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The Astron Astrophys Rev (2003) 12: 1–41 Digital Object Identifier (DOI) 10.1007/s00159-003-0021-9 THE ASTRONOMY AND AS...

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The Astron Astrophys Rev (2003) 12: 1–41 Digital Object Identifier (DOI) 10.1007/s00159-003-0021-9

THE

ASTRONOMY AND ASTROPHYSICS REVIEW

The heating of the solar corona R. W. Walsh1 , J. Ireland2 1 Centre for Astrophysics, University of Central Lancashire, Preston, Lancashire PR1 2HE, UK 2 L3 Communications EER Systems Inc, NASA Goddard Spaceflight Center, Code 682.3,

Building 26, Room G-1, Greenbelt, MD 20771, USA Received 6 February 2003 / Published online 14 November 2003 – © Springer-Verlag 2003

Abstract. The heating of the solar corona has been a fundamental astrophysical issue for over sixty years. Over the last decade in particular, space-based solar observatories (Yohkoh, SOHO and TRACE) have revealed the complex and often subtle magnetic-field and plasma interactions throughout the solar atmosphere in unprecedented detail. It is now established that any energy release mechanism is magnetic in origin - the challenge posed is to determine what specific heat input is dominating in a given coronal feature throughout the solar cycle. This review outlines a range of possible magnetohydrodynamic (MHD) coronal heating theories, including MHD wave dissipation and MHD reconnection as well as the accumulating observational evidence for quasi-periodic oscillations and small-scale energy bursts occurring in the corona.Also, we describe current attempts to interpret plasma temperature, density and velocity diagnostics in the light of specific localised energy release. The progress in these investigations expected from future solar missions (Solar-B, STEREO, SDO and Solar Orbiter) is also assessed. Key words: Sun: corona – Sun: magnetic fields – MHD – Sun: activity – Sun: oscillations

1. Introduction: A new view of the solar corona from space Space-based observations of the solar corona have revolutionised our understanding and appreciation of its surprising beauty and incessant variability. The outer atmosphere of our closest star is revealed to be an inhomogeneous, complex, dynamic system; subtle plasma and magnetic-field interactions occur over a wide range of spatial and temporal scales creating a plethora of coronal structures. Investigating the corona remains central to astronomy as well as physics, since we can observe this star in greater detail than others, and can examine numerous plasma processes that are impossible to reproduce in a laboratory on Earth. In particular, the existence of a counter-intuitive high temperature corona (on average 1–2 million K but can be substantially higher in some localised Correspondence to: [email protected]

2

R.W. Walsh, J. Ireland

Table 1. Main characteristics of a selection of instruments from SOHO (CDS: Coronal Diagnostic Spectrometer; SUMER: Solar Ultraviolet Measurements of Emitted Radiation; EIT: Extreme ultraviolet Imaging Telescope; MDI: Michelson Doppler Interferometer), Yohkoh (SXT: Soft Xray Telescope) and TRACE; (1 = 1 arcsec ≈ 750 km on the Sun). See Huber and MalinovskyArduini (1992) Instrument

Description

Spectral range

Pixel resolution

SOHO CDS SOHO SUMER SOHO EIT

EUV spectrometer EUV spectrometer EUV imager

2 × 1.7 1 2.5

SOHO MDI Yohkoh SXT TRACE

Interferometer Soft X-ray Imager EUV imager

˚ 513–633 A˚ 307–379 A, ˚ 500–1600 A ˚ 195 A, ˚ 171 A, ˚ 304 A ˚ 284 A, ˚ ˚ 6767.8 A±190 mA 0.25 to 4.0 keV ˚ 195 A, ˚ 284 A, ˚ 171 A, ˚ Lyman α, 304 A, ˚ three about 1550 A

4.0 (full disc) 2.5 0.5 –1.0

regions) above the much “cooler” photosphere (at 6000K) has puzzled solar physicists for several decades – it is now known as the solar coronal heating problem. In that regard, the Solar and Heliospheric Observatory (SOHO) (Domingo et al., 1994) has made a major impact in probing the corona. Launched in 1995, SOHO resides 1.5 million km sunwards from the Earth. From this location, SOHO’s twelve instruments observe the Sun twenty-four hours a day, monitoring continuously the activity of the star. Table 1 summarises the nature and main characteristics of four of the SOHO instruments that will be referred to in the following sections.Also mentioned is the Japanese/UK/USA spacecraft Yohkoh which has onboard the Soft X-ray Telescope (SXT; Tsuneta et al., 1991)1 and the Transition Region and Coronal Explorer (TRACE), operated by the Stanford-Lockheed Institute for Space Research (Handy et al., 1999). In particular the latter is producing superior resolution movies which display a wealth of small-scale, dynamic detail. This review paper will concentrate upon recent major advances in coronal observations and theoretical modelling relevant to heating such a multi-scale (in space, temperature and time) environment. In Sect. 2, we outline briefly the background to this coronal heating puzzle. Section 3 deals with possible energy release mechanisms (whether via magnetohydrodynamic waves (3.1) or small scale magnetic reconnection events (3.2)) and the corresponding possible observational signatures that are now being detected. Section 3.3 decribes investigations into the localisation of the heat input in observed coronal structures (mainly active region loops) while Sect. 4 discusses the implications of the above in the light of future solar missions. 1 unfortunately the last contact we had with Yohkoh was 15th December 2001.

The heating of the solar corona

3

Fig. 1. Simultaneous (a) SOHO/MDI magnetogram (white (black) indicates the line-of-sight component of the magnetic field out of (in to) the Sun) and (b) SOHO/EIT 171 A˚ image

2. The coronal heating problem At the end of the nineteenth century, the presence of certain lines in the coronal spectrum presented the powerful new science of spectroscopy with a major dilemma. The socalled coronal “green line” did not match with any known element on Earth. Thus it was surmised that a new element (that only existed in the solar atmosphere, coronium) was responsible. It was not until the late 1930’s and early 1940’s that Grotrian (1939) and Edlén (1942) made the breakthrough. These unusual coronal lines were in fact emitted by iron, calcium and nickel in states of high ionisation – this meant that the coronal environment was at a very high temperature (millions of degrees) with each element having a substantial number of electrons removed. However, this “solution” only leads to another more mystifying puzzle. Under normal thermodynamic considerations, the atmosphere above the photosphere should decrease in temperature as one travels away from the Sun and should not increase dramatically. The extra amount of energy required to balance coronal losses from thermal conduction, optically thin radiation and mass loss (from the solar wind and solar eruptions such as flares and coronal mass ejections) is small (only ≈ 0.01 %) compared to the total energy output of the Sun (at about 6 × 1010 erg cm−2 s−1 )). However, given the presence of million degree coronal plasma, some energy source(s) must be depositing heat somewhere in the corona. Figure 1a displays a SOHO/MDI image of the photospheric magnetic field; using Zeeman splitting, MDI creates a line-of-sight magnetic map of the full disc of the Sun (a magnetogram) at least every 96 minutes. Figure 1b is a simultaneous SOHO/EIT EUV ˚ (at a peak temperature of approximately 1 MK) image of the corona. It can be 171 A seen clearly that the regions of brightest EUV emission correspond to the regions of strongest magnetic field. With an estimated field strength of 10 to 100 Gauss, the corona is considered a low β plasma; typically β = 2µp0 /B0 2 ≈ 0.01, where B0 2 /µ and p0 are the magnetic and plasma pressure respectively. Coronal structures are dominated by the


e

-1

0

chromosphere

4

15

Log Density (cm-3 )

N 5

photosphere

Log Temperature (K)

6

corona

transition region

4

10 Te 1

2

3

Height above visible limb (Mm)

Fig. 2. Sketch of the variation of electron temperature Te and density Ne with height for an average model solar atmosphere

magnetic field and can be described using Magnetohydrodynamics (MHD). A detailed description of the Solar MHD equations and their applicability to a range of coronal phenomena is beyond this present paper – the reader is referred to Priest (1982) and Walsh (1998). It is now accepted that the coronal magnetic field embedded in the turbulent motions of the photosphere plays the most vital role in maintaining this atmospheric temperature gradient. Figure 2 displays a sketch of the “traditional” view of how the temperature and density varies with height through the solar atmosphere. The dramatic temperature increase of two orders of magnitude from the chromosphere to the corona is connected through a narrow (< 1 Mm) transition region. However, the picture suggested by these average curves has been challenged as limiting, confusing or maybe just wrong by EUV observations over a wide spectral range. Consider Fig. 3 which displays a SOHO/EIT global ˚ image of the Sun with a close-up snapshot of the active region on the limb observed 171 A by TRACE. The region viewed through this narrow-band filter consists of a multitude of fine plasma threads that outline the magnetic field structure. The inhomogeneity and complexity of this million degree plasma is evident and is certainly not representative of a gravitationally stratified, plane-parallel atmosphere as is implied in Fig. 2. Similiarly, Fig. 4 shows a typical SOHO/CDS image of an active region on the solar limb for six spectral lines. CDS is a rastering spectrometer that has the advantage of sampling a wide temperature range simultaneously. Entire loops in typical transition region lines (for example, O V at 2.5 × 105 K) are seen, clearly at odds with the notion of a purely thermally stratified atmosphere. Thus theorists and observers are now concentrating upon individual structures in the corona (the “building blocks” of this environment as spelled out by Vaiana and Rosner, 1978) to try and determine the heating mechanism. With this in mind, it must be noted that the phrase “coronal heating” is a very sweeping and general term. When confronted with “coronal heating” does the solar physicist then consider these well defined closed magnetic loops which are observed at a wide range of temperatures (Fig. 5a) or the “diffuse” corona, radiating at over 2×106 K


5

˚ global image of the solar disc with a close-up snapshot of active region Fig. 3. SOHO/EIT 171 A loops from the higher resolution TRACE instrument in the same spectral line

but not confined within these “brighter” loops (of course the entire corona is filled with magnetic field; Fig. 5b)? Or what form of coronal heating is operating in plumes that are observed in “coronal emission lines” with their open magnetic-field structure within coronal holes (Fig. 5c)? Maybe one should concentrate upon the formation of many small-scale brightenings across the Sun (Fig. 5d) or the energy requirements within a cool (104 K), dense prominence as an important aspect that should not be ignored either (Fig. 5e). If there is a “favoured” heating mechanism, it should be able to explain all of the above if it is going to represent the complete solution to the “coronal heating problem”. However, it is more likely that a range of energy release mechanisms are operating with perhaps one dominating under certain circumstances. In fact, the variety of structures in the corona may be due directly to spatial and temporal variations in the energy input or to differing ways in which the plasma is heated.

6


Fig. 4. SOHO/CDS image of an active region on the solar limb displaying entire loop structures recorded in spectral lines over a range of temperatures Table 2. Typical values for a number of solar coronal quantities (see Bray et al., 1991) Quantity

Forumla

Coronal value

Length of structure Temperature Electron number density Pressure Magnetic field strength Sound speed Alfvén speed Radiative loss Conductive loss Acoustic timescale Alfvén timescale Radiative timescale Conductive timescale

L T ρ P B √ VS = 5P /3ρ VA = B 2 /4πρ LR LC τS = L/VS τA = L/VA τR = P /LR τC = P /LC

108 m 2 × 106 K 1015 m−3 6 × 102 Pa 100 G 2.5 × 105 m s−1 2 × 106 m s−1 2 × 10−5 W m−3 2 × 10−4 W m−3 500 s 50 s 3000 s 800 s

Crucially, this all depends on a balance between the time it takes information to propagate along the magnetic field (Alfvén timescale τA on the order of tens of seconds in the corona) and the particular timescale that the field is being jostled or oscillated at (τD ) (see Table 2 for typical timescales in the corona by Bray et al., 1991). If τA > τD , the enhanced energy content is stored as waves which must be dissipated by resistivity and viscosity (an AC mechanism). On the other hand, if τD > τA then the magnetic structure


7

Fig. 5. How is coronal heating operating (a) in TRACE 171A˚ loops; (b) throughout a SOHO/EIT 171 A˚ image of the solar disc at solar minimum; (c) within a close-up SOHO/EIT 195 A˚ image of a coronal hole; (d) in dynamic, small scale brightenings (Ireland, et al., 1999) and (e) when a prominence erupts?

is stressed up slowly over a longer period of time, which can result in the energy being released suddenly and explosively when the magnetic field becomes unstable (a DC mechanism). Both of these concepts are outlined below.

8


3. Energy release mechanisms 3.1. AC mechanisms: MHD wave heating It seems intuitively obvious that waves should be present in the corona; it is a dynamic environment and contains many different structures on which waves may be supported. Waves carry energy and can be dissipated in the medium in which they travel, qualitities that make MHD waves worthy of further study in regard to the coronal heating problem. Wave mechanisms face the same problem as any other type of mechanism, namely transfering energy from longer lengthscales to shorter ones. The need for short lengthscales arises because the magnetic diffusivity of the coronal plasma is expected to be very small. However, we note that no definitive measurement of this parameter exists. The problem can be readily seen by considering the induction equation (Priest, 1982); ∂B (1) = ∇ × (v × B) + νm ∇ 2 B, ∂t where B is the magnetic induction, v is the fluid velocity, νm is the magnetic diffusivity and t is time. The ratio of the advective term to the dissipative term expresses their relative “strength” in a number commonly referred to as the magnetic Reynolds number: Rm =

|∇ × (v × B)| lv = νm ∇ 2 B νm

(2)

where l is a characteristic length scale and v is a characteristic fluid velocity. For typical coronal values of l ranging from 106 m to 108 m, v ≈ 1–100 kms−1 and νm ≈ 1 m2 s−1 , the value of Rm lies between 1010 and 1013 , i.e., the advective term far outweighs dissipation. From the definition of Rm it is clear that dissipation only becomes important when lengthscales are small. Thus dissipative effects are significant only on small lengthscales and so to heat the plasma, energy must move by some mechanism from longer to shorter lengscales, and this must occur fast enough to explain the heating that we see. Another way of characterising the plasma is to use the Lundquist number S which can be defined as the ratio of the dissipative timescale (whether due to magnetic diffusivity or fluid viscosity) to an Alfvén timescale. For typical values in the corona, S ≈ 1010 to 1012 , implying that magnetic diffusion occurs on a vastly longer timescale than Alfvén timescales i.e., years (simple magnetic diffusivity time scales) as opposed to seconds (Alfvén timescales). Clearly something else must be happening in the corona and MHD waves have been harnessed as a possible way out of the time and lengthscale problems outlined above. Sections 3.1.1 and 3.1.3 outline two major branches of research in this approach, phase mixing and resonant absorption respectively. Section 3.1.2 considers the evidence for the existence of Alfvén waves in the corona, essential for the viability of the phasemixing mechanism. Finally, Sects. 3.1.4 to 3.1.6 describe classes of oscillations in the solar corona and discuss their implications for wave heating. 3.1.1. Theories of coronal heating: Alfvén–wave phase mixing Phase–mixed Alfvén waves were first proposed as a coronal heating mechanism by Heyvaerts and Priest (1983). An illustration of the basic geometrical set up is presented


9 Z

wave dissipates as z increases

v (x) A

background inhomogeneous Alfvén velocity profile

x footpoint motions excite Alfvén waves on background field

y

Fig. 6. Phase mixing geometry: Alfvén waves on neighbouring field lines move out of phase with each other leading to dissipation across the wavefront at larger z. See Sect. 3.1.1 for more details

in Fig. 6. Alfvén waves are generated at z = 0 through some excitation process; for instance, the geometry of Fig. 6 could represent the base of a coronal loop system, or the base of a coronal hole. Photospheric footpoint motions cause Alfvén waves to be generated on the +z directed field lines. The field is structured in the x-direction and so the Alfvén speed varies from field line to field line. As the waves propagate upwards they move out of phase relative to each other because of the varying Alfvén speed vA (x). This causes gradients to appear across the wavefront which dissipate, heating the corona. For waves of angular frequency ω and wavenumber k = ω/vA (x), the damping of the wavefront varies as [kz]3 exp − 6Rtot where

k2 ω νm + νv k 2 is a total Reynolds number for the plasma, including both magnetic diffusivity νm and kinematic viscosity νv . The cubic power that appears here corresponds to the strong phase-mixing case i.e., the background Alfvén speed is highly structured. Effectively, Rtot =

10

R.W. Walsh, J. Ireland 1/3

the damping lengthscale scales as Rtot . This suggests very rapid damping compared to the (approximate) exp(−z/L) damping present in the non-phase-mixed case of uniform 3 /ν ω2 , which varies as R approximately. Alfvén speed, where L = 2vA m tot The phase–mixing mechanism has undergone much examination and development. Browning and Priest (1984) find that phase–mixed Alfvén waves are rapidly disrupted by the Kelvin–Helmholtz instability and that this leads to turbulence and increased dissipation. Ireland and Priest (1997) decompose the evolution of the phase–mixed wavefront into Fourier components to follow in detail the energy cascade down to smaller scales as the wave propagates, finding that the original Heyvaerts and Priest (1983) solution breaks down at points in the wavefront where phase mixing is weak. Hood et al. (1997a) and Hood et al. (1997b) describe self-similar solutions to the original phase–mixing equations of Heyvaerts and Priest (1983) which express neatly the range of length and time scales required for phase mixing to be a viable coronal heating mechanism, given the enormous value of the Lundquist number in these models. It is found that coronal holes may be heated by this mechanism (Moore et al., 1991) or that it can provide the necessary heat input to accelerate the solar wind (Parker, 1991) but short lengthscales – on the order of 1 km (Woo, 1996) – may be required (Hood et al., 1997a). Coronal loops can also be modelled with the geometry of Fig. 6. Abdelatif (1987) considers a simple loop model which includes a transition region. The Alfvén waves are generated at the underlying chromosphere. Alfvén waves of period 300s deposit little energy in the corona; 5 s period waves deposit more, but not enough to balance losses. For these loops, phase–mixing can occur in time rather than in space i.e, the phase of waves on neighbouring field lines change relative to each other depending on time and the wave decays as exp(−[t/τlam ]3 ) where τlam = (6Rtot )1/3 /ω (Heyvaerts and Priest 1983). Hood et al. (1997b) show that phase mixing can deposit heat on timescales faster than the radiative cooling timescale (i.e., faster than about 3000 s). Commonly occuring solar situations have also been included into the basic mechanism. A background fluid flow adds an extra lengthscale to the mechanism in the same way as the background Alfvén wave does. Also important is the direction of flow relative to the Alfvén wave propagation direction; if they are oppositely directed, the wavelength of the Alfvén wave is effectively shortened, promoting phase mixing as the phase changes faster in a given distance. If both are in the same direction, the opposite effect occurs and phase mixing is depressed relative to the zero flow case (Nakariakov et al., 1998; Ryutova and Habbal, 1995). Inclusion of a density stratification introduces a heightdependent Alfvén velocity, influencing the efficacy of phase mixing. Ruderman et al. (1998) and De Moortel et al. (1999) explored the effect of an exponentially stratified atmosphere on phase mixing and found that the decreasing density stretches the oscillation wavelengths and thereby reduces the generation of transverse gradients. Ohmic heating is spread out more over the system, whereas viscous dissipation is more or less unaffected when compared to the unstratified case. The net effect is that heat will be deposited higher up in the atmosphere. Ruderman et al. (1998) and De Moortel et al. (2000a) also consider Alfvén-wave phase-mixing in diverging atmospheres. Ruderman et al. (1998) consider an exponentially diverging field and find that phase mixing is much faster so that the energy flux decays approximately as exp(−c(x) exp(z/H )) (with c(x) being a function of the direction transverse to the propagation direction and height scale H ). De Moortel et al.


11

(2000a) look at a radially diverging field and also find an enhanced but different energy decay rate of approximately exp(−q(θ )r 7 /7) (for some q(θ), an inverse lengthscale raised to the seventh power where θ is the azimuthal angle). These studies show that the geometry of the system affects the decay rate by shortening the Alfvén-wave wavelength along the field lines, hence promoting phase mixing. An interesting variant of phase mixing can be found in the work of Similon and Sudan (1989). The authors consider the behaviour of Alfvén-wave packets in stochastic three dimensional (3D) magnetic fields. Such areas of field are characterised by exponentially diverging field lines. Alfvén waves on neighbouring field lines have exponentially stretching wavenumbers and so move out of phase with each other. This leads to dissipation lengthscales that vary as ln R and thus lead to very much shorter lengthscales than predicted for the type of geometries discussed by Heyvaerts and Priest (1983). In addition, Similon and Sudan (1989) suggest that the decay timescale should vary as ln R also which was confirmed numerically by Petkaki et al. (1998). These authors also confirm that such fast dissipation rates exist in 3D fields that contain very small chaotic regions in quasi-uniform magnetic structures. Further, Malara et al. (2000) show that the decay timescale’s dependence on R relies on the degree to which the supporting field is three-dimensional. For fields that are two-dimensional, the R 1/3 characteristic of “classical” phase-mixing dependence dominates but as the 3D nature of the field is increased the dependence moves more towards ln R. It is also shown that for plasmas with large Lundquist number like the corona, the field need only be weakly 3D for the decay timescales to fall into the fast ln R regime, lending support to this mechanism’s claim as a coronal heater. The propagation of Alfvén waves in a phase-mixing context continues to attract much exploration and it remains a viable coronal heating candidate. It is, however dependent on the existence of Alfvén waves in the corona, a subject to be tackled in the following section. 3.1.2. Alfvén waves in the corona? Evidence for Alfvén waves (or the existence of phase-mixing mechanisms) in the corona has been difficult to obtain through the direct detection of an oscillating magnetic field. In addition, there are no instruments at present that are capable of measuring the magnetic field in the corona. Instead, indirect measurements are used to infer the presence of Alfvén waves. McClements et al. (1991) show that heating caused by Alfvén waves can contribute to the observed line width, depending on the orientation of the supporting magnetic structure to the observer’s line of sight. The contribution to the line width is predicted to be larger when the field is normal to the line of sight than when the magnetic structure is along the line of sight. If the heating in the structure is due to acoustic wave heating, then the opposite behaviour is seen. The difference occurs as in an Alfvén wave, the wave velocity vector is normal to the background field and so is a maximum when the magnetic field is normal to the line of sight. This suggests an observational program to determine which wave mode dominates the heating: following a loop as it traverses the disk and measuring the line width. Hara and Ichimoto (1999) test the McClements hypothesis on loop systems and present evidence indicating that an Alfvén wave may be the source of heating. However,

12


the nonthermal velocity (derived by carefully analysing emission line widths) ascribed to the presence of Alfvén waves (3–54 km s−1 ) is not sufficient to explain all the nonthermal velocities (14–26 km s−1 ) reported in their observations (Saba and Strong, 1991, report nonthermal velocities of 40–60 km s−1 in the corona). Erdélyi et al. (1998) take a slightly different approach by looking at quiet-sun line widths from disk centre outward; they claim to see a broadening in quiet-sun line widths in SOHO/SUMER data going from disk centre to limb, indicative of Alfvén waves heating the atmosphere. Lee et al. (2000) examine SOHO/SUMER quiet-sun UV data taken at the solar limb and find that the observed nonthermal broadening variation with height above the limb can be explained by undamped Alfvén waves in the medium. Harrison et al. (2002) use line widths in Mg ˚ (formed at 1 MK) observed at the limb by SOHO/CDS, to look for evidence X 629 A of Alfvén waves. It is found that the line widths narrow at higher altitudes, which is interpreted as an observation of dissipative Alfvén waves. The studies mentioned above infer the existence (or not) of Alfvén waves through indirect means. However through magnetically sensitive lines, photospheric magnetic field is measurable and so one might hope that a magnetic field oscillation may be observed in this region of the atmosphere. Ulrich (1996) observes correlated magnetic field/velocity fluctuations indicative of the presence of outgoing Alfvén waves in Mount Wilson magnetograph data of active regions. Observational support of a detectable, oscillating magnetic component – an important step in identifying an Alfvén wave– is sparse and, as yet inconclusive (Gurman and House, 1981; Horn et al., 1997; Lites et al., 1998; Rüedi et al., 1998; Norton et al., 1999; Balthasar 1999; Norton and Ulrich, 2000). The problem of identifying conclusively a magnetic component to the fluctuations comes in interpreting the observations. Line formation can influence the interpretation; for example, Bellot Rubio et al. (2000) detect magnetic field-strength and velocity oscillations derived from the inversion of full Stokes profiles of three Fe I lines at 15650 A˚ taken with the Vacuum Tower Telescope. However, synthesis of the profiles shows that the observed magnetic oscillations can be well described by opacity fluctuations moving up and down the region where the spectral lines are sensitive to magnetic fields. Norton and Ulrich (2000) correlate SOHO/MDI and ASP (Advanced Stokes Polarimeter) active region data to show that the observed magnetic and velocity fluctuations are consistently described by a flux tube sweeping into (or out of) an instrument resolution element by horizontal p-mode components. Finally, the instrument itself can create spurious signals. Fabry-Perot interferometers commonly sample across the emission line and recreate the emission profile from this sampling process. However, if the timescale of variation of the line is faster than the sampling time, then the resulting measurement does not reflect accurately the true variation of the line. This leads to line profiles that, when inverted, show the apparent presence of magnetic-field fluctuations. Calculations of this effect are presented in Settele et al. (2002), who comment that the simulated cross-talk is of the same order of magnitude as that seen by Horn et al. (1997) and Balthasar (1999) (although the phases appear to be different). Settele et al. (2002) point out that the same effect is also present in SOHO/MDI, which uses filters to sample across the line; they show that it is possible to generate a fake magnetic signal from artificial profiles that have a velocity signal only. Although this fake field is not enough to explain the all fluctuations seen in SOHO/MDI data, it may be a significant source of error in weak field regions.


13 Z

surface wave disturbance on flux tube

resonant layers

background inhomogeneous Alfvén velocity profile

v (x) A

exterior

exterior

x

interior

Fig. 7. A resonant absorption geometry. Energy from the surface wave is absorbed in one or more resonant layers in the coronal loop. See Sect. 3.1.3 for more details

As for phase mixing itself, there is little direct observational evidence. Ofman and Aschwanden (2002) claim evidence for phase mixing in an analysis of timescales seen in tranversely oscillating coronal loops (see Sect. 3.1.4). This conclusion has been questioned by Goossens et al. (2002) who suggest that the decay observed in these events is due to resonant absorption (see Sect. 3.1.3) of the oscillation energy rather than phasemixing. 3.1.3. Theories of coronal heating: resonant absorption mechanisms This concept has received much detailed discussion in the literature since it was first posited as a heating mechanism for coronal loops by Ionson (1978). Essentially, the mechanism relies on the existence of a resonance condition inside the loop which enables the transfer of the energy present in MHD surface waves to internal field lines that satisfy the resonance condition. The basic geometry is shown in Fig. 7. A surface MHD wave of given frequency ω is generated on the outer surface of a loop. Consider a much simplified situation (Hollweg, 1987a), where we ignore the other side of the loop and concentrate instead on the fundamental physics of what happens to the

14


system when a surface MHD wave occurs at the boundary between two regions having different Alfvén speeds. The surface disturbance affects internal field lines and so these field lines are also disturbed. However, each field line has its own natural frequency and so field lines at which the resonance condition holds act like classical oscillators subject to a harmonic driver (see also Steinolfson and Davila, 1993). Velocity oscillations on this field line increase quickly; neighbouring field lines are nearly resonant and so also support large velocities, forming what has been termed a resonant layer inside the loop. This creates gradients across the plasma on small length scales, enabling the transfer of energy (via phase-mixing). Thus this mechanism transfers energy from the larger-scale surface wave to the much smaller-scale resonant layer, where it may be used to heat the plasma. The resonant layer is thin (Steinolfson and Davila, 1993) and varies as R −1/3 where R is the Reynolds number (Goossens and Ruderman, 1995; Goossens et al., 1995; confirmed numerically by Poedts et al., 1990). Estimates for typical coronal values suggest that resonant layers have thicknesses from 0.3 km to 250 km (Davila, 1987); therefore, direct imaging of resonant layers would appear to be unlikely with instrumentation that will be available in the near future (although see Solar Orbiter in Sect. 4). The velocity of the resonant layer scales as R 1/3 (Ruderman and Wright, 2000: Hollweg, 1987b). Davila (1987) suggests that for typical coronal values the resonant layer velocity is 60 times the amplitude of the driver (estimated at 0.01vA , for a coronal Alfvén velocity of about 1000 km s−1 ) outside the system. Such large velocities are not observed; however, Davila (1987) points out that within the confines of the model, an averaged root-meansquare velocity on the order of 2–6 km s−1 (a commonly observed range of values) yields enough energy input to account for typical soft X-ray radiation losses. This mechanism has undergone much development and scrutiny with numerical work supporting and extending theoretical advances. Using a numerical Alfvén wave loop model driven by a single frequency source, Ofman et al. (1998) show that resonant heating causes the density profile of the loop to change at the resonant field line. This detunes the resonant absorption at this field line. However, the changed density profile creates new resonant layers; effectively, the resonant layers move, spreading the heat around the loop. The source of heat in the corona comes ultimately from further down in the solar atmosphere; therefore, energy must be transferred from those lower regions, through the chromosphere and transition region, to the corona where it is deposited. Beliën et al. (1999) discuss the effect of including a chromosphere and transition region on resonant absorption. Their numerical model excites a cylindrical flux tube via single frequency torsional Alfvén waves applied at the chromospheric level. An important result of this work is that only a few percent of the energy in the driver is deposited in the corona by resonant absorption. This is due to principally the relatively efficient nonlinear generation of compressive slow magneto-acoustic waves from the initial Alfvén waves at the chromosphere and transition region. This reduces the Alfvén wave energy available for resonant absorption in the corona. In addition, the loops in this model are shown to be poor absorbers of the incoming Poynting flux and are poor at converting this energy into heat. This work shows that the conversion of Alfvénic disturbances into other wave modes is an important factor to consider in resonant absorption. De Groof et al. (2002) study a


15

related resonantly absorbing system which contains Alfvén waves, fast magneto-acoustic waves and a parameter (the azimuthal wave number) that controls the degree of coupling between the two modes. These waves are excited by a single frequency footpoint driver that is polarized in the azimuthal direction. When the azimuthal wave number is zero, the wave modes are linearly decoupled from each other. When the coupling is non-zero, the azimuthally polarized footpoint motions indirectly drive fast magneto-acoustic waves, which couple to Alfvén waves. As a consequence, energy that would have gone into the resonance layer now goes into the formation of other wave modes. This has a deleterious effect on the amount of Alfvénic energy that is available for resonance at most driving frequencies. However, if the driving frequency is close to or at one of the loop quasi-mode2 frequencies (Tataronis and Grossman, 1973; Poedts and Kerner, 1991; Tirry and Goossens, 1996), then the Alfvén resonance can be enhanced beyond that of the uncoupled case. Driving near quasi-mode frequencies is clearly not realistic and so in a companion paper using a similar model, De Groof and Goossens (2002) show that a random driver can create resonant surfaces all over the loop with short enough lengthscales for effective dissipation (see also Wright and Rickard 1995 for comments on resonant absorption in nonuniform magnetohydrodynamic media with random drivers). The observational evidence supporting resonant absorption relies on consistency arguments because the resonant layers themselves are too small to be observable with current instrumentation. Goossens et al. (2002) argue that resonant absorption can explain the phenomena of damped transverse coronal loops (see Sect. 3.1.4) and Davila (1987) contends that observed Doppler velocities are consistent with the predictions of resonant absorption. McKenzie and Mullan (1997) examine high cadence YohkohSXT images of oscillating loops and find that the observed intensity oscillations, plasma β’s and Alfvén and sound speeds are all consistent with aspects of resonant absorption models; for example, the derived qualities of the suspected resonating loops are consistent with those found numerically by Ofman et al. (1995). The observations may be interpreted as loops oscillating in their global mode. Koutchmy et al. (1983) report on Doppler-velocity oscillations in the green coronal 5303 A˚ line of Fe-XIV. The appearance of near harmonic frequencies is viewed as suggestive of an oscillating loop and indeed, the coronal loop and oscillation model used fit the observations well. However, the energy flux in these oscillations is not sufficient to account for radiative losses. Mullan and Johnson (1995) take Einstein and ROSAT (Röntgen Satellite) X-ray observations of four flare stars and find periodicities in the emission. Coronal loop models which suppport Alfvén waves are applied and are found to be consistent with the observations. Although not a direct observation of a mechanism heating stellar loops, this consistency renders resonant absorption a viable explanation for these observations. The resonant absorption mechanism remains to be of great relevance in the coronal heating debate. It continues to be developed both theoretically and computationally, with the paucity of direct observations being a consquence of the expected small lengthscales 2 The quasi-mode arises in structured ideal plasmas as a “collective” mode of oscillation which

is exponentially damped in time. The damping of these modes is due to a resonant coupling into localised Alfvén waves (Tirry and Goossens, 1996). This situation is analogous to the phenomenon of Landau damping in the particle description of a collisionless plasma, where wave energy goes into the acceleration of resonant particles (Sturrock, 1994).

16


direction of loop oscillation

footpoint

footpoint

Fig. 8. A schematic loop undergoing a transverse oscillation. The magnetic field is aligned with the loop and the whole loop undergoes oscillations transverse to this direction. Observationally, we only see the component in the plane of the sky. See Sect. 3.1.4 for more details

generated by this process. Therefore, indirect observations will remain the best bet for confirming the presence of this mechanism in the solar atmosphere for the forseeable future. 3.1.4. Transversally oscillating coronal loops Transversally oscillating coronal loops have been observed recently in active regions by ˚ and Fe XII 195 A ˚ bandpasses (Aschwanden et al., 1999a; TRACE in the Fe XII 171 A Aschwanden et al., 2002). The oscillations appear to be triggered in the corona by a flare or filament destabilisation. The loop is observed to oscillate in a direction transverse to its longest direction which lies in the plane of the sky (Fig. 8). This previously unknown phenomenon was first reported by Schrijver et al. (1999) in a review paper of results from the TRACE instrument. Further description and analysis including the periodicities and amplitudes of loop oscillations are provided by Aschwanden et al. (2002). The possible implications for coronal heating were first pointed out by Nakariakov et al. (1999), who show that interpreting a decaying loop oscillation as a decaying fundamental (global) kink mode implied a dimensionless magnetic Reynolds number (or Lundquist number) that is some eight to nine orders of magnitude smaller than the classical value (see Sect. 3.1). If true, the implications for coronal heating in general are profound. The drive behind most thinking about coronal heating has been to create mechanisms that counteract the large Reynolds and Lundquist numbers: energy has to be transferred from larger lengthscales that we can observe to shorter ones that we cannot observe but where dissipation is important. Phase-mixing and resonant absorption mechanisms do this, as can be shown by considering the properties of waves in the medium. A Reynolds or Lundquist number of the size claimed by Nakariakov et al. (1999) would sidestep many of these problems. The cost of accepting this value is to admit that there is some


17

microphysics operating in the corona that we do not yet understand. This would shift the emphasis of coronal physics dramatically. It is assumed that these events are purely wave-based phenomena and so wave theories can be applied. Wave-propagation and wave-heating theories have advanced to the point that they can now be used to diagnose the state of the corona and thus provide much needed tools in a complex part of the solar atmosphere. This represents something of a change of priorities in the wave-heating community; now that hard data is available, it is no longer satisfactory to speculate on the required parameter ranges as the theory can be applied directly and its predictions tested. In some sense, coronal wave-propagation and heating theories are coming of age. For instance, Ofman (2002) shows that the oscillation decay mechanism posited by De Pontieu et al. (2001) – enhanced chromospheric damping at the footpoints of the coronal loop due to ion-neutral damping of Alfvén waves – cannot account for the observed loop oscillation decay time of the 14 July 1998 event observed by Nakariakov et al. (1999). However, Ofman (2002) also points out that the plausibility of this mechanism depends on a number of observed and estimated parameters that will vary from loop to loop. Thus, the decay mechanism needs to be examined on a case-by-case basis. The approach of using wave theory and observation as diagnostic tools has lead to the concept of “coronal seismology”, as advanced by Nakariakov and Ofman (2001). The idea is that the data can be used in conjunction with theory and numerical simulation to diagnose quantities of direct interest to solar physicists, such as a coronal magnetic field. Such quantities are hard to determine by observations and yet they have a direct bearing on the coronal heating problem. More examples have been discovered since the event that was studied by Nakariakov et al. (1999); they are listed in Schrijver et al. (2002) and analysed in Aschwanden et al. (2002). Nevertheless, the best example of a decaying loop oscillation remains that of Nakariakov et al. (1999). The oscillations are triggered by flares or filament destabilizations. Typically the oscillations have most periods in the range 2 min to 11 min, decay times of 3–21 min and amplitudes on the order of 100 km to 8800 km. The identification of many more examples has spurred much new effort in this area: Ireland and De Moortel (2002) apply the work of De Moortel et al. (2002d) to explore carefully the effect of error propagation on the oscillation properties both found and assumed by Nakariakov et al. (1999); they find that the decay properties (such as for example, decay time) are not well defined by the data. Ofman and Aschwanden (2002) claim evidence for the existence of phase-mixing mechanisms (see Sect. 3.1.1) based on an analysis of the damping timescale dependence. Ruderman and Roberts (2002) revisit the theory of resonant absorption in inhomogeneous loops to suggest that only loops with small scale density variations oscillate for long enough to be observable. In this work, the loop oscillation is damped through energy transfer to a resonant layer in the loop. Also, Goossens et al. (2002) point out that the rate of removal of energy from the kinetic motion of the loop via damped quasi-modes obviates the need for a drastically different Lundquist number. Crucial to energy estimates is the actual size of oscillation. Cooper et al. (2003) point out that the column depth along the line of sight can either amplify or attenuate the observed amplitude of a coronal kink oscillation: the observed amplitude depends on the orientation of the oscillation

18


to the line of sight. This effect needs to be taken into account when estimating the true oscillation amplitude. At the heart of coronal seismology in its current form lies the idea of trying to explain the phenomenon by using a wave interpretation. One intriguing counter suggestion (Schrijver and Brown, 2000) is that the oscillations observed in the corona are merely the coronal response to field rearrangements at the photospheric level. This proposal conveniently accounts for the fact that only very few coronal field lines respond to the triggering event since only those field lines that have the correct photospheric disturbance are seen to oscillate higher up in the corona. As more and more examples are collected, one hopes for significant progress in this field. Unfortunately, the declining solar cycle suggests that new examples will be observed less frequently. In addition, near future missions such as SDO and Solar-B have pixel sizes no better than that of TRACE, currently the only instrument with which we can observe these events (however see Sect. 3.1.5 below for a caveat). This is frustrating given that the spatial oscillations are damped within a few periods and more pixels per arcsecond at the Sun would allow these fascinating events to be followed in greater detail (Ireland and De Moortel, 2002). 3.1.5. Transverse oscillations again Coronal oscillations have recently been seen as a variation in Doppler velocity of high temperature lines observed by SOHO/SUMER. The first report by Kliem et al. (2002) describes an oscillating flow exhibited in the Doppler velocity of the lines Fe XXI ˚ T ≈ 107 K) and C II (λ1335.7 A, ˚ T ≈ 2 × 104 K) in a flaring active region (λ1354.1 A, on the solar limb. The measured Doppler velocities (greater than 100 km s−1 with a periodicity of 11.7 min and a decay time of 8 min) imply enormous displacements far in excess of those measured by TRACE in other, lower temperature transversally oscillating loops (see Sect. 3.1.4). Thus these measurements may describe reconnection-sourced flows rather than loop oscillations. However, Wang et al. (2002a,b) describe another set of SOHO/SUMER Doppler velocity oscillations in high temperature lines that are interpreted as wave modes: the identification is made by comparing the panoply of theoretically available wave-mode oscillation periods with the experimentally derived one. In this case, the fundamental mode of a slow standing wave fits the observations best (Roberts et al., 1984). The ˚ at ≈ 6.3 MK) and have periods in the range oscillations were seen in Fe-XIX (1118 A 14 min to 18 min, exponential decay time of 12 min to 19 min, a peak velocity of 77 km s−1 and a derived amplitude in the range 2000 km to 9000 km. In addition, cooler lines in the study do not show any evidence of oscillating and no dynamic brightening (such as a flare) occurred before or during these observations. Note however, that a slow standing-wave is compressive but no brightness fluctuations with the same periodicity were observed; this does not support this interpretation. Wang et al. (2002b) go on to consider a fundamental kink mode as a possible explanation and show that this requires either a density 25 times higher, or, a field 5 times smaller, than that typically expected. The place of these events in the sparse gallery of coronal oscillations is not yet fixed. Clearly, more observations are needed to fully characterise these events, in terms of their triggers, phenomenology, relevant dynamical parameters, and their diagnostic capabilites


19

for exploring the corona and coronal heating. Most satisfying would be spectroscopic imaging of these oscillations. This would go a long way towards explaining the relative roles of fluid flow and true transversal loop displacement in understanding these events. This should be possible with the XRT (X-Ray Telescope) of Solar-B and thus, we look forward to new data and further insight into these newly observed oscillations. 3.1.6. Longitudinally oscillating coronal loops The second, well-documented coronal oscillation was first noted by Berghmans and ˚ 1.6 × 106 K bandpass active-region Clette (1999) in the SOHO/EIT Fe XII 195 A, data. The oscillation, originally termed a “propagating disturbance” appears as a lowamplitude, propagating intensity variation along very long, essentially open, field lines rooted in active regions. Shortly after this report, De Moortel et al., (2000b) described a single loop in an active region observed in the TRACE 171 A˚ bandpass supporting a very similar propagating disturbance. Bridging these two observations lies Robbrecht et al., (2001) who describe simultaneous observations in TRACE 171 A˚ and SOHO/EIT 195 A˚ data of a propagating disturbance. Also, Marsh et al., (2003) analyse a similiar scenerio but with co-spatial and co-temporal TRACE 171 A˚ and SOHO/CDS observations of a active region loop. A period of approximately 300 s is detected in the TRACE data which is also observed in the CDS He-I, O-V and Mg-IX lines. A full description of many examples of this phenomena as observed in the TRACE ˚ bandpass can be found in De Moortel et al., (2002a). The disturbance propagates 171 A along the loop with an estimated speed of 122 km s−1 ± 43 km s−1 . The variation in oscillation intensity is 4.1% ± 1.5% at the base of the loop. These disturbances are found to decay very quickly (into the noise eventually) with a damping length of 8.9 Mm ± 4.4 Mm (or 37% ± 19% of the estimated loop length). In the set of oscillations described by De Moortel et al. (2002a), the oscillation is found to have an average period of 282 s ± 93 s (although there is some indication that two separate populations may exist – see below). The energy carried by the average oscillation is small, estimated to be 342 erg cm−2 s−1 ± 126 erg cm−2 s−1 . This is not enough to make a significant contribution to the coronal heating budget of active regions. These propagating disturbances have been identified as slow magneto-acoustic waves through comparison of their measured propagation speed with that expected from theory √ (cs = 152 T m s−1 = 150 km s−1 for TRACE 171 A˚ bandpass, where T is measured in MK). As was noted above, these waves do not have sufficient energy to heat the corona in active regions. These observations are also significant in that they have a sufficient temporal cadence (10 s and 30 s) to begin to test the predictions of Porter et al. (1994a,b), who claim that slow-mode waves with periods of less than 100 s can damp sufficiently fast to satisfy the coronal heating budget in active regions. No such waves are detected in the data, indicating that, if they exist, their intensity amplitude must be (on average) less than 4% of the background amplitude (in a range of 0.7% to 14.6%). This implies a density variation of less than 2% for the waves postulated by Porter et al., (1994a). Better signal-to-noise ratios at similar spatial and temporal resolutions will be needed to further constrain the existence of these waves. Slow magneto-acoustic waves have also been found in other parts of the corona. De Forest and Gurman (1998) describe slow-mode waves in polar plumes, which were

20


modelled subsequently by Ofman et al. (1999). Based on an analysis of the periods found in the SOHO/CDS Grazing-Incidence-Spectrometer data, Marsh et al. (2002) attribute slow mode oscillations to the longer periods (> 200s) found and conclude that fast-mode oscillations are consistent with the shorter periods (50 s to 100 s) detected. Theoretical effort has also gone into constructing models of these waves. Nakariakov et al. (2000) describe a one-dimensional model that incorporates effects due to nonlinearity, gravitational stratification along the loop and dissipation due to finite viscosity and thermal conduction. This model supposes long loops (observationally, the loop length is not known but it is assumed that they are closed loops and not open field regions) and predicts a downwardly propagating wave of an amplitude much smaller than the upwardly propagating one. This downward wave has not been observed. De Moortel et al. (2002b) use a linear wave model to show that dissipation resulting from a slightly increased enhanced thermal conduction effect is sufficient to account for the observed damping lengths and wavelengths as well as the observed correlation between period and damping length. Another feature that needs to be explained is the apparent existence of two separate populations of longitudinal oscillation. De Moortel et al. (2002c) classify the TRACE ˚ intensity oscillations according to their period. Two classes are found: the first 171 A class have periods 172 s ± 32 s and appear to be rooted in sunspots (Gurman et al., 1982 describe transition region Doppler oscillations in sunspots in an overlapping period range). The second class have periods of the order 321 s ± 74 s and are not associated with sunspots. This suggests that these oscillations are driven somewhere low in the atmosphere, possibly in the photosphere, and propagate through the transition region and into the corona. A series of observations using SOHO/SUMER (Brynildsen et al., 1999a,b), SOHO-CDS (Maltby et al., 1999) and TRACE (Brynildsen et al., 2002) confirm the existence of 3 min oscillations from the corona down to the chromosphere. The entire umbral transition region takes part in the oscillation, whereas only parts of the ˘ zda et al., 1983; ˚ bandpass display oscillations. Theory (Zug˘ corona in the TRACE 171 A Settele et al., 2001) predicts resonant peaks, spaced about 1 mHz apart in the frequency power spectra, yet the observations show one dominant peak at around 6 mHz. A better understanding of wave propagation in this system is required, particularly with regard to how the wave energy can penetrate into the corona, where it is presumably converted into heat. 3.2. DC mechanisms: can magnetic reconnection heat the corona? The theory of magnetic reconnection is an enormous subject area spanning over half a century of research. As outlined in Sect. 3.1, in the case of the low plasma-β coronal environment, the induction equation (1) yields (under “normal” circumstances) a large magnetic Reynolds number. Effectively, the plasma is frozen to the magnetic field. However, if the lengthscales are reduced (a few metres for the corona), the diffusion term in Eq. (1) will become important. The fieldlines can diffuse through the plasma and reconnect. For a more detailed description of reconnection theory, the reader is refered to the excellent book by Priest and Forbes (2000). Magnetic reconnection in two dimensions is now very well understood – separatrix curves divide up the plane into topologically distinct regions with reconnection and transfer of magnetic flux associated with X-points


21

in the field. In three dimensions, the volume is subdivided by separatrix surfaces with null points (i.e., where the field vanishes) being the possible location of several differing types of three-dimensional reconnection (Priest and Titov, 1996). Of course, EUV images of the corona reveal clearly the complex three-dimensional nature of the plasma responding to the coronal magnetic field. Magnetic reconnection is at the centre of solar flare theory (see the review in this journal by Priest and Forbes (2002)) and recently Fletcher et al. (2001) report on multi-wavelength observations of a flare trigger-site that can be explained qualitatively by three-dimensional reconnection of the magnetic field. In the context of coronal heating, Parker (1988) put forward the concept of nanoflares (with approximately 1024 erg per event). He postulated that the interaction between the forcing motions of the photosphere and the dynamics created by the coronal magnetic field and plasma could lead to the possibility that the energy release is due to the cumulative effect of many small-scale, discrete current sheets and that these events may make up the majority of the heat that is deposited in the solar atmosphere. However, it should be noted that convective motions do not only twist or braid the coronal magnetic field structures as Parker envisaged it. They also are altering constantly the flux source distribution by coalesence, fragmentation, annihilation and emergence from or disappearance into the photosphere. Recent SOHO/MDI magnetogram-observations reveal that the expected lifetime of a flux element is on the order of 14 hr (Hagenaar, 2001) within this “magnetic carpet”. The fact that an individual flux fragment can, on average, only be tracked for such a short time period of time, has significant implications for the energy budget of the solar corona. With this in mind, Priest et al. (2002) have examined a “coronal tectonics” model where each coronal loop we can observe is actually connected to many intense, smaller scale flux sources. As these sources move, separatrix current sheets form in the corona which reconnect and heat the plasma. However, with a scale of < 100 km per intense flux element, this scenerio is beyond testing by current instrumental resolution. In the following sections we outline two approaches to tackling this problem of discrete heating episodes from both global and individual event prespectives. 3.2.1. Pinning down the power law index It is observed that the frequency distribution (F ) of flare energy (E) follows a power law, F (E) = F∗ E α . Hudson (1991) demonstrated that for a coronal heating mechanism to have a dominant contribution comprising of nanoflares, their energy component must have a power scaling index that is much steeper (α < −2) than their larger flare counterparts (−1.8). Power-law behaviour is a signature that a system is undergoing self-organised criticality (SOC). Thus the corona is considered to be an externally driven, dissipative, dynamical system. This arises from the competition between the external photospheric driver and the redistribution that occurs whenever local field-gradients exceed some threshold value. Essentially the connectivity of the field is allowed to change suddenly via magnetic reconnection, releasing energy into the surrounding medium. Although very localised to begin with, this energy release can affect adjacent regions which may themselves become unstable and release energy – an avalanche occurs. This has been studied extensively for modelling solar flare energy release (see review by Charbonneau

22


Fig. 9. Typical peak lumosity frequency distribution from a self-organised criticality (SOC) model that produces a double power law (from M. Georgoulis)

et al., 2001 and references therein). In the coronal heating context, recent investigations into this power-law behaviour have addressed the issue of increasingly sophisticated numerical modelling as well as detecting the global extent of the smallest intensity brightenings in high time-resolution observations. Lu and Hamilton (1991) were the first to apply SOC modelling to solar flares. They also showed that the total-energy power-index is approximately equal to −1.8, in line with observations. Vlahos et al. (1995) as well as Georgoulis and Vlahos (1996, 1998) extended the above concept to include the role of anisotropy into a statistical flare model and were able to reproduce a steeper power law for the smallest events (see Fig. 9). MacKinnon and MacPherson (1997) and MacPherson and MacKinnon (1999) argue that energy released at one location may trigger rapid and remote energy release at other sites. “Non-local” communication within the corona could occur by either accelerated particles travelling from one energy-release location to another potential site or by intense, coherent electromagnetic radiation from accelerated particles that could alter the particle distribution function at other regions in the corona. They show that if too much communication is occuring, too many remote sites are activated and large enough energy events can then occur that relax the system completely. If this happens too frequently, a state of SOC cannot be reached. Kopp and Poletto (1993) employed a semi-analytical approach to modelling the coronal plasma response to nanoflare energy release. They examine very short, 2 Mm to 5 Mm loops and impose, rather than investigate the creation of a power law index of −4 for the nanoflare regime. Building upon previous studies (Cargill 1994; Cargill and Klimchuk, 1997), Klimchuk and Cargill (2001) consider coronal loops that are built up of thousands of thin plasma strands which are heated repeatedly by nanoflares within a narrow energy range (5 × 1023 erg to 2 × 1024 erg). By employing an analytical approximation to mimic the cooling of recently-heated coronal plasma (initally by conduction


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Table 3. Power-law indices calculated from both X-ray (1) and EUV (2–7) observations Author 1. Shimizu & Tsuneta (1997) 2. Berghmans et al. (1998) 3. Krucker & Benz (1998) 4. Parnell & Jupp (2000) 5. Aschwanden et al. (2000c,d) 6. Benz & Krucker (2002) 7. Winebarger et al. (2002a)

Index −1.74 −1.35 −2.3 to −2.6 −2.0 to −2.6 −1.83 −2.31 −2.8 to −3.0

and then by optically thin radiation), the authors provide diagnostic values and line intensities for a range of spectral lines that could be observed directly by SOHO/CDS and SOHO/SUMER. In particular, they suggest that the classical tools for analysing solar plasma spectrocopically, namely emission measure, filling factor and density or temperature determination from line ratios, are excellent ways for examining an impulsively heated corona (although Judge (2000) has challenged these techniques). Vekstein and Katsukawa (2000) extend the model by Cargill (1994) to include the expansion of thermalised plasma across fieldlines at the energy deposition site – the resulting scaling laws are similiar to those found by Cargill and Klimchuk (1997). Moreover, this recent method has the advantage that it gives an estimate of the magnetic-field strength (between 20 Gauss to 50 Gauss) in the soft x-rays loops under consideration. We will return to the diagnostics of the heat input in coronal loops in Sect. 3.3. Both two- and three-dimensional MHD models of magnetic-flux braiding (see for example, Georgoulis et al., 1998 and Galsgaard and Nordlund, 1996 respectively) exhibit bursty Joule dissipation but only over a limited dynamic range. Galtier and Pouquet (1998) model the dynamics of small-scale dynamic dissipative events in coronal loops by introducing a set of forced, compressible MHD equations within a slab geometry. This allows for extended spatial and temporal resolution as compared to previous numerical experiments that had been performed on three-dimensional grids with lower resolution. Encouragingly, the results of Galtier and Pouquet (1998) reflect the power-law distribution function of flares found in both the SOC models and observations. Walsh and Galtier (2000) investigated the temporal variations only of the plasma response within a coronal loop to this bursty dissipation and found that the time-dependent energy input can maintain the loop at typical coronal temperatures. Table 3 gives a range of indices derived from both EUV and X-ray observations of small scale brightenings. Shimizu and Tsuneta (1997) provide an interesting deep survey of solar nanoflares within an active region observed by SXT. By looking at intensity changes in the light curves of what they call macropixels (having an area of 9.8 ×9.8 ), they find many small brightenings in localised parts of long loop structures, particularly in the core of the observed active region. The time resolution for these light curve measurements was 96 seconds and the authors believe that better temporal and spatial resolution observations over a wide range of temperatures are required to understand fully these localised enhancements. In particular, Krucker and Benz (1998), Benz and Krucker (2002) and Parnell and Jupp (2000) were the first to give a value for α less than the critical value of −2 for

24


nanoflare dominant heating. Also, an even steeper power law is found by Winebarger et al. (2002a) who tie in their specific brightenings to a class known as explosive events (see Sect. 3.2.2). However, the power-law derived by Berghmans et al. (1998) is very flat (at −1.35) compared to the others while the value found by Aschwanden et al. (2000c,d) remains close to that observed for flares. Thus, as indicated by Benz and Krucker (2002) and investigated by the nanoflare modelling of Mitra-Kraev and Benz (2001), there are still a number of quite basic issues to be decided concerning the detection of these small-scale brightenings. Firstly, there is the question of how a specfic event in X-ray or EUV dataset is defined. In most cases, an event is selected when the value of the emission measure in a given pixel or set of pixels reaches a maximum that is above background by a specified number of standard deviations, σ . For example, Parnell and Jupp (2000) only choose events > 2σ . In constrast, Aschwanden et al. (2000c,d) have a much stricter criteria; they consider events that only if they appear in both 171-A˚ and 195-A˚ observations. This weights the distribution towards larger events and hence increases the power law index. Also, there is a question of how one has to define events that occur over a number of adjacent pixels. In prescribing the area of an event, a near synchronous time evolution of each pixel must occur. This may be the reason for the larger index determined by Berghmans et al. (1998); their method places all neighbouring brightening pixels together in a single event, possibly at the expense of single pixel bursts. In addition, McIntosh and Charbonneau (2001) and McIntosh et al. (2002) point out a geometrical effect arising from the relationship between the emitting area A and the underlying emitting volume V . Their avalanche models for a flaring plasma suggest that V ≈ Aγ with γ = 1.41. However, if one assumes that the emitting volume is a cylinder, then γ = 1; on the other hand, a loop model has γ = 1.5. The net effect is that models employing γ = 1 steepen the derived distribution and those with γ = 1.5 flatten it. Simple estimates of this effect are made for α values −3, −4 and −5 (cf. Table 3) leading to a correction of the values of α to −1.77 to −1.94, −1.84 ± 0.04 and −1.81 ± 0.09 respectively; these lie much closer to each other and are larger than the critical value of −2. Moreover, there is the issue of how to calculate the total energy released by such events. This can be done either from the peak emission-measure and temperature observed in an event or from how the line intensities over a wide wavelength range increase or decrease during an event. At present, these estimates place the energy input to the quiet corona at only ≈ 12% relative to the total output from the observed region (Benz and Krucker, 2002). Also, Katsukawa and Tsuneta (2001) show that the Gaussian noise component in Yohkoh/SXT data varies with a mean intensity and is larger than that of the predicted photon-noise distribution. They suggest that the X-ray fluctuations may be due to nanoflares with the energy of a single energy burst estimated to be 1021 erg to 1022 erg. This would correspond to approximately 106 events per second for a single active region. However, it must be remembered that in these brightenings, we are observing the consequences of the heating event – most likely evaporation of the chromosphere and the filling of small loops with hot material – rather than the actual energy release itself. The analysis of observations so far have only considered “coronal” parts of the solar spectrum, owing to current instrumental limitations in the spatial and temporal resolutions at “cooler” wavelengths. Of course, there may be sizeable event contributions at other temperatures. Also, it must be realised that the loss of kinetic energy due to


25

plasma motion and the possible production of MHD waves at a reconnection site could also carry energy away and thus, calculating the total energy budget for a nanoflare is a non-trival matter. Finally, this leads onto the fundamental question as to whether the largest flares are the cumulative effect of numerous smaller nanoflares. One may also ask whether the powerlaw continues down to pico- or femto-flares as well? One possible approach requires investigating whether all elementary heating episodes are governed by the same physical process as are larger flares or whether a different mechanism produces a steeper power law. In that regard, the role of statistical flare heating has been considered for other magnetically active stars. Güdel et al. (2003) investigate long duration flare observations of AD Leo and find a value for α of −2.0 to −2.5 in their flare power-law; this is very similar to the value discussed above. Thus, if this α value is partly a reflection of the activity of the star, maybe the contribution made by nanoflares on the sun is the same as that made by much larger flares in other more active, stellar coronae. Thus, now may be the time to concentrate upon trying to understand the physics behind individual events first and let generalisations and extrapolations follow later. This is dealt with in the next section. 3.2.2. The physical properities of individual atmospheric brightenings There has been an extensive search for small-scale atmospheric transient phenomena; therefore, we will only discuss here an illustrative cross-section of the wide range of events now being reported. Starting at transition region temperatures (around 105 K): following on from Dere et al. (1991) and Dere (1994), Innes et al. (1997) report on explosive events in SOHO/SUMER data. They result in non-Gaussian line profiles which display distinctive red and blue shifted jets with velocities > 160 km s−1 . Innes et al. (1997) argue that these bi-directional jets are manifestations of magnetic reconnection in the quiet Sun. On average, these events last for ≈ 40 s, have a size of about 2 and are believed to be located above regions of mixed weak magnetic polarity or at the edge of regions of strong magnetic flux (Chae et al., 1998). Pérez and Doyle (2000) point out that such events could also be associated with magnetic cancellation. Pérez et al. (1999) examine two specific explosive events in detail – one over an active region (Fig. 10), the other in a coronal hole. Madjarska and Doyle (2002) use high cadence (10 s) SOHO/SUMER data in Ly-6 (at 20,000 K) and S-VI (200,000 K) lines to determine the time evolution of explosive events and find that there is a time delay in the plasma response at these temperatures (namely, S-VI lags Ly-6 by up to 40s). In contrast to this, Brković, Solanki and Rüedi (2002) examine quiet sun variability with SOHO/SUMER and SOHO/CDS. In their datasets, they find a high correlation in variablity between two lines (He-I and O-V) at the same location. Teriaca et al. (2003) find no coronal counterpart to these events and thus, it is not clear what role (if any) they play in heating plasma at coronal temperatures. In that regard, Winebarger et al. (2002a) calculate the global energy release for their observed explosive events to be ≈ 4 × 104 erg cm−2 s−1 ; this would mean that these specific events are energetically insignificant for the coronal heating problem. In a series of papers, Roussev et al. (2001a,b,c) investigate a two-dimensional MHD dissipative numerical scheme of X-point reconnection in the transition region of a solar atmosphere model. They are able to produce blue-shifted jets

26


Fig. 10. A time series for an explosive event observed by SOHO/SUMER in the O-VI line at 1032 A˚ over an active region on 10 July 1996 (from Pérez et al., 1999, courtesy G. Doyle)

at about 100 km s−1 but the red-shifted counterpart are an order of magnitude slower than those observed. Sarro et al. (1999) employ a one-dimensional radiative hydrodynamic simulation of a small (13,000 km) coronal-loop atmosphere to investigate explosive events. They place a short-lived, localised energy burst below the transition region and convert the resulting temporal evolution of the plasma (as manifested by flows etc) into C-IV line profiles; these indicate a strong deviation away from ionization equilibrium. Transition region blinkers (Harrison, 1997; Harrison et al., 1999) are observed by SOHO/CDS in O-V and O-IV lines as local intensity enhancements of ≈ 2 above backgrond levels. They are longer lived (about 1000 s) and five times larger (10 ) than explosive events and have velocities around 20 km s−1 . Priest et al. (2002) suggest five possible physical mechanisms for their origin. These are: the heating of cool (≈ 104 K) spicules; short (5 Mm) loops with 105 K material confined within them; the movement of a thin layer of plasma at 105 K within a large magnetic loop connecting the corona to the chromosphere; the heating and cooling of plasma in a loop in response to changes in the heating rate; and the cooling of already hot coronal material, when coronal heating is absent. However, observations by Bewsher et al. (2002) appear to negate some of the above theories. These authors use an automated blinker detection scheme on SOHO/CDS quietsun data and calculate a global occurrence rate for blinkers of 7.5 per second (which is


27

several orders of magnitude less than the observed rate of spicules). From the flat ratio of the oxygen lines (O-III, O-IV and O-V), Bewsher et al. (2002) deduce that blinkers are a phenomenon associated with an increase of the filling factor or the density rather than an increase in temperature; hence, they rule out the heating of loop plasma through a temperature increase and flow of material. The authors find no corresponding signal at coronal temperatures with 99% of the blinker events being located over network boundaries and 75% occurring over regions of a single magnetic polarity (thus how can a low-lying, cool loop form?). Bewsher et al. (2002) suggest the alternative mechanism of the compression of isothermal plasma along existing fieldlines by granulation. This would need to occur at a rate longer than the thermal conduction timescale (> 1000s) but would lead to a density increase only. Walsh et al. (1997) examine high-cadence (13 s) SOHO/CDS observations across an active region and identify two events that fit the above description of a blinker. Gallagher et al. (1999) search for periodicities in blinkers and conclude that they must be produced by rapid compression of the plasma. Also, Parnell et al. (2002) repeat the analysis by Bewsher et al. (2002) but on SOHO/CDS active region data and in this case, there appear coronal signatures to the events in Mg lines. At coronal temperatures, Shimizu (1995) introduces the term active-region transient brightening (ARTB) to describe single- and multiple-loop events in Yohkoh SXT observations. Ireland et al. (1999b), present a study of 27 dynamic brightenings in TRACE ˚ data, classifying them by their shape and lifetime (cf. Fig. 5d). Berghmans, (171 A) McKenzie and Clette (2001) combine simultaneous observations of brightenings by SXT, SOHO/EIT and TRACE in X-ray (ARTBs) and EUV radiation. They find that there is no simple one-to-one correspondence between events; some ARTBs are associated with several EUV brightenings, other weaker ARTBs (or EUV events) have no EUV (of soft x-ray) component at all. Given the power-law behaviour outlined in Sect. 3.2.1, this begs the following question: are all the small-scale brightenings described above essentially the same “physical event” but with a differing energy output, related to say, the magnetic field strength? That is, are we examining the same physical process, with a number of instruments with differing sensitivity, over a range of temperatures and then naming individually each event that is observed? Conversely, it may be possible that all of these brightenings are “unique”, occuring in distinct magnetic topologies and therefore displaying differing physical characteristics. Overall, the improved spatial and temporal resolution from SOHO and TRACE has pushed the lower boundary on this event distribution down into the nanoflare regime. However, this is at the very edge of our current instrumental abilities and until there are further improvements in resolution, there will continue to be much discussion over whether the corona is heated by a “swarm” of small-scale heating bursts.

3.3. Determining the form of the local heating function It is now becoming possible to use observational data to constrain the location of the dominant heat input (and hence the range of the possible theoretical coronal heating mechanisms operating). So far, much of this research has concentrated upon mini-solar

28


atmospheres confined within magnetic loop structures (cf. Fig. 3). This has been investigated as follows. 3.3.1. Coronal heating and scaling laws Active regions are obvious locations to search for signatures of specific energy release mechanisms as these are places where the coronal heating problem is at its most acute. A landmark advance in the analysis of active regions was presented by Rosner et al. (1978, who used Skylab X-ray data and hydrostatic loop modelling to derive two scaling laws. The first states that; Tmax = 1.4 × 103 (pL)1/3 K, where the maximum loop-top temperature Tmax is a function of the loop length L (centimetres) and pressure p (dyn cm−2 ) only. The second comments on the nature of the coronal heating mechanism by calculating the heat deposition rate EH as; EH = 9.8 × 104 p 7/6 L−5/6 ergs−1 cm−2 . These relationships form an important bridge between theory and observation.The reader is refered to Serio et al. (1981) for modified versions taking into account pressure and heating deposition scale heights in the corona with more recent updates in Aschwanden and Schrijver (2002). However, since the ultimate source of the energy of coronal heating is the magnetic field, a link must be made between the observed emission and the magnetic field in order to determine its role in the coronal heating mechanism. Golub et al. (1980) presented a first attempt at making this connection using Skylab soft X-ray data and ground-based magnetograms. This has latterly been updated and refined by Fisher et al. (1998), who usedYohkoh/SXT and ground-based vector magnetograms to demonstrate that the X-ray flux varies as φ 1.19 , where φ is the total unsigned magnetic flux of the active region. They find that, although Alfvén-wave models predict the correct relation between Xray flux and φ, estimates of the energy available are insufficient to account for the observed emission. On the contrary, estimates arising from nanoflare models yield too much energy and also do not show the same measured correlation between emission and field. The minimum-current corona model is consistent with the observed relationship between soft X-ray emission and magnetic field. In this model, coronal heating occurs as a series of small reconnection events in the quasi-static evolution of the coronal magnetic fields (Longcope, 1996). Heating occurs along separators; i.e., along field lines which differentiate one distinct portion of magnetic field from another. Photospheric flux tube motions create intense current ribbons along the separators and this stored energy is liberated eventually by reconnection. However, a quantitive estimate of the energy input from this model is still lacking. Similar studies have made use of other emission lines. Schrijver (1987) found powerlaw relationships between total unsigned magnetic flux and chromospheric C-II and coronal EUV Mg-X emission and commented that the data appears compatible with coronal heating by dissipation of magnetic shear (Parker, 1983). Schrijver et al. (1989) find a power law relationship between longitudinal magnetic flux density and Ca II K emission (a lower temperature line identified with the solar chromosphere). Increasing longitudinal magnetic flux density leads to an increasing Ca II K emission. Harvey and


29

White (1999) find similar power law relationships in the same variables for specific features such as active region plage, decaying active regions, the enhanced network, the weak network and the quiet network. Fludra and Ireland (2002) use SOHO/CDS EUV data and SOHO/MDI magnetic data (Mandrini et al., 2000) to show that the magnetic reconnection in the current-sheet model of Parker (1983) and the high-frequency, boundary-excitation model of Galsgaard and Nordlund (1996) best fit the observed EUV radiation and the magnetic field power-law relationships. Other approaches on the relationship between active-region emission and magnetic field have been pursued. Fludra and Ireland (2003) assume that the radiance of EUV line ˚ (with a peak formation temperature of 2 MK) in an individual coronal Fe-XVI 360.76A loop is related by a power law to the footpoint magnetic field. The authors use a Laplacetransform approach to sum the distribution of field elements and derive the exponent of the power-law relating to the EUV flux magnetic field . This approach lies in between the idea of summing over the entire active region to characterise it (Fisher et al. 1998) and looking at each loop in the active region individually as presented by, for example, Aschwanden et al. (2000b). Porter and Klimchuk (1995), who had used Yohkoh/SXT data, report that the model of Parker (1983) best fits their results, whilst Aschwanden et al. (2000b) comment that since the EUV loops they considered are far from steady state, the mechanism is necessarily of an intermittent nature, such as nanoflares, dissipated Alfvén waves, or mass injections. 3.3.2. Determining the thermal structure of loops: theory One-dimensional hydrodynamic modelling of coronal loops has been worked upon since the late 1970’s (see the review on one-dimensional fluid models by Peres, 2000). These simulations have been applied to a wide range of scenarios, including the formation of cool condensations in prominences, post-flare loop cooling as well as heating diagnostics. Often the main driver in the system is some imposed, generic heating function. When investigating the hydrostatic temperature profile along a coronal magnetic loop, one requires that there be a balance between the energy sources and sinks at each point. Conduction can contribute to both heat loss or gain depending on the direction of heat flow (which is predominantly along the field). Optically thin radiation peaks at lower transition region temperatures before dropping off as one heads towards the chromosphere where optically thick effects become important (see Fig. 11). Finally, there is the energy gained by the coronal heating term. Differing heating mechanisms can produce heating with spatially different forms. Alfvén waves dissipated by phase-mixing or resonant absorption would tend to heat preferentially close to the loop summit where the amplitude of the fundamental mode would be largest. Also, if a loop broadened substantially at its apex, flux braiding would tend to accumulate there and so give enhanced heating at that location. Loops with uniform cross-sections (Klimchuk, 2000) could give a more uniform braiding (and therefore heating) profile. As a simple test, consider a thin plasma strand observed in the corona as being modelled along a single magnetic field line; with gravity neglected, the temperature T

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Fig. 11. Piecewise approximations to the radiative-loss function in the solar atmosphere (— Hildner, 1974; -.-.- Rosner et al., 1978; - - - Cook et al., 1989)

along the strand obeys the equation ∂T ρ2 ∂ κ = χ T α − H (s), ∂s ∂s µR ˜

(3)

where s is the distance along the loop; ρ is the gas density; κ = κ0 T 5/2 W m−1 K−1 is the coefficient of thermal conductivity parallel to the field with κ0 = 10−11 for the corona; R is the molar gas constant (8.3 × 103 m2 s−2 K−1 ) and µ˜ is the mean molecular weight with µ˜ = 0.6 in the ionised corona. The first term on the right-hand side of equation (3) is the effect of the radiative loss (e.g. Cook et al., 1989). The function H is the spatially dependent energy input to the system. Following Walsh (1999), consider thermal profiles with a hot summit temperature (> 106 K) and cool footpoints embedded in the chromosphere (≈ 104 K) . It is assumed that the loop is symmetrical about the loop apex (dT /ds = 0) and therefore only half of the length of the loop needs to be modelled. Figure 12 displays the dependence of the thermal structure on how this energy is distributed for a 60 Mm coronal loop (−30 Mm ≤ s ≤ 30 Mm) with a total fixed amount of energy being deposited of 1.6 × 1025 erg s−1 . That is, in each case, the total amount of energy being deposited in the loop is exactly the same. If heating is applied uniformly along the loop (b), an apex temperature of about 1.85 × 106 K results. However, if the heat is deposited predominantly at the apex in the rarer coronal part of the loop (a) , the temperature at this point is higher (2.25×106 K) than in the uniform case. The temperature gradient along the loop has increased and therefore conduction plays a vital role in redistributing the heat. If the same total amount of energy is released preferentially at the base of the loop (c), the thermal profile becomes very flat with an apex temperature dropping in value to about 106 K. In this case, conduction is greatly reduced in the coronal part of the loop while most of the deposited energy


31

Fig. 12. Comparison of T (s) with H (s) where the total energy input to the loop structure remains constant

is radiated away. Thus, it is evident that the location of the dominant heat input to the plasma thread has an important and possibly observable effect. 3.3.3. Determining the thermal structure of loops: observations There has been a recent concentration of effort in determing the temperature structure along magnetic loops. Employing variations of the model outlined in the preceding Section, the goal has been to match observed T (s) with a thermal profile that will yield a unique H (s) for that given case. However, this has turned out to not be as straightforward as it would first appear.

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Fig. 13. The differential emission measure at a single SOHO/CDS pixel over an active region (courtesy of Piet Martens)

Firstly, Priest et al. (2000) introduced a hydrostatic loop model that balances only thermal conduction and H (s). This model is then compared with coronal temperature measurements along a large, diffuse, soft x-ray loop observed by Yohkoh/SXT. The authors find that a spatially uniform heat input provides the best fit to the data. However, Mackay et al. (2000) have challenged this analysis, stating that the conclusion of uniform heating lacks statisical significance. Extending the loop temperature down to the transition region imposed a further constraint in the length of the loop and the analysis of Mackay et al. points toward the energy being deposited close to the foot-points of the loop. Reale (2002) also reanalyses the same loop and after subtracting the background from the loop image is taken, deduces that the loop is heated at the apex. That three different data interpretation techniques applied to the same dataset each reach radically different conclusions about the heat input is amazing, if not alarming. This controversy has continued over into the analysis of EUV loops. Aschwanden et al. (2000b, 2001) use filter ratios of SOHO/EIT and TRACE EUV bands (171 A˚ to ˚ say) to argue that the near isothermal loops observed indicate an H (s) weighted 195 A towards heating at the loop base. However, the filter-ratio technique has been critised as being too simplistic. Temperature discrimination from two-dimensional images of the corona is problematic due to the optically-thin nature of the environment:- every pixel in the image is the sum along the line of sight of the radiance of plasma over a wide range of temperatures and densities. Thus the concept of the differential emission measure (DEM) must be employed as a means of calculating the amount of emitting material present. The DEM is the integral of the electron density along the line of sight as a function of temperature in the coronal plasma; Figure 13 shows an example of the DEM at a single SOHO/CDS pixel over an active region. With this in mind, Schmelz et al. (2001) derive a DEM distribution for several pixels along an isolated loop using spectral-line data from SOHO/CDS and broadband data from Yohkoh/SXT. They find that the calculated T (s) is clearly inconsistent with an


33

isothermal (and hence footpoint heated) loop. Schmelz (2002) takes the analysis further by reproducing what SOHO/EIT would observe of the aforementioned SOHO/CDS loop and obtains an isothermal structure. Martens et al. (2002) explains that these results are due to the existence of a broad, flat plateau in the DEM from ≈ 0.7 MK to 2.8 MK (Fig. 13). This indicates that equal amounts of plasma within this temperature range exist along the line of sight. The SOHO/EIT and TRACE narrowband filters fall within this range, hence leading to an isothermal ratio. Testa et al. (2002) argue that diagnostics by use of filter ratios are ambiguous as their TRACE temperature calculations yield both very hot (> 5 MK) and cool (≈ 105 K) loops rather than isothermal ones at 1 MK. On the other hand, Aschwanden (2001) suggests that when broadband filters are used to diagnose a multi-temperature system, there is a bias towards a hydrostatic weighting. Also, Chae et al. (2002) argue that by comparing two filter ratios simultaneously (171 A˚ to ˚ and 195 A ˚ to 284 A), ˚ an unambiguous temperature can be found. 195 A It should be noted that there are other fundamental obstacles that need to be overcome before T (s) can be determined properly from observations. Firstly, Lenz et al. (1999) deduced from long-lived TRACE loops that the structures may consist of a bundle of filamentary loop threads at a range of temperatures which, when averaged over, give the appearance of isothermal loops. Similiarly, Fig. 14 displays a simultaneous images of the same portion of the solar limb taken by SOHO/CDS in the Mg-IX line (representing a temperature of approximately 1.0 MK) and by TRACE in the 171-A˚ bandpass. The closeup of a small area on the right-hand side demonstrates clearly that the filamentary nature of the corona observed by TRACE is averaged out by the SOHO/CDS pixel resolution. Within every CDS pixel, there may be multiple, multi-thermal plasma strands which could be interweaved with one another. Thus the DEM observations from SOHO/CDS will be the spatial average across a bundle of plasma threads. Secondly, as already mentioned, the solar atmosphere is highly dynamic with rapid loop brightenings (Nightingale et al., 1999) and evolving plasma flows (Winebarger et al., 2002b). Thus, taking a thermal snapshot of a plasma strand and fitting an equilibrium model through the data-points is but a first step. A time series of thermal profiles would be more appropriate. In fact, Kano and Tsuneta (1996) use Yohkoh/SXT observations to derive the temperature structure along a > 4 MK loop and find “bumps” in the thermal profiles that are greater than the observational uncertainity. Equilibrium profiles always produce a smoothly varying T (s) – any localised deviations away from these smooth changes may indicate that small-scale, time-dependent heating is occurring. This important aspect has been recognised by several authors. Reale et al. (2000b) use a hydrodynamic model to simulate the temporal evolution of coronal plasma along a particular loop observed by TRACE (Reale et al., 2000a). They are able to recreate the observed emission by using an asymetric, implusive heating source followed by folding the simulation through the appropiate instrument response functions. Warren et al. (2002) investigate bright EUV loops that persist longer than the characterisitc radiative cooling time for a 1 MK corona. They argue that the behaviour of these loops can be reproduced by a collection of smaller plasma threads that are repeatedly heating and cooling down. Spadaro et al. (2003) show that the problem of overdense loops (Aschwanden et al., 2001), where the observed density is in excess of that predicted by scaling laws (see Sect. 3.3.1), can be explained by having a transient heating burst close to one loop footpoint. The plasma parameters at certain stages of their evolution exhibit a higher

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Fig. 14. Simultaneous images taken by SOHO/CDS (in the Mg-IX line at a temperature of ap˚ bandpass (also about 1 MK – see Schrijver et al., 1999). proximately 1.0 MK) and TRACE 171-A The close-up of the same region on the right demonstrates that the filamentary nature of the corona observed by TRACE is averaged out by the CDS pixel resolution


35

density than expected. Walsh et al. (1997) consider discrete energy bursts over a wide energy (1024 erg to 1028 erg) and temporal ranges and find that the larger events do not occur frequently enough to maintain typical coronal temperatures. It should also be noted that the problem of determining T (s, t) is compounded when using a rastering spectrometer like the Normal Incidence Spectrometer (NIS) on SOHO/CDS. The NIS slit is exposed only for a certain time over the target while it sweeps the field from right to left in discrete steps, building up a complete image. Thus if plasma is evolving in some way while CDS is building up an image at another position with the field under consideration, a spatio-temporal smearing of the diagnosed plasma parameters occurs (Walsh, 2002). The extent of this smearing depends upon (i) the timescale of the plasma changes themselves relative to the exposure time of the CDS raster and (ii) the orientation of the loop on the Sun relative to the position of the moving vertical slit. This could be overcome by setting the slit at one location in the loop (apex or footpoint say) and tracking the temperature/density changes at that point. This could indicate the possible heating timescale operating in a specific loop. Thirdly, from a planar image, it is difficult to determine the basic three-dimensional geometry of the loop. For example; what is its length, inclination to the solar surface or aspect ratio? These are all important quantities required for modelling. Attempts have been made to deal with this problem (e.g., Aschwanden et al., 1999b, 2000a) but eventually true three-dimensional imaging is required. This will be addressed by the STEREO mission (see Sect. 4). Finally, the question must be posed as to whether there are distinct loop classes observed at differing wavelengths (for example, X-ray, EUV, cool and post-flare loops) or whether they are all the same apart from, say, the magnitude of the energy input. Thus, it is vital to obtain T (s) along a wide range of loop structures. 4. Summary and future missions This review has considered some of the most recent and significant advances in tackling the coronal heating problem. An incredible amount of new information about the Sun’s outer atmosphere has been obtained as a result of the Yohkoh, SOHO and TRACE missions. In particular, the wave-heating model has been revitalised by new observational evidence of quasi-periodic oscillations throughout the solar atmosphere. The small-scale episodic heating approach (nanoflares) is finding new constraints for the theory from both individual small-scale brightenings as well as power-law observations at the very limit of current instrumental capabilities. Also, a possible new diagnostic tool for the heating has been suggested, namely determining the thermal structure of coronal loops. However, accurate modelling, coupled with a clear understanding of the observing technique and interpretation, is required to constrain possible spatial- and time-dependent energy release mechanisms. Such new observations drive both the direction for future instrumentation as well as theoretical modelling. As outlined in Sect. 1, further progress in resolving the coronal heating problem requires almost exclusively space observations. Therefore, we mention here space-based solar observatories that are being currently developed: – Solar-B: Due for launch in 2006, this is the Japanese/US/UK follow-up mission to Yohkoh. Using optical, EUV and X-ray instruments, Solar-B is designed to study

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Table 4. Description of a selection of future instrumentation to be flown on SolarB (EIS: Extreme ultraviolet Imaging Spectrometer; XRT: X-ray Telescope), STEREO (EUVI: Extreme UltraViolet Imager), SDO and Solar Orbiter (EUS: Extreme Ultraviolet Spectrometer; EUI: Extreme Ultraviolet Imager with FSI (Full Sun Imager) and HRI (High Resolution Imager)) Instrument

Description

Best pixel Size (km)

Best time Resolution (s)

Solar-B EIS Solar-B XRT STEREO EUVI SDO Solar orbiter EUS Solar orbiter EUI(FSI) Solar orbiter EUI(HRI)

EUV spectrometer X-ray imager EUV imager EUV imager EUV spectrometer EUV full sun imager EUV partial field imager

725–1450 1450 ≈ 900 ≈ 900 75 1300 35

1–10 2 10 10 1 10 10

the linkage between the magnetic field and the corona. In particular the EUV spectrometer will be optimised for observing active region dynamics. – STEREO: This mission, also scheduled for launch in 2006, will obtain simultaneous images of the Sun from two lines of sight. Using two spacecraft at 1 AU which drift apart slowly, this will allow the stereoscopic reconstruction of three-dimensional images of active regions and coronal mass ejections as they erupt from the Sun. For example, having two viewpoints of the same transversal loop oscillation will tell us much more about the dynamics of coronal loops. – Solar Dynamics Observatory (SDO): A cornerstome mission of NASA’s “Living with a Star” Programme The primary goal of SDO is to investigate the nature and source of solar variations and how they affect life and society. Due for launch in 2007, SDO will be placed in a geosynchronous orbit that will allow for nearly continuous high-telemetry contact. The data rate is about a thousand times that of SOHO with effectively full disc TRACE quality images transmitted every 10 seconds in a range of wavelengths. Mission objectives include understanding the mechanisms for solar variability over a very large range of timescales, specifically of small-scale magnetic flux interactions and brightenings (over seconds to hours), of active region evolution (over hours to days) and of the solar cycle (over weeks to months to years). SDO will also examine how the Sun influences space weather and possible climate change on the Earth. – Solar Orbiter: A unique ESA observatory, the Solar Orbiter will approach the Sun to within 0.2 AU at one part of its orbit, to enable close-up remote sensing of the atmosphere. Also, by matching the speed of the spacecraft with the Sun’s rotation, Orbiter will “hover” over an active region for several days. Finally, by increasing the inclination of the orbital plane, the mission will climb out of the ecliptic to ≈ 30◦ to view the solar poles. Through being so close to the Sun, its effective spatial resolution may allow us to resolve the possible existence of even smaller heating events on the Sun or to decompose the currently known ones into their constituent parts. Such spatial resolution can also help us to begin to answer some questions


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about the presence of resonance layers in loop systems and from there, the viability of wave-based coronal heating mechanisms. Table 4 describes the improved resolution of future spectrometers and atmospheric imagers. In all of the above, there will be greatly enhanced spectral, spatial and temporal capabilities that we know now are needed to probe the dynamic solar atmosphere; with closer linkage to the theoretical modelling than ever before, we look forward to a much better understanding of the long-standing puzzle of how the solar corona is heated. Acknowledgements. The authors would like to thank Gerry Doyle, Piet Martens and Alan Hood for providing a number of figures and for helpful comments and suggestions. We would also like to thank Martin Huber for his patience and constructive critisism of manuscript. RWW was supported in this work by a Leverhulme Trust Research Fellowship. SOHO is a project of international cooperation between ESA and NASA. SOHO images are courtesy of SOHO CDS/EIT/MDI consortia. TRACE images are courtesy of the Stanford-Lockheed Institute for Space Research.

References T.E Abdelatif: Ap. J. 322, 494 (1987) M.J. Aschwanden: Ap. J. 559, L171 (2001) M.J. Aschwanden, L. Fletcher, C.J. Schrijver, D. Alexander: Ap. J. 520, 880 (1999a) M.J. Aschwanden, J.S. Newmark, J.-P. Delaboudinière, W.M. Neupert, J.A. Klimchuk, G.A. Gary, F. Portier-Fozzani, A. Zucker: Ap. J. 515, 842 (1999b) M.J. Aschwanden, D. Alexander, N. Hurlburt, J.S. Newmark, W.M. Neupert, J.A. Klimchuck, G.A. Gary: Ap. J. 531, 1129 (2000a) M.J. Aschwanden, R.W. Nightingale, D. Alexander: Ap. J. 541, 1059 (2000b) M.J. Aschwanden, R.W. Nightingale, T.D. Tarbell, C.J. Wolfson: Ap. J. 535, 1027 (2000c) M. Aschwanden, C.J. Schrijver, Ap. JSS. 142, 269 (2002) M. Aschwanden, C.J. Schrijver, D. Alexander: Ap. J. 550, 1036 (2001) M. Aschwanden, T.D. Tarbell, R.W. Nightingale, C.J. Schrijver, A. Title, C.C. Kanelborg, P. Martens, H.P. Warren: Ap. J. 535 1047 (2000d) M.J. Aschwanden, B. De Pontieu, C.J. Schrijver, A. Title: Solar Phys. 206, 99 (2002) H. Balthasar: Solar Phys. 187, 389 (1999) A.J.C. Beliën, P.C.H. Martens, R. Keppens: Ap. J. 526, 478 (1999) L.R. Bellot Rubio, M. Collados, B. Ruiz Cobo, I. Rodriguez Hidalgo: Ap. J. 534, 989 (2000) A.O. Benz, S. Krucker: Ap. J. 568, 413 (2002) D. Berghmans, F. Clette, D. Moses: A&A 336, 1039 (1998) D. Berghmans, F. Clette: Solar Phys. 186, 207 (1999) D. Berghmans, D. McKenzie, F. Clette: A&A 369, 291 (2001) R.J. Bray, L.E. Cram, C.J. Durrant, R.E. Loughhead: Plasma Loops in the Solar Corona (CUP, 1991) D. Bewsher, C.E. Parnell, R.A. Harrison: Solar Phys. 206, 21 (2002) A. Brkovic, S.K. Solanki, I. Rüedi: A&A 385, 257 (2002) P.K. Browning, E.R. Priest: A&A 131, 283 (1984) N. Brynildsen, T. Leifson, O. Kjeldseth-Moe, P. Maltby, K. Wilhelm: Ap. J. 511, L121 (1999a) N. Brynildsen, P. Maltby, T. Leifson, O. Kjeldseth-Moe, K. Wilhelm: Solar Phys. 191, 129 (1999b) N. Brynildsen, P. Maltby, T. Fredvik, O. Kjeldseth-Moe: Solar Phys. 207, 259 (2002) P.J. Cargill: Ap. J. 422, 381 (1994) P.J. Cargill, J.A. Klimchuk: Ap. J. 478, 799 (1997)

38


J. Chae, H. Wang, C.Y. Lee, P.R. Goode, U. Schuhle: Ap. J. 497, L109 (1998) J. Chae, Y.-D. Park, Y.-J. Moon, H. Wang, H.S. Yun: Ap. J. 567, L159 (2002) P. Charbonneau, S.W. McIntosh, H.-L. Liu, T.J. Bogdan: Solar Phys. 203, 321 (2001) J.W. Cook, C.-C. Cheng, V.L. Jacobs, S.K. Antiochos: Ap. J. 338, 1176 (1989) F.C. Cooper, V.M. Nakariakov, D. Tsiklauri: A&A 397, 765 (2003) J.M. Davila: Ap. J. 317, 514 (1987) C.E. De Forest, J.B. Gurman: Ap. J. 501 (1998), L217 A. De Groof, M. Goossens: Ap. J. 386, 691 (2002) A. De Groof, K. Paes, M. Goossens: Ap. J. 386, 681 (2002) I. De Moortel, A.W. Hood, J. Ireland, T.D. Arber: A&A 346, 641 (1999) I. De Moortel, A.W. Hood, T.D. Arber: A&A 354, 334 (2000a) I. De Moortel, J. Ireland, R.W. Walsh: A&A 355, L23 (2000b) I. De Moortel, J. Ireland, A.W. Hood, R.W. Walsh: Solar Phys. 209, 61 (2002a) I. De Moortel, A.W. Hood, J. Ireland, R.W. Walsh: Solar Phys. 209, 89 (2002b) I. De Moortel, J. Ireland, A.W. Hood, R.W. Walsh: A&A 387, L13 (2002c) I. De Moortel, A.W. Hood, J. Ireland: A&A 381, 311 (2002d) P.C.H. B. De Pontieu, P.C.H. Martens, H.S. Hudson: Ap. J. 558, 859 (2001) K.P. Dere: Adv. Space Res. 14(4), 13 (1994) K.P. Dere, J.-D.F. Bartoe, G.E. Brueckner, J. Ewing, P. Lund: J. Geophys. Res. 96, 9399 (1991) V. Domingo, B. Fleck, A.I. Poland: Space Sci. Rev. 70, 7 (1994) B. Edlén: Z. Astrophys. 22, 30 (1942) R. Erdélyi, J.G. Doyle, M.E. Pérez, K. Wilhelm: A&A 337, 287 (1998) G.H. Fisher, D.W. Longcope, T.R. Metcalf, A. Pevtsov: Ap. J. 508, 885 (1998) L. Fletcher, T.R. Metcalf, D. Alexander, L.A. Ryder, D. Brown, R.W. Nightingale: Ap. J. 554, 541 (2001) A. Fludra, J. Ireland: ESA-SP 508, 267 (2002) A. Fludra, J. Ireland: A&A (2003) in press P.T. Gallagher, K.J.H. Phillips, L.K. Harra-Murnion, F. Baudin, F.P. Keenan: A&A 348, 251 (1999) K. Galsgaard, A. Nordlund: JGR 101, 13445 (1996) S. Galtier, A. Pouquet: Solar Phys. 179, 141 (1998) M. Georgoulis, L. Vlahos: Ap. J. 469, 135 (1996) M. Georgoulis, L. Vlahos: A&A 336, 721 (1998) M. Georgoulis, M. Velli, G. Einaudi: Ap. J. 497, 957 (1998) L. Golub, C. Maxson, R. Rosner, S. Serio, G.S. Vaiana: Ap. J. 238, 343 (1980) M. Goossens, J. Andries, M.J. Aschwanden: A&A 394, L39 (2002) M. Goossens, M.S. Ruderman: Phys. Scr. T60, 171 (1995) M. Goossens, M.S. Ruderman, J.V. Hollweg: Solar Phys. 157, 75 (1995) W. Grotrian: Naturwissen 27, 214 (1939) M. Güdel, M. Audard, V.L. Kashyap, J.J. Drake, E.F. Guinan: Ap. J. 582, 423 (2003) J.B. Gurman, L.L. House: Solar Phys. 71, 5 (1981) J.B. Gurman, J.W. Leibacher, R.A. Shine, B.E. Woodgate, W. Henze: Ap. J. 253, 939 (1982) H.I. Hagenaar: Ap. J. 555, 448 (2001) L.W. Handy et al.: Solar Phys. 187 229 (1999) H. Hara, K. Ichimoto: Ap. J. 513, 969 (1999) R.A. Harrison: Solar Phys. 175, 467 (1997) R.A. Harrison, A.W. Hood, C.D. Pike: A&A 392, 319 (2002) R.A. Harrison, J. Lang, D.H. Brooks, D.E. Innes: A&A 351, 111 5 (1999) K.L. Harvey, O.R. White: Ap. J. 515, 812 (1999) J. Heyvaerts, E.R. Priest: A&A. 117, 220 (1983) E. Hildner: Solar Phys. 35, 123 (1974)


39

J.V. Hollweg: Ap. J. 312, 880 (1987a) J.V. Hollweg: Ap. J. 320, 875 (1987b) A.W. Hood, J. Ireland, E.R. Priest: A&A 318, 957 (1997a) A.W. Hood, D. Gonzáles-Delgado, J. Ireland: A&A 324, 11 (199b) T. Horn, J. Staude, V. Landgraf: Solar Phys. 172, 69 (1997) M.C. Huber, M. Malinovsky-Arduini: Space Sci. Rev. 61(3–4), 301 (1992) H.S. Hudson: Solar Phys. 133, 357 (1991) D.E. Innes, B. Inhester, W.I. Axford, K. Wilhelm: Nature 386, 811 (1997) J.A. Ionson: Ap. J. 226, 650 (1978) J. Ireland, I. De Moortel: A&A 391, 339 (2002) J. Ireland, E.R. Priest: Solar Phys. 173, 31 (1997) J. Ireland, M. Wills-Davey, R.W. Walsh: Solar Phys. 190, 207 (1999) P.G. Judge: Ap. J. 531, 585 (2000) R. Kano, S. Tsuneta: PASJ 48, 535 (1996) Y. Katsukawa, S. Tsuneta: Ap. J. 557, 343 (2001) D.E. McKenzie, D.J. Mullan: Solar Phys. 176, 127 (1997) B. Kliem, I.E. Dammasch, W. Curdt, K. Wilhelm: Ap. J. 568, L61 (2002) J.A. Klimchuk: Solar Phys. 193, 53 (2000) J.A. Klimchuk, P.J. Cargill: Ap. J. 553, (2001) 440 R.A. Koop, G. Poletto: Solar Phys. 133, 357 (1993) ˘ zda, V. Loc˘ans: A&A 120, 185 (1983) S. Koutchmy, Y.D. Zug˘ S. Krucker, A.O. Benz: Ap. J. 501, L213 (1998) H. Lee, H.S. Yun, J. Chae: JKAS 33, 57 (2000) D.D. Lenz, E.E. DeLuca, L. Golub, R. Rosner, J.A. Bookbinder, C. Litwin, F. Reale, G. Peres: Solar Phys. 190, 131 (1999) B.W. Lites, J.H. Thomas, T.J. Bogdan, P.S. Cally: Ap. J. 497, 464 (1998) D.W. Longcope: Solar Phys. 169, 91 (1996) E.T. Lu, R.J. Hamilton: Ap. J. 380, L89 (1991) D.M. Mackay, K. Galsgaard, E.R. Priest, C.R. Foley: Solar Phys. 193, 93 (2000) A.L. MacKinnon, K.P. Macpherson: A&A 326, 1228 (1997) K.P. MacPherson, A.L. MacKinnon: A&A. 350, 1040 (1999) M.S. Madjarska, J.G. Doyle: A&A 382, 319 (2002) F. Malara, P. Petkaki, P. Veltri: Ap. J. 533, 523 (2000) P. Maltby, N. Brynildsen, T. Fredvik, O. Kjeldseth-Moe, K. Wilhelm: Solar Phys. 190, 129 (1999) C.H. Mandrini, P. Démoulin, J.A. Klimchuk, Ap. J. 530, 999 (2000) M.S. Marsh, R.W. Walsh, B.J.I. Bromage: A&A 393 (2002) 649 M.S. Marsh, R.W. Walsh, I. De Moortel, J. Ireland: A&A 404, L37 (2003) P.C.H. Martens, J.W. Cirtain, J.T. Schmelz: Ap. J. 577, L115 (2002) K.G. McClements, R.A. Harrison, D. Alexander: Solar Phys. 131, 41 (1991) S.W. McIntosh, P. Charbonneau: Ap. J. 563, L165 (2001) S.W. McIntosh, P. Charbonneau, T.J. Bogdan, H.-L. Liu, J.P. Norman: Phys. Rev. E 65, 046125 (2002) U. Mitra-Kraev, A.O. Benz: A&A 373, 318 (2001) R.L. Moore, Z.E. Musielak, S.T. Suess, C.-H. An: Ap. J. 378, 347 (1991) D.J. Mullan, M. Johnson: Ap. J. 444, 350 (1995) V.M. Nakariakov, L. Ofman: A&A 372, L53 (2001) V.M. Nakariakov, L. Ofman, E.E. DeLuca, B. Roberts, J.M. Davila: Science 285, 862 (1999) V.M. Nakariakov, B. Roberts, K. Murawski: A&A 332, 795 (1998) V.M. Nakariakov, E. Verwichte, D. Berghmans, E. Robbrecht, A&A 362, 1151 (2000) R.W. Nightingale, M.J. Aschwanden, N.E. Hurlburt: Solar Phys. 190, 249 (1999)

40


L. Nocera, B. Leroy, E.R. Priest: A&A 133, 387 (1984) A.A. Norton, R.K. Ulrich: Solar Phys. 192, 403 (2000) A.A. Norton, R.K. Ulrich, R.I. Bush, T.D. Tarbell: Ap. J. 518, L123 (1999) L. Ofman: Ap. J. 568, L13 (2002)5 L. Ofman, M.J. Aschwanden: Ap. J. 576, L153 (2002) L. Ofman, J. Davila, R.S. Steinolfson: Ap. J. 444, 471 (1995) L. Ofman, J.A. Klimchuk, J.M. Davila: Ap. J. 493, 474 (1998) L. Ofman, V.M. Nakariakov, C.E. Deforest: Ap. J. 514(1), 441 (1999) E.N. Parker: Ap. J. 264, 642 (1983) E.N. Parker: Ap. J. 330, 474 (1988) E.N. Parker: Ap. J. 376, 355 (1991) C.E. Parnell, D. Bewsher, R.A. Harrison: Solar Phys. 206, 249 (2002) C.E. Parnell, P.E. Jupp: Ap. J. 529, 554 (2000) G. Peres: Solar Phys. 193, 33 (2000) M.E. Pérez, J.G. Doyle, R. Erdélyi, L.M. Sarro: A&A 342, 279 (1999) M.E. Pérez, J.G. Doyle: A&A 360, 331 (2000) P. Petkaki, F. Malara, P. Veltri: Ap. J. 500, 483 (1998) K.J.H. Phillips, P.D. Read, P.T. Gallagher et al.: Solar Phys. 193, 259 (2000) S. Poedts, J.P. Goedbloed: A&A 321, 935 (1997) S. Poedts, M. Goossens, W. Kerner: Ap. J. 360, 279 (1990) S. Poedts, W. Kerner: Phys. Rev. Lett. 66(22), 2871 (1991) L.J. Porter, J.A. Klimchuk, P.A. Sturrock: Ap. J. 435, 435 (1994a) L.J. Porter, J.A. Klimchuk, P.A. Sturrock: Ap. J. 435, 502 (1994b) L.J. Porter, J.A. Klimchuk: Ap. J. 454, 499 (1995) E.R. Priest: Solar Magnetohydrodynamics (D. Reidel, Dordrecht 1982) E.R. Priest, C.R. Foley, J. Heyvaerts, T.D. Arber, D. Mackay, J.L. Culhane, L.W. Acton: Ap. J. 539, 1002 (2000) E.R. Priest, T. Forbes: Magnetic Reconnection: MHD Theory and Applications (CUP 2000) E.R. Priest, T. Forbes: Astron. Astrophys. Rev. 10, 313 (2002) E.R. Priest, J. Heyvaerts, A. Title: Ap. J. 576, 533 (2002) E.R. Priest, A.W. Hood, D. Bewsher: Solar Phys. 205, 249 (2002) E.R. Priest, V.S. Titov: Phil. Trans. Roy. Soc. 354, 2951 (1996) F. Reale: Ap. J. 580, 566 (2002) F. Reale, G. Peres, S. Serio, R.M. Betta, E.E. DeLuca, L. Golub: Ap. J. 535, 412 (2000a) F. Reale, G. Peres, S. Serio, R.M. Betta, E.E. DeLuca, L. Golub: Ap. J. 535, 423 (2000b) E. Robbrecht, E. Verwichte, D. Berghmans, J.F. Hochedez, S. Poedts, V.M. Nakariakov: A&A 370, 591 (2001) B. Roberts, P.M. Edwin, A.O. Benz: Ap. J. 279, 857 (1984) R. Rosner, W.H. Tucker, G.S. Vaiana: Ap. J. 220, 643 (1978) I. Roussev, R. Erdélyi, J.G. Doyle, K. Galsgaard: A&A 370, 298 (2001a) I. Roussev, K. Galsgaard, R. Erdélyi, J.G. Doyle: A&A 375, 228 (2001b) I. Roussev, J.G. Doyle, K. Galsgaard, R. Erdélyi: A&A 380, 719 (2001c) M.S. Ruderman, B. Roberts: Ap. J. 577, 475 (2002) M.S. Ruderman, V.M. Nakariakov, B. Roberts: A&A 338, 1118 (1998) M.S. Ruderman, A.N. Wright: Phys. Plasmas 7(9), 3515 (2000) I. Rüedi, S.K. Solanki, J.O. Stenflo, T. Tarbell, P.H. Scherrer: A&A 335, L97 (1998) M.P. Ryutova, S.R. Habbal: Ap. J. 451, 381 (1995) J.L.R. Saba, K.T. Strong: Ap. J. 375, 789 (1991) L.M. Sarro, R. Erdélyi, J.G. Doyle, M.E. Pérez: A&A 351, 721 (1999) J.T. Schmelz, R.T. Scopes, J.W. Cirtain, H.D. Winter, J.D. Allen: Ap. J. 556, 896 (2001)


41

J.T. Schmelz: Ap. J. 578, L161 (2002) C.J. Schrijver: A&A 172, 111 (1987) C.J. Schrijver, J. Coté, C. Zwaan, S.H. Saar: Ap. J. 337, 964 (1989) C.J. Schrijver et al: Solar Phys. 187, 261 (1999) C.J. Schrijver, D.S. Brown: Ap. J. 537, L69 (2000) C.J. Schrijver, M.J. Aschwanden, A.M. Title: Solar Phys. 206, 69 (2002) S. Serio, G. Peres, G.S. Vaiana, L. Golub, R. Rosner: Ap. J. 243, 288 (1981) A. Settele, T.A. Carroll, I. Nickelt, A.A. Norton: A&A 386, 1123 (2002) A. Settele, J. Staude, Y.D. Zhugzhda: Solar Phys. 202, 281 (2001) T. Shimizu: PASJ 47, 251 (1995) T. Shimizu, S. Tsuneta: Ap. J. 486, 1045 (1997) P.L. Similon, R.N. Sudan: Ap. J. 336, 442 (1989) D. Spadaro, A.F. Lanza, A.C. Lanzafame, J.T. Karpen, S.K. Antiochos, J.A. Klimchuk, P.J. MacNeice: Ap. J. 582, 486 (2003) R.S. Steinolfson, J.M. Davila: Ap. J. 415, 354 (1993) P.A. Sturrock: Plasma Physics: An introduction to the theory of astrophysical, geophysical, and laboratory plasmas (Cambridge University Press, 1994) J. Tataronis, W. Grossman: Z. Physik 261, 203 (1973) L. Teriaca, M.S. Madjarska, J.G. Doyle: A&A 392, 309 (2003) P. Testa, G. Peres, F. Reale, S. Orlando: Ap. J. 580, 1159 (2002) W.J. Tirry, M. Goossens: Ap. J. 471, 501 (1996) S. Tsuneta, L. Acton, M. Bruner, J. Lemen, W. Brown, R. Caravalho, R. Catura, S. Freeland, B. Jurcevich, J. Owens: Solar Phys. 136, 37 (1991) D. Tsiklauri, V.M. Nakariakov: A&A 379, 1106 (2001) R.K. Ulrich: Ap. J. 465, 436 (1996) G.S. Vaiana, R. Rosner: Ann. Rev. Astron. Astrophys. 16, 393 (1978) G. Vekstein, Y. Katsukawa: Ap. J. 541, 1096 (2001) L. Vlahos, M. Georgoulis, R. Kluiving, P. Paschos: A&A 229, 897 (1995) R.W. Walsh: Lect. Notes in Phys. 507, 187 (1998) R.W. Walsh: ESA SP-446, 687 (1999) R.W. Walsh: ESA SP-508, 335 (2002) R.W. Walsh, S. Galtier: Solar Phys. 197, 57 (2000) R.W. Walsh, J. Ireland, R.A. Harrison, E.R. Priest: ESA SP 404, 717 (1997) T. Wang, S.K. Solanki, W. Curdt, D.E. Innes, I.E. Dammasch: ESA SP-508, 465 (2002a) T. Wang, S.K. Solanki, W. Curdt, D.E. Innes, I.E. Dammasch: Ap. J. 574, L101 (2002b) H.P. Warren, A.R. Winebarger, P.S. Hamilton: Ap. J. 579, L41 (2002) A.R. Winebarger, A.G. Emslie, J.T. Mariska, H.P. Warren: Ap. J. 565, 1298 (2002a) A.R. Winebarger, H.P. Warren, A. Van Ballegooijen, E.E. DeLuca, L. Golub: Ap. J. 567, L89 (2002b) A.N. Wright, G.J. Rickard: Ap. J. 444, 458 (1995) R. Woo: Nature 379, 321 (1996) ˘ zda, V. Loc˘ans, J. Staude: Solar Phys. 82, 369 (1983) Y.D. Zug˘

The Astron Astrophys Rev (2003) 12: 43–69 Digital Object Identifier (DOI) 10.1007/s00159-003-0020-x

THE


Circulating subbeam systems and the physics of pulsar emission Joanna M. Rankin1,∗ , Geoffrey A.E. Wright2 1 Sterrenkundig Instituut, University of Amsterdam, Kruislaan 403, Amsterdam 1098 SJ,

The Netherlands (e-mail: [email protected]) 2 Astronomy Centre, University of Sussex, Falmer BN1 9QJ, UK

(e-mail: [email protected]) Received 8 May 2003 / Published online 14 November 2003 – © Springer-Verlag 2003

Abstract. The purpose of this paper is to suggest how detailed single-pulse observations of “slow” radio pulsars may be utilized to construct an empirical model for their emission. It links the observational synthesis developed in a series of papers by Rankin in the 1980’s and 90’s to the more recent empirical feedback model of Wright (2003a) by regarding the entire pulsar magnetosphere as a non-steady, non-linear interactive system with a natural built-in delay. It is argued that the enhanced role of the outer gap in such a system indicates an evolutionary link to younger pulsars, in which this region is thought to be highly active, and that pulsar magnetospheres should no longer be seen as being “driven” by events on the neutron star’s polar cap, but as having more in common with planetary magnetospheres and auroral phenomena. Key words: stars: pulsars: Polarisation – Radiation mechanisms: non-thermal

Introduction A visitor to a pulsar observing session will see on the oscillograph something quite unlike anything in the rest of astrophysics: a never-ending dancing pattern of pulses: sometimes bright, sometimes faint, sometimes in regular patterns, sometimes disordered, sometimes switching off entirely only to resurge with greater vigour. Variations can be found on every time scale down to tiny fractions of seconds. Astrophysics is a field used to dealing with objects which evolve over millions, over thousands of millions of years, perhaps occasionally punctuated by dramatic cataclysmic Correspondence to: [email protected] ∗ On leave from: Physics Department, University of Vermont, Burlington, VT 05405, USA

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J.M. Rankin, G.A.E. Wright

events, but generally affording no more than an unvarying image through the telescope. How are we then to deal with a phenomenon which is so alien to the common astrophysical experience? It can be argued that the study of pulsars is more than a study of complex physics: that it is a study of complexity itself. Beyond the original insights, some 30 years ago now, that pulsars are rotating magnetised neutron stars, emitting coherently in the radio band from a roughly conical region above the magnetic polar caps, little has been elicited from the welter of information gathered over the decades to point us towards some fundamental understanding of the underlying mechanism by which the pulsars emit. This impasse has arisen partly because pulsars have been treated primarily as steadystate astrophysical objects undergoing minor fluctuations which we detect in subpulses, rather than as intrinsically non-steady, nonlinear systems whose subpulses contain valuable information about the nature of the system. Yet before any detailed physics can be undertaken, it is essential to unravel the embedded complexity and to discern the structure of the underlying system. This point is well understood in many branches of terrestrial physics where irregular time series are commonplace. Why is it so difficult to predict the weather? Why do animal populations dramatically rise and fall in an apparently random manner? The point of course is that although complexity may arise through the operation of complex systems (as with the weather), it can also do so through simple systems operating under simple conditions – as in the classic population studies of Prof. Robert May (for a review see [79]). And it is essential to distinguish between them, and to know which we are dealing with. In the case of pulsars emphasis has certainly been laid on the former of these assumptions. Theorists have explored the properties of time-independent magnetosphere models (often axisymmetric about the rotation axis, so they would not even pulse!) and assumed that the observed radio phenomena are complex temporal or geometrical “perturbations” of some underlying equilibrium. Furthermore, many emission models have seen pulsar “events” as being driven and determined by conditions on the polar cap surface, reflecting the traditional view of classical dynamics that systems have starting and ending points, that causality has only one direction. The problem of this approach is that detailed time-structured observations have little to say in the construction and verification of these models. Perhaps it is possible to take an alternative approach, well started in a series of papers by one of us and her collaborators (“Towards An Empirical Theory of Pulsar Emission”, I–VIII; hereafter ETI–ETVIII), to use the observations to determine the model – to ask the pulsars themselves how they work. This approach is shared by another of us in a paper [134], which attempts to construct an empirical pulsar model from known observations. The physical features of such a model necessarily remain only sketched, but intriguingly suggest a link to the auroral properties of terrestrial and planetary magnetospheres, and entail a feedback system capable of generating quasi-chaotic phenomena. Where appropriate, throughout this review we will draw attention to links between observations and this model, and possible tests of its validity. Following the spirit of these ideas we therefore adopt the view that, although apparently complex, pulsar observations at both radio frequencies and in the optical, x-ray and γ -ray regions may be the by-products of a single simple underlying system. As far

Circulating subbeam systems and the physics of pulsar emission

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as possible special pleading or exceptional circumstances will not be introduced in order to explain difficult results. The thesis explored in this review is that the simple picture of a dipole rotating alone in vacuo, when inclined at different angles and viewed from different angles, can give rise to the myriad of beautiful complex phenomena observed in pulsars at many wavelengths over the past decades. This thesis will be put to the test.

Geometry is pivotal Let us assume that the only permanent features of any pulsar are its underlying magnetic geometry and our particular view of it. Knowledge of these is the prerequisite to establishing the degree of complexity (or simplicity) the underlying flow of the emitting particles needs to possess to account for the highly non-steady observations. So what results, developed over the many years of pulsar research, can confidently be regarded as indicators of a pulsar’s magnetic field geometry and thus give a starting point in our quest? Below are listed the three most influential ideas, all of which are closely associated with a pulsar’s most fundamental observational property: its remarkably stable and individual integrated profile. – The most fundamental result – as fundamental today as it was over 30 years ago for Radhakrishnan & Cook [101; hereafter R&C] and Komesaroff [60] – is the conal, single-vector-model (SVM) geometry implicit in many profile forms and polarization position-angle (hereafter PA) traverses. Without question this is the most successful theoretical idea yet articulated as it relates the magnetic inclination and sightline impact angles α and β to the PA sweep behavior. Of course, it is probably a simplification or abstraction of the actual physical situation. And we must question whether its underlying assumptions are entirely correct. But (as with the dipolar assumption below) the best means of assessing its correctness is to assume it true and then study any resulting discrepancies. – Second, the extension and development of the foregoing models (also Backer [9]) into a profile classification system – the starting point of the “Empirical Theory” noted above – and their subsequent evolution into several broadly compatible means of estimating angles α and β characterizing a star’s emission geometry [73; hereafter LM]; ETVIa,b). This in turn has led to the provisional conclusion that the integrated emission from most pulsars stems from one or all of three different emission beams, the core and the inner/outer cones, each roughly centered on the magnetic axis. (See ETI: Fig. 21 and ETVIa: Fig. 1 for a schematic description of the classification system.) – Third, it has emerged that pulsar emission beams are nearly circular! While various workers have cogently explored whether they might be latitudinally or longitudinally extended, no strong evidence has emerged to the effect that they are non-circular [18, 80]. Indeed, probably they are somewhat so, but their departures from circularity are evidently small and less systematic than mere axial extension [1, 28]. On the basis of the first two points it may provisionally be concluded that pulsar emission appears to reflect a magnetic field configuration which is nearly dipolar in the emission region. While many of us have at times appealed to “non-dipolar effects”

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to explain sundry mysteries, no single instance yet exists where this explanation can be clearly demonstrated. Indeed, although theory of neutron stars and observations of them in other contexts (e.g., x-ray binaries) suggest that pulsar surface magnetic fields are probably not entirely dipolar – particularly in the case of millisecond pulsars – our very failure to identify concrete instances of non-dipolar effects in ordinary pulsars argues that the fields must be nearly dipolar at the emission-region heights that the observations reflect. Furthermore, clear evidence for non-dipolarity will probably come only by pushing the dipolar assumption so far that counterexamples emerge. Many theorists have plausibly argued that the magnetic field in the outer magnetosphere will be distorted by current flows and relativistic effects (e.g., [89, 17, 86, 121]). But one must be beware of overlooking more fundamental concepts by using multipole structures close to the surface to explain difficult observations – i.e., one may fall into the trap of using complexity to explain complexity. Support for the third point, also consistent with the dipole hypothesis, follows from the identification of circulating subbeams systems in B0943+10 [25] and B0809+74 [67]: it is then this subbeam circulation which produces the average conal form, and thus makes them roughly circular in shape – i.e., symmetrical about the magnetic axis. The subbeam circulation (first identified observationally as subpulse “drift” by Drake & Craft [27] and systematized by Backer [8]) may be provisionally regarded as a general characteristic of conal beams – but the subbeams need not be regularly spaced, nor steady over time; they can equally well be formed in a sporadic or chaotic manner while still retaining a circular symmetry about the magnetic axis. For these reasons, the form of pulsar beams can best be explained by assuming circularity and then assessing any evidence for departures. We can therefore adopt three assumptions, the SVM, dipolarity and conal beam circularity, to jointly provide a standpoint for constructing simple geometrical models for most pulsars (e.g., [26]; hereafter DR01). To these we can add three basic electrodynamic concepts, also geometric in nature, which were established in the early days of pulsar research. First, a light cylinder, at which corotating particles would attain the speed of light. Second, a corotating zone whose bounding field line would be the last to close within the light cylinder; emission would thus be confined to the open field lines in a region close to the polar cap and surrounding the magnetic axis. Third, a surface on which the charge density would be formally zero in a quasi-steady state, and which would therefore be capable of forming an “outer gap” accelerator [53]. It is in this last region that γ - and x-ray pulses are thought by many [20, 116, 118, 50, 21] to be formed in young pulsars, and it is not unreasonable to believe that it may continue to play an important role even after its high-energy phase is past [19, 134]. These are the geometric considerations which play a central role in our approach, but attempts at “ab initio” theorising will be eschewed: three decades of experience and history have shown that general pulsar theories – physical theories of pulsars attempting to deduce the behaviour of real pulsars from first principles – have not yet proved capable of yielding significant, specific, falsifiable expectations about the observed emission of an actual individual pulsar. Future more successful theories must be able to do so, and simple semi-empirical models of the emission geometry along the lines summarised here provide the essential point of connection between our natural observations and the ramifications of physical theories. However in this article, we stress again, the reader


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will find geometry put not only to its traditional use of disentangling the observer’s perspective of pulsar “events”, but given a prominent role in determining their nature.

The pulsar family Although the main focus of this article will be on “slow” radio pulsars, it is important to stress that their properties are likely to be closely related both to those of faster, younger pulsars such as the Crab and Vela, which also emit in the high-energy bands, and to the family of older but rapidly spinning millisecond pulsars.

Young pulsars Through their capacity to produce optical, x-ray and γ -ray emission, young pulsars have often been seen as a class apart – not least because they are observed by a distinctly different community of astronomers! Yet this is a dangerous view if we are to regard pulsars as exhibiting a continuum of behaviour which evolves as a pulsar ages. It has seemed likely that the high-energy photons of young pulsars are produced by a different mechanism – and probably in a different region of the magnetosphere – from the coherent radio emission. It is then easy to believe that those who study radio pulsars have little to learn from the high-energy studies, and vice versa. The stress we are laying on the role of geometric features in determining phenomena should warn us against this view. Indeed, it is largely through geometric arguments that the outer gap has been identified by some [20] a possible source of γ rays: and the outer gap is directly linked by magnetic field lines to what is certainly the site of the radio emission in slower pulsars. Does outer-gap pair creation cease as soon as the high-energy emission becomes undetectable? It is possible to construct a viable emission model in which this process plays a critical role [134], and if verified, could provide a natural link between radio pulsars and their high-energy siblings.

Millisecond pulsars These pulsars, thought to be older neutron stars which have been “spun-up” through a history of accretion, have relatively weak magnetic fields and often unusual profiles which do not conform to the pattern of slow pulsars [62, 63]. There are good theoretical arguments for believing that their surface magnetic fields are highly distorted (e.g., [120]), which may cause profile distortion. However, virtually nothing is known of their single pulse behaviour. For this reason they lie outside much of the analysis here, but again we would caution against rushing to multipole geometries as quick explanations. At any large distance from the star the dipole component will dominate, and, as we will strongly suggest, dipole geometries are capable of creating great intrinsic complexity.

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Subbeam circulation and pulsar phenomenology Pulsar profiles as attractors It is no coincidence that the three fundaments listed in the opening section are all deductions based on the properties of integrated profiles. A pulsar’s profile is its indelible, individual and stable characteristic. This extraordinary property has been recognized since the early days of pulsar research. However, the invariance of profiles is probably responsible for seducing many theorists into taking it as evidence of some underlying stability in the emission system, such that the ever-changing behaviour of the individual pulses can conveniently be ignored. Yet they are nothing of the sort. Studies of non-linear dynamical systems have repeatedly revealed the presence of strange attractors, features which confine the highly timedependent variables of the system to a specific region of variable space, but in no way indicate convergence to a steady state. A pulsar’s profile represents a two-dimensional cross-section (Poincaré section) created by our sightline intersecting an otherwise unseen three-dimensional attractor. Nothing in the pulsar emits radiation in the form of a profile. Profiles contain valuable information about the quasi-chaotic system, but they are not the system itself. A powerful result of the 1980’s was the claim that pulsars have attractors in the form of nested cones (ETI, ETVIa), and even that cones have approximately consistent radii from pulsar to pulsar (relative to the size of the polar cap) (ETVIa,b). Over the years there have been associated claims that the true attractor structures are less [73] or more [33, 41] ordered, but nonetheless the implications of these findings remain profound. It has long been assumed that pulsar emission emanated from particles closely bound to the magnetic field lines, so that the emission components followed the contours of that field. The consequence of any observations which suggest consistent profile structure from pulsar to pulsar (such as the “Empirical Theory”) is then that certain field lines are preferentially selected by the particles – and very nearly the same field lines in each pulsar. Explanations for this in terms of the classic [119] (hereafter R&S) model then have to appeal to multipole features in the surface magnetic field [37, 38, 5], yet this begs the obvious question as to why each pulsar would have similar multipoles. Alternatively, it has been suggested that the cones are formed by multiple refractions within the magnetosphere (e.g., [96]), or by the novel mechanism of induced inverseCompton scattering [100]. But then, precisely because profiles are only attractors and not the actual emission, we would expect the subpulses in the inner and the outer cones to have similar subpulse behaviour – and this seems to be far from the case. However, if we abandon the unwritten assumption of these models that pulsar magnetospheres are systems driven from the polar cap – that the tiny tail wags the substantial dog – then we are forced to postulate that somehow the outer magnetosphere selects the critical fieldlines. The natural choice for these fieldlines, on both geometric and physical grounds, would be the cones which connect the outer gap’s upper and lower extrema to the polar cap (as exemplified in the model of Fitzpatrick & Mestel [30, 31]). There is anyway strong evidence that the outer gap plays a critical role in the production of γ rays in young pulsars [118] via cascades of pair-production. In the older pulsars we are concentrating on here, we may conjecture that – long after the cascades have died out – sporadic photon-photon pair-production may still occur in the outer gap region


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Fig. 1. A carousel depicting the structure and themes of this paper: the individual topics are linked to the underlying principles via their geometric interpretations

and interact with the polar cap. Thus the outer gap might continue to play an important, if not directly detectable, role in slower pulsars. The opening angles of these critical field lines seem, on reasonable assumptions about the emission heights, to have the right proportions to account for the attractor cones of the ET [35, 134] and at these heights the magnetic field is almost purely dipolar. It is not impossible that the precise fieldlines preferred in any given pulsar may be at some intermediate value, especially in more inclined pulsars – and may vary in time, resulting in multiconal attractors. We are consequently led to understand that it is the downward-moving particles which determine the emission site. These particles must be accelerated over the vast distances from the outer gap towards the pole [85, 17], and particles of opposite sign must be accelerated back to the gap. This concept thus shares many features with the free-acceleration models of Arons & Scharlemann [3], Mestel [86], Mestel & Shibata [88] and Jessner et al. [55], although the scale of operation is greater than envisaged by these authors. More recently, by invoking inverse-Compton scattering as the principle emission mechanism for producing pairs in older pulsars, promising models have begun to appear [98, 99, 134, 48, 49, 44–46] in which the acceleration zone is extended further up into the magnetosphere, and in which pair creation may fail to quench the local electric field in slow pulsars, thus leaving a residual potential difference extending to “infinity” – a feature which could naturally correspond to the magnetosphere-wide scale requirements of the empirical model. However, in all these models the implied so-called

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“return flow” should in the present view be seen as the primary flow, and none have explored the possibility of azimuthally-dependent emission implied by both observations and the feedback system of Wright [134] (see Fig. 2). The new model may therefore theoretically reproduce the system attractors – the double cone. But to develop it further on the empirical basis we have promised above, we must focus our attention on the pulse-sequence behaviours, and deduce the model’s properties from them. The behaviours can be conveniently discussed under four headings which summarize four basic emission phenomena: “drift”, core emission, modechanging, and nulling. These headings are largely suggested by the manner of their detection and observation. However, it is essential to bear in mind that some or all are often present in a single pulsar (e.g., B0031–07, B1237+25), and may well spring from different aspects of the same physical mechanism. A fifth heading, “emission cycles”, is therefore added, under which we discuss the apparent “rules” or “memories” which may link these phenomena. The principle headings of our discussion are gathered together graphically in the carousel of Fig. 1. “Drift”/non-“drift” Subpulse “drift” is a crucial clue towards solving the pulsar puzzle, as it exhibits the stunningly beautiful capacity for order in pulsar radio emission. It is a feature found only in conal regions of the profile – and indeed only then when our sightline passes obliquely along the outer edge of the emission cone (thus producing a conal single, or Sd profile). And this drift can range from being gradual – with subpulses moving slowly across the pulse window over up to 20 rotation periods – to being rapid – presenting an on-off effect to the observer. Its intermittent presence in the emission of predominantly “slow” pulsars is powerful evidence of the unpredictable regularity characterisitic of quasi-chaotic systems. The emission of some pulsars varies systematically, although not periodically or even predictably, between discrete drifting patterns (e.g., B0031–07, B1944+17, or B2319+60), but many/most stars usually exhibit much less order in their pulse sequences (PSs). No pulsar is known which permanently emits with one single drifting pattern. On the other hand, few pulsars have conal emission which is fully chaotic. Most at least occasionally exhibit sequences which, however brief, are more or less orderly. It is possible that higher orders of regularity are present, even in apparently chaotic emission, which defy detection by current methods. It may be that we are limited by current analytical tools, designed to identify specific correlations rather than to measure the underlying complexity. Power spectra and cross-correlations pick up strong periodicities at specific phases of the pulse window and are powerful tools when the emission is highly regular. But how, for example, could a systematically decaying or oscillating drift rate be detected? Near-chaotic systems can exhibit great subtlety in their behaviour. How do the differing geometrical circumstances found within the pulsar population produce the immense variety of patterns – both in the emission of a single star and among those with ostensibly similar characteristics? It is suspected that slow systematic drift over many periods may be a characteristic of pulsars with small magnetic inclination angles (well known in this category are B0809+74, B0031–07 and B0818–13 – all thought to be aligned within about 15◦ on geometrical grounds; see LM and/or ETVI), a


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result which would suggest that the entire magnetosphere – and not just conditions near the surface – plays a role in fixing the subpulse behaviour. However, it is no less important to understand an unusual Sd pulsar with no apparent drift, such as B0628–28, and to account for the more irregular patterns found in those pulsars with larger magnetic inclinations as it is to understand the regularities of B0943+10 or B0809+74. Also a puzzle are the properties of the conal double (type D) stars, where our sightline cuts the emission cone more centrally (e.g., B0525+21 and B1133+16); here some subpulse regularity is observed but apparentlyfar less than in their close kin, the Sd stars. Nonetheless, from both an observational and theoretical standpoint the natural starting point of any study of “drift” is to examine those pulsars with the most regularly behaved drifting subpulses, and by far the best and brightest known exemplars are B0943+10 and B0809+74. Observations of these have given us the telling image of a circular “carousel” of emitting subbeams ([25]; DR01). B0943+10 in particular, when emitting in its highly regular “B” mode, exhibits precisely 20 subbeams which circulate around the magnetic axis about every 37 rotation periods (or about 41 s). This star has provided us our first opportunity to count the number of subbeams and to confirm the geometric aspects of the R&S model. Yet it is now known that even this “B” mode adopts slightly varying circulation speeds on largely unpredictable time spans [114]. And the well-known pulsar B0809+74, after being thought for decades to have a nearclockwork regularity in its drifting pattern, has recently been found to drift on occasions at a consistently slower rate [67]. The task of accounting for drifting subpulses has only made limited progress over the years since the publication of the 1975 R&S polar gap model. Recently Gil and coworkers have described multipole models in which “sparks” on the polar cap can be made to adequately mimic the observed drift of certain pulsars (e.g., [36]), but this inevitably involves some arbitrariness in the choice of the magnetic field structure. However, it is possible to produce drifting subbeams naturally, and without invoking multipoles, through the operations of the feedback model sketched in the previous subsection [134]: one can suppose the formation of pair-creation “nodes” in regions both around the polar cap close to the surface, and in the outer gap, which “fire” particles at each other and thus create a self-sustaining system. The nodes will appear to precess in tandem both about the magnetic axis and around the outer gap. This system, although still owing much in its physical processes to the R&S model (i.e., pair creation and the E×B particle drift), depends on interactions between widely separated regions of the magnetosphere. Thus a natural time delay is built into the system, and hence leads to the possibility of chaotic or quasi-chaotic behaviour. The system can equally well be viewed as being “driven” from the polar cap as from the outer gap, although in reality it is a self-sustaining system with no starting and no end point. The promise of this approach is that such a feedback model has within it the capacity to explain more complex phenomena than the simple steady circulation of an axisymmetric system. As the magnetic inclination of a pulsar increases (while yet retaining near dipolar geometry at relevant heights), the system naturally causes the emission in the circulating “carousel” to develop a patchiness and asymmetry reminiscent of many observed features. In this view, the subbeam “carousel”, although always possessing a near-circular form, is no more than a distorted “reflection” of the outer-gap nodes, which circulate in tandem with those above the polar cap in an extended quasi-elliptical path

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Fig. 2. The emission geometry for pulsars at a low angle of inclination. Note that although the rings of nodes both near the pulsar surface (dark ring) and their mirrors on the null surface (finely dotted ring) encircle the magnetic axis, only the mirror ring also includes the rotation axis. The dotted straight lines representing the null surface separating negatively and positively charged regions of the magnetosphere, and their intersection with the last closed field-line defines the site of an “outer gap” (see [134] for details)

about both the rotation and magnetic axes (Fig. 2). Although no time dependence is built into it, the model bears a striking resemblance to auroral models in terrestrial and planetary magnetospheres [comparisons with the recently discovered “drifting” x-ray hot spots around Jupiter’s poles ([40] – see Fig. 3) are particularly apposite since the Jovian radius (67,000 km) is comparable to the height of the outer gap!], and one may speculate that phenomena known from these fields – such as flares and magnetic reconnection – may be found to play an analogous role.


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Fig. 3. A multi-frequency image of Jupiter taken from the Chandra website (http://chandra.harvard.edu/). The (blue) UV ring and the (red) x-ray spots are superimposed on the well-known optical image. It is thought that the x-rays must originate from particles reflected from pole to pole. In the movie from which this picture is taken, the intensity of the spots varies on the timescale of the interpole travel time. Image reproduced with kind permission of its creator, Dr. R. Gladstone. (See [40] and the website credits)

Core emission Core emission, as its name suggests, is emission which appears to be propagated in a narrow pencil beam surrounding the magnetic axis. Its angular dimensions are such that, if deemed to be coming directly from the polar cap surface, it would fill exactly the area enclosed by the “feet” of the last closed field lines. A great mystery, of course, is the relationship between this and the drift emission often found in the surrounding cones. We understand the gross distinctions between them in terms of their beam topology and modulation characteristics (ETI–V), but we understand virtually nothing about their commonality; and if the magnetosphere is truly operating as an integrated system, it seems most likely that both types of radio emission stem from the same sets of accelerated charged particles. It is tempting – yet at present no more than a speculation – to see at least a part of the core emission simply as the radial reflection of the emission of cascading downwardly flowing particles [90, 135]. Such particles are an important component of the feedback model, and will certainly be powerful emitters as they are accelerated immediately above and towards the polar cap. Above all they will move down the last closed field lines from the outer gap and naturally define the limits of the polar cap.

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Support for the interdependence of core and conal radiation comes from pulsars such as B1237+25, where our sightline runs almost directly over the magnetic axis. In the single pulse trains of this pulsar, the core region is dormant while the outer components have a strong and regular periodicity, but when the core brightens (as it does on quasiperiodical timescales) the conal modulation is interrupted, and only recommences when the core subsides [42]. A case could be made to view the core emission from all pulsars as generally being inhibitive to regular periodicity in the conal components. This is certainly supported by observations of the well known pulsar B0329+54 (e.g., [14, 126, hereafter SP98; 127, hereafter SP02]), which has multiple cones as well as a dominant central core component, yet has never been reported to show any periodic behaviour. Surprisingly, core emission has still not been well studied. In part this is because it was identified after the heyday of enthusiasm for single-pulse investigations. It is also an unfortunate coincidence that most of the bright exemplars of core emission lie outside the declination limits of the Arecibo instrument. This is only a part of the story, however: the Vela pulsar, perhaps the prime example of core emission in the sky, is far from well studied though some solid new efforts are being made (e.g., [56, 64]). No well measured (polarized? time-aligned?) set of profiles is available, so we can only speculate about either its polarization or profile modes or how its conal emission develops at high frequencies. Many other things have been studied about this nearly unique and remarkably influential star (e.g., [65, 102]), but many of the basics remain a matter of guesswork. The Vela pulsar B0833–45 is probably an excellent example of the core-single St class – those with a single core component at meter wavelengths. ETIV has shown that it lies at the short-period end of a group whose component widths scale as P −1/2 – just as does the angular width of the polar cap. As the rotation period P increases, there is a tendency for stars first to acquire an inner cone, and later an outer cone (ETVI). One might therefore suggest that as pulsars slow and lose their outer-gap high-energy emission (and by implication their capacity to create self-sustaining pair production here), sporadic low-energy pair-creation at either limit of the outer gap may still be permitted, and this in turn could generate conal radio emission through the feedback mechanism outlined above [134]. As the pulsar further slows, these limits will become inaccessible to the sustaining surface x-rays, leading finally to the extinction of first the inner and then the outer cone. This picture, again based on geometric argument, corresponds well to the observational analyses of ETI–VI. It also creates, yet again, the possibilty of a feedback system: when pair-creation becomes prolific in the outer gap, the downwardly-moving particles quench the potential and polar cap pair creation needed for conal radiation [20]. This reduces the heating of the polar cap, which therefore cools until its thermal x-rays cannot support the outer-gap pair avalanche, and the mechanism for creating conal radiation can recommence. Thus, the core emission can be seen as one component of a thermostatic process! On the evidence above, the core emission is a very large and significant piece of the pulsar-emission jigsaw puzzle. In our future research we therefore should set about answering a series of guideline questions:


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– How can we test whether the appearance of a core component in the radio emission is evidence of the onset of (possibly short-lived) runaway pair-creation in the outer gap? Some kind of statistical test for quasi-chaotic behaviour may be appropriate. – Does the core component have significant structure within itself? If the conjecture of Wright [134] that core emission is in part reflected conal emission is correct, then the core structure may mimic the conical structure of the outer components. Such structure does seem to occur in B0329+54 (SP02), but in faster pulsars it is often difficult to discern whether the observed structure [22] is to be interpreted as truly core or conal. – If core activity is responsible for disrupting quasi-periodic conal modulation, can we detect this in the conal emission of pulsars which do not have a central sightline traverse? How do the statistics of periodicity loss in pulsars with only conal emission compare with those where the core is visible? These questions are clearly related to the phenomenon of profile moding, discussed in the next subsection. – How common is quasi-periodicity in core components? And whether periodic or not, can any pattern of rise or fall or non-stochastic behaviour be discerned? Moding: changes in subpulse patterns Historically, this phenomenon has often been associated with, and identified through, discrete variations in the profile shape. It was first identified by Backer [6] in B1237+25, but later in a wide range of pulsars including B0329+54 [71; SP98, SP02], B1822–09 [32], B2319+60 [137], B0943+10 [124, 125; DR01]) and most recently B2303+30 [115]. Moding may well be universal, especially now that even B0809+74 – long a considered a bastion of near-steady regularity [72] – has been shown to have a second mode [67]. This effectively means that no well studied pulsar has been found to be free of moding. However detected, moding is always associated with changes in the subpulse pattern. In those exemplars listed just above, the moding is easy to identify through clear and sudden changes in the profile shape. In others, such as B0031–07 [54] and B1944+17 [24], the mode change is seen as an immediate and significant change in subpulse drift rate, with later analysis then revealing an associated profile change [137, 138]. The changes are often easy to identify, but in some prominent pulsars exhibiting profile moding without any regular subpulse modulation (e.g., B0329+54), it is important to identify what changes in the PSs correlate with the mode changes, work already well started by Suleymanova & Pugachev [SP98, SP02]. Interestingly, it seems that at least some pulsars “anticipate” their mode changes. This has been demonstrated in both B0329+54 [SP98, SP02] and B0943+10 [125] where subtle intensity variations begin some hundreds of pulses before the more dramatic – almost instantaneous – mode change actually occurs. It is curious (and hard to account for theoretically) that this slow anticipatory modulation does not seem, in the case of the exquisite “drifter” B0943+10, to affect the periodicity of its drift. Work is underway to see if B2303+30, which in many ways resembles B0943+10 but whose mode changes are more frequent, also shares this property. On the basis of these observations it may be useful from a theoretical standpoint to distinguish between two types of modes: “ordered” modes in which the subpulses exhibit regular behaviour such as drift, and “disordered” modes, where the emission is

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predominantly chaotic. Thus, B0031–07 and B1944+17 have three modes of the first kind, B0809+74 [67] has at least two of the same, B1237+25 one of each, and both B0943+10 and B2303+30 may have several ordered and one disordered mode [114, 115]. Often the changes between the ordered modes may be gradual, as in B2016+28 [95]. In most of the pulsars with more than two ordered modes, it has been found that mode changes do follow some systematic “cycle” (generally accelerating the drift rate through increasing values before returning to the “start”). Examples are B0031–07, B1944+17 and B2319+60, and this may well be a common feature at least of slow-drift pulsars. This apparent memory is a powerful clue and we must learn how to interpret it (see the Emission cycles section below). In pulsars with “disordered” modes, we must ask if this might always correspond to the onset of core emission, even if that emission is fortuitously invisible to us. This question is closely related to our discussion of B1237+25 in the previous section. The apparently spontaneous switching from one emission mode to another, whether ordered or not, is, of course, the hallmark of a quasi-chaotic system. It need not imply that the switch is “caused” by any external agency either from the interstellar medium or the neutron star crust. Nor need the moment of change be at all predictable. Nevertheless, time series generated from these changes may not be entirely chaotic and it may be possible to borrow analytical techniques from studies of non-periodic phenomena in other fields to mine underlying information about the physical system which produces moding. Our understanding that the integrated profile forms are produced by a system of circulating subbeams, which is highly symmetric about the magnetic axis, constrains our possible interpretations. When a mode change occurs between ordered modes, it is crucial to know which parameters have concurrently changed. It was originally believed – for example in the case of B0031–07 – that the repetition rate P3 altered suddenly, but that the driftband separation, P2 , remained unchanged. This would imply geometrically that the emitting regions, and their corresponding nodes, would remain on the same fieldlines but accelerate their drift motion. This appears to be true, at least to first order, for the five or six pulsars where this phenomenon is known. Some doubt was cast on this by the discovery that the profiles of the successive modes did actually widen [137], a result later confirmed by Vivekanand & Joshi [132]. These latter authors further claim that their driftband measurements suggest significant increases in P2 from mode to mode (i.e., as P3 decreases). Such measurements are notoriously difficult to make, not least because P2 varies across the pulse window and may be subject to polarization and “absorption” effects (see next section). However van Leeuwen et al. [67] identify a similar effect in B0809+74, where an increase in P3 is associated with a narrowing profile and an increase in P2 . If confirmed, the change in P2 , though slight, would imply (pointed out by van Leeuwen et al. [67]) that the emission beam has rapidly moved radially across fieldlines, and in terms of our geometric model here this would mean the outer gap nodes would have migrated to different latitudes on the outer gap and the polar nodes to new radii on the polar cap. This is perfectly possible (given that we do not know the nature of the underlying cause for the mode change!) and would reveal interesting properties for


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the model, but it is first necessary to confirm this result in more detail: again, it is the observations which must be the arbiter of the form the model takes. Nulling “Null” pulses are identified by a complete absence of intensity throughout the entire pulse window, and appear to interrupt pulse sequences without warning. Often they persist for many periods (some pulsars are known which remain in a “null” state most of the time), and then emission reappears as suddenly as it ceased. The phenomenon is more common in older, longer-period pulsars, although it is no longer believed that pulsars “die” through gradually “nulling away” (see ETIII). In certain pulsars nulls and subpulse drift have long been understood as closely associated [130, 29, 72], but we still have remarkably little physical understanding of these nulls. It is possible that there are several different kinds of nulls (see [7]), an idea also hinted at in analyses of the slow-drifting, moding pulsar B0031–07 [131], who found a bimodal distribution of null length. Vivekanand did not, however, identify where the two types of nulls occurred in the PSs. It is very possible that the shorter nulls tended to occur within a single mode (i.e., the mode persists following the null) and that the longer “nulls” occurred between different modes. One might also take B0809+74 as evidence for this idea, as its slower drift mode(s) always seem to follow long null intervals [67]. By contrast, in fast-drifting pulsars there are now strong indications that nulls are associated with subbeam circulation in a broader context: pulsar B2303+30 rarely seems to null when in its bright and well ordered drift mode, but it exhibits deep nulls in PSs which are less orderly or chaotic [115]. Pulsar B0834+06 exhibits mostly one-pulse nulls which appear to fall on the weak phase of its nearly even-odd PS modulation. Can it be that in a pulsar (e.g., B1133+16) with sporadic pulse-to-pulse modulation, there are occasionally “empty” sightline traverses through the average emission-beam pattern which simply fail to encounter significant radiation? In order to answer such questions, new investigations of pulsar nulling are required which investigate the link between nulling and subpulse behaviour. A recent result of this new approach is the success in understanding the null/drifting interaction in B0809+74. van Leeuwen et al. [67, 68] have shown not only that each transition to the second mode is preceded by a null sequence, but that during every null sequence the phase of the subpulse is “remembered” and then gradually accelerates either to its previous mode or a new mode. This is a more subtle interaction than previously suspected [72]. Knowing the source and growth of nulls in the magnetosphere would give great insight into their nature. The onset and ending of a “null” are so rapid that they are hard to catch in the moment – though such a population should occur statistically in many pulsars. We do not know how close to simultaneous is the onset at different frequencies (and by implication at differing locations in the emission zone), nor whether it ends as fast as it commences. Currently the Multi-Frequency, Multi-Observatory Pulsar Polarimetry (MFO) Project (http://www.astron.nl/mfo/) is gathering simultaneous broad-band observations which are providing the first general opportunity to address such questions. Does the entire “carousel” of subbeams switch off together? A study of nulling in conal double (D) pulsars might help resolve this. From an observational point

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of view it is difficult to distinguish between short “nulls” (with absolutely no emission) and very weak emission, so the observations required are not easy to obtain. The statistics of null and burst length in a given pulsar are as important as the null fraction. Where null pulses occur within PSs is equally crucial. An interesting analogy to nulling – and to mode changing too – is the incidence of terrestrial earthquakes or avalanches, where larger earthquakes (avalanches) occur less frequently according to a specific law (the Gutenberg-Richter law). It is known that statistics of these “selfordered critical systems” (SOC’s) reveal characteristics of the underlying physical processes, typically through the presence of power-law distributions [10]. This procedure has also successfully been applied to solar flares and magnetic reconnection, and would be interesting to pursue in this context. There are virtually no working theories which adequately account for nulling, and hence there is no agreement as to whether nulling occurs because the engine producing the emitting particles temporarily “switches off”, or whether the emission process itself breaks down. For example, in the feedback model outlined here, the flow from the suface to the null line and back may not be continuous and may contain irregular or even “void” stretches of low particle density creating lapses in the emission, which we experience as nulls. Alternatively, or additionally, nulls may arise through a breakdown in the mechanism which maintains the coherent radiation. This latter could arise simply because the rapidly changing flow cannot hold the flow steady enough for the conditions producing coherence to develop. Thus the nulling phenomenon could be seen as the visible yet ‘superficial’ response to one of a range of deeper underlying conditions. One might then predict that nulls will be more prevalent in highly irregular stretches of emission, and there is some suggestion of this in the observations of a number of pulsars (e.g., B2303+30), but it is important to test this in more careful analyses of observations. Emission cycles In a number of pulsars, so far 4, the emission modes are characterized by a progressive increase in drift-rate through at least 3 modes. These pulsars (B0031–07 [54], B1918+19 [41a], B1944+17 [24], B2319+60 [137]) all have very low drift-rates in their principal modes, and the magnetic axes of all are thought to be weakly inclined with respect to their rotation axes. What is remarkable about them is that the mode sequences appear to follow certain “rules”. For example, B0031–07 has 3 identified modes, A, B and C, which have repetition periodicities (P3 s) of about 12, 8 and 5 periods respectively. These modes are interspersed by null stretches, both within a mode and between modes. But often a mode-change occurs without an intervening null, and then it is found that only transitions A to B or B to C are allowed [54, 138]. The transitions take place within a few rotation periods at most, possibly within a single period. In other words, sudden, nullfree mode changes in which the driftbands retain their identity can only occur when the mode change corresponds to an increase in the drift rate. This gives the impression that the pulsar emission is executing a kind of cycle, from A to B to C, which may last some hundreds of pulses. Not all cycles include C, which is anyway of short duration. These properties are shared by the remaining 3 pulsars, and recently the pulsar B0809+74, also with a slow drift rate and low inclination, has also been shown to have


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smooth transitions (preserving drift-band identity) from a slow mode to fast, but only fast to slow following a long null [67]. All this suggests that the subpulse sequences possess direction, even “memory”. This behaviour is known in many branches of nonlinear studies. Near-chaotic systems can move from one pattern to another, apparently unpredictably, migrating from one limit cycle to another with a corresponding change in attractor. Regarding profiles as attractors, this is precisely what the changing pulsar profiles reveal: the profiles of the emission modes do seem to widen as the driftrate increases, and by a similar amount in each pulsar. A further curious fact about these pulsars is that the ratios of their successive modal drift rates are about the same: all (including B0809+74) appear to increase their driftrates by about 1.6 as they move from one mode to the next. Whether this increase entirely stems from a reduction in the pattern repetition rate (P3 ), or whether also the band spacings (P2 ) are slightly reduced (as Vivekanand & Joshi [132] and van Leeuwen et al. [67] find for B0031–07 and B0809+74, respectively) is important to clarify. It is fascinating to speculate as to what is physically happening during these “cycles”. It seems unlikely that additional nodes [134] or sparks [37–39] are created as the mode transitions occur, for they seem to be smooth and no act of node/spark creation is observed. The conclusion is that the emission region, and hence the nodes/sparks, must migrate radially to an inner set of field lines. In Wright’s model, the outergap mirror points must move along the gap further from the star. The cycle would then begin with a slow drift in outer fieldlines, possibly those bounding the corotating zone, and progress towards the axis. This spiral inwards is reminiscent of the model suggested many years ago for B1237+25 by Hankins & Wright [42], although in this strongly inclined pulsar the entire sequence lasts only 2.8 periods. Note also that the slow drift rate of the weakly-inclined pulsars implies (in the model of Wright [134]) that the outergap nodes are nearly corotating with the star – appropriate to the corotating zone boundary. Then, as the modes progress, they spin faster (in the corotating frame) counter to the rotation of the star, and eventually become closer to being stationary in the observer frame and nearer the light cylinder. The fact that we have only 4 established examples so far of this cyclic behaviour may be because lengthy and detailed studies of the subpulse sequences are necessary before the mode-change “rules” become apparent. But if subpulse behaviour does result from magnetospheric feedback [134], it also may be because at the more common larger angles of inclination (say between 20◦ and 50◦ ) the structure of the magnetosphere’s potential becomes highly asymmetric, with both faster driftrates and more blurred mode changes. Hence slow long-term cycles may only be a feature of nearly-aligned pulsars. Integrated profile questions or attractor analyses Although we have stressed the importance of single pulse analyses and implied that they are the true currency of a pulsar’s emission, the fact remains that single pulse analysis is only possible for a small minority of the pulsar population. Only 10–20 pulsars have so far had their single pulse behaviour well documented, and for some of these the description is only preliminary (e.g., B1112+50 [139]) or relatively inaccessible (e.g., [4, 7]) Many more bright pulsars, some recently discovered (e.g., [69]), are deserving of greater study, and we feel a major effort should be made to accelerate their analysis.

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We are therefore forced to accept that for the majority of pulsars (there are some 1700 known to date) only their integrated profile is available for study. Yet, so long as we continue to bear in mind their nature as attractors, it is possible to mine a great deal of information, particularly of a geometric nature, from this population. This is essentially what was done by one of us (ETI,ETII,ETIII) and Lyne & Manchester [73] in the eighties, when perhaps 200 usable profiles were available. What now needs to be done is to look at these results in the light of our twin hypotheses of nearly circular subbeam circulation, and a pan-magnetosphere feedback system. We will take in turn a number of crucial aspects of profile analyses, and pursue the consequences.

Double-cone beam structure While several pulsars with five distinct components had long been known (e.g., B1237+25, B1857–26), suggesting two conal rings as well as a central core beam, it was not until 1993 (ETVI) that firm evidence was given for two cones with coherent geometrical characteristics (then confirmed by Gil et al. [35], Kramer et al. [61], Mitra & Deshpande [91]). Specifically, the respective inner and outer cones in double-cone (M) stars were found to have outside, half-power, 1-GHz radii of 4.33◦ P −1/2 and 5.75◦ P −1/2 – and the single cones of triple (T) pulsars were found to be one or the other. Then, ETVII showed that while outer cones exhibit an ever larger low-frequency radii (known as RFM, see below), inner-cone emission radii appear to be nearly constant over the entire radio band. It is still not understood why some pulsars have two concentric cones and what is the relation of the subpulse modulation in the two cones. Even for the paragon of this phenomenon, B1237+25, there is very much still to learn. One line of approach has assumed that double-cone emission probably comes from the same set of emitted charges, whether sparks or beams (e.g., [26]), while Gil and collaborators [36–39] have envisioned several concentric rings of sparks on the stellar surface which are thought to be associated with the various cones and even the core. The implications of these assumptions are very different, and almost no work has been devoted to pursuing their study through PS analyses. There are now almost 20 stars with well identified doublecone profiles (see ETVI), so a systematic study is possible and feasible – though perhaps no more than half a dozen are strong enough for PS analysis. In any case, that rotating subbeams are responsible for the generation and modulation of these cones gives us new ways of studying and assessing their character and origin.

RFM/no RFM The phenomenon that prominent conal double profiles (e.g., B1133+16) become progressively wider with wavelength was well noted very early [60], and many workers participated in documenting the effect, often by fitting pairs of power-law functions to the asymptotic high and low frequency profile widths or component spacings (e.g., [71, 123]. Thorsett [129] demonstrated that a function of the form ϕ0 +(f/f0 )−a fitted the full low to high frequency behaviour well. von Hoensbroech & Xilouris [52] have provided


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a full review of work on “radius-to-frequency mapping” (hereafter RFM) in the course of extending the range of the high frequency observations. The question of RFM has perhaps become more interesting with the conclusion that it is mainly or exclusively a characteristic of outer-conal beams (Mitra & Rankin 2002; ETVII). This study included the beam geometry for the first time, so that conclusions are framed in terms of conal beam radii and emission heights. In addition, two different types of RFM behaviour were identified among the outer cones – those which approach a constant radius at the highest frequencies and those that do not. Nonetheless, in many other ways the emission from inner and outer conal beams is indistiguishable, so that it again becomes a question of how a rotating subbeam system radiates in such a manner that its envelope does or does not exhibit a frequency dependent radius. Closely related questions arise in considering the significance of the altered profile forms produced by mode changes. This was first noted in the context of pulsar B0329+54 [71], but excellent examples are now also B0611+22 [93] and recent studies of B0809+74 [67, 68]. The problem is aggravated by the fact that there is no agreed model for the production of emission. Assuming that the coherent radiation is emitted tangentially to field lines in the polar cap region some hundreds of kilometers above the stellar surface, the critical problem is then to determine precisely which fieldlines are carrying the emission and at which height [58]. This is no easy task given the likely effects of aberration and timedelay [77, 33; ETVII]. From the standpoint of the feedback model, this work is very important, since it will determine the nature and true positioning of the link to the outer gap. “Absorption” This phenomenon relates to the gross asymmetry which is evidenced in certain pulsar profiles, yet only within certain frequency ranges, suggesting that the asymmetry is not an intrinsic property of the profile but that some intervening medium has partly “absorbed” the emission. Although first discussed in the context of multi-frequency alignment anomalies in the relatively stable pulsar B0809+74 [23, 12, 13], where the drifting subpulses become blurred and attenuated as they pass through a specific longitude, the phenomenon is now also known to be closely associated with profile mode changing, as (e.g., in B0943+10) the degree and character of the “absorption” is strongly correlated with the profile mode. Thus much of what was said above in regard to profile modes is equally applicable here. Indeed, perhaps profile-mode changing and “absorption” should be viewed together as two faces of one phenomenon – the temporal and profile-spectral manifestations of a single cause which is also manifested in the PS pattern. From an observational standpoint we now can see why “absorption” is most clearly or usually identified in pulsars where the impact angle β is comparable to the conal beam radius ρ (i.e., usually stars which are members of the Sd profile class), whereas profile mode changing is most easily identified in multiply-peaked pulsars with |β|/ρ much less than unity. A more recent variation of this topic has come with the discovery of mysterious “notches” in the profiles of a number of very different pulsars [84]. These are found in certain wide-profile pulsars, are narrow double-dip in character, and tend to follow

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the profile centroid by about 60◦ longitude. The critical question is whether they are intrinsic to the profile or are truly absorption. There is a need for frequency-dependent studies to resolve this, since if not intrinsic the notches could for the first time identify very localised regions of the magnetosphere where the absorption takes place. Defining the location of absorption, given the geometric theme of this paper, is something of a challenge. Assuming that the effect is not occuring within the circulating subbeams, we have to track the likely path of the radiation as it escapes the magnetosphere. Three things will be crucial to this: 1) the longitude in the profile, which defines the moment and angle of emission, 2) the rotation period, which fixes the scale of the magnetosphere, and 3) the angle of inclination, which locates the position of the null surface, the outer gaps and the distance from the magnetic pole to the light cylinder. A start on this problem very much in keeping with the “keep-it-simple” geometrical ideas of this article has recently been made on the issue of profile notches: it can be shown that if, as generally assumed, the emission frequency is height-dependent, then double-notches can arise through time-delay and aberration in quite natural geometries and need no appeal to “distorted” field-lines [135].

RF spectra, rotation energy loss & RF efficiency That conal beams are produced by systems of rotating subbeams gives us the possibility of estimating the full radiation pattern of a given pulsar in terms of what we observe in the course of our particular sightline traverse. A first effort in this direction was made by Deshpande & Rankin [25] for pulsar B0943+10. Then, the emission from the full beam pattern at a given frequency can be integrated over the pulsar’s full spectrum and compared with its rotational energy loss to estimate its overall RF radiation efficiency. Such efforts, carried out for a substantial group of stars promise to provide an important quantitative point of connection with physical theories of pulsar emission. The above work depended on low frequency observations made over many years at the Pushchino Radio Astronomy Observatory and the catalogues of pulsar spectra and luminosity estimates compiled by Malofeev and colleagues there (e.g., [74, 75]). Otherwise, only limited progress has been made in understanding why pulsars exhibit different radio-frequency spectra. Some attention has been paid to spectral-index differences at centimeter wavelengths (i.e., [78]) as well as the breaks in such indices exhibited by certain stars [94, 16, 81]. However, equally important is the issue of whether a pulsar’s spectrum turns over at low frequencies [15, 76]. Some pulsars (e.g., B0329+54) exhibit spectral turnovers at 100–300 MHz, and thus are observable at low frequencies only with great difficulty, if at all. Other pulsars – and it seems all of those best known for their regular drifting-subpulse systems (e.g., B0031–07, B0809+74, B0943+10) – are observable to very low frequencies. B0943+10 in particular exhibits no spectral turnover down to some 30 MHz [26]. It should thus now be possible to gain some insights into the physical reasons for such different behaviours.


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Emission questions Microstructure and giant pulses A number of observations and developments have begun to narrow the possible interpretations of microstructure. Apparently, the fine temporal structure of microstructure has been resolved, and additionally there is evidence that its autocorrelation length scale is roughly proportional to the pulsar period [97]. Observations using the Effelsberg and Westerbork instruments seem to show in pulsars like B0329+54 that micropulses occur in all three main components [66, 104] so that the phenomenon – as with nulling – affects both core and conal components. It is, however, far from clear what connection, if any, micropulses have with subbeams in Sd stars such as B0809+74 or whether there is any orderliness to their polarization characteristics. Much work then needs to be done in order to assess how closely associated microstructure is with the other primary pulsar phenomena – and the study of microstructure in a pulsar with a very orderly rotatingsubbeam system such as B0809+74 undoubtedly has much to teach us about the nature of microstructure. In a small, but now growing, number of fast pulsars microstructure is found to be associated with the phenomenon of “giant pulses”. Such pulses are narrow but exhibit an intensity far in excess of the mean pulse energy. They were first found in the Crab pulsar [47, 70, 43], but recently have also been found in spun-up millisecond pulsars (e.g., [59]). They have a distinctive power-law energy distribution – possibly suggestive of self-organised criticality (see the earlier section on Nulling, and [140]), suggesting they might be the response to a simple generating physical system operating on a wide range of scales in a self-similar manner. Furthermore, they often occur at phases close to those of the high-energy profile components [117]. Assuming high-energy emission is indeed emitted from outer gaps, all this intriguingly hints at an independent physical radio source for giant pulses and at an interrelationship between polar cap and outer gap radio emissions.

Polarization issues The origin of the orthogonal polarization modes (OPM) – wherein, the radiation exhibits two preferred PAs about 90◦ apart – is one of the great mysteries of the pulsar emission problem. Those stars so far well studied in terms of their OPM characteristics are almost all conal dominated, so we have virtually no good examples apart from B0329+54 [14, 34; SP98, 02] of core components that can indicate what role the OPM play in core emission. What is increasingly clear is that conal pulsar beams are highly modal in their angular beaming characteristics [26, 113, 114]. OPM has historically been assumed to be a characteristic of the pulsar emission mechanism, but there is now theoretical work to the effect that it may result from propagation effects [2, 11, 96]. Basic questions about whether the two modes occur simultaneously in individual samples and whether they are fully or partially polarized remain. The issue of how such characteristics vary with frequency, and whether they might be implicated in the generally lower levels of polarization at very high frequencies, has only been touched. Again, each of these questions can fruitfully be studied in the context of a rotating subbeam system, because

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the modulated character of the signals gives one an additional method by which to separate the combined effects of the modal interactions. The work of McKinnon & Stinebring [82, 83] has provided a much sounder statistical and interpretive foundation for OPM work, but analyses based on sensitive and fully calibrated recent observations are needed to carry this work further. Just why pulsars have polarization and depolarization remains a mystery. The modal character of the rotating subbeam systems which produce conal beams is probably almost entirely responsible for the complex variety of characteristics observed in different pulsars with conal profiles. Rankin & Ramachandran [113] have explored the character of this beam-edge depolarization in stars with conal components pairs where our sight-line passes close to the magnetic axis as well as in conal single (Sd ) stars where our sightline makes an oblique traverse, finding that a virtually identical beam configuration can produce the full range of observed effects. Therefore, it should be possible to model the depolarization of the conal emission in a wide variety of situations to both improve our knowledge of the conal emission geometry as well as the nature of the modal emission which produces the polarization and depolarization. This is a rich area for immediate study and a good example of how the context for PS analysis and interpretation has been changed almost completely by our expectation that rotating subbeam systems produce the emission which both polarizes and depolarizes conal components. A closely related question is the polarimetric relation between inner and outer conal beams. We often see evidence for two active modes on the outer edge of the emission beam and only one in interior regions of the profile (or beams). In a double-cone star (e.g., B1237+25) this means both modes are active in the outer cone, but only a single mode is apparent in the inner cone. However, we also see cases of inner-cone D or T stars where both modes are active on the outside edges of their inner cones. Must this circumstance not bear importantly on how the OPM is generated – that is, whether it is an emission or propagation effect? X-ray, optical & γ -ray emission We close our carousel of pulsar phenomenology (Fig. 1) with a discussion of high-energy pulsar observations and their relation to the radio emission. Although nearly 2000 radio pulsars have now been discovered, only a handful of these have been detected at high-energy wavelengths. Future satellites promise to greatly expand this number, but there remains a feeling that we are dealing with two classes of pulsars: one population where the x-ray and shorter wavelength emission is closely correlated with young pulsars having large values of B12 /P 2 together with prominent or exclusive core emission beams at radio wavelengths, the other with no high-energy emission and exhibiting predominantly conal features. The contrast is exacerbated by the fact that pulse-sequence analysis is still impossible for the high-energy emission, and that therefore only profile (i.e., attractor) studies are available. This has further fostered the impression that such pulsars are in a steady state, and furthermore emit from different regions by a different mechanism. Yet this dichotomy may be an illusion, brought about simply by the differing means by which the high-energy and radio emisson are detected: a major point stressed in Wright’s work [134] is that even in slow pulsars the radio emisson may require the


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interactions between differing regions of the magnetosphere. Thus a highly-energetic pulsar with core emission and an old pulsar with only outer cone radio emission above the level of detectability represent opposite ends of an evolutionary spectrum. Younger pulsars with energetic outer gaps would “quench” the electric field in the conal regions above the poles [20], and the downflowing particles would somehow generate the core emission, possibly by reflection of incident radiation generated just above the polar cap surface. Measurements of correlations between core and high-energy emission must become possible in the near future and provide an opportunity to test and develop these ideas. For example, certain x-ray pulsars, such as B0611+22 [93], exhibit slow quasi-periodic profile changes which could be interpreted as a very slow rotation of one or more subbeams [57], and it would be interesting to know whether the x-ray emission is modulated or correlated with these radio profile variations. The evolutionary picture has received some theoretical support from the recent studies by Harding and her coworkers [44–46] of pair creation in the polar cap region. Building on the earlier work of Hibschman & Arons [48, 49], which incorporates the effects of backflowing particles in determining the height of the acceleration zone, they envisage a pulsar’s radio emission as a two-phase process: above the polar caps of young pulsars the principle radiation mechanism by which pairs are produced is curvature radiation, which generates sufficient pairs to screen the ambient electric field. However in older, “slow” pulsars, this gives way to radiation dominated by inverse Compton scattering – and crucially the electric field above the acceleration zone cannot now be fully screened. This implies that particles will continue to be slowly accelerated towards the outer gap, where Wright [134] envisages the occurence of further pair creation. Intriguingly, Hirotani & Shibata [51] have recently shown that the precise location of the outer gap will itself depend on the inflow and outflow of current, suggesting further non-steady feedback processes. The implication of these exercises is that we ignore interactions between the polar cap and outer gap at our peril. Conclusions This paper represents an attempt to take a novel view of the pulsar phenomenon. By abandoning the view that a pulsar’s magnetosphere is in a near-steady state, and further that its behaviour on all scales of time and space is determined by so far unexplained, yet complex events on the tiny polar caps, it is argued that a promising new approach is possible. Thus the magnetosphere is seen as having an inclined, essentially dipolar, structure, whose apparently complex emission arises not from abitrarily complex magnetic field components, but from subtle time-delayed interactions between regions relatively remote from one another. The principle interaction exists between the magnetic polar regions of the neutron star and the outer gap. But it is also arguable that, quite possibly, a similar aurora-like mirror interaction occurs between the poles – a feature which might be mathematically represented as a particle “pressure” exerted within or at the surface of the closed corotating “dead” zone [87]. Each region of the magnetosphere is then dependent on every other, yet never in a steady state and always with a natural time lag. This idea is distinctly different from the more conventional view that the flow is driven

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smoothly from the tiny polar regions to the light cylinder, and opens a whole new line of pulsar investigation. In developing our specific ideas we lean on both the observational analyses of one of us (ETI-VIII) and the recently developed concepts of the other [134], where the geometry of the feedback process has been examined in greater detail and successfully compared with observations in a few highly-organised pulsars. Such a feedback system can naturally proceed to bifurcations (i.e., alternate states) and ultimately to fully chaotic emission without any need to invoke strange geometries or external influences. This behaviour is highly reminiscent of what is found in real pulsars, and thereby hints at the possibility of uniting theory and observations. Here an attempt is made to link these new ideas to the principal long-standing conundrums found in the study of older, slow pulsars. But the wider purpose is to suggest that future theoretical investigations may benefit from links to existing studies of the properties of time-dependent non-linear systems, which demonstrate that highly complex behaviour can be found in even the simplest systems. Similarly, the subtle statistics of time series, often used to mine information from apparent chaos in fields far removed from astrophysics, might be usefully applied to pulse-sequence observations. It would not be the first time that cross-discipline studies have given unexpected insights. Acknowledgements. We thank our referee as well as Leon Mestel, Nikos Papanicolaou, Ben Stappers and Svetlana Suleymanova for critical comments or discussions which have significantly improved the paper. One of us (JMR) wishes to acknowledge the support both of the US National Science Foundation Grant AST 99-87654 and of a visitor grant from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek. The other (GAEW) thanks the University of Sussex for a Visiting Research Fellowship, and also the University of Vermont for support from the abovementioned US NSF grant.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

P.N. Arendt Jr., J. Eilek: ApJ 581, 451 (2002) J. Arons, J.J., Barnard: ApJ 302, 120 (1986) J. Arons, E. Scharlemann, ApJ 231, 854 (1979) M. Ashworth: Ph.D. Thesis, University of Manchester, UK (1982) E. Asseo, D. Khechinasvili: MNRAS 334, 743 (2002) D.C. Backer: Nature 227, 692 (1970) D.C. Backer: Ph.D. thesis, Cornell Univ. (1971) D.C. Backer: ApJ 182, 245 (1973) D.C. Backer: ApJ 209, 895 (1976) P. Bak: How Nature Works: The Science of Self-Organised Systems. Copernicus, New York (1996) J.J. Barnard, J. Arons: ApJ 302, 138 (1986) N. Bartel, N.S. Kardeshev, A.D. Kuzmin, N.Ya. Nikolaev, M.V. Popov, W. Sieber, T.V. Smirnova, V.A. Soglasnov, R. Wielebinski: A&A 93, 85 (1981) N. Bartel: A&A 97, 384 (1981) N. Bartel, D. Morris, W. Sieber, T.H. Hankins: ApJ 258, 776 (1982) G. Benford, R. Bushauer: MNRAS 179, 189 (1977) V.S. Beskin, A.V. Gurevich, Y.N. Istomin: Soviet Astronomy Letters 14, 93 (1988)


67

17. V.S. Beskin, A.V. Gurevich, Ya.N. Istomin: Physics of the Pulsar Magnetosphere, Cambridge University Press (1993) 18. J.D. Biggs: MNRAS 245, 514 (1990) 19. Chen, K. & Ruderman, M. 1993, ApJ 402, 264 20. K.S. Cheng, C. Ho, M. Ruderman: ApJ 300, 500 (1986) 21. K.S. Cheng, M. Ruderman, L. Zhang: ApJ 537, 964 (2000) 22. F. Crawford, R.N. Manchester, V.M. Kaspi: AJ 122, 2001 (2001) 23. J.G. Davies, A.G. Lyne, F.G. Smith, V.A. Izvekova, A.D. Kuz’min, Yu.P. Shitov: MNRAS, 211, 57 (1984) 24. W.T.S. Deich, J.M. Cordes, T.H. Hankins, J.M. Rankin: ApJ 300, 540 (1986) 25. A.A. Deshpande, J.M. Rankin: ApJ 524, 1008 (1999) 26. A.A. Deshpande, J.M. Rankin: MNRAS, 322, 438 (DR01) (2001) 27. F.D. Drake, H.D. Craft Jr.: Nature 220, 231 (1968) 28. J. Eilek, P.N. Arendt Jr.: ApJ (in preparation) 29. A.V. Filippenko, V. Radhakrishnan: ApJ 263, 828 (1982) 30. R. Fitzpatrick, L. Mestel: MNRAS 232, 277 (1988a) 31. R. Fitzpatrick, L. Mestel: MNRAS 232, 303 (1988b) 32. L.A. Fowler, G.A.E. Wright, D. Morris: A&A 93, 54 (1981) 33. R.T. Gangadhara, Y. Gupta: ApJ 555, 31 (2001) 34. J.A. Gil, A.G. Lyne: MNRAS 276, 55 (1995) 35. J.A. Gil, J. Kijak, J. Seiradakis: A&A 272, 268 (1993) 36. J.A. Gil, M. Sendyk: ApJ 541, 351 (2000) 37. J.A. Gil, G.I. Melikidze, D. Mitra: A&A 388, 235 (2002a) 38. J.A. Gil, G.I. Melikidze, D. Mitra: A&A 388, 246 (2002b) 39. J.A. Gil, G.I. Melikidze: ApJ 577, 900 (2002) 40. G.R. Gladstone et al.: Nature 415, 1000 (2002) 41. Y. Gupta, R.T. Gangadhara: ApJ 584, 418 (2003) 41a. T.H. Hankins, A. Wolszczan: ApJ 318, 410 (1987) 42. T.H. Hankins, G.A.E. Wright: Nature 288, 681 (1980) 43. T.H. Hankins, J.S. Kern, J.C. Weatherall, J.A. Eilek: Nature 422, 141 (2003) 44. A. Harding, A. Muslimov: ApJ 556, 987 (2002a) 45. A. Harding, A. Muslimov: ApJ 568, 864 (2002b) 46. A. Harding, A. Muslimov, B. Zhang: ApJ 576, 366 (2002) 47. C. Heiles, D. Campbell, J.M. Rankin: Nature 226, 529 (1970) 48. J.A. Hibschmann, J. Arons: ApJ 554, 624 (2001a) 49. J.A. Hibschmann, J. Arons: ApJ 560, 871 (2001b) 50. K. Hirotani, S. Shibata: MNRAS 308, 54 (1999) 51. K. Hirotani, S. Shibata: ApJ 558, 216 (2001) 52. A. von Hoenschbroech, K.M. Xilouris: AA 324, 981 (1997) 53. N.J. Holloway: Nature 246, 6 (1975) 54. G.R. Huguenin, J.H. Taylor, T.H. Troland: ApJ 162, 727 (1970) 55. A. Jessner, H. Lesch, T. Kunzl: ApJ 547, 959 (2001) 56. S. Johnston, W. van Straten, M. Kramer, M. Bailes: ApJ 549, L101 (2001) 57. J.S. Kern: M.S. Thesis, University of Vermont, Burlington (1998) 58. J. Kijak, J.A. Gil: A&A 397, 969 (2003) 59. A. Kinkhabwala, S.E. Thorsett: ApJ 535, 365 (2000) 60. M.M. Komesaroff: Nature 225, 612 (1970) 61. M. Kramer, R. Wielebinski, A. Jessner, J.A. Gil, J.H. Seiradakis: A&AS 107, 515 (1994) 62. M. Kramer, K.M. Xilouris, D.R. Lorimer, O. Doroshenko, A. Jessner, R. Wielebinski, A. Wolszczan, F. Camilo: ApJ 501, 270 (1998)

68


63. M. Kramer, C. Lange, D.R. Lorimer, D.C. Backer, K.M. Xilouris, A. Jessner, R. Wielebinski: ApJ 526, 957 (1999) 64. M. Kramer, S. Johnston, W. van Straten: MNRAS 334, 523 (2002) 65. S. Krishnamohan, G.S. Downs: ApJ 265, 372 (1983) 66. Ch. Lange, M. Kramer, R. Wielebinski, A. Jessner: A&A 332, 111 (1998) 67. A.G.J. van Leeuwen, M.L.A. Kouwenhoven, R. Ramachandran, J.M. Rankin, B.W. Stappers: A&A 387, 169 (2002) 68. A.G.J. van Leeuwen, B.W. Stappers, J.M. Rankin, R. Ramachandran: A&A 399, 223 (2003) 69. D.R. Lorimer, M. McLaughlin: private communication (2002) 70. S.C. Lundgren, J.M. Cordes, M. Ulmer, S.M. Matz, S. Lomatch, R.S. Foster, T.H. Hankins: ApJ 453, 433 (1995) 71. A.G. Lyne: MNRAS 153, 27P (1971) 72. A.G. Lyne, M. Ashworth: MNRAS 204, 477 (1983) 73. A.G. Lyne, R.N. Manchester: MNRAS 234, 519 (1988) 74. V.M. Malofeev: in Pulsars: Problems & Progress. ASP Conference Series 105, 271 (1996) 75. V.M. Malofeev: Catalog of Pulsar Radio Spectra. Pushchino (1999) 76. V.M. Malofeev, I. Malov: Ap&SS 78, 73 (1981) 77. I.F. Malov, S.A. Suleimanova: Astron. Rep. 42, 388 (1998) 78. O. Maron, J. Kijak, M. Kramer, R. Wielebinski: A&AS, 147, 195 (2000) 79. R. May: Proc Roy Soc B228, 241 (1986) 80. M.M. McKinnon: ApJ 413, 317 (1993) 81. M.M. McKinnon: ApJ 475, 763 (1997) 82. M.M. McKinnon, D.R. Stinebring: ApJ 502, 883 (1998) 83. M.M. McKinnon, D.R. Stinebring: ApJ 529, 435 (2000) 84. M. McLaughlin, J. Rankin: in preparation 85. L. Mestel, J.A. Robertson, Y.-M. Wang, K.C. Westfold: MNRAS 217, 443 (1985) 86. L. Mestel: Stellar Magnetism. Oxford University Press (1999) 87. L. Mestel, J. Mestel, S. Goodwin, G.A.E. Wright: MNRAS (submitted) 88. L. Mestel, S. Shibata: MNRAS 271, 621 (1994) 89. F.C Michel: Theory of Neutron Star Magnetospheres. University of Chicago Press, Chicago (1991) 90. F.C. Michel, in: The Magnetospheric Structure and Emission Mechanisms of Radio Pulsars. eds T.H. Hankins, J.M. Rankin, J.A. Gil, Pedagogical University Press, Zielona Gora, p. 236 (1992) 91. D. Mitra, A.A. Deshpande: A&A 346, 906 (1999) 92. D. Mitra, J.M. Rankin: ApJ 577, 322 (2002) (ETVII) 93. L.A. Nowakowski, N.S. Rivera: AAS meeting, 197, 130.04 (2000) 94. Yu. Ochelkov, V. Usov: Nature 308, 332 (1984) 95. L. Oster, D.A. Hilton, W. Sieber: AA 57, 10 (1977) 96. S.A. Petrova: AA 360, 592 (2000) 97. M.V. Popov, N. Bartel, W.H. Cannon, A. Novikov, Yu. V.I. Kondratiev, V.I. Altunin: AA 196, 171 (2002) 98. G.J. Qiao, W.P. Lin: AA 333, 172 (1998) 99. G.J. Qiao, J.F. Liu, B. Zhang, J.L. Han: AA 377, 964 (2001) 100. G.J. Qiao, X.D. Wang, H.G. Wang, R.X. Xu: Chin. J. Astron. Astrophys. 377, 964 (2002) 101. V. Radhakrishnan, D.J. Cooke: ApLett, 3, 225 (RC) (1969) 102. V. Radhakrishnan, A.A. Deshpande: AA 379, 551 (2001) 103. V. Radhakrishnan, J.M.. Rankin: ApJ 352, 258 (1990) (ETV) 104. R. Ramachandran: private communication (2001) 105. R. Ramachandran, J.M. Rankin, B.W. Stappers, M.L.A. Kouwenhoven, A.G.L. van Leeuwen: AA 381, 993 (2002)

Circulating subbeam systems and the physics of pulsar emission 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140.

69

J.M. Rankin: ApJ 274, 333 (1983a) (ETI) J.M. Rankin: ApJ 274, 359 (1983b) (ETII) J.M. Rankin: ApJ 301, 901 (1986) (ETIII) J.M. Rankin: ApJ 325, 314 (1988) J.M. Rankin: ApJ 352, 247 (1990) (ETIV) J.M. Rankin: ApJ 405, 285 (1993a) (ETVIa) J.M. Rankin: ApJs, 85, 145 (1993b) (ETVIb) J.M. Rankin, R. Ramachandran: ApJ 590, 411 (2003) (ETVIII) J.M. Rankin, S.A. Suleymanova, A.A. Deshpande: MNRAS 340, 1076 (2003) J.M. Rankin, G.A.E. Wright: MNRAS (in preparation) R.W. Romani: ApJ 470, 469 (1996) R.W. Romani, S. Johnston: ApJ 557, L93 (2001) R.W. Romani, I.-A. Yadigaroglu: ApJ 438, 314 (1995) M.A. Ruderman, P.G. Sutherland: ApJ 196, 51 (1975) M.A. Ruderman, T. Zhu, K. Chen: ApJ 492, 267 (1998) S. Shibata: MNRAS 276, 537 (1995) S. Shibata, K. Hirotani: ApJ 558, 216 (2001) W. Sieber, R. Reinecke, R. Wielebinski: AA 38, 169 (1975) S.A. Suleymanova, V.A. Izvekova: Soviet Astronomy 28, 32 (1984) S.A. Suleymanova, V.A. Izvekova, J.M. Rankin, N. Rathnasree: J. Astrophys. Astron. 19, 1 (1998) S.A. Suleymanova, V.D. Pugachev: Astronomy Reports 42, 252 (1998) S.A. Suleymanova, V.D. Pugachev: Astronomy Reports 46, 34 (2002) J.H. Taylor, G.R. Huguenin, R.M. Hirsch, R.M. Manchester: ApLett 9, 205 (1971) S.E. Thorsett: ApJ 377, 263 (1991) S.C. Unwin, A.C.S. Readhead, P.N. Wilkinson, M.S. Ewing: MNRAS 182, 711 (1978) M. Vivekanand: MNRAS 274, 785 (1995) M. Vivekanand, B.C. Joshi: ApJ 477, 431 (1997) A. von Hoenschbroech, K.M. Xilouris: AA 324, 981 (1997) G.A.E. Wright: MNRAS 344, 1041 (2003) G.A.E. Wright: in preparation (2003) G.A.E. Wright, L.A. Fowler: AA 101, 356 (1981a) G.A.E. Wright, L.A. Fowler: in: IAU Symposium 95 Pulsars, eds W. Sieber, R. Wielebinski, Reidel, Dordrecht, p. 221 (1981b) G.A.E. Wright, W. Sieber, A. Wolszczan: AA 160, 402 (1985) R.X. Xu, J.F. Liu, J.L. Han, G.J. Qiao: ApJ 535, 354 (2000) M. Young, B.G. Kenny: in Pulsars: Problems Progress. ASP Conference series, 105, 179 (1996)


THE


X-ray astronomy of stellar coronae Manuel Güdel Paul Scherrer Institut, Würenlingen and Villigen, 5232 Villigen PSI, Switzerland Received 27 February 2004 / Published online 25 August 2004 – © Springer-Verlag 2004

Abstract. X-ray emission from stars in the cool half of the Hertzsprung-Russell diagram is generally attributed to the presence of a magnetic corona that contains plasma at temperatures exceeding 1 million K. Coronae are ubiquitous among these stars, yet many fundamental mechanisms operating in their magnetic fields still elude an interpretation through a detailed physical description. Stellar X-ray astronomy is therefore contributing toward a deeper understanding of the generation of magnetic fields in magnetohydrodynamic dynamos, the release of energy in tenuous astrophysical plasmas through various plasma-physical processes, and the interactions of high-energy radiation with the stellar environment. Stellar X-ray emission also provides important diagnostics to study the structure and evolution of stellar magnetic fields from the first days of a protostellar life to the latest stages of stellar evolution among giants and supergiants. The discipline of stellar coronal X-ray astronomy has now reached a level of sophistication that makes tests of advanced theories in stellar physics possible. This development is based on the rapidly advancing instrumental possibilities that today allow us to obtain images with sub-arcsecond resolution and spectra with resolving powers exceeding 1000. High-resolution X-ray spectroscopy has, in fact, opened new windows into astrophysical sources, and has played a fundamental role in coronal research. The present article reviews the development and current status of various topics in the X-ray astronomy of stellar coronae, focusing on observational results and on theoretical aspects relevant to our understanding of coronal magnetic structure and evolution. Key words: X-rays: stars – Stars: coronae – Stars: flare – Stars: late-type – Stars: magnetic fields For my part I know nothing with any certainty, but the sight of the stars makes me dream. Vincent van Gogh (1853–1890) This article is dedicated to the late Rolf Mewe, a prominent astrophysicist who contributed

major work to the field of stellar X-ray astronomy and spectroscopy. He died on May 4, 2004.

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Contents 1. 2. 3. 4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The study of stellar coronae . . . . . . . . . . . . . . . . . . . . . . . . . . The early days of stellar coronal X-ray astronomy . . . . . . . . . . . . . . A walk through the X-ray Hertzsprung-Russell diagram . . . . . . . . . . . 4.1. Main-sequence stars . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. The coolest M dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Brown dwarfs (and planets?) . . . . . . . . . . . . . . . . . . . . . 4.4. A-type stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. X-ray emission from normal A stars . . . . . . . . . . . . 4.4.2. Chemically peculiar A stars . . . . . . . . . . . . . . . . 4.4.3. Herbig Ae/Be stars . . . . . . . . . . . . . . . . . . . . . 4.5. Giants and supergiants . . . . . . . . . . . . . . . . . . . . . . . . 4.6. Close binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7. Contact binary systems . . . . . . . . . . . . . . . . . . . . . . . . 5. X-ray activity and rotation . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Rotation-activity laws . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Activity and rotation in stars with shallow convection zones . . . . 5.3. Rotation and saturation; supersaturation . . . . . . . . . . . . . . . 5.4. Physical causes for saturation and supersaturation . . . . . . . . . . 5.5. Rotation and activity in pre-main sequence stars, giants and binaries 6. Flux-flux relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Chromosphere-transition region-corona . . . . . . . . . . . . . . . 6.2. Radio – X-ray correlations . . . . . . . . . . . . . . . . . . . . . . 7. Thermal structure of stellar coronae . . . . . . . . . . . . . . . . . . . . . 7.1. Thermal coronal components . . . . . . . . . . . . . . . . . . . . . 8. High-resolution X-ray spectroscopy . . . . . . . . . . . . . . . . . . . . . 9. The differential emission measure distribution . . . . . . . . . . . . . . . . 9.1. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1. The DEM of a static loop . . . . . . . . . . . . . . . . . . 9.2.2. The DEM of flaring structures . . . . . . . . . . . . . . . 9.3. Reconstruction methods and limitations . . . . . . . . . . . . . . . 9.4. Observational results . . . . . . . . . . . . . . . . . . . . . . . . . 9.5. Coronal temperature-activity relations . . . . . . . . . . . . . . . . 10. Electron densities in stellar coronae . . . . . . . . . . . . . . . . . . . . . 10.1. Densities from Fe line ratios . . . . . . . . . . . . . . . . . . . . . 10.2. Line ratios of He-like ions . . . . . . . . . . . . . . . . . . . . . . 10.3. Spectroscopic density measurements for inhomogeneous coronae . 11. The structure of stellar coronae . . . . . . . . . . . . . . . . . . . . . . . . 11.1. Loop models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Coronal structure from loop models . . . . . . . . . . . . . . . . . 11.2.1. Loop parameters . . . . . . . . . . . . . . . . . . . . . . 11.2.2. Loop-structure models . . . . . . . . . . . . . . . . . . . 11.2.3. Conclusions and limitations . . . . . . . . . . . . . . . .

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74 77 78 81 81 84 85 86 86 87 88 88 89 89 90 90 92 92 93 94 95 95 96 97 97 98 100 100 100 100 102 103 107 108 110 110 112 115 117 117 119 119 119 121

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11.3. 11.4. 11.5. 11.6. 11.7. 11.8. 11.9. 11.10.

Coronal structure from densities and opacities . . . . . Coronal constituents: Emission-measure interpretation Coronal imaging: Overview . . . . . . . . . . . . . . Active-region modeling . . . . . . . . . . . . . . . . . Maximum-entropy image reconstruction . . . . . . . . Lucy/Withbroe image reconstruction . . . . . . . . . . Backprojection and Clean image reconstruction . . . . Coronal structure inferred from eclipses . . . . . . . . 11.10.1. Extent of eclipsed features . . . . . . . . . . 11.10.2. Structure and location of coronal features . . 11.10.3. Thermal properties of coronal structures . . . 11.11. X-ray coronal structure in other eclipsing binaries . . . 11.12. Inferences from rotational modulation . . . . . . . . . 11.13. Rotationally modulated and eclipsed X-ray flares . . . 11.14. Inferences from Doppler measurements . . . . . . . . 11.15. Inferences from surface magnetic fields . . . . . . . . 11.16. Extended or compact coronae? . . . . . . . . . . . . . 12. Stellar X-ray flares . . . . . . . . . . . . . . . . . . . . . . . 12.1. General properties and classifications . . . . . . . . . 12.2. General flare scenario . . . . . . . . . . . . . . . . . . 12.3. Cooling physics . . . . . . . . . . . . . . . . . . . . . 12.4. Interpretation of the decay time . . . . . . . . . . . . 12.5. Quasi-static cooling loops . . . . . . . . . . . . . . . 12.6. Cooling loops with continued heating . . . . . . . . . 12.7. Two-Ribbon flare models . . . . . . . . . . . . . . . . 12.8. Hydrodynamic models . . . . . . . . . . . . . . . . . 12.9. Magnetohydrodynamic models . . . . . . . . . . . . . 12.10. Summary of methods . . . . . . . . . . . . . . . . . . 12.11. Observations of stellar X-ray flares . . . . . . . . . . . 12.12. Flare temperatures . . . . . . . . . . . . . . . . . . . 12.13. Flare densities . . . . . . . . . . . . . . . . . . . . . . 12.14. Correlation with UV and optical flares . . . . . . . . . 12.15. Correlation with radio flares . . . . . . . . . . . . . . 12.16. The “Neupert Effect” . . . . . . . . . . . . . . . . . . 12.17. Non-thermal hard X-rays? . . . . . . . . . . . . . . . 13. The statistics of flares . . . . . . . . . . . . . . . . . . . . . . 13.1. Correlations between quiescent and flare emissions . . 13.2. Short-term coronal X-ray variability . . . . . . . . . . 13.3. Stochastic variability – what is “quiescent emission”? . 13.4. The solar analogy . . . . . . . . . . . . . . . . . . . . 13.5. The flare-energy distribution . . . . . . . . . . . . . . 13.6. Observables of stochastic flaring . . . . . . . . . . . . 14. X-ray absorption features and prominences . . . . . . . . . . 15. Resonance scattering and the optical depth of stellar coronae . 16. The elemental composition of stellar coronae . . . . . . . . . 16.1. Solar coronal abundances: A brief summary . . . . . .

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16.2. 16.3.

Stellar coronal abundances: The pre-XMM-Newton/Chandra view . Stellar coronal abundances: New developments with XMM-Newton and Chandra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.4. Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . 16.5. Coronal and photospheric abundances . . . . . . . . . . . . . . . . 16.6. Flare metal abundances . . . . . . . . . . . . . . . . . . . . . . . . 16.7. Theoretical models for abundance anomalies . . . . . . . . . . . . 17. X-ray emission in the context of stellar evolution . . . . . . . . . . . . . . 17.1. Main-sequence stars . . . . . . . . . . . . . . . . . . . . . . . . . 17.2. Giants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3. Dividing lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.4. Hybrid stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.5. Evolution of X-ray emission in open stellar clusters . . . . . . . . . 17.5.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 17.5.2. Rotation-age-activity relations . . . . . . . . . . . . . . . 17.5.3. Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.5.4. Co-eval clusters . . . . . . . . . . . . . . . . . . . . . . . 17.5.5. Toward older clusters . . . . . . . . . . . . . . . . . . . . 17.5.6. Toward younger clusters . . . . . . . . . . . . . . . . . . 18. X-ray coronae and star formation . . . . . . . . . . . . . . . . . . . . . . . 18.1. T Tauri stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1.2. X-ray luminosity and age . . . . . . . . . . . . . . . . . 18.1.3. X-ray luminosity, saturation, and rotation . . . . . . . . . 18.1.4. The widely dispersed “field WTTS” samples . . . . . . . 18.1.5. Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1.6. The circumstellar environment . . . . . . . . . . . . . . . 18.1.7. Accretion-driven X-ray emission? . . . . . . . . . . . . . 18.2. Protostars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2.2. Flares and magnetic fields . . . . . . . . . . . . . . . . . 18.2.3. The stellar environment . . . . . . . . . . . . . . . . . . 18.2.4. “Class 0” objects . . . . . . . . . . . . . . . . . . . . . . 18.3. Young brown dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . 19. Young populations in the solar neighborhood . . . . . . . . . . . . . . . . . 20. Long-term variability and stellar magnetic cycles . . . . . . . . . . . . . . 20.1. Clusters and field star samples . . . . . . . . . . . . . . . . . . . . 20.2. Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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178 182 183 186 187 188 188 190 192 193 194 194 196 199 200 201 201 201 202 202 203 204 205 206 207 207 207 207 208 209 210 211 213 213 214 215 215

1. Introduction More than half a century ago, the presence of a very hot, tenuous gas surrounding the Sun, the X-ray corona, was inferred indirectly from optical coronal lines of highly ionized species (Grotrian 1939; Edlén 1942) and more directly by detecting X-ray photons in


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the course of a rocket flight (Burnight 1949)1 . Around the same time, radio observations revealed a radio corona as well (Hey 1946). Of course, the sheer beauty of the solar corona has been admired in scattered visible light ever since humans first wondered about solar eclipses, but only during the last very few decades have we started to seriously grasp solutions to some of the fundamental astrophysical problems within the field of solar and stellar astronomy. Magnetic fields have come to the center of our attention in this endeavor. They seem to be ubiquitous among stars, but neither do we understand precisely why, nor have we fully understood the bewildering variety of plasma physical mechanisms that act in stellar environments. We have found magnetic fields on stars that ought to have none so long as we appeal to our limited understanding of magnetic field production and amplification. We witness various processes of energy transport and energy release intimately related to those very magnetic fields; the fields not only guide mass and energy flows, they are the sources of energy themselves. But our understanding of energy dissipation has remained patchy, in particular in magnetically active stars. The coronal magnetic fields reach into the stellar environment, structuring it and governing heating and particle acceleration. Nevertheless, except in the case of the Sun, we have very little, and usually only indirect evidence of the topology of magnetic fields. In very young stars, magnetic fields may reach out to the circumstellar accretion disks. Again, their role is manifold: they transport angular momentum and thus control the spin rate of the star. They guide mass flows, thus take a leading role in the mass accretion process. They release energy and thus ionize the stellar molecular environment, possibly altering the physics and chemistry of accretion disks and thereby influencing the formation of planets. At later stages, they control stellar rotation through angular momentum transport via a stellar wind and thus engage in a feedback loop because the magnetic field production is rooted in precisely this rotation. The magnetic field thus plays a fundamental role in the evolution of the radiative environment of a star, with far-reaching consequences for the chemical development of planetary atmospheres and, eventually, the formation of life. These and many further challenges have stimulated our field of research both in theory and observation, producing a rich treasure of ideas and models from stellar evolution to elementary plasma-physical processes that reach way beyond specific coronal physics problems. Yet, it has proven surprisingly difficult to study these magnetic fields in the outer stellar atmospheres and the stellar environments. Thus, the essence of a stellar corona is not yet accessible. It is the mass loading of magnetic fields that has given us specific diagnostics for magnetic activity to an extent that we often consider the hot plasma and the accelerated high-energy particles themselves to be our primary subjects. Although often narrowed down to some specific energy ranges, coronal emission is intrinsically a multi-wavelength phenomenon revealing itself from the meter-wave radio range to gamma rays. The most important wavelength regions from which we have learned diagnostically on stellar coronae include the radio (decimetric to centimetric) range and the X-ray domain. The former is sensitive to accelerated electrons in magnetic 1 T. Burnight wrote, “The sun is assumed to be the source of this radiation although radiation

of wave-length shorter than 4 angstroms would not be expected from theoretical estimates of black body radiation from the solar corona.” The unexpected has prevailed all through the history of coronal physics indeed!

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fields, and that has provided the only direct means of imaging stellar coronal structure, through very long baseline interferometry. The most productive spectral range for stellar coronal physics has, however, been the soft X-ray domain where the mysteriously heated bulk plasma trapped in the coronal fields radiates. The X-ray diagnostic power has been instrumental for our understanding of physical processes in coronae, and the recent advent of high-resolution X-ray spectroscopy with the Chandra and XMM-Newton X-ray observatories is now accessing physical parameters of coronal plasma directly. This review is predominantly concerned with the soft X-ray domain of stellar coronal physics, and partly with the closely related extreme ultraviolet range. Radio aspects of stellar coronae have been reviewed elsewhere (Güdel 2002) and will be occasionally addressed when they provide complementary information to our present subject. Notwithstanding the importance of these two wavelength regimes, I emphasize that further diagnostics are available at other photon energies. Although optical and ultraviolet spectroscopy refers predominantly to cooler layers of stellar atmospheres, a few coronal emission lines detected in this wavelength range promise some complementary diagnostics in particular through the very high spectral resolving power available. And second, the hard X-ray and γ -ray range, recognized as the fundamental source of information for energy release physics in the solar corona, will be of similar importance for stars although, at the time of writing, it remains somewhat of a stellar terra incognita, waiting for more sensitive instruments to detect these few elusive photons. A review of a field that has accumulated massive primary literature from three decades of continuous research based on numerous satellite observatories, necessarily needs to focus on selected aspects. The review in hand is no exception. While trying to address issues and problems across the field of stellar X-ray astronomy, I have chosen to put emphasis on physical processes and diagnostics that will help us understand mechanisms not only in stars but in other astrophysical environments as well. Understanding energyrelease physics, magnetic-field generation mechanisms, and evolutionary processes of magnetic structures from protostars to giants will eventually contribute to our understanding of the physics in other astrophysical objects. Examples are accretion-driven mechanisms in disks around active galactic nuclei, the physics of large-scale galactic magnetic fields, or the heating and cooling of galaxy cluster gas. In the course of this review, a number of controversial issues and debates will deliberately be exposed – this is where more investment is needed in the future. Also, while I will address some topics relatively extensively, I will touch upon others in a somewhat more cursory way. My hope is that various previous reviews help close the gaps. They themselves are far too numerous to name individually. I would recommend, among others, the following reviews as entry points to this field: The extreme-ultraviolet domain has recently been summarized extensively by Bowyer et al. (2000). Haisch et al. (1991a) summarized the multi-wavelength view of stellar and solar flares. Two early comprehensive reviews of X-ray astrophysics of stellar coronae were written by Rosner et al. (1985) and Pallavicini (1989), and very recently Favata and Micela (2003) have presented a comprehensive observational overview of stellar X-ray coronae. An interesting early summary of nonradiative processes in outer stellar atmospheres that comprises and defines many of our questions was given by Linsky (1985). Mewe (1991) reviewed X-ray spectroscopic methods for stellar coronae. High-energy aspects


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in the pivotal domain of star formation and early stellar evolution were comprehensively summarized by Feigelson and Montmerle (1999). Topics that are – despite their importance for stellar astronomy – predominantly the subject of solar physics are not discussed here. In particular, plasma-physical mechanisms of coronal heating, the acceleration of (solar and stellar) winds, and the operation of internal dynamos will only be touched upon in so far as stellar observations are contributing specifically to our knowledge. I also note that insights relating to our subject provide diagnostics that reach out to entirely different fields, such as studies of the rotational history of stars, the ionization structure and large-scale evolution of star-forming molecular clouds, the structure and the composition of galactic stellar populations, and dynamo theory for various types of stellar systems. Beyond what I can address in this summary, I need to refer the reader to the more specialized literature. 2. The study of stellar coronae The study of stellar coronae, of course, starts with the Sun. This provides a rather important advantage for stellar astronomers: that of having a nearby, bright standard example available at high spatial and spectral resolution. What, then, should we expect from the study of stellar coronae? In the context of the solar-stellar connection, stellar X-ray astronomy has introduced a range of stellar rotation periods, gravities, masses, and ages into the debate on the magnetic dynamo. Coronal magnetic structures and heating mechanisms may vary together with variations of these parameters. Parameter studies could provide valuable insight for constraining relevant theory. Different topologies and sizes of magnetic field structures lead to different wind mass-loss rates, and this will regulate the stellar spin-down rates differently. As is now clear, on the other hand, rotation is one of the primary determinants of the magnetic dynamo. This point could not be demonstrated by observing the Sun: The Sun’s magnetic activity is in fact strongly modulated (due to the 11-year magnetic spot cycle, Fig. 1), but this effect is not directly dependent on the rotation period. Conversely, the well-studied solar activity cycle motivates us to investigate similar magnetic modulations in stars in order to confine the underlying dynamo mechanism. Stars allow us to study long-term evolutionary effects by observing selected samples with known and largely differing ages. While models of the solar interior and its evolution predict that the young Zero-Age Main-Sequence (ZAMS) Sun was fainter by ≈ 25% than at present, stellar X-ray astronomy has revealed that the solar high-energy emission was likely to be hundreds of times more intense at such young ages. The increased level of ionizing and UV radiation must then have had an important impact on the formation and chemistry of planetary atmospheres. At younger stages still, the radiation at short wavelengths may have been pivotal for ionizing the circumstellar accretion disk. This must have resulted in at least five significant effects that determine the further process of planet formation and stellar evolution. First, stellar magnetic fields couple to the inner disk and thus guide mass accretion onto the star; second, and at the same time, torques mediated by the magnetic fields regulate the rotation period of the star; third, winding-up magnetic fields between star and disk may release further magnetic energy that may lead to jet (and indirectly, to molecular outflow) activity; fourth, permeation of the weakly ionized disk by magnetic

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Fig. 1. Yohkoh images of the Sun during activity maximum (left, in 1991) and minimum (right, in 1995). The light curve in the lower panel illustrates the long-term “cyclic” variability of the solar soft X-ray output

fields induces instabilities (e.g., the Balbus-Hawley instability) that are relevant for the accretion process and planet formation; and fifth, the X-ray irradiation may directly influence the disk chemistry and thus the overall evolution of the dust disk (e.g., Glassgold et al. 2000). Including stars into the big picture of coronal research has also widened our view of coronal plasma physics. While solar coronal plasma resides typically at (1 − 5) × 106 K with temporary excursions to ≈ 20 MK during large flares, much higher temperatures were found on some active stars, with steady plasma temperatures of several tens of MK and flare peaks beyond 100 MK. Energy release in stellar flares involves up to 105 times more thermal energy than in solar flares, and pressures that are not encountered in the solar corona.

3. The early days of stellar coronal X-ray astronomy While this review is entirely devoted to (non-solar) stellar studies, an important anchor point would be missing if the success of the Skylab mission in the early seventies were not mentioned. The high-quality images of the full-disk Sun in X-rays formed, together with data from previous rocket flights, our modern picture of the solar and therefore stellar coronae. The solar X-ray corona is now understood as a dynamic ensemble of magnetic


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loops that contain hot plasma in ever-changing constellations, yet always related to the underlying photospheric magnetic field. Interacting loops may episodically evolve into flares that release much of their energy as soft X-rays. Coronal holes, characterized by low X-ray emission and predominantly open magnetic field lines along which the solar wind escapes at high speed, fill volumes between bright coronal active regions. From a stellar astronomer’s point of view, the early solar coronal studies culminated in the formulation of scaling laws for coronal structures. Best known is the seminal paper by Rosner et al. (1978) in which several of the basic ideas of coronal structure and static loops were developed or extended. These concepts paved the way to interpreting stellar coronae without requiring the imaging capabilities that have been so central to solar studies. The field of stellar coronal X-ray astronomy was in fact opened around the same time, in 1975 when Catura et al. (1975) reported the detection of Capella as the first stellar coronal X-ray source on the occasion of a rocket flight. They estimated the X-ray luminosity at 1031 erg s−1 – four orders of magnitude above the Sun’s – and the plasma electron temperature at about 8 × 106 K, again several times higher than the Sun’s. I note in passing that the latter measurement is in quite close agreement with modern values. This result was confirmed by Mewe et al. (1975) from observations with the ANS satellite; they were the first to interpret the soft X-rays as solar-like coronal emission at an enhanced level. Around the same time, Heise et al. (1975) monitored the first stellar coronal X-ray flares (on YZ CMi and UV Cet) with ANS; one of the flares was recorded simultaneously with an optical burst. The possible contributions of stellar X-ray flares to the diffuse galactic soft X-ray background and of associated particles to the cosmicray particle population were immediately recognized and discussed. Numerous flare observations followed, opening up new avenues of research on energy release physics familiar from the Sun. For example, White et al. (1978) related a soft X-ray flare on HR 1099 with a simultaneous radio burst. Further detections followed suit. Algol was next in line, defining another new class of stellar X-ray sources (Schnopper et al. 1976; Harnden et al. 1977). The initial discussion related the X-rays to an accretion mass stream, however, while modern interpretation ascribes them to coronal structures on the K-type secondary. A series of detections with HEAO 1, namely of RS CVn and HR 1099 (Walter et al. 1978a), Capella (Cash et al. 1978), and UX Ari (Walter et al. 1978b) established the RS CVn binaries as a class of coronal X-ray sources that may also be significant contributors to the galactic soft X-ray background. The unusually high X-ray production of this class was confirmed in the survey by Walter et al. (1980a), also based on HEAO 1. Main-sequence (MS) stars were brought on stage with the first discovery of Proxima Centauri in the extreme ultraviolet range by Haisch et al. (1977), while Nugent and Garmire (1978) identified the “solar twin” α Cen as an inactive coronal source at a luminosity level similar to the Sun. Several further single MS stars at the high end of the activity scale were found, putting our own Sun into a new perspective as a rather modest X-ray star (Walter et al. 1978c; Cash et al. 1979a; Walter et al. 1980b). Discoveries soon extended the coronal range into the A spectral class (Mewe et al. 1975; Topka et al. 1979) although these early detections have not been confirmed as coronal sources, from the present-day point of view. (Mewe et al. 1975 suggested the white dwarf in the Sirius system to be the X-ray source.)

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An important new chapter was opened with the introduction of medium-resolution X-ray spectroscopy. Cash et al. (1978) used HEAO 1 to obtain the first coronal X-ray spectrum of Capella. They correctly interpreted excess emission between 0.65 and 1 keV as being due to the Fe xvii/xviii complex. The earliest version of a (non-solar) stellar coronal emission measure distribution can be found in their paper already! They noticed that the high temperature of Capella’s corona requires magnetic confinement unless we are seeing a free-flowing coronal wind. Another element of modern coronal X-ray interpretation was introduced by Walter et al. (1978b) when they realized that subsolar abundances were required to fit their medium-resolution spectrum of UX Ari. The first explicit X-ray spectra of (non-solar) stellar flares were obtained by Kahn et al. (1979). The thermal nature of the emission was confirmed from the detection of the 6.7 keV Fe Kα line. The Einstein satellite revolutionized the entire field of coronal X-ray astronomy, transforming it from a domain of mostly exotic and extreme stars to a research area that eventually addressed X-ray emission from all stars across the Hertzsprung-Russell diagram, with no lack of success in detecting them either as steady sources (Vaiana et al. 1981) or during large outbursts (Charles et al. 1979). The field of star formation entered the scene when not only star formation regions as a whole, but individual young stars such as T Tau stars were detected as strong and unexpectedly variable X-ray sources (Ku and Chanan 1979; Ku et al. 1982; Gahm 1980; Walter and Kuhi 1981), including the presence of strong flares (Feigelson and DeCampli 1981). The solid-state spectrometer on board Einstein also provided spectroscopic access to many coronal X-ray sources and identified individual emission-line blends of various elements (Holt et al. 1979). These spectra permitted for the first time multi-temperature, variable-abundance spectral fits that suggested the co-existence of cool and very hot 7 (> ∼ 2 × 10 K) plasma in RS CVn binaries (Swank et al. 1981; Agrawal et al. 1981). Lastly, grating spectroscopy started to resolve individual spectral lines or blends in coronal X-ray spectra. Mewe et al. (1982) described spectroscopic observations of Capella that separated Fe and O lines in the 5–30 Å region using the Einstein objective grating spectrometer with a resolving power up to at least 30. Only few high-resolution stellar spectra were obtained with the Focal Plane Crystal Spectrometer (FPCS) on Einstein and the Transmission Grating Spectrometer (TGS) on EXOSAT. The instruments offered spectral resolving powers of 50–500 in the X-ray band (FPCS) and of < ∼ 60 in the EUV band (TGS), respectively. The former instrument was used in narrow wavelength bands only; examples include observations of σ 2 CrB (Agrawal et al. 1985) and Capella (Vedder and Canizares 1983). While these instruments marked a breakthrough in Xray spectroscopy at the time, the S/N achieved was not sufficient to derive detailed information on emission measure (EM) distributions. Nevertheless, rough models were derived that grossly resemble the results from modern high-sensitivity spectroscopy (Vedder and Canizares 1983). Later, the TGS was used to derive information on the EM distribution of bright X-ray sources (Lemen et al. 1989) and to study loop models (Schrijver et al. 1989b). The ultimate breakthrough in stellar coronal physics came with the initial Einstein survey that led to three significant insights. First, X-ray sources abound among all types of stars, across the Hertzsprung-Russell diagram and across most stages of evolution (Vaiana et al. 1981). Stars became one of the most prominent classes of cosmic X-ray


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sources. Second, the X-ray luminosities and their distribution now uncovered along the main sequence could not be in agreement with the long-favored acoustic heating theories; the X-ray emission was now interpreted as the effect of magnetic coronal heating. And third, stars that are otherwise similar reveal large differences in their X-ray output if their rotation period is different (Pallavicini et al. 1981; Walter and Bowyer 1981). These systematics have been in the center of dynamo theory up to the present day, and it is fair to say that no dynamo theory will be deemed fully successful without addressing the latter two points in some detail. The initial findings were rapidly consolidated (e.g., Johnson 1981; Ayres et al. 1981a) but cool-star X-ray astronomy has remained an active research area to the present day, with no lack of debate. The following chapters are devoted to our still exciting era of stellar X-ray astronomy.

4. A walk through the X-ray Hertzsprung-Russell diagram A look at the Hertzsprung-Russell diagram (HRD) of detected X-ray stars in Fig. 2, compiled from selected catalogs of survey programs (Alcalá et al. 1997; Berghöfer et al. 1996; Hünsch et al. 1998a,b, 1999; Lawson et al. 1996), shows all basic features that we know from an optical HRD (we plot each star at the locus of the optically determined absolute magnitude MV and the color index B−V regardless of possible unresolved binarity). Although the samples used for the figure are in no way “complete” (in volume or brightness), the main sequence is clearly evident, and so is the giant branch. The top right part of the diagram, comprising cool giants, is almost devoid of detections, however. The so-called corona vs. wind dividing line (dashed in Fig. 2; after Linsky and Haisch 1979) separates coronal giants and supergiants to its left from stars with massive winds to its right. It is unknown whether the wind giants possess magnetically structured coronae at the base of their winds – the X-rays may simply be absorbed by the overlying wind material (Sect. 17.3). The few residual detections may at least partly be attributed to low-mass companions. The large remaining area from spectral class M up to at least mid-F comprises stars that are – in the widest sense – solar-like and that define the subject of this review. I now turn to a few selected domains within the HRD that have attracted special attention. The domain of star formation and pre-main sequence evolution will be discussed in a wider context toward the end of this review (Sect.18).

4.1. Main-sequence stars The main sequence (MS henceforth) has arguably played the most fundamental role in the interpretation of stellar magnetic activity. It is here that we find a relatively clear correspondence between mass, radius, and color. On the other hand, evolutionary processes map poorly on the MS, providing us with a separate free parameter, namely age or, often equivalently, rotation rate. Current wisdom has it that the most massive coronal MS stars are late-A or early F stars, a conjecture that is supported both by observation and by theory. Theory predicts the absence of a magnetic dynamo in earlier A stars, given the

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Fig. 2. Hertzsprung-Russell diagram based on about 2000 X-ray detected stars extracted from the catalogs by Berghöfer et al. (1996) (blue), Hünsch et al. (1998a,b) (green and red, respectively), and Hünsch et al. (1999) (pink). Where missing, distances from the Hipparcos catalog (Perryman et al. 1997) were used to calculate the relevant parameters. The low-mass pre-main sequence stars are taken from studies of the Chamaeleon I dark cloud (Alcalá et al. 1997; Lawson et al. 1996, yellow and cyan, respectively) and are representative of other star formation regions. The size of the circles characterizes log LX as indicated in the panel at lower left. The ranges for the spectral classes are given at the top (upper row for supergiants, lower row for giants), and at the bottom of the figure (for main-sequence stars)

lack of a significant outer convection zone. (In earlier-type stars of spectral type O and B, shocks developing in unstable winds are the likely source of X-rays.) MS stars define by far the largest stellar population for systematic survey studies (Maggio et al. 1987; Fleming et al. 1988; Schmitt et al. 1990a; Barbera et al. 1993). The ROSAT All-Sky Survey (RASS) from which the samples shown in Fig. 2 were drawn has contributed invaluably to our science by providing volume-limited samples including stars down to the end of the MS and to the minimum levels of X-ray activity. Comprehensive surveys of cool MS stars, some of them complete out to more than 10 pc, were presented by Schmitt et al. (1995), Fleming et al. (1995), Schmitt (1997) and


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Table 1. Symbols and units used throughout the text Symbol, acronym

Explanation

R∗ R M Prot or P p L T ne nH B f FX LX Lbol = 0 T γ Ro RTV loop VAU loop 2-R flares HRD EM Q, DEM EMD (ZA)MS PMS (W, C)TTS BD

Stellar radius [cm] Solar radius [7 × 1010 cm] Solar mass [2 × 1033 g] Rotation period [d] Pressure [dyne cm−2 ] Coronal loop semi-length [cm] Coronal electron temperature [K] Electron density [cm−3 ] Hydrogen density [cm−3 ] Magnetic field strength [G] Surface filling factor [%] Loop area expansion factor (apex to base) X-ray surface flux [erg s−1 cm−2 ] X-ray luminosity [erg s−1 ] Stellar bolometric luminosity [erg s−1 ] Cooling function [erg s−1 cm3 ] Rossby number Constant cross-section loop after Rosner et al. (1978) Expanding cross-section loop after Vesecky et al. (1979) Two-Ribbon flares Hertzsprung-Russell Diagram Emission Measure Differential Emission Measure Distribution (discretized, binned) Emission Measure Distribution (Zero-Age) Main Sequence Pre-Main Sequence (Weak-lined, classical) T Tauri Star Brown Dwarf

Hünsch et al. (1999), with detection rates as high as 95% per spectral class, except for the intrinsically faint or X-ray dark A stars. The survey sensitivities were sufficient to suggest a lower limit to the MS X-ray luminosity probably around a few times 1025 erg s−1 (Schmitt et al. 1995) which translates to a lower limit to the surface X-ray flux that is similar to that of solar coronal holes (Schmitt 1997). Such studies have contributed much to our current understanding of coronal physics, in particular with regard to the dependence of magnetic activity on rotation, the ingredients controlling the coronal heating efficiency, and the feedback loop between activity and evolution, subjects broadly discussed across this review. Before moving on to giants and binaries, I now specifically address three fundamental issues within the main-sequence domain: that of very low-mass stars, brown dwarfs, and A stars with very shallow convective zones.

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4.2. The coolest M dwarfs Beyond spectral type M5, the internal structure of dwarf stars changes significantly as they become fully convective. The classical αω dynamo can thus no longer operate. On the other hand, a distributed (or α 2 ) dynamo may become relevant (e.g., Giampapa et al. 1996 and references therein). One would then naturally expect that both the magnetic flux on the surface and the topology of the magnetic fields in the corona systematically change across this transition, perhaps resulting in some discontinuities in the X-ray characteristics around spectral class dM5. Observations do not seem to support this picture, however. The long-time lowestmass X-ray detection, VB 8 (M7e V) has shown steady emission at levels of LX ≈ 1026 erg s−1 (Johnson 1981; Fleming et al. 1993; J. Drake et al. 1996) and flares up to an order of magnitude higher (Johnson 1987; Tagliaferri et al. 1990; J. Drake et al. 1996). If its X-ray luminosity LX or the ratio of LX /Lbol are compared with other late M dwarfs, a rather continuous trend becomes visible (Fleming et al. 1995, Fig. 3, although there have been scattered claims to the contrary, see, e.g., Barbera et al. 1993). The maximum levels attained by these stars (LX ≈ 10−3 Lbol ) remains the same across spectral class M. If a change from an αω to a distributive dynamo indeed does take place, then the efficiencies of both types of dynamos must be very similar, or the transition must be very

Fig. 3. Diagram showing LX /Lbol for lowest-mass stars later than spectral type M5. Flare and nonflaring values for several detections are marked (figure courtesy of T. Fleming and M. Giampapa, after Fleming et al. 2003)


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smooth and gradual, with the two regimes possibly overlapping (Fleming et al. 1993; Weiss 1993; J. Drake et al. 1996). The same question also arose in the context of the coolest M dwarfs, namely relating to the boundary toward the substellar regime (around masses of 0.07M ). A change in the magnetic behavior is suggested there, for the following reason. The photospheres of such stars are dominated by molecular hydrogen, with a very low ionization degree of approximately 10−7 . Electric currents flow parallel to the coronal magnetic field lines in the predominant non-flaring force-free configuration, but since currents cannot flow into the almost neutral photosphere, any equilibrium coronal configuration will be potential, that is, not capable of liberating energy for heating (Fleming et al. 2000 and references therein). A precipitous drop of LX would thus be expected. Heating could be due to episodic instabilities in more complex magnetic configurations that then produce prominent flares. Indeed, stars at the bottom of the main-sequence (Fleming et al. 2000; Schmitt and Liefke 2002) and evolved brown dwarfs (see below) have been detected in X-rays during flares but not generally at steady levels, similar to what is seen in Hα observations (see references in Fleming et al. 2003). This picture has become somewhat questionable with the X-ray detection of VB 10 (M8e) during 3.5 hrs at a level of LX ≈ 2.4 × 1025 erg s−1 and log LX /Lbol ≈ −4.9 by Fleming et al. (2003) who claim this emission to be non-flaring. It is, however, inherently difficult to identify a steady process in data with very low signal-to-noise ratios (Sect. 13.3), so that the last word on the emission type in those stars may not have been spoken. A most productive strategy is to push the limit further toward lower-mass objects, as discussed below. 4.3. Brown dwarfs (and planets?) Below the stellar mass limit at 0.07M , the realm of brown dwarfs (BD) has attracted immense attention in recent years. The field is, at the time of writing, still quite poorly explored in X-rays. Whereas young X-ray emitting BDs have now amply been detected in star forming regions, these objects behave like contracting T Tauri stars rather than evolved, low-mass MS stars. Recent findings on young BDs are therefore summarized in Sect. 18.3 in the context of star formation. At some quite early point in their evolution (before the age of 100 Myr), they must drop to quite low activity levels. Krishnamurthi et al. (2001) could not detect any BD in their Pleiades field down to a sensitivity limit of LX ≈ 3 × 1027 erg s−1 . First X-ray detections among older, contracted BDs now exist, but a number of anomalies come to light. The first X-ray detected evolved brown dwarf, LP 944-20, was recorded exclusively during a flare, with LX ≈ 1.2 × 1026 erg s−1 and with a decay time of ≈ 5400 s (Rutledge et al. 2000). Although this star is old (≈ 500 Myr), it has not spun down (Prot ≤ 4.4 hrs). While it should thus be in a “supersaturated” regime (Sect. 5), it shows no detectable steady X-ray emission, quite in contrast to its strong and also flaring radio radiation (Berger 2002). Tsuboi et al. (2003) found the BD companion of TWA 5 (with an age of 12 Myr) at levels of LX ≈ 4 × 1027 erg s−1 and, again, below the empirical saturation limit, with a rather soft spectrum (kT = 0.3 keV). Finally, Briggs and Pye (2004) reported a weak detection of Roque 14 in the Pleiades (age 100 Myr), with LX ≈ 3 × 1027 erg s−1 . This time, the emission is not compatible with a flare if the decay time is shorter than 4 ks.

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Ultimately, X-ray observations offer the possibility to detect (X-ray dark) planets as they eclipse part of the corona of their parent star while in transit. Such methods are particularly promising for low-mass stars as a Jupiter-like planet could eclipse a rather significant coronal area. Briggs and Pye (2003) presented an example of a Pleiades member star that showed a significant dip in a flaring light curve (Sect. 11.13). The requirements for such a flare eclipse to occur are somewhat implausible, however, unless enhanced magnetic activity is induced by star-planet interactions (see Briggs and Pye 2003).

4.4. A-type stars The outer convection zones of stars become very shallow toward early F stars and disappear in A-type dwarfs. These stars are therefore not capable of operating a classical αω-type dynamo. Even if magnetic fields existed in early A-type stars, efficient coronal energy release is not expected because no strong surface convective motions are present to transport energy into non-potential coronal fields. Coincidentally, the acoustic flux from the interior reaches a maximum for late A and early F stars (Vaiana et al. 1981, Schrijver 1993 and references therein), a fact that has provoked several early survey programs to look for strong X-ray emission in these stars (Vaiana et al. 1981; Pallavicini et al. 1981; Topka et al. 1982; Walter 1983; Schmitt et al. 1985a). Acoustic heating has meanwhile been widely ruled out as the principal coronal heating mechanism along the main sequence (Vaiana et al. 1981; Stern et al. 1981, although the issue re-surfaces from time to time, e.g., Mullan and Cheng 1994a and Mullan and Fleming 1996, for M dwarfs). However, a significant “base” contribution of acoustic waves in particular to the heating of the lower atmospheres of A-F stars remains a viable possibility (Schrijver 1993; Mullan and Cheng 1994b). Investigations of magnetic activity in A-type stars have proceeded along three principal lines: i) Search for genuine magnetic activity in single, normal A-type and early F stars; ii) study of magnetic activity in chemically peculiar Ap/Bp stars; iii) search for signatures of magnetic fields in very young, forming A-type stars (e.g., Herbig Ae/Be stars). Some selected results are briefly summarized below. 4.4.1. X-ray emission from normal A stars Volume-limited stellar samples reveal a rather abrupt onset of X-ray emission around spectral type A7-F0, with a large range of luminosities developing across spectral class F (Schmitt 1997). The drop in X-rays toward earlier stars is appreciable: The definitive X-ray detection of Altair (A7 V) shows a very soft spectrum at low luminosity (log LX ≈ 27.1, log LX /Lbol ≈ −7.5, Schmitt et al. 1985a), with a temperature of only ≈ 1 MK (Golub et al. 1983; Schmitt et al. 1990a). Quite in general, ostensibly single A-to-early F stars show distinctly soft spectra if detected in X-rays (Panzera et al. 1999). Optically selected samples have produced a number of additional detections up to early A stars, among them quite luminous examples. However, there are several reasons to believe that unidentified cooler companions are responsible for the X-rays. Given the rapid evolution of A-type stars, a companion of, say, spectral type K or M would still be quite active. The companion hypothesis is thus particularly likely for X-ray


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luminous examples with a hard spectrum (Golub et al. 1983). Late-B and A-type stars in the Pleiades, for example, have X-ray properties that are indeed consistent with the presence of a cooler coronal companion (Daniel et al. 2002; Briggs and Pye 2003). Another indication is the break-down of any correlation between rotation and LX or rotation and B − V among these stars, once again indicating that the X-rays may not actually be related to the A star (Simon et al. 1995; Panzera et al. 1999), although F stars are considered to be coronal sources in any case (see below). Illustrative examples of the complications involved in A-star X-ray astronomy are nearby A-star binaries. The X-ray detections of the A-type binary Castor, even as a strong flaring source (Pallavicini et al. 1990b; Schmitt et al. 1994b; Gotthelf et al. 1994), opened up new speculations on A-star coronae. Spatially resolved observations (Güdel et al. 2001a; Stelzer and Burwitz 2003) with XMM-Newton and Chandra showed that both components are X-ray active. However, Castor is in fact a hierarchical quadruple system consisting of two A stars that are each surrounded by a low-mass (K-M type, Güdel et al. 2001a and references therein) companion. They are additionally accompanied by the well-known X-ray strong M-dwarf binary YY Gem. Both Castor components are frequently flaring (Güdel et al. 2001a; Stelzer and Burwitz 2003) and reveal X-ray spectra and fluxes that are quite similar to M dwarfs. Restricting our attention now to the few genuine late A- or early F-type coronal emitters, we find that their weak dynamo operation is generally not able to brake the rapidly spinning star considerably during their short lifetime (Schmitt et al. 1985a). One step further, several authors (Pallavicini et al. 1981; Walter 1983; Simon and Landsman 1991) have questioned the presence of any activity-rotation relation from spectral class A to F5 (beyond which it holds) altogether. These coronae are also conspicuous by their severe deficit of X-ray emission compared to chromospheric and transition region fluxes; the latter can be followed up to mid-A type stars at quite high levels (Simon and Drake 1989, 1993; Simon and Landsman 1991, 1997). Whether or not these atmospheres are indeed heated acoustically and drive an “expanding”, weak and cool corona (Simon and Drake 1989) or whether they are heated magnetically, the X-ray deficit and the low coronal temperatures clearly attest to the inability of these stars to maintain substantial, hot coronae in any way comparable to cooler active stars, their appreciable chromospheres notwithstanding. 4.4.2. Chemically peculiar A stars Magnetic chemically peculiar stars of spectral type Bp or Ap are appreciable magnetic radio sources (Drake et al. 1987), but they have produced quite mixed results in X-rays. While a number of detections were reported early on (Cash et al. 1979b; Cash and Snow 1982; Golub et al. 1983), most Bp/Ap stars remained undetected, and only few of them can be identified as probably single stars (S. Drake et al. 1994b). When detected, their X-ray luminosities are quite high (log LX ≈ 29.5–30, log LX /Lbol ≈ −6) and do not follow the systematics of earlier-type stars. Given the strong surface magnetic fields in Bp/Ap stars, the currently favored models involve dipolar magnetospheres either featuring equatorial reconnection zones that heat plasma (S. Drake et al. 1994b) or winds that are magnetically guided to the equatorial plane where they collide and heat up (Babel and Montmerle 1997).

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A suspiciously high detection rate of CP stars was reported for the open cluster NGC 2516 by Dachs and Hummel (1996), Jeffries et al. (1997), and Damiani et al. (2003) (6 or 7 detected out of 8 observed CP stars in the latter study, amounting to one half of all detected stars optically identified as A-type). Such statistical samples may argue in favor of some of the Ap stars in fact being the sites of the X-ray emission. As for nonmagnetic Am stars, only scattered evidence is present that some may be X-ray sources (Randich et al. 1996b; Panzera et al. 1999), but again the caveats with undetected cooler companions apply. 4.4.3. Herbig Ae/Be stars The nature of strong X-ray emission from pre-main sequence Herbig Ae/Be stars has remained rather controversial. Models include unstable stellar winds, colliding winds, magnetic coronae, disk coronae, wind-fed magnetospheres, accretion shocks, the operation of a shear dynamo, and the presence of unknown late-type companions. Some X-ray properties are reminiscent of hot stars (Zinnecker and Preibisch 1994), others point to coronal activity as in cool stars, in particular the presence of flares (Hamaguchi et al. 2000; Giardino et al. 2004) and very high temperatures (T > ∼ 35 MK, Skinner et al. 2004). For reviews – with differing conclusions – I refer the reader to the extensive critical discussions in Zinnecker and Preibisch (1994), Skinner and Yamauchi (1996), and Skinner et al. (2004).

4.5. Giants and supergiants The evolution of X-ray emission changes appreciably in the domain of giants and supergiants. The area of red giants has attracted particular attention because hardly any X-rays are found there. The cause of the X-ray deficiency is unclear. It may involve a turn-off of the dynamo, a suppression by competing wind production, or simply strong attenuation by an overlying thick chromosphere (Sect. 17.3). This region of the HRD was comprehensively surveyed by Maggio et al. (1990) using Einstein, and by Ayres et al. (1995), Hünsch et al. (1998a), and Hünsch et al. (1998b) using the ROSAT AllSky Survey. A volume-limited sample was discussed by Hünsch et al. (1996). Several competing effects influence the dynamo during this evolutionary phase especially for stars with masses > ∼ 2M : While the growing convection zone enhances the dynamo efficiency, angular momentum loss via a magnetized wind tends to dampen the dynamo evolution. These processes occur during the rather rapid crossing of the Hertzsprung gap toward M type giants and supergiants. The systematics of the X-ray emission are still not fully understood. A rather exquisite but very small family of stars is defined by the so-called FK Com stars, giants of spectral type K with an unusually rapid rotation and signs of extreme 32 −1 activity. Their X-ray coronae are among the most luminous (LX > ∼ 10 erg s ) and hottest known (with dominant temperatures up to 40 MK; e.g., Welty and Ramsey 1994; Gondoin et al. 2002; Gondoin 2004b; Audard et al. 2004). These stars are probably descendants of rapidly rotating B-A MS stars that, during the fast evolution across the Hertzsprung gap, have been able to maintain their rapid rotation as the convection zone


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deepened, while now being in a stage of strong magnetic braking due to increased magnetic activity (Gondoin et al. 2002; Gondoin 2003a). The leading hypothesis, however, involves a merger of a close binary system, in which the orbital angular momentum of the companion is transferred to the primary (Bopp and Stencel 1981).

4.6. Close binaries Close, tidally interacting binaries keep their fast rotation rates often throughout their MS life and possibly into the subgiant and giant evolution. Their rotation-induced dynamos maintain high magnetic activity levels throughout their lifetimes, making them ideal laboratories for the study of magnetic dynamo theory. The most common binary systems available for study are RS CVn-type systems that typically contain a G- or K-type giant or subgiant with a late-type subgiant or MS companion. The similar class of BY Dra-type binaries contain two late-type MS stars instead. If their separation is sufficiently small, the two components may come into physical contact, defining the class of W UMa-type contact systems (see Sect. 4.7 below). And finally, Algol-type binaries are similar to RS CVn systems, but the MS component is of early type (typically a B star). The cool subgiant fills its Roche lobe, and mass transfer may be possible. Extensive X-ray surveys of RS CVn-type binaries were presented by Walter and Bowyer (1981), Drake et al. (1989), Drake et al. (1992), Dempsey et al. (1993a), Dempsey et al. (1993b), and Fox et al. (1994). Comparative studies suggested that the secondary star plays no role in determining the activity level of the system other than providing the mechanism to maintain rapid rotation (Dempsey et al. 1993a). However, the surface X-ray activity does seem to be enhanced compared to single stars with the same rotation period (Dempsey et al. 1993a). The X-ray characteristics of BY Dra binaries are essentially indistinguishable from RS CVn binaries so that they form a single population for statistical studies (Dempsey et al. 1997). The X-ray emission of Algols was surveyed by White and Marshall (1983), McCluskey and Kondo (1984) and Singh et al. (1995). White et al. (1980) were the first to indicate that X-rays from Algol-type binaries are also coronal (with X-ray sources located on the late-type secondary), and that they resemble RS CVn-type binaries in that respect. However, Algols are underluminous by a factor of 3–4 compared to similar RS CVn binaries (Singh et al. 1996b) . It is therefore rather unlikely that possible accretion streams contribute significantly to the X-ray emission in Algol. Ottmann et al. (1997) presented the first survey of Population II binaries. They concluded that their overall X-ray emission is weaker than what is typical for similar Pop I RS CVn binaries. Here, part of the trend may, however, be explained by the Pop II sample containing fewer evolved stars. On the other hand, the reduced metallicity may also inhibit efficient coronal radiation.

4.7. Contact binary systems W UMa systems are contact binaries of spectral type F-K with rotation periods from 0.1 – 1.5 d. They were first detected in X-rays by Caroll et al. (1980) and surveyed by

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Cruddace and Dupree (1984). Their rapid rotation periods suggest enhanced activity, and this is indeed confirmed by more recent comprehensive surveys (St¸epie`n et al. 2001). However, early work already found an order-of-magnitude deficiency in LX /Lbol when compared to similar detached systems (Cruddace and Dupree 1984; Vilhu and Rucinski 1983; Vilhu 1984). This phenomenon is also known as “supersaturation” (see Sect. 5). A survey by McGale et al. (1996) with ROSAT essentially confirmed the luminosity deficit in all targets and additionally reported somewhat lower maximum temperatures and a smaller amount of very hot plasma when compared with detached RS CVn binaries. The related near-contact binaries do not share a common envelope but may in fact be evolutionary precursors of contact systems. They were studied by Shaw et al. (1996) who found luminosities similar to those of contact systems but again significantly lower than those of RS CVn binaries.

5. X-ray activity and rotation 5.1. Rotation-activity laws Stellar rotation and magnetic activity operate in a feedback loop; as a single low-mass MS star ages, it sheds a magnetized wind, thus spinning down due to angular momentum transport away from the star. This, in turn, weakens the internal dynamo and thus reduces magnetic activity (e.g., Skumanich 1972). This negative feedback loop tends to converge toward a definitive rotation period P that depends only on mass and age once the star has evolved for a few 100 Myr (e.g., Soderblom et al. 1993). It is thus most likely rotation, and only indirectly age, that determines the level of magnetic activity, a contention confirmed in recent studies by Hempelmann et al. (1995). X-rays offer an ideal and sensitive tool to test these dependencies, and corresponding results were found from the initial Xray survey with Einstein. Pallavicini et al. (1981) suggested a relation between X-ray luminosity and projected rotational velocities vsini (where v is measured in km s−1 ) LX ≈ 1027 (vsini)2 [erg s−1 ]

(1)

(although the stellar sample included saturated stars, which were recognized only later). A similar trend was visible in a sample shown by Ayres and Linsky (1980). The overall relation was subsequently widely confirmed, e.g., by Maggio et al. (1987) for F-G MS and subgiant stars, or by Wood et al. (1994) for a large sample of nearby stars based on EUV measurements (with somewhat smaller indices of 1.4 – 1.6). For the surface flux FX or the ratio LX /Lbol , a relation like (1) implies FX ,

LX ∝ 2 ∝ P −2 Lbol

(2)

where is the angular rotation velocity and we have, for the moment, ignored the photospheric-temperature term distinguishing the two measures on the left-hand side. Walter (1981) reported LX /Lbol ∝ but his sample included saturated stars (not recognized as such at that time). He later introduced broken power-laws and thus in fact corrected for a saturation effect in rapid rotators (Walter 1982, see below). Schrijver et al. (1984) included other determining factors, concluding, from a common-factor analysis,


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that the specific emission measure ζ (total EM divided by the stellar surface area) is related to P and the (dominant) coronal temperature as ζ = 1028.6±0.2 T 1.51±0.16 P −0.88±0.14

(3)

where here T is given in MK, P in d, and ζ in cm−5 . Since the dynamo efficiency also depends on the convection zone depth, Noyes et al. (1984) and Mangeney and Praderie (1984) introduced the Rossby number Ro as the ratio of the two relevant time scales of rotation and convection (Ro = P /τc , where τc is the convective turnover time). The most general rotation-activity diagrams that may include stars of various spectral classes and radii are now conventionally drawn for the variables Ro and LX /Lbol (Dobson and Radick 1989) although there has been considerable discussion as to which parameters are to be preferred (Rutten and Schrijver 1987; Basri 1987). A critical appraisal of the use of Ro for activity-rotation relations was given, for example, by St¸epie`n (1994) who described some limitations also with regard to the underlying theoretical concepts. The overall rotation-activity relation was perhaps best clarified by using large samples of stars from stellar clusters. The comprehensive diagram in Fig. 4 clearly shows a regime where LX /Lbol ∝ Ro−2 for intermediate and slow rotators (from Randich et al. 2000). However, in fast rotators LX appears to become a unique function of Lbol , LX /Lbol ≈ 10−3 regardless of the rotation period (Agrawal et al. 1986a; Fleming et al. 1988; Pallavicini et al. 1990a). The tendency for a corona to “saturate” at this level once the rotation period (or the Rossby number) is sufficiently small, or v sufficiently large, was identified and described in detail by Vilhu and Rucinski (1983), Vilhu (1984), Vilhu and Walter (1987), and Fleming et al. (1989). It is valid for all classes of stars but the onset of saturation varies somewhat depending on the spectral type. Once MS coronae are saturated, LX also becomes a function of mass, color, or radius simply owing to the fundamental properties of MS stars.

Fig. 4. Activity-rotation relationship compiled from several samples of open cluster stars. Key to the symbols: circles: Pleiades; squares: IC 2602 and IC 2391: stars: α Per; triangles: single Hyades stars; crossed triangles: Hyades binaries; diamonds: IC 4665; filled symbols: field stars (figure courtesy of S. Randich, after Randich et al. 2000, by the kind permission of the Astronomical Society of the Pacific)

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5.2. Activity and rotation in stars with shallow convection zones The shallow convection zones toward early F stars express themselves through two effects. First, the maximum LX /Lbol ratio or the maximum surface flux FX decrease when compared to the nearly constant values for cooler stars (Walter 1983; Vilhu and Walter 1987; Gagné et al. 1995b, also Wood et al. 1994 for EUV emission). In other words, the dynamo becomes less efficient. And second, little or no dependence of LX on rotational parameters is found in early F stars (Pallavicini et al. 1981; Walter 1983; Simon and Drake 1989, 1993; Stauffer et al. 1994). These results were initially taken to suggest a change in the dynamo mode (possibly from non-solar-like to solar-like at a spectral type of ≈F5 V), or a change in the surface magnetic field configuration as the convection zone deepens (Schrijver and Haisch 1996), or a change from acoustic to magnetic coronal heating (Simon and Drake 1989). Comprehensive surveys by Mangeney and Praderie (1984), Schmitt et al. (1985a), and Dobson and Radick (1989), however, put the absence of an activity-rotation relation into question. If activity is correlated with the Rossby number, then in fact the same dependence is recovered for early F-type stars as for later stars. Consideration of the convective turnover time may indeed be important for these stars because, in contrast to the range of cooler stars, τc varies largely across the F spectral class (e.g., Stauffer et al. 1994; Randich et al. 1996a). Once a “basal” flux is subtracted from the observed chromospheric flux, one also finds that all convective stars, including late-A and F stars, follow the same coronal-chromospheric flux-flux relations (Sect. 6; Schrijver 1993). It is essentially the dynamo efficiency (i.e., the surface magnetic flux density for a given rotation rate) that decreases toward earlier F stars while the basic dynamo physics may be identical in all convective main-sequence stars (except, possibly, for late-M dwarfs; Sect. 4.2). At the same time, the magnetic braking efficiency is reduced in early-F stars. The dynamo and, as a consequence, the magnetic flux production are never sufficient in these stars to “saturate” the way cooler stars do. 5.3. Rotation and saturation; supersaturation The issue of which parameters most favorably represent the activity-rotation relation was studied in great detail by Pizzolato et al. (2003) for MS stars in the context of saturation. They reported the following results (see also Micela et al. 1999a for a qualitative description): i) The rotation period is a good activity indicator for non-saturated stars for which it correlates with the unnormalized LX regardless of mass. The slope of the power law is – 2. ii) The period at which saturation is reached increases with decreasing mass (≈ 1.5 d for an 1.05M star, ≈ 3.5 d for a 0.7M star, and rapidly increasing further for lower masses), therefore reaching to progressively lower maximum LX . iii) In the saturation regime, LX /Lbol becomes strictly independent of rotation and mass with the possible exception of stars with masses > 1.1M . iv) A modified, empirical convective turnover time (hence a modified Rossby number Ro ) can be derived as a function of stellar mass with the goal of defining a universal function LX /Lbol = f (Ro ) that is valid for all cool stars irrespective of mass. The empirical turnover time is found to be −1/2 similar to the calculated τc , and it scales with Lbol . As a consequence, the two descrip tions, LX vs. P and LX /Lbol vs. Ro become fully equivalent for non-saturated stars. v)


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The saturation is triggered at a fixed Ro ≈ 0.1, and the critical period where saturation starts is Psat . The full description of the rotation-activity relation in this picture is, then,  LX   ∝ Ro−2 and LX ∝ P −2 for P > ∼   Lbol Lbol −1/2 (4) Psat ≈ 1.2  L  LX  −3 ≈ 10 for P < ∼ Lbol As rotational equatorial velocities exceed ≈ 100 km s−1 , the LX /Lbol values begin to slightly decrease again. This “supersaturation” phenomenon (Prosser et al. 1996; Randich et al. 1996a; James et al. 2000, Fig. 4) may be ascribed to a fundamental change of the dynamo action or to a decrease of the surface coverage with active regions (see Sect. 5.4).

5.4. Physical causes for saturation and supersaturation Considering all aspects described above, it seems fair to say that all spectral classes between F and M are capable of maintaining coronae up to a limit of log (LX /Lbol ) ≈ −3.0. Some decrease of the maximum (“saturation”) level toward earlier F and late-A stars may be real because of the shallowness of the convection zone in these stars. The physical causes of saturation and supersaturation are not well understood. Ideas include the following: 1. The internal dynamo saturates, i.e., it produces no more magnetic flux if the rotation period increases (Gilman 1983; Vilhu and Walter 1987). 2. The surface filling factor of magnetic flux approaches unity at saturation (Vilhu 1984). This is also motivated by a strong correlation between saturated LX and radius rather than LX and surface temperature (Fleming et al. 1989). However, if the entire solar surface were filled with normal active regions, its X-ray luminosity would amount to only ≈ (2 − 3) × 1029 erg s−1 (Vaiana and Rosner 1978; Wood et al. 1994), with LX /Lbol ≈ 10−4 (Vilhu 1984), short of the empirical saturation value by one order of magnitude. To make up for this deficiency, one requires enhanced densities, larger coronal heights, or different mechanisms such as continuous flaring (see Sect. 13). The detection of rotational modulation in some saturated or nearly saturated stars (Güdel et al. 1995; Kürster et al. 1997; Audard et al. 2001a, see Sect.11.12) casts some doubt on a stellar surface that is completely covered with an ensemble of similar active regions. 3. Jardine and Unruh (1999) argued that the radius where centrifugal forces balance gravity (the co-rotation radius) approaches the outer X-ray coronal radius in rapid rotators. As the rotation rate increases, centrifugal forces lead to a rise in pressure in the outer parts of the largest loops. Once the co-rotation radius drops inside the corona, the local gas pressure may increase sufficiently to blow open the magnetic structures, thus leading to open, X-ray dark volumes. This mechanism confines the coronal height. This coronal “stripping” overcomes effects due to increased pressure, leading to approximately constant emission in the saturation regime. As the rotation rate increases further and the corona shrinks, a more structured low corona is

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left behind that is less luminous (“supersaturated”) and is more prone to rotational modulation (Jardine 2004). Deep rotational modulation has indeed been found in the supersaturated young G star VXR45 (Marino et al. 2003a, see Sect. 11.12). 4. An alternative explanation was given by St¸epie`n et al. (2001) who conjectured that rapid rotation produces, through a strong centrifugally induced gradient of the effective gravity from the equator to the pole, a heat flux excess toward the poles in the stellar interior. Consequently, an excess convective updraft develops at the poles, accompanied by poleward circulation flows in the lower part of the convection zone, and equatorward surface return flows. This circulation system sweeps magnetic fields from the generation region in the lower convection zone toward the poles. This effect strongly amplifies with rotation rate, thus leaving progressively more of the equatorial region free of strong magnetic fields. Therefore, the filling factor decreases. The effect is particularly strong in W UMa-type contact binaries although an additional suppression, presumably due to equatorial flows between the components, is found. The suppression of equatorial activity has an interesting side effect in that loss of angular momentum through a wind is strongly suppressed (St¸epie`n et al. 2001).

5.5. Rotation and activity in pre-main sequence stars, giants and binaries Among giants and supergiants, the dependence between rotation and activity becomes much less evident (Maggio et al. 1990). Whereas cooler giants follow the same dependence as MS stars, this does not hold for warmer giants (Ayres et al. 1998). The evolution across the Hertzsprung gap features two competing effects, namely a deepening convection zone that strengthens the dynamo, and rapid spin-down that weakens it. It is likely that the rapid evolution through this regime does not leave sufficient time for the stars to converge to a unified rotation-activity relation. There are also mixed results from pre-main sequence stars. Whereas the standard behavior including saturation applies to some star-forming regions such as Taurus, other regions show all stars in a saturation regime, up to rotation periods of 30 d. This effect could be related to the long convective turnover time in these stars, as discussed by Flaccomio et al. (2003c) and Feigelson et al. (2003) (see Sect. 18.1 for further details). Close binary systems are interesting objects to study the effect of rapid rotation that is maintained due to tidal interactions with the orbiting companion. Walter and Bowyer (1981) found LX ∝ (5) Lbol (and no dependence on v) although this relation contains much scatter and may in fact be a consequence of a relation between stellar radius and orbital period in close binaries, larger stars typically being components of longer-period systems and being bolometrically brighter (Walter and Bowyer 1981; Rengarajan and Verma 1983; Majer et al. 1986; Dempsey et al. 1993a); this explanation was however questioned again by Dempsey et al. (1997). In general, caution is in order with regard to activity-rotation relationships in these binaries because many of them are at or close to the saturation limit.


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6. Flux-flux relations 6.1. Chromosphere-transition region-corona Flux-flux (or luminosity-luminosity) relations from the chromosphere to the corona contain telltale signatures of the overall heating process and of systematic deficiencies at any of the temperature layers. The standard relation between normalized luminosities from transition-region emission lines such as C iv and coronal X-ray luminosities is non-linear, with a power-law slope of about 1.4 – 1.5 (Ayres et al. 1981b; Vilhu 1984; Agrawal et al. 1986a; Haisch et al. 1990c; Ayres et al. 1995); the power-law becomes steeper if chromospheric lines are used, e.g., Mg ii; thus LMg II 3 LX LC IV 1.5 LX ≈ ; ≈ (6) Lbol Lbol Lbol Lbol (see Fig. 5). These relations hold for RS CVn-type binaries as well (Dempsey et al. 1993a), although Mathioudakis and Doyle (1989) reported a near-linear correlation between the Mg ii and and X-ray surface fluxes in dMe and dKe dwarfs. Schrijver and co-workers suggested that a color-dependent basal component be subtracted from the chromospheric (and partly transition region) stellar line fluxes to obtain the magnetically induced excess flux H K in the Ca ii H&K lines (Schrijver 1983, 1987; Schrijver

Fig. 5. “Flux-flux” diagram for LX and the C iv luminosity. Different groups of stars are schematically represented by different shading, labeled as follows: 1 standard relation for main-sequence stars; 2 X-ray deficient G supergiants; 3, 4 G-K0 III giants; 5 low-activity K0-1 III giants, 6 X-ray deficient F-G0 Hertzsprung gap stars; 7 probable region of red giants (Aldebaran, Arcturus); the black circles mark “hybrid” stars (figure courtesy of T. Ayres, after Ayres 2004)

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et al. 1992; Rutten et al. 1991 and further references cited therein). The justification for this procedure is that the flux-flux power-law relations tighten and become colorindependent. They flatten somewhat but remain non-linear between X-rays and chromospheric fluxes: FX ∝ 1.5−1.7 . On the other hand, this procedure results in little change HK for the X-ray vs. transition region flux correlation (Rutten et al. 1991; Ayres et al. 1995). The basal chromospheric flux is then independent of activity and was suggested to be the result of steady (non-magnetic) acoustic heating (Schrijver 1987). No such basal flux is found for X-rays (Rutten et al. 1991) which may imply that any lower limit to the average X-ray surface flux may be ascribed to a genuine minimum magnetic heating. If done so, the lower limit to the X-ray surface flux empirically found by Schmitt (1997) implies, however, a minimum magnetic chromospheric flux that is still much in excess of the basal fluxes for G-M stars, thus putting into question whether truly basal stars are realized, except possibly for F-type stars (see also Dempsey et al. 1997). The flux-flux relations must be rooted in the magnetic flux on the stellar surface. Whereas chromospheric fluxes appear to depend non-linearly on the average photospheric magnetic flux density f B (f is the surface filling factor of the magnetic fields) both for solar features and for entire stars (Schrijver et al. 1989a; Schrijver and Harvey 1989), the stellar coronal correlation between X-ray surface flux and f B becomes nearly linear (Schrijver et al. 1989a). This suggests that an important cause of the non-linearities in the chromospheric-coronal flux-flux correlations is actually rooted in the behavior of the chromospheric radiative losses. On the other hand, Ayres et al. (1996) explained the non-linearity in the corona-transition region flux-flux relation by the increasing coronal temperatures with increasing activity (Sect. 9.5), bringing a progressively larger fraction of the emission into the X-ray band. For various solar features (active regions, bright points, etc), a strong linear correlation was reported between LX and total unsigned magnetic flux (Fisher et al. 1998); the principal determining factor is the surface area of the feature. Interestingly, this correlation extends linearly over orders of magnitude to magnetically active stars. Because the entire stellar coronae may be made up of various solar-like features, the overall correlation suggests that a common heating mechanism is present for all solar and stellar coronal structures (Pevtsov et al. 2003). Empirically, a somewhat different relation was suggested by St¸epie`n (1994) if the stellar color (or the photospheric effective temperature) was also taken into account, namely FX ∝ T 8.3 B 1.9 where B is the surface magnetic field strength. There are interesting deviations from the flux-flux correlations, in particular in the giant and supergiant domain. These are briefly addressed in the context of evolution and coronal structure in Sect. 17.2 and 17.4. Also, several flux-flux relations have been reported between flaring and low-level emission. I describe those in Sect. 13.1.

6.2. Radio – X-ray correlations There is considerable interest in correlating emissions that connect different parts of causal chains. As I will discuss further in Sect.12.2, standard flare models involve electron beams (visible at radio wavelengths) that heat the chromospheric plasma to X-ray emitting temperatures. The heating processes of the quiescent coronal plasma


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may be entirely different, however. Nevertheless, average radio and X-ray luminosities are nearly linearly correlated in magnetically active stars (Güdel and Benz 1993), LX /LR ≈ 1015.5 [Hz]2 with some scatter, and this correlation appears to mirror the behavior of individual solar flares (Benz and Güdel 1994). This flux-flux relation applies to quite different classes of active stars such as RS CVn binaries (Drake et al. 1989, 1992; Dempsey et al. 1993a, 1997; Fox et al. 1994) and active M dwarfs (Güdel et al. 1993). It is not entirely clear what the underlying cause is, but the most straightforward interpretation is in terms of chromospheric evaporation of frequent, unresolved flares that produce the observed radio emission and at the same time heat the plasma to coronal temperatures.

7. Thermal structure of stellar coronae 7.1. Thermal coronal components The large range of temperatures measured in stellar coronae has been a challenge for theoretical interpretation from the early days of coronal research. Whereas much of the solar coronal plasma can be well described by a component of a few million degrees, early investigations of RS CVn binaries with low-resolution detectors already recognized that active stellar coronae cannot be (near-)isothermal but require a parameterization in terms of at least two largely different temperature components, one around 4–8 MK and the other around 20 − 100 MK (Swank et al. 1981, also Holt et al. 1979, White et al. 1980, and Agrawal et al. 1981 for individual cases). First estimates based on static loop models showed that a simple active corona requires either very high pressures (of order 100 dynes cm−2 ), implying very compact sources with small filling factors, or extremely extended magnetic loops, with a possibility to connect to the binary companion (Swank et al. 1981). The solar analogy had thus immediately reached its limitation for a proper interpretation of stellar data. This theme and its variations have remained of fundamental interest to the stellar X-ray community ever since. Although even low-resolution devices provide meaningful temperature measurements, there has been a long-standing debate on the interpretation of “1-T ” or “2-T ” models. Historically, the opinions were split; some argued that the individual temperature components represent separate plasma features (Schrijver et al. 1984; Mewe and Schrijver 1986; Singh et al. 1987; Pallavicini et al. 1988; Lemen et al. 1989; Pasquini et al. 1989; Schrijver et al. 1989b; Dempsey et al. 1993b; Singh et al. 1995, 1996a,c; Rodonò et al. 1999); others suggested that they parameterize a continuous distribution of EM in temperature and thus represent a continuum of source types (Majer et al. 1986; Schmitt et al. 1987, 1990a; Schmitt 1997; Drake et al. 1995b, 2001). As we have been learning from high-resolution spectroscopy, the correct solution may be a diplomatic one. There is little doubt (also from the solar analogy and simple physical models) that coronae display truly continuous EM distributions, but there are a number of superimposed features that may trace back to individual physical coronal structures. The differential emission measure distribution (DEM) thus became an interesting diagnostic 2 Note that the radio luminosity L is conventionally derived from a flux density measured at R

a fixed frequency such as 4.9 GHz or 8.4 GHz, per unit frequency interval.

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tool for coronal structure and heating (see, for example, Dupree et al. 1993; Brickhouse et al. 1995; Kaastra et al. 1996; Güdel et al. 1997a; Favata et al. 1997c; Griffiths and Jordan 1998, to mention a few). The temperatures determined from low-resolution spectral devices may in fact also be driven by detector characteristics, in particular the accessible energy range as well as the spectral behavior of the detector’s effective area (Majer et al. 1986; Schmitt et al. 1987; Pasquini et al. 1989; Schmitt et al. 1990a; Favata et al. 1997c). Overall, there is little doubt that the gross temperature determinations of low-resolution devices are correct, but a comprehensive description of the emission measure distribution requires high-resolution spectra that allow for more degrees of freedom and thus independent parameters, although the accuracy of the spectral inversion remains limited on principal mathematical grounds (see Sect. 9.3). I will in the following focus on more recent results that are based on reconstructions of full DEMs mainly from high-resolution devices, first reviewing some general data and basic definitions.

8. High-resolution X-ray spectroscopy With the advent of Chandra and XMM-Newton, high-resolution X-ray spectroscopy has opened a new window to stellar coronal research. The Chandra High-Energy Transmission Grating Spectrometer (HETGS), the Low-Energy Transmission Grating Spectrometer (LETGS) as well as the two XMM-Newton Reflection Grating Spectrometers (RGS) cover a large range of spectral lines that can be separated and analyzed in detail. The spectra contain the features required for deriving emission measure distributions, abundances, densities, and opacities as discussed throughout this paper. Here, I give only a brief description of sample spectra and some distinguishing properties that are directly related to the thermal structure. Figures 6 and 7 show examples of spectra obtained by XMM-Newton and Chandra, respectively. The stars cover the entire range of stellar activity: HR 1099 representing a very active RS CVn system, Capella an intermediately active binary, and Procyon an inactive F dwarf. The spectrum of HR 1099 reveals a considerable amount of continuum and comparatively weak lines, which is a consequence of the very hot plasma in this corona (T ≈ 5–30 MK). Note also the unusually strong Ne ix/Fe xvii and Ne x/Fe xvii flux ratios if compared to the other stellar spectra. These anomalous ratios are in fact due to an abundance anomaly discussed in Sect. 16.3. The spectrum of Capella is dominated by Fe xvii and Fe xviii lines which are preferentially formed in this corona’s plasma at T ≈ 6 MK. Procyon, in contrast, shows essentially no continuum and only very weak lines of Fe. Its spectrum is dominated by the H- and He-like transitions of C, N, and O formed around 1–4 MK. The flux ratios between H- to He-like transitions are also convenient temperature indicators: The O viii λ18.97/O vii λ21.6 flux ratio, for example, is very large for HR 1099 but drops below unity for Procyon.

HR 1099

C VI Lyα

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Fig. 6. Three high-resolution X-ray spectra of stars with largely differing activity levels: HR 1099, Capella, and Procyon. Data from XMM-Newton RGS

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Fig. 7. Extracts of two high-resolution X-ray spectra from HR 1099 and Capella, showing the region of the Fe L-shell transitions. Strong lines in the Capella spectrum without identification labels correspond to those labeled in the HR 1099 spectrum (data from Chandra HETGS, courtesy of N. Brickhouse)

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9. The differential emission measure distribution 9.1. Theory The flux φj observed in a line from a given atomic transition can be written as 1 ne nH dV φj = AGj (T ) dlnT 4πd 2 dlnT

(7)

where d denotes the distance, and Gj (T ) is the “line cooling function” (luminosity per unit EM) that contains the atomic physics of the transition as well as the ionization fraction for the ionization stage in question, and A is the abundance of the element with respect to some basic tabulation used for Gj . For a fully ionized plasma with cosmic abundances, the hydrogen density nH ≈ 0.85ne . The expression ne nH dV (8) dlnT defines the differential emission measure distribution (DEM). I will use this definition throughout but note that some authors define Q (T ) = ne nH dV /dT which is smaller by one power of T . For a plane-parallel atmosphere with surface area S, (8) implies 1 dT −1 H (T ) = (9) Q(T ) = ne nH SH (T ), T ds Q(T ) =

where H is the temperature scale height. 9.2. Interpretation Equations (7) and (8) introduce the DEM as the basic interface between the stellar X-ray observation and the model interpretation of the thermal source. It contains information on the plasma temperature and the density-weighted plasma mass that emits X-rays at any given temperature. Although a DEM is often a highly degenerate description of a complex real corona, it provides important constraints on heating theories and on the range of coronal structures that it may describe. Solar DEMs can, similarly to the stellar cases, often be approximated by two power laws Q(T ) ∝ T s , one on each side of its peak. Raymond and Doyle (1981) reported low-temperature power-law slopes of s = 0.9 for the coronal hole network, s = 2.1 for the quiet Sun, and s = 3.1 for flares. The Sun has given considerable guidance in physically interpreting the observed stellar DEMs, as the following subsections summarize. 9.2.1. The DEM of a static loop The DEM of a hydrostatic, constant-pressure loop was discussed by Rosner et al. (1978) (= RTV), Vesecky et al. (1979) (= VAU), and Antiochos and Noci (1986). Under the conditions of negligible gravity, i.e., constant pressure in the entire loop, and negligible thermal conduction at the footpoints, 1

Q(T ) ∝ pT 3/4−γ /2+α

1 − [T /Ta ]2−γ +β

1/2

(10)


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Fig. 8. Left: Calculated differential emission measures of individual static loops. The solid curves refer to uniform heating along the loop and some fixed footpoint heating flux, for different loop halflengths labeled above the figure panel in megameters. The dashed curves illustrate the analytical solutions presented by Rosner et al. (1978) for uniform heating. The dotted lines show solutions assuming a heating scale height of 2 × 109 cm (figure courtesy of K. Schrijver, after Schrijver and Aschwanden 2002). Right: Examples of discrete stellar emission measure distributions derived from spectra of solar analogs. The slopes below log T ≈ 6.5 are only approximate (figure courtesy of A. Telleschi)

(Bray et al. 1991) where Ta is the loop apex temperature, and α and β are power-law indices of, respectively, the loop cross section area S and the heating power q as a function of T : S(T ) = S0 T α , q(T ) = q0 T β , and γ is the exponent in the cooling function over the relevant temperature range: (T ) ∝ T γ . If T is not close to Ta and the loops have constant cross section (α = 0), we have Q(T ) ∝ T 3/4−γ /2 , i.e., under typical coronal conditions for non-flaring loops (T < 10 MK, γ ≈ −0.5), the DEM slope is near unity (Antiochos and Noci 1986). If strong thermal conduction is included at the footpoints, then the slope changes to +3/2 if not too close to Ta (van den Oord et al. 1997), but note that the exact slope again depends on γ , i.e., the run of the cooling function over the temperature range of interest. The single-loop DEM sharply increases at T ≈ Ta (Fig. 8). Such models may already resemble some stellar DEMs (Ayres et al. 1998), and they are close to observed solar full-disk DEMs that indicate Q ∝ T 3/2 (Jordan 1980; Laming et al. 1995; Peres et al. 2001). However, the DEMs of many active stars are much steeper (see below; Fig. 8). Loop expansion (α > 0) obviously steepens the DEM. Increased heating at the loop footpoints (instead of uniform heating) makes the T range narrower and will also increase the slope of the DEM (Bray et al. 1991; Argiroffi et al. 2003). Further, if the heating is non-uniform, as for example in loops that are predominantly heated near the footpoints, the DEM becomes steeper as well (see numerical calculations of various loop examples by Schrijver and Aschwanden 2002 and Aschwanden and Schrijver 2002). Examples are illustrated in Fig. 8 together with discrete emission measure distributions derived from stellar spectra. Comprehensive numerical hydrostatic energybalance loop models undergoing steady apex heating have been computed by Griffiths (1999), with applications to observed DEMs, and by the Palermo group (see Sect. 11.2). If the loops are uniformly distributed in Ta , and one assumes a heating rate proportional to the square of the magnetic field strength, B 2 , then Q is dominated by the hottest

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loops because these produce more EM at any given T than cooler loops (Antiochos and Noci 1986). In the more general case, the descending, high-T slope is related to the statistical distribution of the loops in Ta ; a sharp decrease of the DEM indicates that only few loops are present with a temperature exceeding the temperature of the DEM peak (Peres et al. 2001). Lemen et al. (1989) found that EM is concentrated at temperatures where the cooling function (T ) has a positive slope or is flat; these are regions insensitive to heating fluctuations. This idea was further discussed by Gehrels and Williams (1993) who found that most 2-T fits of low-resolution RS CVn spectra show plasma in two regions of relative stability, namely at 5–8 MK and above 25 MK. 9.2.2. The DEM of flaring structures Antiochos (1980) (see also references therein) discussed DEMs of flaring loops that cool by i) static conduction (without flows), ii) evaporative conduction (including flows), and iii) radiation. The inferred DEMs scale, in the above order, like Qcond ∝ T 1.5 ,

Qevap ∝ T 0.5 ,

Qrad ∝ T −γ +1 .

(11)

Since γ ≈ 0 ± 0.5 in the range typically of interest for stellar flares (5 − 50 MK), all above DEMs are relatively flat (slope 1 ± 0.5). If multiple loops with equal slope but different peak T contribute, then the slope up to the first DEM peak can only become smaller. Non-constant loop cross sections have a very limited influence on the DEM slopes. Stellar flare observations are often not of sufficient quality to derive temperature and EM characteristics for many different time bins. An interesting diagnostic was presented by Mewe et al. (1997) who calculated the time-integrated (average) DEM of a flare that decays quasi-statically. They find Q ∝ T 19/8 (12) up to a maximum T that is equal to the temperature at the start of the decay phase. Sturrock et al. (1990) considered episodic flare heating. In essence, they showed how loop cooling together with the rate of energy injection as a function of T may form the observed solar “quiescent” DEM, i.e., the latter would be related to the shape of the cooling function (T ): the negative slope of between 105 K and a few times 106 K results in an increasing Q(T ). Systems of this kind were computed semi-analytically by Cargill (1994), using analytic approximations for conductive and radiative decay phases of the flares. Here, the DEM is defined not by the internal loop structure but by the time evolution of a flaring plasma (assumed to be isothermal). Cargill argued that for radiative cooling, the (statistical) contribution of a flaring loop to the DEM is, to zeroth order, inversely proportional to the radiative decay time, which implies Q(T ) ∝ T −γ +1

(13)

up to a maximum Tm , and a factor of T 1/2 less if subsonic draining of the cooling loop is allowed. Simulations with a uniform distribution of small flares within a limited energy range agree with these rough predictions, indicating a time-averaged DEM that is relatively flat below 106 K but steep (Q[T ] ∝ T 4 ) up to a few MK, a range in which


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the cooling function drops rapidly. Güdel (1997) used a semi-analytical hydrodynamic approach formulated by Kopp and Poletto (1993) to compute the time-averaged DEM for typical stellar conditions up to several 107 K for a power-law distribution of the flare energies (see also Sect. 13.6), finding two DEM peaks that are dominated by the large number of small, cool flares (“microflares” producing the cooler plasma) and by the much less frequent energetic, hot flares, respectively. Let us next assume – in analogy to solar flares – that the occurrence rate of flares is distributed in energy as a power law with an index α (dN/dE ∝ E −α ) and that the peak emission measure EMp of a flare is a power-law function of its peak temperature Tp at least over a limited range of temperatures: EMp ∝ Tpb as found by Feldman et al. (1995) (see also Sect. 12.12 for a larger flare sample). Then, an analytic expression can be derived for the time-averaged DEM of such a flare ensemble, i.e., a “flare-heated corona”, revealing a power law on each side of the DEM peak (Güdel et al. 2003a): 2/ζ T for T < Tm Q(T ) ∝ (14) T −(α−2)(b+γ )−γ for T > Tm where we have assumed the same luminosity decay-time scale for all flares. Here, Tm (a free parameter) is the temperature of the DEM peak, and b ≈ 4.3 ± 0.35 (Sect. 12.12) in the temperature range of interest for active-stellar conditions. The parameter ζ ≡ τn /τT , τn and τT being the e-folding decay times of density and temperature, respectively, is found to vary between ζ = 0.5 (strong heating during the decay) and ζ = 2 (no heating, see Reale et al. 1997, Sect. 12.6). This model produces DEM slopes below Tm that are steeper than unity and range up to a maximum of four.

9.3. Reconstruction methods and limitations Deriving DEMs or their discretized, binned equivalents, the “emission measure distributions” (EMD) in log T from X-ray spectra has been one of the central issues in observational stellar X-ray astronomy. As implied by (7), it is also of considerable importance in the context of determining the coronal composition (see Sect. 16). Although a full description of the methodology of spectral inversion is beyond the scope of this review, I will briefly outline the available strategies as well as the current debate on optimizing results. This may serve as an introduction and guide to the more technical literature. If a spectrum of an isothermal plasma component with unit EM is written in vector form as f(λ, T ), then the observed spectrum is the weighted sum g(λ) = f(λ, T )Q(T )dlnT ≡ F · Q. (15) In discretized form for bins log T , F is a rectangular matrix (in λ and T ). Equation (15) constitutes a Fredholm equation of the first kind for Q. Its inversion aiming at solving for Q is an ill-conditioned problem with no unique solution unless one imposes additional constraints such as positivity, smoothness, or functional form, most of which may not be physically founded. A formal treatment is given in Craig and Brown (1976). The problem is particularly serious due to several sources of unknown and systematic uncertainties,

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such as inaccurate atomic physics parameters in the spectral models, uncertainties in the instrument calibration and imprecise flux determinations, line blends (see detailed discussion in van den Oord et al. 1997 and Kashyap and Drake 1998 and references therein) and, in particular, unknown element abundances. The latter need to be determined from the same spectra. They are usually assumed to be constant across the complete DEM although this hypothesis is not supported by solar investigations (Laming et al. 1995; Jordan et al. 1998). The following constrained inversion techniques have turned out to be convenient:3 1. Integral inversion with regularization. A matrix inversion of (15) is used with the additional constraint that the second derivative of the solution Q(log T ) is as smooth as statistically allowed by the data. Oscillations in the data that are due to data noise are thus damped out. This method is appropriate for smooth DEMs, but tends to produce artificial wings in sharply peaked DEMs (Mewe et al. 1995; Schrijver et al. 1995; Cully et al. 1997). A variant using singular value decomposition for a series of measured line fluxes was discussed by Schmitt et al. (1996b) . 2. Multi-temperature component fits. This approach uses a set of elementary DEM building blocks such as Gaussian DEMs centered at various T but is otherwise similar to the traditional multi-component fits applied to low-resolution data (examples were given by Kaastra et al. 1996 and Güdel et al. 1997b). 3. Clean algorithm. This is both a specific iteration scheme and a special case of (2) that uses delta functions as building blocks. The observed spectrum (or part of it) is correlated with predictions from isothermal models. The model spectrum with the highest correlation coefficient indicates the likely dominant T component. A fraction of this spectral component is subtracted from the observation, and the corresponding model EM is saved. This process is iterated until the residual spectrum contains only noise. The summed model EM tends to produce sharp features while positivity is ensured (Kaastra et al. 1996). 4. Polynomial DEMs. The DEM is approximated by the sum of Chebychev polynomials Pk . For better convergence, the logarithms of the EM and of T are used: log[Q(T )dlog (T )] = N−1 k=0 ak Pk (log T ) which ensures positivity. The degree N of the polynomial fit can be adjusted to account for broad and narrow features (Lemen et al. 1989; Kaastra et al. 1996; Schmitt and Ness 2004; Audard et al. 2004). 5. Power-law shaped DEMs of the form Q(T ) ∝ (T /Tmax )α up to a cutoff temperature Tmax are motivated by the approximate DEM shape of a single magnetic loop (Pasquini et al. 1989; Schmitt et al. 1990a). 3 I henceforth avoid expressions such as “global” or “line-based methods” that have often been used in various, ill-defined contexts. Spectral inversion methods should be distinguished by i) the range and type of the data to be fitted, ii) the parameters to be determined (model assumptions), iii) the iteration scheme for the fit (if an iterative technique is applied), iv) the convergence criteria, v) the constraints imposed on the solution (e.g., functional form of DEM, smoothness, positivity, etc), and vi) the atomic database used for the interpretation. Several methods described in the literature vary in some or all of the above characteristics. Most of the methods described here are not inherently tailored to a specific spectral resolving power. What does require attention are the possible biases that the selected iteration scheme and the constraints imposed on the solution may introduce, in particular because the underlying atomic physics tabulations are often inaccurate or incomplete (“missing lines” in the codes).


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The ranges and types of data may vary depending on the data in use. Low-resolution spectra are commonly inverted as a whole because individual features cannot be isolated. If a high-resolution spectrum is available, then inversion methods have been applied either to the entire spectrum, to selected features (i.e., mostly bright lines), or to a sample of extracted line fluxes. As for iteration schemes, standard optimization/minimization techniques are available. Various methods have been developed for fits to samples of line fluxes (e.g., Lemen et al. 1989; Huenemoerder et al. 2001, 2003; Osten et al. 2003; Sanz-Forcada et al. 2003; Telleschi et al. 2004), with similar principles: 1. The DEM shape is iteratively derived from line fluxes of one element only, typically Fe (xvii-xxvi in X-rays, covering T up to ≈100 MK), e.g., by making use of one of the above inversion schemes tailored to a sample of line fluxes. Alternatively, one can use T -sensitive but abundance-independent flux ratios between He-like and H-like transitions of various elements to construct the DEM piece-wise across a temperature range of ≈ 1–15 MK (Schmitt and Ness 2004). 2. The Fe abundance (and thus the DEM normalization) is found by requiring that the continuum (formed mainly by H and He) agrees with the observations. 3. The abundances of other elements are found by comparing their DEM-predicted line fluxes (e.g., assuming solar abundances), with the observations. The advantage of such schemes is that they treat the DEM inversion and the abundance determination sequentially and independently. Huenemoerder et al. (2001) and Huenemoerder et al. (2003) used an iteration scheme that fits DEM and abundances simultaneously based on a list of line fluxes plus a continuum. Kashyap and Drake (1998) further introduced an iteration scheme based on Markov-chain Monte Carlo methods for a list of line fluxes. This approach was applied to stellar data by Drake et al. (2001). Genetic algorithms have also, albeit rarely, been used as iteration schemes (Kaastra et al. 1996 for low-resolution spectra). There has been a lively debate in the stellar community on the “preferred” spectral inversion approach. Some of the pros and cons for various strategies are: Methods based on full, tabulated spectral models or on a large number of individual line fluxes may be compromised by inclusion of transitions with poor atomic data such as emissivities or wavelengths. On the other hand, a large line sample may smooth out the effect of such uncertainties. Consideration of all tabulated lines further leads to a treatment of line blends that is self-consistent within the limits given by the atomic physics uncertainties. A most serious problem arises from weak lines that are not tabulated in the spectral codes while they contribute to the spectrum in two ways: either in the form of excess flux that may be misinterpreted as a continuum, thus modifying the DEM; or in the form of unrecognized line blends, thus modifying individual line fluxes and the pedestal flux on which individual lines are superimposed. A careful selection of spectral regions and lines for the inversion is thus required (see discussion and examples in Lepson et al. 2002 for the EUV range). If DEMs and abundances are iterated simultaneously, numerical cross-talk between abundance and DEM calculation may be problematic, in particular if multiple solutions exist. Nevertheless, each ensemble of line flux ratios of one element determines the same DEM and thus simultaneously enforces agreement. If a list of selected line fluxes

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is used, e.g., for one element at a time, DEM-abundance cross talk can be avoided, and the influence of the atomic physics uncertainties can be traced throughout the reconstruction process. But there may be a strong dependence of the reconstruction on the atomic physics uncertainties and the flux measurements of a few lines. The lack of a priori knowledge on line blends affecting the extracted line fluxes will introduce systematic uncertainties as well. This can, however, be improved if tabulated potential line blends are iteratively included. The presence of systematic uncertainties also requires a careful and conservative choice of convergence criteria or smoothness parameters to avoid introduction of spurious features in the DEM. The result is a range of solutions that acceptably describe the data based on a goodness-of-fit criterion, in so far as the data can be considered to be represented by the spectral database in use. Within this allowed range, “correctness” cannot be judged on by purely statistical arguments. The spectral inversion is non-unique because the mathematical problem is ill-posed – the atomic data deficiencies cannot be overcome by statistical methodology but require external information. Direct comparisons of various methods, applied to the same data, are needed. Mewe et al. (2001) presented an EMD for Capella based on selected Fe lines that compares very favorably with their EMD derived from a multi-T approach for the complete spectra, and these results also seem to agree satisfactorily with previously published EMDs from various methods and various data sets. EMDs of the active HR 1099 found from spectra of XMM-Newton RGS (Audard et al. 2001a) and from Chandra HETGS (Drake et al. 2001) agree in their principal features, notwithstanding the very different reconstruction methods applied and some discrepancies in the abundance determinations. Telleschi et al. (2004) determined EMDs and abundances of a series of solar analogs at different activity levels from polynomial-DEM fits to selected spectral regions and from an iterative reconstruction by use of extracted line-flux lists. The resulting EMDs and the derived abundances of various elements are in good agreement. Schmitt and Ness (2004) compared two approaches within their polynomial DEM reconstruction method, again concluding that the major discrepancies result from the uncertainties in the atomic physics rather than from the reconstruction approach, in particular when results from EUV lines are compared with those from X-ray lines. A somewhat different conclusion was reported by Sanz-Forcada et al. (2003) from an iterative analysis of Fe-line fluxes of AB Dor; nevertheless, their abundance distribution is in fact quite similar to results reported by Güdel et al. (2001b) who fitted a complete spectrum. The evidence hitherto reported clearly locates the major obstacle not in the inversion method but in the incompleteness of, and the inaccuracies in, the atomic physics tabulations. Brickhouse et al. (1995) gave a critical assessment of the current status of Fe line emissivities and their discrepancies in the EUV range, together with an analysis of solar and stellar spectra. The effects of missing atomic transitions in the spectral codes were demonstrated by Brickhouse et al. (2000) who particularly discussed the case of Fe transitions from high n quantum numbers, i.e., of transitions that have only recently been considered.


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9.4. Observational results If the caveats and the principal mathematical limitations of the present state of the art in the derivation of EMDs discussed above are properly taken into account, then the physical implications of some of the more secure results offer access to the underlying coronal physics. Most EMDs have generally been found to be singly or doubly peaked (Mewe et al. 1995, 1996, 1997; Drake et al. 1995b, 1997; Rucinski et al. 1995; Schrijver et al. 1995; Kaastra et al. 1996; Schmitt et al. 1996b; Güdel et al. 1997a,b) and confined on either side approximately by power laws (e.g., Mathioudakis and Mullan 1999; Güdel et al. 2003a). Examples are shown in Figs. 8 and 9, where stellar and solar EMDs are

Fig. 9. Emission measure distributions of two intermediately active stars and the Sun. The axes are logarithmic, with the EM given in units of 1050 cm−3 , and the temperature in K. The blue and red circles refer to EMDs for ξ Boo and Eri, respectively. The histograms refer to full-disk solar EMDs derived from Yohkoh images at solar maximum, including also two versions for different lower cutoffs for the intensities in Yohkoh images. Note the similar low-T shapes but the additional high-T contributions in the stars that reveal EMDs similar to bright solar active regions (figure courtesy of J. Drake, after Drake et al. 2000)

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compared. These power laws open up interesting ways of interpretation as discussed in Sect. 9.2.1 and 9.2.2. It is notable that the complete EMD shifts to higher temperatures with increasing stellar activity (see also Sect. 9.5), often leaving very little EM at modest temperatures and correspondingly weak spectral lines of C, N, and O (Kaastra et al. 1996). For example, Haisch et al. (1994) found only highly-ionized spectral lines in the EUV spectrum of the intermediately active solar analog χ 1 Ori (Fe xvi and higher) whereas the EUV spectrum of Procyon and α Cen is dominated by lower ionization stages, corresponding to a DEM peaking at 1–2 MK, similar to the full-disk, non-flaring solar DEM (Mewe et al. 1995; Drake et al. 1995b, 1997). Double peaks are often found for active stars. They then reveal a minimum in the range of 10–20 MK (Lemen et al. 1989; Mewe et al. 1996; Güdel et al. 1997a; Huenemoerder et al. 2003). Filling in this trough does not seem to lead to consistent solutions (e.g., Lemen et al. 1989; Sanz-Forcada et al. 2001), although bias could be introduced by inaccurate atomic physics. On the other hand, the two peaks may have a physical foundation. Continual flaring has been proposed (Güdel 1997), or separate families of magnetic loops dominated by two different temperature regimes (Sciortino et al. 1999). In less active stars, the hotter peak disappears, leaving a marked single EMD maximum just below 10 MK (Dupree et al. 1993; Brickhouse and Dupree 1998; Sanz-Forcada et al. 2001, 2002). EMDs are often steeper on the low-T side than single, constant-cross section loop models (e.g., the static loop models by Rosner et al. 1978) predict, and this is particularly true for the more active stars (Pasquini et al. 1989; Schmitt et al. 1990a; Dempsey et al. 1993b; Laming et al. 1996; Laming and Drake 1999; Drake et al. 2000; Sanz-Forcada et al. 2002; Scelsi et al. 2004; Telleschi et al. 2004). For example, the cooler branches of the stellar EMDs in Fig. 9 follow approximately Q ∝ T 3 . One remedy may be loops with an expanding cross section from the base to the apex, as computed by Vesecky et al. (1979). In that case, there is comparatively more hot plasma, namely the plasma located around the loop apex, than cooler plasma. The EMD and the DEM would consequently steepen. Spectral fits using individual loops require, in specific cases, expansion factors , i.e., the ratio between cross sectional areas at the apex and at the footpoints, of between 2 and 50. Still, this model may fail for some sources (Schrijver et al. 1989b; Ottmann 1993; Schrijver and Aschwanden 2002). Alternatively, the steep low-T EMD slopes may be further evidence for continual flaring (Güdel et al. 2003a); (14) predicts slopes between 1 and 4, similar to what is often found in magnetically active stars (see Sect. 13.6). An extremely steep (slope of 3–5) EMD has consistently been derived for Capella (Brickhouse et al. 1995; Audard et al. 2001b; Behar et al. 2001; Mewe et al. 2001; Argiroffi et al. 2003). Here, the EMD shows a sharp peak around 6 MK that dominates the overall spectrum. These EM results also agree well with previous analyses based on EUV spectroscopy (Brickhouse et al. 2000). 9.5. Coronal temperature-activity relations Early low-resolution spectra from HEAO 1, Einstein, EXOSAT, and ROSAT implied the persistent presence of considerable amounts of plasma at unexpectedly high temperatures, T > 10 MK (e.g., Walter et al. 1978b; Swank et al. 1981), particularly in extremely


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active stars. This is now borne out by EMDs of many active stars that show significant contributions up to 30–40 MK, if not higher. One of the surprising findings from stellar X-ray surveys is a relatively tight correlation between the characteristic coronal temperature and the normalized coronal luminosity LX /Lbol : Stars at higher activity levels support hotter coronae (Vaiana 1983; Schrijver et al. 1984; Stern et al. 1986; Schmitt et al. 1990a; Dempsey et al. 1993b; Maggio et al. 1994; Gagné et al. 1995a; Schmitt et al. 1995; Hünsch et al. 1996; Güdel et al. 1997a; Preibisch 1997a; Schmitt 1997; Singh et al. 1999). Instead of explicit temperature measurements, some authors used spectral hardness as a proxy for T , and the surface flux FX or the EM per unit area can be used instead of LX /Lbol , but the conclusions remain the same. The example of solar analogs is shown together with the Sun itself during its activity maximum and minimum in Fig. 10. Here, LX ∝ T 4.5±0.3 EM ∝ T 5.4±0.6

(16) (17)

where LX denotes the total X-ray luminosity, but EM and T refer to the “hotter” component in standard 2-T fits to ROSAT data. Such relations extend further into the pre-main sequence domain where exceedingly hot coronae with temperatures up to ≈100 MK are found (Imanishi et al. 2001a). The cause of this relation is not clear. Three classes of models might apply: Phenomenologically, as the activity on a star increases, the corona becomes progressively more dominated by hotter and denser features, for example active regions as opposed to quiet areas or coronal holes. Consequently, the average stellar X-ray spectrum indicates more hot plasma (Schrijver et al. 1984; Maggio et al. 1994; Güdel et al. 1997a; Preibisch 1997a; Orlando et al. 2000; Peres et al. 2000; see Sect. 11.4). Increased magnetic activity also leads to more numerous interactions between adjacent magnetic field structures. The heating efficiency thus increases. In particular, we expect a higher rate of large flares. Such models naturally produce the temperatureactivity correlation: The increased flare rate produces higher X-ray luminosity because chromospheric evaporation produces more EM; at the same time, the plasma is heated to higher temperatures in larger flares (as we will discuss in Sect. 12.12). This mechanism was simulated and discussed by Güdel et al. (1997a), Güdel (1997), and Audard et al. (2000) (see also Sect. 13). Jordan et al. (1987) and Jordan and Montesinos (1991) studied an EM-T relation based on arguments of a minimum energy loss configuration of the corona, assuming a fixed ratio between radiative losses and the coronal conductive loss. They suggested a relation including the stellar gravity g of the form EM ∝ T 3 g

(18)

which fits quite well to a sample of observations with T taken from single-T fits to stellar coronal data. The authors suggested that this relation holds because coronal heating directly relates to the production rate of magnetic fields, and the magnetic pressure is assumed to scale with the thermal coronal pressure. Equation (18) then follows directly.

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solar analogs

Temperature (MK)

10

ROSAT higher T XMM, EM weighted mean T Sun (min-max)

1 26

27

28

logLX (erg s-1)

29

30

31

Fig. 10. Coronal temperature vs. X-ray luminosity for solar analogs. The filled circles are from the sample of Güdel et al. (1997a) and Güdel et al. (1998) and refer to the hotter component in 2-T fits to ROSAT data. The solar points (triangles), covering the range from sunspot minimum to maximum, were taken from Peres et al. (2000). The open circles refer to EM-weighted averages of log T ; these values were derived from full reconstructed EMDs (Telleschi et al. 2004) and, for α Cen (at LX ≈ 1027 erg s−1 ), from multi-T fits (Raassen et al. 2003a). In both of the latter cases, XMM-Newton data were used

10. Electron densities in stellar coronae With the advent of high-resolution spectroscopy in the EUV range (by EUVE and Chandra) and in X-rays (by XMM-Newton and Chandra), spectroscopic tools have become available to measure electron densities ne in coronae. Coronal electron densities are important because they control radiative losses from the coronal plasma; observationally, they can in principle also be used in conjunction with EMs to derive approximate coronal source volumes. The spectroscopic derivation of coronal densities is subtle, however. Two principal methods are available. 10.1. Densities from Fe line ratios The emissivities of many transitions of Fe ions in the EUV range are sensitive to densities in the range of interest to coronal research (Mewe et al. 1985, 1995; Schmitt et al. 1994a, 1996c; Mathioudakis and Mullan 1999). Brickhouse et al. (1995) have provided extensive tabulations of the relevant emissivities together with a critical review of their overall reliability. The different density dependencies of different lines of the same Fe ion then also make their line-flux ratios, which (apart from blends) are easy to measure, useful diagnostics for the electron density.


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A review of the literature (see also Bowyer et al. 2000) shows a rather unexpected segregation of coronal densities into two realms at different temperatures. The cool coronal plasma in inactive stars is typically found at low densities of order 109 cm−3 – 1010 cm−3 . In active stars, the cooler components may show elevated densities, but extreme values up to > 1013 cm−3 have been reported for the hotter plasma component. A few notable examples follow. For the inactive α Cen, Mewe et al. (1995) derived ne = 2×108 cm−3 – 2×109 cm−3 , in reasonable agreement with a measurement from EUVE (Drake et al. 1997) and with typical solar coronal densities (Landi and Landini 1998). For the similarly inactive Procyon, Schmitt et al. (1994a, 1996c) and Schrijver et al. (1995) found somewhat higher values of approximately 3 × 109 cm−3 – 4 × 109 cm−3 from lines of Fe x–xiv, with an allowed range from 109 cm−3 to 1010 cm−3 . This picture does not change much for intermediately active stars such as Eri (ne ≈ 10 −3 3 × 109 cm−3 , Laming et al. 1996; Schmitt et al. 1996b), or ξ Boo A (ne > ∼ 10 cm , Laming and Drake 1999). In general, the more active stars tend to show somewhat higher densities. An appreciable change comes with higher activity levels when we consider the hotter plasma. Some extremely high densities have been reported from line ratios of highly ionized Fe, for example: Capella (ne = [0.04 − 1.5] × 1013 cm−3 from Fe xix-xxii; Dupree et al. 1993; Schrijver et al. 1995), UX Ari (ne = [4.5 ± 2] × 1012 cm−3 from Fe xxi; Güdel et al. 1999, also Sanz-Forcada et al. 2002), AU Mic (ne = [2 − 5] × 1012 cm−3 from Fe xxi-xxii; Schrijver et al. 1995), σ Gem (ne ≈ 1012 cm−3 from Fe xxi-xxii; Schrijver et al. 1995, also Sanz-Forcada et al. 2002), ξ UMa B (ne = 5 × 1012 cm−3 from Fe xxi-xxii; Schrijver et al. 1995), 44i Boo (ne > 1013 cm−3 from Fe xix; Brickhouse and Dupree 1998), HR 1099 (ne = [1.6 ± 0.4] × 1012 cm−3 from Fe xix, xxi, xxii; Sanz-Forcada et al. 2002; somewhat higher values in Osten et al. 2004), II Peg (ne = [2.5 − 20] × 1012 cm−3 from Fe xxi and xxii; Sanz-Forcada et al. 2002), AB Dor (ne = [2 − 20] × 1012 cm−3 from Fe xx-xxii; Sanz-Forcada et al. 2002), β Cet (ne = [2.5 − 16] × 1011 cm−3 from Fe xxi; Sanz-Forcada et al. 2002), and several short-period active binaries (ne ≈ [3 − 10] × 1012 cm−3 from Fe xxi, Osten et al. 2002). However, most of these densities are only slightly above the lowdensity limits for the respective ratios, and upper limits have equally been reported 12 −3 (for σ 2 CrB, ne < ∼ 10 cm from Fe xxi, Osten et al. 2000, 2003; for HD 35850, 11 −3 ne ≤ [4 − 50] × 10 cm from Fe xxi, Mathioudakis and Mullan 1999; Gagné et al. 1999). Mewe et al. (2001) used several line ratios of Fe xx, xxi, and xxii in Chandra data 12 −3 of Capella, reporting ne < ∼ (2–5) × 10 cm , in mild contradiction with EUVE reports cited above. More stringent upper limits of log ne = 11.52 were obtained for Algol from Fe xxi EUV line ratios (Ness et al. 2002b). From a detailed consideration of Fe xxi line ratios in the Chandra HETG spectrum of Capella, Phillips et al. (2001) even concluded that the density measured by the most reliable Fe xxi line ratio, f (λ102.22)/f (λ128.74), 12 −3 is compatible with the low-density limit of this diagnostic (i.e., ne < ∼ 10 cm ); in fact, these authors re-visited previous measurements of the same ratio and suggested that they all represent the low-density limit for Capella. Likewise, Ayres et al. (2001a) find contradictory results from different density indicators in the EUV spectrum of β Cet, and suggest low densities. Finally, Ness et al. (2004) measured various Fe line ratios in a

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large sample of coronal stars. None of the stars showed high densities from all line ratios, and all values were again close to the low-density limit; moreover, a given line flux ratio appears to be identical for all considered stars, within the uncertainties. Because it is unlikely that all coronae reveal the same densities, a more natural assumption is that all measurements represent the low-density limit. The observational situation is clearly unsatisfactory at the time of writing. It is worrisome that most measurements referring to the hotter plasma straddle the low-density limit of the respective ion but tend to be systematically different for ionization stages that have similar formation temperatures. At face value, it is perhaps little surprising that the densities do not come out even higher, but this circumstance makes the measurements extremely vulnerable to systematic but unrecognized inaccuracies in the atomic physics tabulations, and to unrecognized blends in some of the lines. Slight shifts then have a dramatic effect on the implied densities, as can be nicely seen in the analysis presented by Phillips et al. (2001). The resolution of these contradictions requires a careful reconsideration of atomic physics issues.

10.2. Line ratios of He-like ions The He-like triplets of C v, N vi, O vii, Ne ix, Mg xi, and Si xiii provide another interesting density diagnostic for stellar coronae. Two examples are shown in Fig. 11 (right). The spectra show, in order of increasing wavelength, the resonance, the intercombination, and the forbidden line of the O vii triplet. The ratio between the fluxes in the forbidden line and the intercombination line is sensitive to density (Gabriel and Jordan 1969) for the following reason: if the electron collision rate is sufficiently high, ions in the upper

Fig. 11. Left: Term diagram for transitions in He-like triplets. The resonance, intercombination, and forbidden transitions are marked. The transition from 3 S1 to 3 P1 re-distributes electrons from the upper level of the forbidden transition to the upper level of the intercombination transition, thus making the f/ i line-flux ratio density sensitive. In the presence of a strong UV field, however, the same transition can be induced by radiation as well. Right: He-like triplet of O vii for Capella (black) and Algol (green). The resonance (r), intercombination (i), and forbidden (f) lines are marked. The f/ i flux ratio of Algol is suppressed probably due to the strong UV radiation field of the primary B star (data from Chandra; both figures courtesy of J.-U. Ness)


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level of the forbidden transition, 1s2s 3 S1 , do not return to the ground level, 1s 2 1 S0 , instead the ions are collisionally excited to the upper levels of the intercombination transitions, 1s2p 3 P1,2 , from where they decay radiatively to the ground state (see Fig. 11 for a term diagram). They thus enhance the flux in the intercombination line and weaken the flux in the forbidden line. The measured ratio R = f/ i of the forbidden to the intercombination line flux can be written as R=

f R0 = 1 + ne /Nc i

(19)

where R0 is the limiting flux ratio at low densities and Nc is the critical density at which R drops to R0 /2. For C v and N vi, the photospheric radiation field needs to be considered as well because it enhances the 3 S1 –3 P1,2 transitions; the same applies to higher-Z triplets if a hotter star illuminates the X-ray source (see Ness et al. 2001). The tabulated parameters R0 and Nc are slightly dependent on the electron temperature in the emitting source; this average temperature can conveniently be confined by the temperature-sensitive G ratio of the same lines, G = (i + f )/r (here, r is the flux in the resonance line 1s 2 1 S0 –1s2p 1 P1 ). A recent comprehensive tabulation is given in Porquet et al. (2001); Table 2 contains relevant parameters for the case of a plasma that is at the maximum formation temperature of the respective ion. A systematic problem with He-like triplets is that the critical density Nc increases with the formation temperature of the ion, i.e., higher-Z ions measure only high densities at high T , while the lower-density analysis based on C v, N vi, O vii, and Ne ix is applicable only to cool plasma. Stellar coronal He-like triplets have become popular with Chandra and XMM-Newton. For C v, N vi, and O vii, early reports indicated densities either around or below the low density limit, viz. ne ≈ 109 –1010 cm−3 for Capella (Brinkman et al. 2000; Canizares et al. 2000; Audard et al. 2001b; Mewe et al. 2001; Ness et al. 2001; Phillips et al. 2001), α Cen (Raassen et al. 2003a), Procyon (Ness et al. 2001; Raassen et al. 2002), HR 1099 (Audard et al. 2001a), and II Peg (Huenemoerder et al. 2001). Note that this sample covers an appreciable range of activity. (A conflicting, higher-density measurement, ne ≈ [2–3] × 1010 cm−3 , was given by Ayres et al. 2001b for HR1099 and Capella). A low-density limit (log ne < 10.2) is found for Capella also from the Table 2. Density-sensitive He-like tripletsa Ion

λ(r, i, f ) (Å)

R0

Nc

log ne rangeb

T rangec (MK)

Cv N vi O vii Ne ix Mg xi Si xiii

40.28/40.71/41.46 28.79/29.07/29.53 21.60/21.80/22.10 13.45/13.55/13.70 9.17/9.23/9.31 6.65/6.68/6.74

11.4 5.3 3.74 3.08 2.66d 2.33d

6 × 108 5.3 × 109 3.5 × 1010 8.3 × 1011 1.0 × 1013 8.6 × 1013

7.7–10 8.7–10.7 9.5–11.5 11.0–13.0 12.0–14.0 13.0–15.0

0.5–2 0.7–3 1.0–4.0 2.0–8.0 3.3–13 5.0–20

a data derived from Porquet et al. (2001) at maximum formation temperature of ion b range where R is within approximately [0.1,0.9] times R 0 c range of 0.5–2 times maximum formation temperature of ion d for measurement with Chandra HETGS-MEG spectral resolution

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Ne ix triplet (Ness et al. 2003b). First unequivocal reports on significant, higher densities measured in O vii came for very active main-sequence stars such as AB Dor (Güdel et al. 2001b) and YY Gem (Güdel et al. 2001a), indicating ne of several times 1010 cm−3 . The trend for higher densities in more active main-sequence stars is consistently found across various spectral types (Ness et al. 2002a; Raassen et al. 2003b; van den Besselaar et al. 2003), whereas active binaries may reveal either high or low densities (Ness et al. 2002b; Huenemoerder et al. 2001, 2003), and low-activity stars generally show low densities (Ness et al. 2002a). The most recent, comprehensive compilation of these trends can be found in Ness et al. (2004) who surveyed O vii and Ne ix triplets of a sample of 42 stellar systems across all levels of magnetic activity, and in Testa et al. (2004) who studied a sample of 22 stars with Chandra. As for higher-Z He-like triplets, reports become quite ambiguous, echoing both the results and the problems encountered in the analysis of Fe lines. Mewe et al. (2001) found ne = 3 × 1012 cm−3 – 3 × 1013 cm−3 in Capella from Mg xi and Si xiii as measured by the Chandra LETGS. These high values agree with EUVE measurements (e.g., Dupree et al. 1993), but they contradict simultaneous Chandra measurements obtained from Fe xx-xxii (Mewe et al. 2001). Osten et al. (2003) derived densities from He-like triplets, Fe xxi and Fe xxii line ratios over a temperature range of ≈ 1 − 15 MK. They found a sharply increasing trend: densities from lines formed below 6 MK point at a modest electron density of a few times 1010 cm−3 , while those formed above indicate densities exceeding 1011 cm−3 , possibly reaching up to a few times 1012 cm−3 . Somewhat perplexingly, though, the Si xiii triplet that is formed at similar temperatures as Mg xi suggests ne < 1011 cm−3 , and discrepancies of up to an order of magnitude become evident depending on the adopted formation temperature of the respective ion. The trend for an excessively high density implied by Mg can also be seen in the analysis of Capella by Audard et al. (2001b) and Argiroffi et al. (2003). Clearly, a careful reconsideration of line blends is in order. Testa et al. (2004) have measured densities from Mg xi in a large stellar sample after modeling blends from Ne and Fe, still finding densities up to a few times 1012 cm−3 but not reaching beyond 1013 cm−3 . All measurements from Si xiii imply an upper limit ≈ 1013 cm−3 , casting some doubt on such densities derived from EUV Fe lines (see above). A trend similar to results from O vii is found again, namely that more active stars tend to reveal higher overall densities. In the case of Ne, the problematic situation with regard to line blends is illustrated in Fig. 12. If the density trend described above is real, however, then coronal loop pressures should vary by 3–4 orders of magnitude. This obviously requires different magnetic loop systems for the different pressure regimes, with a tendency that hotter plasma occupies progressively smaller volumes (Osten et al. 2003; Argiroffi et al. 2003). Contrasting results have been reported, however. Canizares et al. (2000), Ayres et al. (2001b), and Phillips et al. (2001) found, from the Chandra HETG spectrum of Capella, densities at, or below the low-density limit for Ne, Mg, and Si. A similar result applies to II Peg (Huenemoerder et al. 2001). A summary of the present status of coronal density measurements necessarily remains tentative. Densities measured from Mg xi and Si xiii may differ greatly: despite their similar formation temperatures, Mg often results in very high densities, possibly induced by blends (see Testa et al. 2004); there are also discrepancies between densities


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Fig. 12. The spectral region around the Ne ix triplet, showing a large number of Fe lines, some of which will blend with the Ne lines of interest if the resolving power is smaller than shown here (data from Chandra HETGS; the smooth red line shows a fit based on Gaussian line components; figure courtesy of J.-U. Ness)

derived from lines of He-like ions and from Fe xxi and Fe xxii line ratios, again for similar temperature ranges; and there is, lastly, disagreement between various authors who have used data from different instruments. The agreement is better for the cooler plasma components measured with C v, N vi, and O vii. There, inactive stars generally show ne < 1010 cm−3 , whereas densities of active stars may reach several times 1010 cm−3 , values that are in fact in good agreement with measurements based on eclipses or rotational modulation (Sect. 11).

10.3. Spectroscopic density measurements for inhomogeneous coronae Density measurements as discussed above have often been treated as physical parameters of an emitting source. However, because X-ray coronae are inhomogeneous, spectroscopic density measurements should not be taken at face value but should be further interpreted based on statistical models and distributions of coronal features. In spectroradiometry parlance, the observed irradiance, also loosely called “flux”, from the stellar corona derives from the sum of the radiances over the entire visible coronal volume. Let us assume, for the sake of argument, an isothermal plasma around the maximum-formation temperature, T . Let us assume, further, that the emitting volumes, −β V , are distributed in electron density as a power-law, dV /dne ∝ ne . We expect β to be positive, i.e., low-density plasma occupies a large volume and high-density plasma is concentrated in small volumes. The densities inferred from the irradiance line ratios Robs of He-like ions are then biased toward the highest densities occurring in reasonably large volumes because of the n2e dependence of the luminosity.

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log(nmin) = 8.5 log(nmax) = 10.0

3

log(nmin) = 9.5

F/I ratio

log(nmax) = 10.5

2 log(nmax) = 11.0

1 log(nmax) = 11.5 log(nmax) = 12.0

0 0

1

2

3 β

4

5

6

4 log(nmin) = 9.5, log(nmax) = 12.0

F/I ratio

3

2

1

0 0

1

2

3 β

4

5

6

Fig. 13. Top: Calculated Robs = F /I irradiance ratios for the He-like O vii line triplet originating in an inhomogeneous corona with a radiance distribution resulting from a power-law volumedensity distribution (see text for details). The R ratio is plotted as a function of the power-law index β. The different curves are for different ranges of densities at which plasma is assumed to exist; the upper cutoff of the adopted range is given by the labels at left, while labels at right give the lower cutoff. The vertical line marks the transition from the low-R to the high-R regime at β = 3. – Bottom: Example illustrating the Robs = F /I irradiance ratio as a function of β (black line), compared with the R ratio that would correspond to an unweighted average of the densities of all volume elements considered (green). Atomic data from Porquet et al. (2001) were used

The observed forbidden and intercombination line irradiances F and I are the contributions of the radiances f and i, respectively, integrated over the distribution dV /dne and corrected for the stellar distance. The resulting observed Robs = F /I ratios are plotted in Fig. 13a as a function of β for reasonable ranges of coronal densities [ne,min , ne,max ] considered for the power-law volume distribution. The transition from low to high R occurs around β = 3, which is a direct consequence of the n2e factor under the integral sign. A slight rearrangement of the distribution of active regions may thus dramatically change Robs . Further, again due to the n2e dependence of the line flux, the “inferred density” is not an average over the coronal volume. In Fig. 13b, the spectroscopically measured R ratios from this distribution are compared with the ratio that the linearly


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averaged density itself would produce (for one example). It illustrates that the inferred densities are considerably biased to higher values, that is, smaller R ratios, for a given volume distribution (or β). In a global coronal picture like that above, then, the Robs values do not describe “densities” but the steepness of the density distribution, and a straightforward interpretation of densities and volumes from the singular spectroscopic values can be misleading. The line ratio instead contains interesting information on the distribution of coronal densities. More active MS stars thus appear to maintain flatter density distributions, which could be a consequence of the finite coronal volume: since the latter must be shared by low- and high-density plasmas, the more efficient heating in more active stars (e.g., the increased production of chromospheric evaporation) produces a larger amount of high-density volume, at the cost of the residual low-density volume, thus flattening the distribution and decreasing R. Alternatively, as Fig. 13a illustrates, the cutoffs of the density distribution could be shifted to higher values for more active stars while the slope β remains similar. The interpretation of coronal density measurements thus naturally connects to coronal structure, which is the subject of the following section. 11. The structure of stellar coronae The magnetic structure of stellar coronae is one of the central topics in our research discipline. The extent and predominant locations of magnetic structures currently hold the key to our understanding of the internal magnetic dynamo. For example, compact or extended coronae may argue for or against the presence of a distributed dynamo. All X-ray inferences of coronal structure in stars other than the Sun are so far indirect. This section describes various methods to infer structure in stellar coronae at X-ray wavelengths, and reviews the results thus obtained. 11.1. Loop models Closed magnetic loops are the fundamental “building blocks” of the solar corona. When interpreting stellar coronae of any kind, we assume that this concept applies as well, although caution is in order. Even in the solar case, loops come in a wide variety of shapes and sizes (Fig. 14) and appear to imply heating mechanisms and heating locations that are poorly understood – see, for example, Aschwanden et al. (2000a). Nevertheless, simplified loop models offer an important starting point for coronal structure studies and possibly for coronal heating diagnostics. A short summary of some elementary properties follows. Under certain simplifying assumptions, loop scaling laws can be derived. These have been widely applied to stellar coronae. Rosner et al. (1978) (= RTV) have modeled hydrostatic loops with constant pressure (i.e., the loop height is smaller than the pressure scale height). They also assumed constant cross section, uniform heating, and absence of gravity, and found two scaling laws relating the loop semi-length L (in cm), the volumetric heating rate (in erg cm−3 s−1 ), the pressure p (in dynes cm−2 ), and the loop apex temperature Ta (in K), Ta = 1400(pL)1/3 ;

= 9.8 × 104 p 7/6 L−5/6 .

(20)

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Fig. 14. Left: Example of a solar coronal loop system observed by TRACE. Right: Flaring loop system (observation by TRACE at 171Å). Although these images show the emission from relatively cool coronal plasma, they illustrate the possible complexity of magnetic fields

Serio et al. (1981) extended these scaling laws to loops exceeding the pressure scale height sp , whereby, however, the limiting height at which the loops grow unstable is (2 − 3)sp : Ta = 1400(pL)1/3 e−0.04L(2/sH +1/sp ) ;

= 105 p 7/6 L−5/6 e0.5L(1/sH −1/sp ) .

(21)

Here, sH is the heat deposition scale height. For loops with an area expansion factor > 1, Vesecky et al. (1979) (= VAU) found numerical solutions that approximately follow the scaling laws (Schrijver et al. 1989b) Ta ≈ 1400 −0.1 (pL)1/3 ;

Ta = 60 −0.1 L4/7 2/7 .

(22)

Accurate analytical approximations to hydrostatic-loop solutions have been given by Aschwanden and Schrijver (2002) for uniform and non-uniform heating, including loops with expanding cross sections and loops heated near their footpoints. I note in passing that the hydrostatic equations allow for a second solution for cool loops (T < 105 K) with essentially vanishing temperature gradients and small heights (on the Sun: < 5000 km, the pressure scale height at 105 K). These are transition region loops that can be observed in the UV region (Martens and Kuin 1982; Antiochos and Noci 1986). There are serious disagreements between some solar-loop observations and the RTV formalism so long as simplified quasi-static heating laws are assumed, the loops being more isothermal than predicted by the models. There is, however, only limited understanding of possible remedies, such as heating that is strongly concentrated at the loop footpoints, or dynamical processes in the loops (see, for example, a summary of this debate in Schrijver and Aschwanden 2002). Unstable solutions of large coronal loops with temperature inversions at the loop apex were numerically studied by Collier Cameron (1988). If such loops are anchored on rapidly rotating stars, they may, in addition, become unstable under the influence of centrifugal forces. Once the latter exceed gravity, the pressure and the electron density


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grow outwards along the magnetic field, enhance the radiative loss rate and lead to a temperature inversion, which grows unstable. Rapid thermal cooling at the distant loop apex may then lead to condensations of prominence-like, magnetically trapped and centrifugally supported, synchronously rotating cold gas, for which there is indeed evidence at distances of ≈ 3R∗ around the rapid rotator AB Dor (Collier Cameron 1988). Further numerical studies, including various assumptions on the base pressure, surface magnetic field, and base conductive flux were presented by Unruh and Jardine (1997).

11.2. Coronal structure from loop models 11.2.1. Loop parameters When we interpret stellar coronal spectra, we assume, to first order, that some physical loop parameters map on our measured quantities, such as temperature and EM (and possibly density), in a straightforward way. In the simplest approach, we assume that the observed luminosity LX is produced by an ensemble of identical coronal loops with characteristic half-length L, surface filling factor f , and an apex temperature T used for the entire loop; then, on using (20) and identifying LX = V , we obtain R∗ 2 f 3.5 L ≈ 6 × 1016 T [cm]. (23) R LX This relation can only hold if L is smaller than the pressure scale height. Based on this expression, the luminous, hot plasma component in magnetically active stars seems to invariably require either very large, moderate-pressure loops with a large filling factor, or solar-sized high-pressure compact loops with a very small (< 1%) filling factor (Giampapa et al. 1985; Stern et al. 1986; Schrijver et al. 1989b; Giampapa et al. 1996; Güdel et al. 1997a; Preibisch 1997a; Sciortino et al. 1999). Schrijver et al. (1984) modeled T and EM of a sample of coronal sources based on RTV loop models and found the following trends: i) Inactive MS stars such as the Sun are covered to a large fraction with large-scale, cool (2 MK) loops of modest size (0.1R∗ ). ii) Moderately active dwarfs are dominated by very compact, high-density, hot (≈20 MK) loops that require large heating rates (up to 20 times more than for solar compact active region loops). iii) The most active stars may additionally form rather extended loops with heights similar to R∗ . 11.2.2. Loop-structure models While the above interpretational work identifies spectral-fit parameters such as T or EMs with parameters of theoretical loop models, a physically more appealing approach involves full hydrostatic models whose calculated emission spectra are directly fitted to the observations. While physically more realistic than multi-isothermal models, the approach has its own limitations because it relies on a host of ad hoc parameters such as the location and distribution of heating sources within a loop, the loop geometry, the type of thermal conduction law inside the loop and, in particular, the unknown statistical distribution of all the loop parameters in a coronal ensemble. Fitting spectra calculated

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by use of full hydrostatic models permits, however, to constrain possible combinations of these physical loop parameters. Giampapa et al. (1985) presented this type of numerical RTV-type loop models and, assuming that one type of loop dominates, fitted them both to stellar X-ray and transition-region UV fluxes. The modest success of the fitting suggested to them that their assumption was questionable and that various structures do coexist in stellar atmospheres. Stern et al. (1986) fitted numerical loop models, characterized by the loop apex temperature Ta , the loop semi-length L, and the expansion factor , to spectra from the Einstein Imaging Proportional Counter (IPC), and the solutions were again constrained by UV observations. The successful fit results indicated magnetic loops of modest size (L < 1010 cm) with modest filling factors (f < 10 − 20%), but with extreme, flare-like −2 pressures (p > ∼ 400 dynes cm ). Giampapa et al. (1996) extended loop studies to M dwarfs observed by ROSAT. They found that the low-T component at ≈ 1 − 2 MK requires loops of small length (L R∗ ) but high pressure (p > p ), whereas the high-T component at ≈ 5 − 10 MK must be confined by rather long loops (L ≈ R∗ ) and high base pressures (p ≈ 20 dynes cm−2 p ) with filling factors of order 0.1. These latter solutions however violate the applicability of the RTV scaling law, since the loop height exceeds the pressure scale-height. Giampapa et al. (1996) therefore speculated that this component is, in fact, related to multiple, very compact flaring regions with a small filling factor, while the cooler, compact component relates to non-flaring active regions. The loop model approach has been extensively developed and further discussed in a series of papers by the Palermo group (Ciaravella et al. 1996, 1997; Maggio and Peres 1996, 1997; Ventura et al. 1998). The most notable results are: 1. To obtain a successful spectral fit to low-resolution data of a single loop, one usually requires at least two isothermal plasma components. The often-found two spectral components from fits to low-resolution spectra must not, in general, be identified with two loop families (Ciaravella et al. 1997). 2. Applications to observations often do, however, require two loop families in any case, but for reasons more involved than the presence of two dominant thermal components. In such cases, one finds relatively cool loops (T = 1.5 − 5 MK) with modest to high pressures (p = 2 − 100 dynes cm−2 ) and hot (T = 10 − 30 MK), extreme-pressure loops (p = 102 − 104 dynes cm−2 ). The latter are – once again – reminiscent of flaring loops with a very small surface filling factor (Maggio and Peres 1997; Ventura et al. 1998). 3. Low-activity stellar coronae, on the other hand, may be sufficiently well described by a single, dominant type of loop. This is the case for Procyon on which short, cool, low-pressure loops should occupy 10% of the surface in this picture. Ottmann et al. (1993) found that the coronal structure on AR Lac can be interpreted with essentially one class of RTV loops with an apex temperature of 38 MK, although a better match may be based on variable cross-section VAU loops, an approach followed by Ottmann (1993), who found loops with a half-length L ≈ 3 × 1011 cm and a filling factor f ≤ 10%. van den Oord et al. (1997) applied analytic loop models including non-zero conductive flux at the loop footpoints and variable expansion factors to EUVE spectra.


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The spectral inversion is problematic because a given spectrum can be modeled by various sets of physical parameters, such as various combinations between loop expansion factors and loop base conductive fluxes. The range of solutions, however, consistently requires loop expansion factors of 2–5, and in several stars, at least two loop families with different apex temperatures. Sciortino et al. (1999) similarly applied tabulated loop models of steady-state coronal (RTV) loops to interpret medium-resolution X-ray spectra of M dwarfs. They again found that at least two classes of magnetic loops, one with an apex temperature of ≈ 10 MK and one with several tens of MK, are required. Although the solutions allow for a large range of base pressures and surface filling factors, both the cooler and the hotter loops are found to be quite compact, with lengths smaller than 0.1R∗ and filling factors of 10−4 to 10−3 . A similar study was presented by Griffiths (1999) who computed comprehensive static energy-balance loop models to interpret EMDs of RS CVn binaries. The doublepeak structure in the EMD again required two loop families with apex temperatures of 8 and 22 MK, respectively, both of modest size. Finally, Favata et al. (2000b) concluded, from modeling of several X-ray flares on AD Leo (Sect. 12.6), that all magnetic loops involved in the flaring corona are of similar, relatively compact dimension (0.3R∗ ). If these are the typical structures that form the overall corona, then their filling factor is no larger than about 6% despite the rather high X-ray luminosity of this star. The loop pressure must consequently be large (70 dyne cm−2 ). 11.2.3. Conclusions and limitations The most essential conclusion from these exercises is perhaps that, within the framework of these simplistic models, the loop heating rate required for magnetically active stars may exceed values for typical solar loops by orders of magnitude, pointing toward some enhanced heating process reminiscent of the energy deposition in flares. The compactness of the hot loops and the consequent high pressures also set these coronal structures clearly apart from any non-flaring solar coronal features. The inferred geometric size has important implications for dynamo theories. The apparent predominance of compact, localized sources suggests a predominance of local, small-scale magnetic fields. Such fields are expected from distributed dynamos that have been postulated for fully convective stars. A possible conclusion for deeply convective M dwarfs is that the solar-type αω dynamo does not operate, in agreement with the absence of a convective boundary inside the star once it becomes fully convective (Giampapa et al. 1996). This conclusion is, however, not entirely valid in the light of other magnetic field measurements that have revealed global components, e.g., by use of radio interferometry (Sect. 11.16). It is also important to note that open solar magnetic fields carry little specific EM, and that large-scale hot loops cannot be dense because the plasma cannot be magnetically confined in that case. Little X-ray emission is therefore expected from such features, even though they may well exist as magnetic structures. While explicit loop models provide an appealing basis for a physical interpretation of coronal structures, the limitations of our diagnostics should be kept in mind: 1. due to the degeneracy of solutions in the product pL (see (20)), multiple, largely differing solutions are usually compatible with observations of finite quality and of

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low energy resolution (e.g., Schmitt et al. 1985b for Procyon, van den Oord et al. 1997 for further sources); 2. the use of models based on one loop or one family of identical loops (in L, Ta and hence p, f , , and the heating profile along the loop) may offer a number of degrees of freedom that is sufficiently large to describe a given spectrum satisfactorily, yet the model is unlikely to describe any real corona. In this sense, like in the case of multi-isothermal models or in “minimum flux” coronal models, loop models parameterize the real situation in a manner that is not straightforward and that requires additional constraints from additional sources of information. I also refer to the extensive, critical discussion on this point by Jordan et al. (1986). 11.3. Coronal structure from densities and opacities Spectroscopically measured densities provide, in conjunction with EMs, important estimates of emitting volumes. For example, Ness et al. (2001) use the RTV scaling laws together with measured coronal temperatures and electron densities inferred from Helike triplets of C, N, and O of Procyon. They concluded that the dominant coronal loops 9 on this star are solar-like and low-lying (L < ∼ 10 cm). For the more active Capella, Mewe et al. (2001) found very similar structures covering a few tens of percent of the surface, but additionally they inferred the presence of a hotter plasma at apparently very high densities (Sect. 10.1). This latter plasma would have to be confined to within 7 very compact loops (L < ∼ 5 × 10 cm) that cover an extremely small area on the star −6 −4 (f ≈ 10 − 10 ). In general, for increasing temperature, progressively higher pressures and progressively smaller volumes are determined (Osten et al. 2003; Argiroffi et al. 2003; Sect. 10.2). The confinement of such exceedingly high densities in compact sources, with a size of a few 1000 km, would then require coronal magnetic field strengths of order 1 kG (Brickhouse and Dupree 1998). In that case, the typical magnetic dissipation time is only a few seconds for ne ≈ 1013 cm−3 if the energy is derived from the same magnetic fields, suggesting that the small, bright loops light up only briefly. In other words, the stellar corona would be made up of numerous ephemeral loop sources that cannot be treated as being in a quasi-static equilibrium (van den Oord et al. 1997). The debate as to how real these densities are, continues, as we mentioned in Sect. 10. Ness et al. (2002b), again using standard coronal-loop models, derived moderately compact loop sizes (L ≈ 109 − 5 × 1010 cm) for Algol, the uncertainty being related to uncertain density measurements. Testa et al. (2004) and Ness et al. (2004) used density information from O vii, Ne ix, Mg xi, and computed a rough stellar surface filling factor f of static loops. They found that f remained at a few percent for cool, O vii emitting material for the most active stars. For less active stars, Ness et al. (2004) reported similar filling factors, whereas Testa et al. (2004) found them to decrease with decreasing activity. For the hotter, Mg xi emitting material, the surface coverage rapidly increases in more active stars. A possible interpretation involves a relatively cool, inactive base corona that remains unaltered while hotter and denser loops are added as one moves to progressively more active stars – a larger rate of magnetic interaction between adjacent active regions could then be assumed to heat the plasma, for example by flares. The lack of measured optical depths τ due to resonance scattering in stellar coronae (see Sect. 15) can also be exploited to set limits to coronal size scales. Mewe et al. (2001)


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and Phillips et al. (2001) used formal upper limits on τ derived from Fe xvii line ratios of Capella together with densities derived from Fe xx-xxii line ratios (with the caveats mentioned above) to estimate that the characteristic size of a single emitting region is in the range of (1 − 3) × 108 cm, i.e., very compact in comparison with Capella’s radius. This procedure, however, is not valid for more complicated geometries: if active regions are distributed across the stellar surface, then optical depths may cancel out in the observations, even if individual larger structures may be involved with non-zero optical depth (Mewe et al. 2001). 11.4. Coronal constituents: Emission-measure interpretation The average X-ray surface flux FX is a direct tracer for the type of structures that can possibly cover the stellar surface. Because we generally have no information on stellar coronal inhomogeneities, the average stellar FX can obviously not be compared directly with FX values of solar coronal structures. We can nevertheless derive quite meaningful constraints. For example, the average FX on Proxima Centauri is only about one fifth of corresponding values for solar active regions while it exceeds solar quiet region values by one order of magnitude. Assuming, then, that the emission is concentrated in equivalents of solar active regions, their surface filling factor would be as much as 20%, compared to 0.01–1% for the Sun at the 1 dyne cm−2 level (Haisch et al. 1980). At the low end of magnetic activity, there seem to be no stars with an X-ray surface flux below FX ≈ 104 erg cm−2 s−1 (Schmitt 1997). This flux coincides with the surface flux of solar coronal holes, suggesting that the least active MS stars are fully covered by coronal holes. Similar results were reported by Hünsch et al. (1996) for giants. If coronal holes, inactive regions, active regions, bright points, small and large flares are characteristically different in their thermal structure and their surface flux, then one may interpret a full-disk EMD as a linear superposition of these various building blocks. We may start from the Sun by attempting to understand how various coronal features contribute to the integrated X-ray light (Ayres et al. 1996; Orlando et al. 2000, 2001; Peres et al. 2000). Full-disk solar EMDs from Yohkoh images reveal broad distributions with steep slopes below the temperature peak and a gradual decline up to 107 K. The interesting aspect is that the EMDs shift to higher temperatures both from activity minimum (peak at ≈ 1 MK) to maximum (peak at ≈ 2 MK) and from X-ray faint to X-ray bright features (see also Fig. 9). On the stellar side, we see similar shifts from a hotter to a cooler EMD on evolutionary time scales as a star ages and becomes less active (Güdel et al. 1997a; Güdel 1997). For example, EMDs of intermediately active stars closely resemble the solar cycle-maximum EMD (Fig. 9), which indicates a nearly complete surface coverage with active regions (Drake et al. 2000). From this point of view, the Sun’s magnetic cycle mimics an interval of stellar activity during its magnetic cycle (Ayres et al. 1996). Moving to very active stars, large-scale structures between active regions and post-flare loops seem to become the dominating coronal components rather than normal active regions and bright points. The increased luminosity is then a consequence of increased filling factors, increased loop base pressures, and higher temperatures (Ayres et al. 1996; Güdel et al. 1997a). Orlando et al. (2001) showed that in a similar manner the increasing X-ray spectral hardness from solar minimum to maximum on the one hand and from low-activity to

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high-activity solar analogs on the other hand can be explained by an increasing proportion of dense and bright coronal features, namely active regions and in particular hot cores of active regions. However, if the Sun were entirely covered with active regions, the X-ray luminosity would amount to only ≈ (2 − 3) × 1029 erg s−1 (Vaiana and Rosner 1978; Wood et al. 1994) with LX /Lbol ≈ 10−4 (Vilhu 1984), short of LX of the most active early G-type analogs of the Sun by one order of magnitude. A similar problem is evident for extremely active, rapidly rotating FK Comae-type giants whose full disk FX exceeds non-flaring solar active region fluxes by up to an order of magnitude (Gondoin et al. 2002; Gondoin 2003a). In those stars, the cooler (< 10 MK) plasma component alone already fills the complete surface under the usual assumptions. The DEMs of such active stars produce excessive emission around 10–20 MK (Güdel et al. 1997a), which incidentally is the typical range of solar flare temperatures. This led to the suggestion that the high-T DEM is in fact due to the superposition of a multitude of superimposed but temporally unresolved flares (Sect. 13). If added to a low-T “quiescent” solar DEM, the time-integrated DEM of solar flares indeed produces a characteristic bump around 10–20 MK that compares favorably with stellar DEMs (Güdel et al. 1997a). This happens because the flare EM decreases rapidly as the temperature decays, leaving a trace on the DEM only at relatively high temperatures, in agreement with (12) for time-integrated flares. If a full distribution of flares contributes, including small flares with lower temperature, then the entire DEM could be formed by the continually heating and cooling plasma in flares (Güdel 1997). The predicted steep low-T slope (up to ≈ 4) of a stochastic-flare DEM compares very favorably with observations of active stars (Güdel et al. 2003a). The reason for an increased fraction of hotter features in more active stars (Fig. 10) may be found in the coronal structure itself. Toward more active stars, magnetic fields interact progressively more frequently due to their denser packing. In this view, an increased heating rate in particular in the form of flares reflects the enhanced dynamo operation in rapidly rotating stars. Since flares enhance the electron density along with the temperature, one finds a predominance of hotter structures in more active stars (Güdel et al. 1997a; cf. also the discussion in Sect. 9.5). Along these lines, Phillips et al. (2001) compared high-resolution spectra of Capella and solar flares, finding a surprising overall agreement; similarly, Güdel et al. (2004) compared the average X-ray spectrum of a large stellar flare with the spectrum of low-level emission of the very active dMe binary YY Gem. The agreement between the spectral features, or equivalently, the EMD, is compelling. The hypothesis of ongoing flaring in active stars that we have now repeatedly invoked will be further discussed in Sect. 13. 11.5. Coronal imaging: Overview As the development of solar coronal physics has amply shown, coronal imaging will be an indispensable tool for studying the structure and heating of stellar coronae in detail. At present, coronal structure recognition based on direct or indirect imaging methods is still highly biased by observational constraints and by the location of physical processes that heat plasma or accelerate particles. Stellar coronal structure resolved at radio wavelengths refers to extended (typically low-density) closed magnetic fields into


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which high-energy electrons have been injected. X-ray emitting plasma traces magnetic fields that have been loaded with dense plasma. But both types of structure, as well as coronal holes that are weak both in X-rays and at radio wavelengths, refer to the underlying global distribution of surface magnetic fields. Presently, only radio structures can be directly imaged by means of radio Very Long Baseline Interferometry (VLBI; for a review see Güdel 2002), whereas thermal coronal sources can be mapped indirectly by using X-ray eclipses, rotational modulation, or Doppler information as discussed below. With these limitations in mind, I now briefly summarize various image reconstruction methods for eclipses and rotational modulation (Sects. 11.6–11.9) and related results (Sects. 11.10–11.13). Sections 11.14 and 11.15 address alternative methods for structure modeling. In its general form, the “image” to be reconstructed consists of volume elements at coordinates (x, y, z) with optically thin fluxes f (x, y, z) assumed to be constant in time. In the special case of negligible stellar rotation during the observation, the problem can be reduced to a 2-D projection onto the plane of the sky, at the cost of positional information along the line of sight (Fig. 15). In general, one thus seeks the geometric brightness distribution f (x, y, z) = fij k (i, j, k being the discrete pixel number indices) from a binned, observed light curve Fs = F (ts ) that undergoes a modulation due to an eclipse or due to rotation.

11.6. Active-region modeling In the most basic approach, the emitting X-ray or radio corona can be modeled by making use of a small number of simple, elementary building blocks that are essentially described by their size, their brightness, and their location. This approach is the 3-D equivalent to standard surface spot modeling. Preferred building block shapes are radially directed, uniformly bright, optically thin, radially truncated spherical cones with their apexes at the stellar center. Free parameters are their opening angles, their heights above the stellar surface, their radiances, and their central latitudes and longitudes. These parameters are then varied until the model fits the observed light curve. For extensive applications to eclipsing binaries, see, for example, White et al. (1990), Ottmann (1993), and Culhane et al. (1990). A minimum solution was presented by Güdel and Schmitt (1995) for a rotationally modulated star. If a rotationally modulated feature is invisible during a phase interval ϕ of the stellar rotation, then all sources contributing to this feature must be confined to within a maximum volume, Vmax , given by Vmax (2π − ϕ)(1 + sin2 i) 2cot(χ /2) ψ − + = 3 R∗ 3 6sini 3tani

(24)

where tanχ = tan(ϕ/2)cosi, sin(ψ/2) = sin(ϕ/2)sini with 0 ≤ ψ/2 ≤ π/2, and χ and ϕ/2 lie in the same quadrant (i is the stellar inclination, 0 ≤ i ≤ π/2). Together with the modulated fraction of the luminosity, lower limits to average electron densities in the modulated region follow directly.

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Fig. 15. Sketch showing the geometry of an eclipsing binary (in this case, α CrB, figure from Güdel et al. 2003b). The large circles illustrate the limbs of the eclipsing star that moves from left to right in front of the eclipsed star (shown in yellow). The limbs projected at different times during ingress and egress define a distorted 2-D array (x, y) of pixels (an example of a pixel is shown in gray)

11.7. Maximum-entropy image reconstruction We follow the outline given in Güdel et al. (2003b) to discuss maximum entropy methods (MEM) for image reconstruction. They are applicable both to rotationally modulated light curves and to eclipse observations. The standard MEM selects among all images fij k (defined in units of counts per volume element) that are compatible with the observation, the one that minimizes the Kullback contrast (“relative entropy”)

fij k fij k ln a (25) K= fij k i,j,k

fija k ,

with respect to an a priori image which is usually unity inside the allowed area or volume and vanishes where no brightness is admitted. Minimizing K thus introduces the least possible information while being compatible with the observation. The contrast K is minimum if fij k is proportional to fija k and thus flat inside the field of view, and it is maximum if the whole flux is concentrated in a single pixel (i, j, k). The compatibility with the observed count light curve is measured by χ 2 ,

(F ∗ − Fs )2 s (26) χ2 = Fs∗ s


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where Fs and Fs∗ are, respectively, the observed number of counts and the number of counts predicted from fij k and the eclipse geometry. Poisson statistics usually requires more than 15 counts per bin. Finally, normalization is enforced by means of the constraint  2

f tot − fij k  ij k

N=

f tot

(27)

where f tot is the sum of all fluxes in the model. The final algorithm minimizes the cost function C = χ 2 + ξ K + ηN .

(28)

The trade-off between the compatibility with the observation, normalization, and unbiasedness is determined by the Lagrange multipliers ξ and η such that the reduced χ 2 is < ∼ 1, and normalization holds within a few percent. For applications of this method and variants thereof, see White et al. (1990) and Güdel et al. (2003b). 11.8. Lucy/Withbroe image reconstruction This method (after Lucy 1974 and Withbroe 1975, the latter author discussing an application to spectral line flux inversion) was extensively used by Siarkowski (1992), Siarkowski et al. (1996), Pre´s et al. (1995), Güdel et al. (2001a), Güdel et al. (2003b) and Schmitt et al. (2003) to image X-ray coronae of eclipsing binaries; it is applicable to pure rotational modulation as well. The method is formally related to maximum likelihood methods although the iteration and its convergence are methodologically different (Schmitt 1996). The algorithm iteratively adjusts fluxes in a given set of volume elements based on the mismatch between the model and the observed light curves in all time bins to which the volume element contributes. At any given time ts during the eclipse, the observed flux Fs is the sum of the fluxes fij k from all pixels that are unocculted:

F (ts ) = fij k ms (i, j, k) (29) i,j,k

where ms is the “occultation matrix” for the time ts : it puts, for any given time ts , a weight of unity to all visible pixels and zero to all invisible pixels (and intermediate values for partially occulted pixels). Since Fs is given, one needs to solve (29) for the flux distribution, which is done iteratively as follows:

fijn+1 k

Fo (ts ) ms (i, j, k) Fmn (ts ) n s = fij k

ms (i, j, k)

(30)

s

Fmn (ts )

where Fo (ts ) and are, respectively, the observed flux and the model flux (or counts) in the bin at time ts , both for the iteration step n. Initially, a plausible, smooth distribution of flux is assumed, e.g., constant brightness, or some r −p radial dependence.

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11.9. Backprojection and Clean image reconstruction If rotation can be neglected during an eclipse, for example in long-period detached binaries, then the limb of the eclipsing star is projected at regular time intervals onto the plane of the sky and therefore onto a specific part of the eclipsed corona, first during ingress, later during egress. The two limb sets define a 2-D grid of distorted, curved pixels (Fig. 15). The brightness decrement during ingress or, respectively, the brightness increment during egress within a time step [ts , ts+1 ] originates from within a region confined by the two respective limb projections at ts and ts+1 . Ingress and egress thus each define a 1-D image by backprojection from the light curve gradients onto the plane of the sky. The relevant reconstruction problem from multiple geometric projections is known in tomography. The limiting case of only two independent projections can be augmented by a CLEAN step, as follows. The pixel with the largest sum of projected fluxes from ingress and egress is assumed to represent the location of a real source. A fraction, g < 1, of this source flux is then subtracted from the two projections and saved on a clean map, and the process is iterated until all flux is transferred onto the latter. This method was described by Güdel et al. (2003b) who applied it to a total stellar eclipse of α CrB, with consideration of different gain factors g and post-fit flux redistributions to study multiple solutions.

11.10. Coronal structure inferred from eclipses I now review selected results from analyses of X-ray eclipses, and, in subsequent subsections, of rotational modulation and Doppler measurements. Some important parameters are summarized in Table 3. 11.10.1. Extent of eclipsed features Some shallow X-ray eclipses in tidally interacting binary systems of the RS CVn, Algol, or BY Dra type have provided important information on extended coronal structure. For example, Walter et al. (1983) concluded that the coronae in the AR Lac binary components are bi-modal in size, consisting of compact, high-pressure (i.e., 50–100 dynes cm−2 ) active regions with a scale height < R∗ , while the subgiant K star is additionally surrounded by an extended (2.7R∗ ) low-pressure corona. This view was supported by an analysis of ROSAT data by Ottmann et al. (1993). In the analysis of White et al. (1990), the association of different regions with the binary components remained ambiguous, and so did the coronal heights, but the most likely arrangement again required at least one compact region with p > 100 dynes cm−2 and favored an additional extended, low-pressure coronal feature with p ≈ 15 dynes cm−2 and a scale height of ≈ R∗ . Further, a hot component pervading the entire binary system was implied from the absence of an eclipse in the hard ME detector on EXOSAT. Culhane et al. (1990) similarly observed a deep eclipse in TY Pyx in the softer band of EXOSAT but a clear absence thereof in the harder band, once more supporting a model including an extended, hot component. From an offset of the eclipse relative to the optical first contact in Algol, Ottmann (1994) estimated the height of the active K star corona to be ≈ 2.8R .


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Table 3. X-ray coronal structure inferred from eclipses and rotational modulation Star

Spectrum

Extendeda height (R∗ )

nbe

Compacta height (R∗ )

nbe

Referencec

AR Lac AR Lac AR Lac AR Lac Algol Algold Algold TY Pyx XY UMa VW Cepd α CrB α CrB EK Dra YY Gem V773 Taud

G2 IV+K0 IV G2 IV+K0 IV G2 IV+K0 IV G2 IV+K0 IV B8 V+K2 IV B8 V+K2 IV B8 V+K2 IV G5 IV+G5 IV G3 V+K4 V K0 V+G5 V A0 V+G5 V A0 V+G5 V dG0e dM1e+dM1e K2 V+K5 V

≈1 1.1–1.6 0.7–1.4 ≈1 0.8 – – ≈1–2 – 0.84 – – – –

0.29 0.2–0.8 0.3–0.8 0.12–1.8 ... – – 0.02–3 – 5 – – – –

0.01 0.06 0.03–0.06 – – < ∼ 0.5 0.1 – ≤ 0.75 – < ∼ 0.2 < ∼ 0.1 < ∼ 0.2 0.25–1 ≈ 0.6

4–6 >5 6–60 – – > ∼ 9.4 < ∼3 – ... – < ∼3 0.1–3 > ∼4 0.3–3 ≥ 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Notes. a Extended structures of order R∗ , compact structures significantly smaller. b Electron density in 1010 cm−3 for extended and compact structures, respectively. c References: 1 Walter et al. (1983); 2 White et al. (1990); 3 Ottmann et al. (1993); 4 Siarkowski et al. (1996); 5 Ottmann (1994); 6 Schmitt and Favata (1999); 7 Schmitt et al. (2003); 8 Pre´s et al. (1995); 9 Bedford et al. (1990); 10 Choi and Dotani (1998); 11 Schmitt and Kürster (1993); 12 Güdel et al. (2003b); 13 Güdel et al. (1995); 14 Güdel et al. (2001a); Skinner et al. (1997). d Refers to observation of eclipsed/modulated flare.

White et al. (1986) inferred, from the absence of X-ray dips or any modulation in the light curve of Algol, a minimum characteristic coronal scale height of 3R (i.e., about 1R∗ ). Similar arguments were used by Jeffries (1998) for the short period system XY UMa to infer a corona that must be larger than 1R unless more compact structures sit at high latitudes. This latter possibility should in fact be reconsidered for several observations that entirely lack modulation. Eclipses or rotational modulation can be entirely absent if the active regions are concentrated toward one of the polar regions. This possibility has found quite some attention in recent stellar research. Detailed studies of light curves that cover complete binary orbits with ASCA raise, however, some questions on the reliability of the derived structure sizes. Unconstrained iterations of the light curve inversion algorithm do converge to structures that are extended on scales of R∗ (Fig 16); but constrained solutions exist that sufficiently represent the light curves with sources no larger than 0.3R∗ (Siarkowski et al. 1996). Nevertheless, detailed studies of the imaging reconstruction strategy and the set-up of initial conditions led Pre´s et al. (1995) to conclude that X-ray bright sources do indeed exist far above the surfaces in the TY Pyx system, most likely located between the two components. The latter configuration includes the possibility of magnetic fields connecting the two stars. Interconnecting magnetic fields would draw implications for magnetic heating through

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phase 0.0

−0.1

0.1

0.2

10 count rate

8 6 4 2

eclipse

a

YY Gem 2000/04/24

0 0.9

1.0

−0.5 3.0

−0.4

−0.3

1.1 1.2 time (JD − 2451659.0)

−0.2

−0.1

phase 0

0.1

1.3

0.2

0.3

0.4

0.5

count rate

2.5 2.0 1.5 1.0 0.5 0.0

b 0

AR Lac 1993/06/01−3

0.2

0.4

0.6

0.8

1.0 time (d)

1.2

1.4

1.6

1.8

Fig. 16. Two examples of eclipses and the corresponding coronal image reconstructions. From top to bottom: Light curve of the YY Gem system (from Güdel et al. 2001a, observation with XMM-Newton EPIC); light curve of the AR Lac system (after Siarkowski et al. 1996, observation with ASCA SIS); reconstructed image of the coronal structure of, respectively, YY Gem (at phase 0.375) and AR Lac (at quadrature). The latter figure shows a solution with intrabinary emission. (The light curve of AR Lac is phase-folded; the actual observation started around phase 0; data and image for AR Lac courtesy of M. Siarkowski.)


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reconnection between intrabinary magnetic fields, as was suggested by Uchida and Sakurai (1984, 1985) and was also proposed from radio observations of the RS CVn-type binary CF Tuc (Gunn et al. 1997), the Algol-type binary V505 Sgr (Gunn et al. 1999), and the pre-cataclysmic binary V471 Tau (Lim et al. 1996). The X-ray evidence remains ambiguous at this time, and alternative X-ray methods such as Doppler measurements (Ayres et al. 2001b) have not added support to this hypothesis (Sect. 11.14). 11.10.2. Structure and location of coronal features The eclipse light curves often require asymmetric, inhomogeneous coronae, with bright features sometimes found on the leading stellar hemispheres (e.g., Walter et al. 1983; Ottmann et al. 1993; Ottmann 1994), but often also on the hemispheres facing each other (Bedford et al. 1990; Culhane et al. 1990; White et al. 1990; Siarkowski 1992; Siarkowski et al. 1996; Pre´s et al. 1995). This may, as mentioned above, have important implications for intrabinary magnetic fields. For the dMe binary YY Gem, Doyle and Mathioudakis (1990) reported a preferred occurrence of optical flares also on the two hemispheres facing each other, and this hypothesis has been supported by the timing of Xray flares (Haisch et al. 1990b). However, X-ray image reconstruction from light curves does not require any emission significantly beyond 2R∗ (Güdel et al. 2001a, Fig. 16): interconnecting magnetic fields are thus not supported in this case. Similarly, a deep eclipse observed on XY UMa (in contrast to an observation reported by Jeffries 1998) places the eclipsed material on the hemisphere of the primary that faces the companion, but judged from thermal loop models, the sources are suggested to be low-lying (Bedford et al. 1990). A concentration of activity on the inner hemispheres could, alternatively, be induced by tidal interactions and may therefore not require any interconnecting magnetic fields (Culhane et al. 1990). Eclipse modulation also confines the latitudes b of the eclipsed material. For AR Lac, b = 10◦ − 40◦ (Walter et al. 1983, and similarly in White et al. 1990, and Ottmann et al. 1993). Bedford et al. (1990) infer −30◦ ≤ b ≤ +30◦ from a deep eclipse on XY UMa. Most active regions on the dMe binary YY Gem (dM1e+dM1e) are concentrated around ±(30◦ − 50◦ ) (Güdel et al. 2001a), in good agreement with Doppler imaging of surface active regions (Hatzes 1995). The confinement of the inhomogeneities leads to the somewhat perplexing result that these most active stars reveal “active” X-ray filling factors of no more than 5–25% despite their being in the saturation regime (Sect. 5; see White et al. 1990; Ottmann et al. 1993). 11.10.3. Thermal properties of coronal structures The presence of distinct compact and extended coronae may reflect the presence of different thermal structures – in fact, the distinction may simply be due to different scale heights if magnetic fields do not constrain the corona further. The average radial density profile of YY Gem with a scale height of ≈ [0.1 − 0.4]R∗ derived from eclipse reconstruction is in good agreement with the pressure scale height of the one component of the plasma that dominates the X-ray spectrum (Güdel et al. 2001a). Compact sources are often inferred with size scales comparable to solar active regions. Based on such arguments, the extended structures are more likely to be associated with the hottest persistent plasma in active binaries (Walter et al. 1983; White et al. 1990; Rodonò et

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al. 1999, but see Singh et al. 1996a and Siarkowski et al. 1996 for alternative views). Inferred pressures of up to >100 dynes cm−2 make these regions appear like continuously flaring active regions (Walter et al. 1983; White et al. 1990). Alternatively, they could contain low-density, slowly cooling gas ejected from large flares. This view would be consistent with radio VLBI observations. The latter have mapped non-thermal flares that expand from compact cores to extended ( 1R∗ ) halos where they cool essentially by radiation (Güdel 2002 and references therein). Conjecture about different classes of thermal sources is again not unequivocal, however. Ottmann et al. (1993) and Ottmann (1994) found equivalent behavior of soft and hard spectral components during eclipses in AR Lac and Algol, respectively, and argued in favor of a close spatial association of hot and cool coronal components regardless of the overall spatial extent. This issue is clearly unresolved.

11.11. X-ray coronal structure in other eclipsing binaries Among wide, non-interacting eclipsing stars, α CrB provides a particularly well-suited example because its X-ray active, young solar analog (G5 V) is totally eclipsed every 17 days by the optical primary, anA0V star that is perfectly X-ray dark. Other parameters are ideal as well, such as the non-central eclipse, the eclipse time-scale of a few hours, and the relatively slow rotation period of the secondary. Eclipse observations obtained by ROSAT (Schmitt and Kürster 1993) and by XMM-Newton (Güdel et al. 2003b) were used to reconstruct projected 2-D images of the X-ray structure. They consistently reveal patches of active regions across the face of the G star; not much material is found significantly beyond its limb (Fig. 17). The structures tend to be of modest size (≈ 5 × 109 cm), with large, X-ray faint areas in between, although the star’s luminosity exceeds that of the active Sun by a factor of ≈30. These observations imply moderately high densities in the emitting active regions, and both studies mentioned above yielded average electron densities in the brightest active regions of a few 1010 cm−3 . 0.6 α CrB 2001/08/27

0.5

count rate

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Fig. 17. Light curve and image reconstruction of the A+G binary α CrB. The left panel shows the light curve from observations with XMM-Newton, the right panel illustrates the reconstructed X-ray brightness distribution on the G star (after Güdel et al. 2003b)


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X-ray light curves of eclipsing contact binary systems have shown sharp dips (Vilhu and Heise 1986; Gondoin 2004a) that could be interpreted as being due to compact sources probably located in the “neck” region that connects the two stars (Vilhu and Heise 1986) although Gondoin (2004a) inferred quite an extended corona from static loop models. Brickhouse and Dupree (1998), in contrast, placed a very compact source, with an extent of order 108 cm, near the polar region of the primary, complemented by a more extended low-density corona that contributes most of the X-ray light. 11.12. Inferences from rotational modulation The Sun often shows rather pronounced rotational modulation in X-rays as few active regions rotate into and out of view. Observations of X-ray rotational modulation are exceptional among stars, one of the main reasons being that the X-ray brightest rapid rotators are highly active; such stars are probably covered with numerous active regions, and intense flaring may further veil low-amplitude modulations. Among somewhat less active stars, the young solar analog EK Dra has shown rotational modulation both at X-ray and radio wavelengths (Güdel et al. 1995), and in X-rays it is predominantly the cooler material that shows this modulation. This argues against flares contributing to the signal. The depth and length of the modulation (Fig. 18a) constrains the X-ray coronal height, and also the electron densities to ne > 4 × 1010 cm−3 , in agreement with spectroscopic measurements (Ness et al. 2004). This leads to the conclusion that much of the emitting material is concentrated in large “active regions”. Collier Cameron et al. (1988) reported a similar finding for a weak modulation in AB Dor: this again suggested that the cooler loops are relatively compact. It is worthwhile mentioning, though, that X-ray rotational modulation has been difficult to identify on this star (S. White et al. 1996 and references therein; Vilhu et al. 1993; Maggio et al. 2000; Güdel et al. 2001b); a weak modulation has been reported by Kürster et al. (1997). Interestingly, radio observations of AB Dor reveal two emission peaks per rotation that probably relate to preferred active longitudes (Lim et al. 1992). 0.30

Rate [cnt/sec]

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Fig. 18. Two examples of X-ray rotational modulation in active solar analogs: a (left): EK Dra (Güdel et al. 1995), and b (right), the supersaturated VXR45 (right figure courtesy of A. Marino, after Marino et al. 2003a). Both light curves are phase-folded

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Because the X-ray luminosity in “supersaturated stars” (Sect. 5) is also below the empirical maximum, rotational modulation would give important structural information on the state of such coronae. A deep modulation in VXR45 (Fig. 18b) suggests that extreme activity in these stars is again not due to complete coverage of the surface with active regions (Marino et al. 2003a). Among evolved stars, the RS CVn binary HR 1099 (K1 IV + G5 V) has consistently shown X-ray and EUV rotational modulation, with an X-ray maximum at phases when the larger K subgiant is in front (Agrawal and Vaidya 1988; J. Drake et al. 1994; Audard et al. 2001a). Because the X-ray material is almost entirely located on the K star (Ayres et al. 2001b), the rotationally modulated material can be located – in contrast to the binaries studied through eclipses – on the K star hemisphere that faces away from the companion (Audard et al. 2001a). A particularly clear example was presented by Ottmann (1994) for Algol that showed a closely repeating pattern over three stellar orbits, testifying to the stability of the underlying coronal structure on time scales of several days. The strong modulation combined with a large inclination angle further suggests that most of the modulated material is located at moderate latitudes. Schmitt et al. (1996d) and Gunn et al. (1997) found strong rotational modulation on the RS CVn-type binary CF Tuc. Here, Gunn et al. (1997) speculated that the emitting corona is associated with the larger K subgiant and is facing toward the smaller companion, thus again opening up a possibility for intrabinary magnetic fields. Somewhat unexpectedly, even extremely active protostars appear to show signs of coronal inhomogeneities. Kamata et al. (1997) observed sinusoidal variations in one such object and tentatively interpreted it as the signature of rapid (P ≈ 1 d) rotation. If this interpretation is correct, then once again we infer that these extremely active stars are not fully covered by coronal active regions. 11.13. Rotationally modulated and eclipsed X-ray flares Rotational modulation of flares, or the absence thereof, contributes very valuable information on densities and the geometric size of flaring structures. Skinner et al. (1997) found compelling evidence for a rotationally modulated flare on the T Tau star V773 Tau. By making use of (24), they inferred, independent of any flare model, a minimum electron density of 2×1011 cm−3 in the flaring region. This immediately implies that the decaying plasma is subject to continuous heating. Otherwise, the plasma would freely cool on a time scale of ≈ 1.5 hrs, an order of magnitude shorter than observed. Geometric considerations then lead to a source of modest size at high latitudes. Stelzer et al. (1999) developed a “rotating flare” model that combines flare decay with self-eclipse of the flaring volume by the rotating star. They successfully fitted light curves of four large stellar flares with slow rises and flat peaks. Alternative explanations for such anomalous light curves are possible, however. If a long-lasting flare with time scales exceeding one orbit period shows no eclipse in its course, then the flare either occurred near one of the polar regions, or it is geometrically large. Kürster and Schmitt (1996) argued in favor of the latter possibility; they modeled a flare light-curve of CF Tuc. Nevertheless, a partial eclipse may also have affected the decay of that flare. Maggio et al. (2000) suggested flaring loops located at latitudes higher than 60◦ based on the absence of eclipse features during a large flare on AB Dor.


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Fig. 19. Limb view of an X-ray flare on Algol, reconstructed from an eclipse light curve. Axis labels are in units of R . Dashed circles give height in steps of 0.1R∗ (figure courtesy of J.-U. Ness, after Schmitt et al. 2003)

This would allow for more modest flare sizes, a possibility that is clearly supported by detailed flare modeling results (Sect. 12). Choi and Dotani (1998) were the first to describe a full eclipse of an X-ray flare in progress in a binary system, namely in the contact binary system VW Cep. During a narrow dip in the flare decay, the X-ray flux returned essentially to the pre-flare level. Geometric considerations then placed the flare near one of the poles of the primary star, with a size scale of order 5.5×1010 cm or somewhat smaller than the secondary star. The authors consequently inferred an electron density of 5 × 1010 cm−3 . A polar location was also advocated for a flare on Algol observed across an eclipse by Schmitt and Favata (1999). The flare emission was again eclipsed completely, and judged from the known system geometry, the flare was located above one of the poles, with a maximum source height of no more than approximately 0.5R∗ , implying a minimum electron density of 9.4 × 1010 cm−3 if the volume filling factor was unity. A more moderate flare was observed during an eclipse in the Algol system by Schmitt et al. (2003) (Fig. 19). In this case, the image reconstruction required an equatorial location, with a compact flare source of height h ≈ 0.1R∗ . Most of the source volume exceeded densities of 1011 cm−3 , with the highest values at ≈ 2 × 1011 cm−3 . Because the quiescent flux level was attained throughout the flare eclipse, the authors argued that its source, in turn, must be concentrated near the polar region with a modest filling factor of f < 0.1 and electron densities of ≈ 3 × 1010 cm−3 . Further candidates for eclipsed flares may be found in Bedford et al. (1990) for the short-period binary XY UMa as suggested by Jeffries (1998), and in Güdel et al. (2001a) for the eclipsing M dwarf binary YY Gem. Briggs and Pye (2003) reported on

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Fig. 20. A flare on the Pleiades member HII 1100 that shows a short dip early in the rise time, with the flux dropping back to the pre-flare level. One hypothesis (that requires confirmation) refers to an eclipsing Jupiter-like planet (figure courtesy of K. Briggs, after Briggs and Pye 2003, based on XMM-Newton observations)

an interesting eclipse-like feature in a flare in progress on an active Pleiades member (Fig. 20). Again, the flux returned precisely to pre-flare values for a short time, only to resume the increase of the flare light-curve after a brief interval. A somewhat speculative but quite possible cause for the observed dip could be a planet in transit. The existence of such a planet obviously needs confirmation. Some important parameters related to the flares discussed in this section are summarized in Table 3. 11.14. Inferences from Doppler measurements Doppler information from X-ray spectral lines may open up new ways of imaging stellar coronae as they rotate, or as they orbit around the center of gravity in binaries. First attempts are encouraging although the instrumental limitations are still severe.Ayres et al. (2001b) found Doppler shifts with amplitudes of ≈ 50 km s−1 in X-ray lines of HR 1099 (Fig. 21). Amplitudes and phases clearly agree with the line-of-sight orbital velocity of the subgiant K star, thus locating the bulk of the X-ray emitting plasma on this star, rather than in the intrabinary region. Periodic line broadening in YY Gem, on the other hand, suggests that both components are similarly X-ray luminous (Güdel et al. 2001a); this is expected, because this binary consists of two almost identical M dwarfs. Huenemoerder et al. (2003) found Doppler motions in AR Lac to be compatible with coronae on both companions if the plasma is close to the photospheric level. For the contact binary 44i Boo, Brickhouse et al. (2001) reported periodic line shifts corresponding to a total net velocity change over the full orbit of 180 km s−1 . From the amplitudes and the phase of the rotational modulation (Brickhouse and Dupree 1998), they concluded that two dominant X-ray sources were present, one being very compact and the other being extended, but both being located close to the stellar pole of the larger companion. A rather new technique employs coronal forbidden lines in the UV or optical range, making use of spectral resolving powers that are still out of reach to X-ray astronomy.


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Fig. 21. Doppler motion in the HR 1099 system measured from line shifts in the Chandra HETGS/MEG spectrum. The predicted radial velocity curves are shown solid (K star) and dashed (G star). The measurements clearly locate the X-ray emission predominantly on the K star (figure courtesy of T. Ayres, after Ayres et al. 2001b)

Maran et al. (1994) and Robinson et al. (1996) were the first to report the detection of the Fe xxi λ1354 line in HST observations of active stars. Linsky et al. (1998) presented a detailed analysis of this line in the Capella system. Ayres et al. (2003b) summarized the current status and presented a survey of further possible UV line candidates. In the UV range, the second promising candidate is the Fe xii λ1349 line while few other transitions are sufficiently strong for detection. An analogous study for the far-UV range was presented by Redfield et al. (2003). In the UV range accessible from the ground, Schmitt and Wichmann (2001) for the first time recorded the Fe xiii λ3388.1 line formed at 1.6 MK in a spectrum of the dMe dwarf CN Leo. The collected results from these observations are still modest – compared to the X-ray bibliography! Tentative results seem promising for further investigation: 1. the lines observed so far are essentially only thermally and rotationally broadened, i.e., significant bulk Doppler shifts due to mass flows in flares have not (yet) been detected; 2. several very active stars appear to show some excess broadening; it could possibly be due to rotational velocities of extended coronal regions located high above the stellar surface. Line broadening may in this case provide some important information on the overall coronal size (Ayres et al. 2003b; Redfield et al. 2003). 11.15. Inferences from surface magnetic fields Information on coronal structure can also be derived indirectly from surface ZeemanDoppler images as developed for and applied to the stellar case by Jardine et al. (2002a), Jardine et al. (2002b), and Hussain et al. (2002) and further references therein. Because Zeeman-Doppler images provide the radial and azimuthal magnetic-field strengths as a function of position, one could in principle derive the coronal magnetic field structure by 3-D extrapolation. This requires a number of assumptions, however. Jardine et al. (2002a) and Jardine et al. (2002b) studied the case of potential field extrapolation, i.e., the coronal magnetic field follows B = −∇, where is a function of the coordinates. Because the field must be divergence free, one requires ∇ 2 = 0. The solution involves

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Fig. 22. Reconstruction of the X-ray corona of AB Dor based on extrapolation from Zeeman Doppler Imaging. Brightness encodes emission measure along the line of sight. The left panel shows a solution for an EM-weighted density of 4×108 cm−3 , the right panel for 1.5×1010 cm−3 (figure courtesy of M. Jardine, after Jardine et al. 2002b)

associated Legendre functions in spherical coordinates, and the boundary conditions, namely the measured magnetic field strengths on the surface, fix the coefficients. The model requires further parameters such as the base thermal pressure with respect to the local magnetic pressure, and some cutoff of the corona at locations where the thermal pressure might open up the coronal field lines. Various computed models (Fig. 22) recover, at least qualitatively, the total EM, the average density, and the low level of rotational modulation observed on very active stars such as AB Dor. The highly complex coronal structure, involving both very large magnetic features and more compact loops anchored predominantly at polar latitudes (as implied by the Doppler images), suppresses X-ray rotational modulation to a large extent. The modeling is delicate because i) part of the star cannot usually be Doppler imaged, ii) fine structures are not recognized in the available Doppler images, in particular so in dark areas, and iii) the active corona is not in a potential configuration. The first point was addressed by Jardine et al. (2002a) and Jardine et al. (2002b) and the last by Hussain et al. (2002) who extended the models to include some form of currents in force-free fields. It is interesting that the models show various locations where the gravity, centrifugal, and Lorentz forces are in equilibrium. These are the places where distant Hα prominences may condense, for which there is indeed evidence in AB Dor out to distances of 5R∗ (Collier Cameron 1988; Donati 1999).

11.16. Extended or compact coronae? As the previous discussions imply, we are confronted with mixed evidence for predominantly extended (source height > R∗ ) and predominantly compact ( R∗ ) coronal structures or a mixture thereof. There does not seem to be unequivocal agreement on the


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type of structure that generally prevails. Several trends can be recognized, however, as summarized below. Compact coronal structure. Steep (portions of the) ingress and egress light curves or prominent rotational modulation unambiguously argue in favor of short scale lengths perpendicular to the line of sight (e.g., for the G star in AR Lac, see Walter et al. 1983; White et al. 1990; Ottmann et al. 1993; or for α CrB, see Schmitt and Kürster 1993; Güdel et al. 2003b). Common to all are relatively high inferred densities (≈ 1010 cm−3 ). The pressures of such active regions may exceed pressures of non-flaring solar active regions by up to two orders of magnitude. Spectroscopic observations of high densities and loop modeling add further evidence for the presence of some rather compact sources (Sects. 10 and 11.2). Flare modeling also provides modest sizes, often of order 0.1–1R∗ , for the involved magnetic loops (Sect. 12). Extended structure. Here, the arguments are less direct and are usually based on the absence of deep eclipses, or very shallow ingress and egress curves (e.g., the K star in AR Lac, see Walter et al. 1983; White et al. 1990). Caution is in order in cases where the sources may be located near one of the polar regions; in those cases, eclipses and rotational modulation may also be absent regardless of the source size. Complementary information is available from flare analysis (see Sect. 12) that in some cases does suggest quite large loops. The caveat here is that simple single-loop models may not apply to such flares. Clear evidence is available from radio interferometry that proves the presence of large-scale, globally ordered magnetic fields (see references in Güdel 2002). The existence of prominent extended, closed magnetic fields on scales > R∗ is therefore also beyond doubt for several active stars. The most likely answer to the question on coronal structure size is therefore an equivocal one: Coronal magnetic structures follow a size distribution from very compact to extended ( > ∼ R∗ ) with various characteristic densities, temperatures, non-thermal electron densities, and surface locations. This is no different from what we see on the Sun even though various features observed on stars stretch the comparison perhaps rather too far for comfort: various structures may predominate, depending on the magnetic activity level, on the depth of the convection zone, or on binary characteristics.

12. Stellar X-ray flares Flares arise as a consequence of a sudden energy release and relaxation process of the magnetic field in solar and stellar coronae. Present-day models assume that the energy is accumulated and stored in non-potential magnetic fields prior to an instability that most likely implies reconnection of neighboring antiparallel magnetic fields. The energy is brought into the corona by turbulent footpoint motions that tangle the field lines at larger heights. The explosive energy release becomes measurable across the electromagnetic spectrum and, in the solar case, as high-energy particles in interplanetary space as well. For a review, I refer the reader to Haisch et al. (1991a). Flares are ubiquitous among coronal stars, with very few exceptions. Apart from the entire main sequence (Schmitt 1994), flares have been found among giants (Welty and Ramsey 1994 for FK Com) and hybrid stars (Kashyap et al. 1994; Hünsch and Reimers 1995), and in clump giants both pre-He-flash (Ayres et al. 1999) and post-He-flash (Ayres

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et al. 2001a, Fig. 25 below), partly with extremely long time-scales of up to several days and with signs of continued activity. Flares have prominently figured in solar studies, and it is once again solar physics that has paved the way to the interpretation of stellar flares, even if not all features are fully understood yet. The complexity that flares reveal to the solar astronomer is inaccessible in stellar flares, especially in the absence of spatially resolved observations. Simplified concepts, perhaps tested for solar examples, must suffice. The following sections summarize the “stellar astronomer’s way” of looking at flares.

12.1. General properties and classifications X-ray flares on the Sun come, roughly speaking, in two varieties, known as compact and long-duration (also “two-ribbon”) flares (Pallavicini et al. 1977). The former variant shows a simple structure, usually consisting of one or a few individual loops that brighten up on time scales of minutes. They are of modest height and show high densities. The most likely mechanism leading to compact flares is an interaction between neighboring loops. In contrast, the second type of flare shows decay time scales of up to 1–2 hours; their magnetic field structures are large (104 −105 km) and the densities are low. Complex loop arcades that are anchored in two Hα ribbons are regularly involved. The most likely flare process relates to an opening up of magnetic fields (e.g., by a filament eruption) and subsequent relaxation by closing the “open” field lines. Related flare classifications have been made for hard X-rays as well. Applications of the solar classification scheme to stars, in particular magnetically active stars, should be treated with caution. The possibility of intrabinary magnetic fields or significant tidal effects in close binary stars, extremely dense packing of magnetic fields, polar magnetic fields, magnetic fields from a distributed dynamo, magnetospheres of global dimensions, and star-disk magnetic fields in pre-main sequence stars may lead to energy release configurations that are unknown on the Sun. The comprehensive EXOSAT survey of MS stellar flares by Pallavicini et al. (1990a) testifies to this problem, with some flares showing more rapid decays than rises, multiple peaks, abrupt drops etc. Nevertheless, these authors did find evidence for a class of flares with short rise times of order of minutes and decay times of order of a few tens of minutes, proposed to be analogs of solar compact flares, and flares with long decay times exceeding one hour, reminiscent of two-ribbon (2-R) flares on the Sun. Flares with a rapid rise on time scales smaller than the dynamical time scale of filament eruption are unlikely to be 2-R flares but are more suggestive of compact flares (van den Oord et al. 1988), while longer rise times may indicate 2-R flares (e.g., van den Oord and Mewe 1989). Typical e-folding decay times of large flares on active stars are found to be several kiloseconds (Gotthelf et al. 1994; Monsignori Fossi et al. 1996; Sciortino et al. 1999; Maggio et al. 2000). Decay times of 5–15 ks are not exceptional for young stars, e.g., in the Pleiades or in star-forming regions (Gagné et al. 1995a; Stelzer et al. 2000). In any case, the natural approach to understanding stellar coronal X-ray flares has been to extend solar concepts to stellar environments. I will now first discuss several flare models that have been repeatedly applied to observations in the literature; the subsequent sections will summarize a few notable results derived from stellar flare observations.


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12.2. General flare scenario A “standard picture” has emerged from numerous solar flare studies, comprising roughly the following features. The flare reconnection region, located somewhere at large coronal heights, primarily accelerates electrons (and possibly ions) up to MeV energies. The accelerated electrons precipitate along the magnetic fields into the chromosphere where they heat the cool plasma to coronal flare temperatures, thus “evaporating” part of the chromosphere into the corona. The high-energy electron population emits radio gyrosynchrotron radiation and, upon impact, non-thermal hard X-ray (HXR) bremsstrahlung, and it generates optical continuum+line radiation. These emissions are well correlated on time scales as short as seconds (e.g., Hudson et al. 1992 for HXR and white light flares; Kosugi et al. 1988 for hard X-rays and gyrosynchrotron emission). The soft Xrays, in contrast, develop only as the closed magnetic fields are filled with plasma on time scales of tens of seconds to minutes. Various elements of this scenario may vary from flare to flare. From the X-ray point of view, the above model implies a characteristic evolution of flare EM and temperature. As the initial energy release suddenly heats part of the chromospheric plasma, very high temperatures are reached rapidly. As large amounts of plasma are streaming into the corona, cooling starts while the luminosity is still increasing as a consequence of increasing densities. The flare temperature thus peaks before the EM does, or analogously, harder emission peaks before softer emission, a feature that is regularly observed in solar and stellar flares4 (Landini et al. 1986; Haisch et al. 1987; Vilhu et al. 1988; Doyle et al. 1988a; van den Oord et al. 1988; van den Oord and Mewe 1989; Haisch et al. 1990b; Stern et al. 1992a; Monsignori Fossi et al. 1996; Güdel et al. 1999; Maggio et al. 2000; Güdel et al. 2004) and in numerical simulations of flares (e.g., Cheng and Pallavicini 1991; Reale et al. 2004). 12.3. Cooling physics Flares cool through radiative, conductive, and possibly also volume expansion processes. We define the flare decay phase as the episode when the net energy loss by cooling exceeds the energy gain by heating, and the total thermal energy of the flare plasma decreases. The thermal energy decay time scale τth is defined as E (31) E˙ where E ≈ 3ne kT is the total thermal energy density in the flaring plasma of electron density ne and temperature T , and E˙ is the volumetric cooling loss rate (in erg cm−3 s−1 ). For conduction across temperature gradients in parallel magnetic fields, the mean loss rate per unit volume is τth =

dT 1 4 κ0 T 7/2 ≈ E˙c = κ0 T 5/2 L ds 7L2

(32)

4 This should not be mistaken for the Neupert Effect (Sect. 12.16); the present effect is entirely due to plasma cooling while the Neupert effect involves a physically different non-thermal population of electrons. The different hard and soft light-curves do not per se require non-thermal plasma, nor multiple components.

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where s is the coordinate along the field lines, and the term κ0 T 5/2 dT /ds is the conductive flux in the approximation of Spitzer (1962), to be evaluated near the loop footpoint where T drops below 106 K, with κ0 ≈ 9 × 10−7 erg cm−1 s−1 K−7/2 . Equations (31, 32) define the conductive time scale τth ≡ τc . The second equation in (32) should be used only as an approximation for non-radiating loops with a constant cross section down to the loss region and with uniform heating (or for time-dependent cooling of a constant-pressure loop without heating; for the factor of 4/7, see Dowdy et al. 1985; Kopp and Poletto 1993). We have used L for the characteristic dimension of the source along the magnetic field lines, for example the half-length of a magnetic loop. Strictly speaking, energy is not lost by conduction but is redistributed within the source; however, we consider energy lost when it is conducted to a region that is below X-ray emitting temperatures, e.g., the transition region/chromosphere at the magnetic loop footpoints. For expressions relevant for loops with varying cross sections, see van den Oord and Mewe (1989). Radiative losses are by bremsstrahlung (dominant for T > ∼ 20 MK), 2-photon continuum, bound-free, and line radiation. We note that the plasma composition in terms of element abundances can modify the cooling function (T ), but the correction is of minor importance because stellar flares are usually rather hot. At relevant temperatures, the dominant radiative losses are by bremsstrahlung, which is little sensitive to modifications of the heavy-element abundances. The energy loss rate is E˙r = ne nH (T )

(33)

(or n2e (T ) in an alternative definition, with nH ≈ 0.85ne for cosmic abundances). For T ≥ 20 MK, (T ) = 0 T γ ≈ 10−24.66 T 1/4 erg cm3 s−1 (after van den Oord and Mewe 1989 and Mewe et al. 1985). Equations. (31, 33) define the radiative time scale τth ≡ τr . 12.4. Interpretation of the decay time Equations (31), (32), and (33) describe the decay of the thermal energy, which in flare plasma is primarily due to the decay of temperature (with a time scale τT ) and density. In contrast, the observed light curve decays (with a time scale τd for the luminosity) primarily due to the decreasing EM and, to a lesser extent, due to the decrease of (T ) with decreasing temperature above ≈ 15 MK. From the energy equation, the thermal energy decay time scale τth is found to be γ 1 1 1 = 1− + (34) τth 2 τT 2τd where the right-hand side is usually known from the observations (see van den Oord et al. 1988 for a derivation). The decay time scale of the EM then follows as 1/τEM = 1/τd − γ /τT . Pan et al. (1997) derived somewhat different coefficients in (34) for the assumption of constant volume or constant mass, including the enthalpy flux. In the absence of measurements of τT , it is often assumed that τth = τd although this is an inaccurate approximation. For a freely cooling loop, τEM = τT (Sect. 12.6), and a better replacement is therefore τth = 2(γ + 1)τd /3.


143

In (34), τth is usually set to be τr or τc or, if both loss terms are significant, (τr−1 + τc−1 )−1 , taken at the beginning of the flare decay (note again that a simple identification of τr with τd is not accurate). If radiative losses dominate, the density immediately follows from Eqs. (31, 33) 3kT τth ≈ (35) ne (T ) and the characteristic size scale of the flaring plasma or the flare-loop semi-length L for a sample of N identical loops follow from EM = ne nH ( + 1)π α 2 N L3 ≈ n2 3

(36)

where α is the aspect ratio (ratio between loop cross sectional diameter at the base and total length 2L) and is the loop expansion factor. The loop height for the important case of dominant radiative losses follows to be (White et al. 1986; van den Oord et al. 1988) 1/3 8 20 EM 2 1/3 2 −1/3 H = Nα τ ( + 1)−1/3 . (37) 9π 4 k 2 T 3/2 r A lower limit to H is found for τr ≈ τc in the same treatment: 0 EM 2 −1 Hmin = . Nα κ0 π 2 T 3.25

(38)

N, α, and are usually unknown and treated as free parameters within reasonable bounds. Generally, a small N is compatible with dominant radiative cooling. This approach gives a first estimate for the flare-loop size, but it provides only an upper limit to and a lower limit to ne , for the following reason. Equation (35) assumes free cooling without a heating contribution. If heating continues during the decay phase, then τobs > τth , hence the implied ne,obs < ne ; in other words, the effective cooling function is reduced and, therefore, the apparent obs > . The effect of continued heating will be discussed in Sect. 12.6 and 12.7. Decay time methods have been extensively used by, among others, Haisch et al. (1980), van den Oord et al. (1988), Jeffries and Bedford (1990), Doyle et al. (1991), Doyle et al. (1992b), Ottmann and Schmitt (1994), Mewe et al. (1997), and Osten et al. (2000) for the interpretation of large flares. For small N , most authors found loop heights of the order of a few 1010 cm and inferred densities of a few times 1011 cm−3 (see Sect. 12.11). Pallavicini et al. (1990a) inferred typical flare densities, volumes, and magnetic loop lengths for various strong flares on M dwarfs, concluding that ne tends to be higher than electron densities in solar compact flares, while the volumes are more reminiscent of solar two-ribbon (2-R) flares. The simplest approach involving full coronal loop models assumes cooling that is completely governed either by conduction or radiation. Antiochos and Sturrock (1976, 1978) have treated a conductively-driven flaring loop, first with static and then with evaporative cooling, i.e., respectively, without mass flow and with subsonic mass upflows (under time-constant pressure). Under the assumption that radiation is negligible, Antiochos and Sturrock obtained as loop-apex temperatures t −2/5 t −2/7 Tstat (t) = T0 1 + , Tevap (t) = T0 1 + . (39) τc,0 τc,0

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Here, the relevant timescale is τc,0 = 5p0 /(2κ0 T0 )(L/1.6)2 (Cargill 1994), and the subscript 0 refers to values at the beginning of the cooling phase. This formulation has been used by Pan et al. (1997) as part of an extended flare model involving variable mass or variable volume. For the more likely case of dominant radiative cooling, Antiochos (1980) and Cargill (1994) give, for static cooling and cooling with subsonic draining, respectively, a temperature at the position s along the loop of  t 1/(1−γ )   T (s) 1 − (1 − γ ) static  0 τr,0 T (s, t) = (40)  3 1 t 1/(1/2−γ )   T0 (s) 1 − draining −γ 2 2 τr,0 where τr,0 is the radiative loss time (35) at the cooling onset. A more general treatment was considered by Pan and Jordan (1995) for a flare on the active main-sequence binary CC Eri, including both radiative and conductive losses. They gave a differential equation for the development of the temperature as a function of the measured EM and T , which then serves to determine L in the conductively-dominated case, and the flaring volume in the radiative case. 12.5. Quasi-static cooling loops van den Oord and Mewe (1989) derived the energy equation of a cooling magnetic loop in such a way that it is formally identical to a static loop (Rosner et al. 1978), by introducing a slowly varying flare heating rate that balances the total energy loss, and a possible constant heating rate during the flare decay. This specific solution thus proceeds through a sequence of different (quasi-)static loops with decreasing temperature. The general treatment involves continued heating that keeps the cooling loop at coronal temperatures. If this constant heating term is zero, one finds for free quasi-static cooling T (t) = T0 (1 + t/3τr,0 )−8/7

(41)

−4

(42)

Lr (t) = Lr,0 (1 + t/3τr,0 ) ne (t) = ne,0 (1 + t/3τr,0 )−13/7

(43)

where Lr is the total radiative loss rate, and τr,0 is the radiative loss time scale (35) at the beginning of the flare decay. This prescription is equivalent to requiring a constant ratio between radiative and 1/4 conductive loss times, i.e., in the approximation of T > ∼ 20 MK ( ∝ T ) T 13/4 τr = const ≈ 0.18. τc EM

(44)

Accordingly, the applicability of the quasi-static cooling approach can be supported or rejected based on the run of T and EM during the decay phase. Note, however, that a constant ratio (44) is not a sufficient condition to fully justify this approach. The quasi-static cooling model also predicts a particular shape of the flare DEM (Mewe et al. 1997) – see (12). van den Oord and Mewe (1989), Stern et al. (1992a),


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Ottmann and Schmitt (1996), Kürster and Schmitt (1996), Mewe et al. (1997) and many others have applied this model. The approach has recently been criticized, however, because the treatment of heating is not physically self-consistent (Reale 2002).

12.6. Cooling loops with continued heating The characteristics of the flare decay itself strongly depend on the amount of ongoing heating. Several models include continued heating with some prescription (e.g., the quasi-static cooling approach, or two-ribbon models). Continued heating in several large flares with a rapid rise has been questioned for cases where the thermal plasma energy content at flare peak was found to be approximately equal to the total radiative energy during the complete flare. If that is the case, the flare energy has been deposited essentially before the flare peak (van den Oord et al. 1988; Jeffries and Bedford 1990; Tagliaferri et al. 1991). Other flares, however, exhibit evidence of reheating or continued heating during the decay phase (e.g., Tsuboi et al. 1998). Whether or not flaring loops indeed follow a quasi-static cooling path is best studied on a density-temperature diagram (Fig. 23). Usually, characteristic values T = Ta and ne = ne,a as measured at the loop apex are used as diagnostics. For a magnetic loop in hydrostatic equilibrium, with constant cross section assumed, the RTV scaling law (20) requires stable solutions (T , ne ) to be located where T 2 ≈ 7.6 × 10−7 ne L (for ne = ni ). On a diagram of log T vs. log ne , all solutions are therefore located on a straight line with slope ζ = 0.5. Jakimiec et al. (1992) studied the paths of hydrodynamically simulated flares with different heating histories. The initial rapid heating leads to a rapid increase of T , inducing increased losses by conduction. As chromospheric evaporation grows,

Fig. 23. Density-temperature diagram of a hydrodynamically simulated flare. The flare loop starts from an equilibrium (S-S, steady-state loop according to Rosner et al. 1978); (a) and (b) refer to the heating phase; at (c), the heating is abruptly turned off, after which the loop cools rapidly (d, e), and only slowly recovers toward a new equilibrium solution (f, g) due to constant background heating (from Jakimiec et al. 1992)

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radiation helps to balance the heating energy input. The flare decay sets in once the heating rate drops. At this moment, depending on the amount of ongoing heating, the magnetic loop is too dense to be in equilibrium, and the radiative losses exceed the heating rate, resulting in a thermal instability. In the limit of no heating during the decay, that is, an abrupt turn-off of the heating at the flare peak, the slope of the path becomes ζ ≡

dln T τn ≡ =2 dln ne τT

(45)

ζ

implying T (t) ∝ ne (t) = n2e (t) (see Serio et al. 1991 for further discussion). Here, τT and τn are the e-folding decay times of the temperature and the electron density, respectively, under the assumption of exponential decay laws. Only for a non-vanishing heating rate does the loop slowly recover and eventually settle on a new equilibrium locus (Fig. 23). In contrast, if heating continues and is very gradually reduced, the loop decays along the static solutions (ζ = 0.5). Observationally, this path is often followed by large solar flares (Jakimiec et al. 1992). Clearly, a comprehensive description of stellar flares should thus consider continued heating throughout the flare. However, the observables typically available to the stellar astronomer are only the run of the X-ray luminosity (hence the EM) and of the characteristic temperature T . The volume and the density ne are unknown and need to be estimated from other parameters. √ To this end, Reale et al. (1997) replaced ne by the observable EM and thus assumed a constant flare volume, and further introduced the following generalization. In the freely cooling case after an abrupt heating turnoff, the entropy per particle at the loop apex decays on the thermodynamic decay time τtd = 3.7 × 10−4

L 1/2

T0

[s]

(46)

where T0 is the flare temperature at the beginning of the decay (Serio et al. 1991; see Reale et al. 1993 for an extension to loops with L up to a pressure scale height). For the general case with continued heating, Reale et al. (1997) wrote τLC = 3.7 × 10−4

L 1/2

T0

F (ζ ) [s]

(47)

where F (ζ ) ≡ τLC /τtd is a correction function depending on the heating decay time via ζ , and τLC is the observed X-ray light curve decay timescale. F (ζ ) is therefore to be numerically calibrated for each X-ray telescope. The important point is that F (ζ ) has been empirically found from solar observations and numerical simulations to be a hyperbolic or exponential function with three parameters that can be determined for a given instrument. With known F , (47) can be solved for L. This scheme thus offers i) an indirect method to study flaring loop geometries (L), ii) a way of determining the rate and decay time scale of continued heating via F (ζ ) and τtd , and iii) implications for the density decay time via τn = ζ τT . Conditions of applicability include ζ ≥ 0.3 and a resulting loop length L of less than one pressure scale height (Reale et al. 1997). Loop sizes derived from this method agree with direct observations on the Sun. Solar observations of moderate flares with the Solar Maximum Mission SMM implied


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ζ between ∼0.5 and 2 (Sylwester et al. 1993), although Reale et al. (1997) found a predominance of values around ∼ 0.3−0.7, i.e., flares with substantial sustained heating. This method has been applied extensively in the interpretation of stellar flares. Modeling of large flares yields reasonable flare loop sizes that are often smaller than those inferred from other methods. Loop sizes comparable with sizes of solar active regions have been found. But such loops may also be of order of one stellar radius for M dwarfs such as Proxima Centauri (Reale et al. 1988, 2004). The flaring region may thus comprise a significant fraction of the stellar corona on such stars. Giant flares with reliable measurements of temperatures are particularly well suited for an application of this method. Examples have been presented for EV Lac (a flare with a >100 fold increase in count rate in the ASCA detectors, reaching temperatures of 70 MK; Favata et al. 2000a, Fig. 25), AB Dor (Maggio et al. 2000), and Proxima Centauri (Reale et al. 2004). The same approach was also used for pre-main sequence stars by Favata et al. (2001), including comparisons with other methods. The moderate loop sizes resulting from this method have important implications for coronal structure (see Sect.11). The magnetic loops related to several flares observed on AD Leo, for example, all seem to be of fairly similar, modest size (half-length L ≈ 0.3R∗ ). They are therefore likely to represent active region magnetic fields, although under this assumption a quite small filling factor of 6% is obtained (cf. Favata et al. 2000b for details). Applications have also often shown that considerable heating rates are present during the decay phase of large stellar flares (e.g., Favata et al. 2000a,b). Values of ζ as small as 0.5 are frequently found; this corresponds to a decay that is ≈ 3–5 times slower than predicted from free cooling on the thermodynamic time scale. 12.7. Two-Ribbon flare models An approach that is entirely based on continuous heating (as opposed to cooling) was developed for the two-ribbon (2-R) class of solar flares. An example of this flare type is shown in Fig. 24. The 2-R flare model devised initially by Kopp and Poletto (1984) is a parameterized magnetic-energy release model. The time development of the flare light-curve is completely determined by the amount of energy available in non-potential magnetic fields, and by the rate of energy release as a function of time and geometry as the fields reconnect and relax to a potential-field configuration. Plasma cooling is not included in the original model; it is assumed that a portion of the total energy is radiated into the observed X-ray band, while the remaining energy will be lost by other mechanisms. An extension that includes approximations to radiative and conductive losses was described in Güdel et al. (1999) and Güdel et al. (2004). 2-R flares are well established for the Sun (Sect. 12.1, Fig. 24); they often lead to large, long-duration flares that may be accompanied by mass ejections. The magnetic fields are, for convenience, described along meridional planes on the star by Legendre polynomials Pn of order n, up to the height of the neutral point; above this level, the field is directed radially, that is, the field lines are “open”. As time proceeds, field lines nearest to the neutral line move inward at coronal levels and reconnect at progressively larger heights above the neutral line. The reconnection point thus moves upward as the flare proceeds, leaving closed magnetic-loop systems underneath. One

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Fig. 24. Trace image of a flaring magnetic loop arcade

loop arcade thus corresponds to one N-S aligned lobe between two zeros of Pn in latitude, axisymmetrically continued over some longitude in E–W direction. The propagation of the neutral point in height, y(t), with a time constant t0 , is prescribed by (y in units of R∗ , measured from the star’s center) y(t) = 1 +

Hm 1 − e−t/t0 R∗

H (t) ≡ [y(t) − 1]R∗

(48) (49)

and the total energy release of the reconnecting arcade per radian in longitude is equal to the magnetic energy lost by reconnection, y 2n (y 2n+1 − 1) 1 dE = 2n(n + 1)(2n + 1)2 R∗3 B 2 I12 (n) dy 8π [n + (n + 1)y 2n+1 ]3

(50)

dE dy dE = dt dy dt

(51)

(Poletto et al. 1988). In (48), Hm is the maximum height of the neutral point for t → ∞; typically, Hm is assumed to be equal to the latitudinal extent of the loops, i.e., Hm ≈

π R∗ n + 1/2

(52)

for n > 2 and Hm = (π/2)R∗ for n = 2. Here, B is the surface magnetic field strength at the axis of symmetry, and R∗ is the stellar radius. Finally, I12 (n) corresponds to


149

[Pn (cosθ )]2 d(cosθ ) evaluated between the latitudinal borders of the lobe (zeros of dPn /dθ ), and θ is the co-latitude. The free parameters are B and the efficiency of the energy-to-radiation conversion, q, both of which determine the normalization of the light curve; the time scale of the reconnection process, t0 , and the polynomial degree n determine the duration of the flare; and the geometry of the flare is fixed by n and therefore the asymptotic height Hm of the reconnection point. The largest realistic 2-R flare model is based on the Legendre polynomial of degree n = 2; the loop arcade then stretches out between the equator and the stellar poles. Usually, solutions can be found for many larger n as well. However, because a larger n requires larger surface magnetic field strengths, a natural limit is set to n within the framework of this model. Once the model solution has been established, further parameters, in particular the electron density ne , can be inferred. The Kopp and Poletto model is applicable after the initial flare trigger mechanism has terminated, although Pneuman (1982) suggested that reconnection may start in the earliest phase of loop structure development. 2-R models have been proposed for interpretation of stellar flares on phenomenological grounds such as high luminosities, long decay time scales, white-light transients, or X-ray absorption possibly by transits of prominences, by Haisch et al. (1981), Haisch et al. (1983), Poletto et al. (1988), Tagliaferri et al. (1991), Doyle et al. (1992b), Franciosini et al. (2001), Güdel et al. (1999), Güdel et al. (2004), to mention a few. Poletto et al. (1988) emphasized the point that large solar flares predominantly belong to this class rather than to compact, single-loop events. Many authors found overall sizes of order R∗ , i.e., they obtained small n. Comparisons of 2-R model predictions with explicitly measured heating rates during large flares indicate an acceptable match from the rise to the early decay phase (van den Oord and Mewe 1989) although the observed later decay episodes are often much slower than any model parameter allows (Osten et al. 2000; Kürster and Schmitt 1996; Güdel et al. 2004). Part of the explanation may be additional heating within the cooling loops. Katsova et al. (1999) studied a giant long-duration flare on the dMe star AU Mic. The observed decay time of this flare exceeded any plausible decay time scale based on pure radiative cooling by an order of magnitude, suggestive of a 2-R flare. Although an alternative model based on a very large, expanding CME-like plasma cloud at low densities has been presented (Cully et al. 1994), the spectroscopically measured high densities of the hot plasma argue for a coronal source undergoing significant posteruptive heating. A very slowly evolving flare observed on the RS CVn-type binary HR 5110, with a decay time of several days, suggested large source scales but showed clear departures from any model fit; the authors proposed that the flare was in fact occurring in intrabinary magnetic fields (Graffagnino et al. 1995). 12.8. Hydrodynamic models Full hydrodynamic calculations aim at solving the equations of mass, momentum, and energy conservation comprehensively and under quite general conditions, although certain simplifying initial conditions, boundary conditions, and plasma physical approximations must be made. The equations treat the plasma as a thermodynamic fluid, an approximation that is sufficiently good except for the critical footpoint region of magnetic loops

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where the mean free path of the electrons exceeds the temperature and pressure scale heights. In this region, effects such as saturation of the conductive flux due to the freestreaming limit to the heat transport must be included. Treatment of time-dependent ionization and recombination is also required at chromospheric levels. The latter define boundary conditions to the coronal simulations, therefore extensive chromospheric models must be included (see, e.g., Reale et al. 1988). Radiation can usually be approximated sufficiently well in terms of a cooling function integrating all continuum, free-bound, and line losses at a given temperature in ionization equilibrium. The presence of nonthermal, accelerated electron populations is often not treated, and the magnetic fields are assumed to be rigid, with the only purpose of confining the plasma. Heating terms are adjusted empirically, with a distribution both in space and time. Accepting these approximations, state-of-the art simulations have given deep insights into the flare process and the nature of spatially unresolved stellar X-ray flares. The methods have been comprehensively tested with, and applied to, solar flares (Pallavicini et al. 1983; Reale and Peres 1995). For a description of various codes and numerical solar flare simulations, see Nagai (1980), Peres et al. (1982), Pallavicini et al. (1983), Peres et al. (1987), and Mariska et al. (1989). For stellar applications, I refer the reader to Cheng and Pallavicini (1991), Katsova et al. (1997), Reale et al. (2002), and Reale et al. (2004). For stellar flare simulations, there are two major unknowns. First, the energy input can be in the form of high-energy particle beams or of direct heating, leading to different preferred heat source locations such as the footpoints or the loop apex. Fortunately, conduction equalizes effects due to spatially non-uniform heating rapidly enough so that the choice is of limited relevance (Peres et al. 1987; Reale et al. 1988). Second, the basic magnetic configuration of the flares is unknown a priori, including initial conditions in the pre-flare plasma such as pressure or density. Pure hydrodynamic models assume single flaring loops (e.g., Peres et al. 1982), or complexes of independent loops (e.g., Reale et al. 2004), while magnetohydrodynamic (MHD) codes allow for an extension to interacting loops or loop arcades (see below). By varying parameters, comparison of the simulations with observed parameters such as the light curve and the temperature development eventually confine magnetic loop geometries, magnetic fields, heating durations, electron densities, and some of the initial conditions. A parameter study appropriate for flares on dMe stars was performed by Cheng and Pallavicini (1991). They pointed out that multiple solutions exist for given light curves, but that all solutions fulfill an overall linear relation between flare peak EM and total energy released in the flare, with good agreement between the simulations and the observations. This relation emerges because larger energy release produces more extensive chromospheric evaporation. The trend saturates, however, once the energy input becomes too large, because increased radiative losses suppress further conductive evaporation. This, then, suggests that extremely large flares cannot be produced in moderately-sized magnetic loops. The simulations further showed plasma evaporative upflows in the early episodes that reach velocities of 500–2000 km s−1 . Such velocities can in principle be measured spectroscopically. Reale et al. (1988, 2004) studied two giant flares on Proxima Centauri using hydrodynamic approaches. Both flares have been suggested to be close analogs of gradual, very large solar events, with the important difference that their geometric sizes (5 × 109 cm –


151

1010 cm), while similar to large-scale solar events, comprise a significant fraction of the stellar corona. For the second flare, Reale et al. (2004) showed explicitly that multiple flaring loops are required to describe the light curve. This led them to suggest that the actual geometry should be a loop arcade in analogy to the 2-R model, of which a few dominant loops with similar heights were modeled like isolated flaring loops. The same flare modeled with the 2-R approach (Sect. 12.7) indeed leads to very similar magnetic loop heights (Güdel et al. 2004). Large flares on late-type M dwarfs therefore constitute large-scale disturbances of the corona possibly inducing global effects, an assertion that has been supported by interferometric radio observations (Benz et al. 1998).

12.9. Magnetohydrodynamic models Shibata and Yokoyama (1999) and Shibata and Yokoyama (2002) discussed novel flare scaling laws based on their earlier MHD work on X-point reconnection in large flares. They reported a simple scaling relation between flare peak temperature T , the loop magnetic field strength B, the pre-flare loop electron density n0 , and the loop semilength L under the condition of dominant conductive cooling (appropriate for the early phase of a flare), −1/7 T ≈ 1.8 × 104 B 6/7 n0 L2/7 [K]. (53) The law follows from the balance between conduction cooling (∝ T 7/2 /L2 , (32)) and magnetic reconnection heating (∝ B 3 /L). Assuming loop filling through chromospheric evaporation and balance between thermal and magnetic pressure in the loop, two further “pressure-balance scaling laws” follow: EM ≈ 3 × 10−17 B −5 n0 T 17/2 [cm−3 ] 3/2

EM ≈

2/3 2 × 108 L5/3 n0 T 8/3

[cm

−3

].

(54) (55)

An alternative scaling law applies if the density development in the initial flare phase is assumed to follow balance between evaporation enthalpy-flux and conduction flux, although the observational support is weaker, EM ≈ 1 × 10−5 B −3 n0 T 15/2 [cm−3 ]. 1/2

(56)

And third, a steady solution is found for which the radiative losses balance conductive losses. This scaling law applies to a steady loop, 13 4 10 T L [cm−3 ] for T < 107 K EM ≈ (57) 1020 T 3 L [cm−3 ] for T > 107 K and is equivalent to the RTV scaling law (20). The advantage of these scaling laws is that they make use exclusively of the flarepeak parameters T , EM, B (and the pre-flare density n0 ) and do not require knowledge of the time evolution of these parameters. The models have been applied to flares on protostars and T Tau stars (see Sect. 12.12).

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12.10. Summary of methods Despite their considerable sophistication, stellar flare models remain crude approximations so long as we have little a priori knowledge of the magnetic field topology. Solar flares reveal complexities that go far beyond any of the standard models described above. Nevertheless, stellar flare scenarios have been useful tools to roughly assess characteristic flare sizes, densities, and heating rates. Several models have been applied to solar flares as well, which has tested their reliability. In some cases, simple light curve decay analysis (35) or the quasi-static cooling model result in excessively large loop semi-lengths L (Schmitt 1994; Favata and Schmitt 1999; Favata et al. 2000a). Alternative methods such as the heating-decay model (Sect. 12.6) may give more moderate values. On the other hand, seemingly different methods may also result in overall agreement for the magnetic structure size. For example, Endl et al. (1997) compared the 2-R approach with the quasi-static cooling formalism for a large flare on an RS CVn binary and found similar heights of the flaring structures (≈ 1R∗ ). Güdel et al. (2004) and Reale et al. (2004) compared the 2-R model, full hydrodynamic simulations and the heating-decay model, again finding good overall agreement (loop sizes of order 1R∗ on Proxima Centauri). Covino et al. (2001) compared loop lengths obtained for several recently-modeled large stellar flares based on a simple decay-time formalism (35) and on the heating-decay model; the agreement was once more rather good. The authors argued that neglecting heating during the decay increases the model length in the decay-time formalism, but at the same time one ignores conductive cooling. The density is thus overestimated, which decreases the model loop size again. In this sense, approaches such as the heating-decay model or the analytic 2-R model are preferred not necessarily (only) because of their predictive power but because of their physically founded basis and hence reliability, and their support from direct solar observations. Full hydrodynamic or MHD simulations of course provide the closest description of the actual processes, but a realistic simulation requires a careful choice of a number of unknown parameters. One of the main results that have come from extensive modeling of stellar X-ray flares is that extremely large stellar flares require large volumes under all realistic assumptions for the flare density. This is because, first, the energy derives from the non-potential portion of the magnetic fields that are probably no stronger than a few 100 G in the corona; and second, small-loop models require higher pressure to produce the observed luminosity, hence requiring excessively strong magnetic fields. This is in line with the findings by Cheng and Pallavicini (1991) from hydrodynamic simulations. This is not to say that magnetic loops must be of enormous length – a number of interpretation methods suggest the contrary even for very large flares. But at this point, the concept of single-loop approaches becomes questionable particularly as large flares on the Sun often involve very complex arrangements of magnetic structures: the large volumes do not necessarily involve large heights but large surface area (see example in Reale et al. 2004). Alternative models are available in the stellar literature, although they have mostly been applied to singular cases. Most notably, I mention the coronal mass ejection model by Cully et al. (1994) that was applied to a giant flare on AU Mic observed by EUVE (Cully et al. 1993). Fisher and Hawley (1990) derived equations for the evolution of a constant-cross section flaring magnetic loop with uniform but time-varying pressure and


153

volumetric heating rate (for time scales that are long compared to the sound transit time, i.e., assuming quasi-hydrostatic equilibrium). Although their model is not quasi-static by requirement, it can be well approximated by “equivalent static loops” having the same length and the same column depth as the evolving loop. A major advantage of this formulation is that it includes the evaporation phase of the flare, i.e., essentially the flare rise phase. The quality of the model was described in detail by Fisher and Hawley (1990), together with applications to a solar and an optical stellar flare. Another application was described by Hawley et al. (1995) for an EUV flare on AD Leo. Table 4 reports the refined results presented by Cully et al. (1997) for a typical low-abundance corona. A further model including evaporative cooling was presented by Pan et al. (1997) in an application to a strong flare on an M dwarf. There are a number of further, “unconventional” models, e.g., star-disk magnetic flares in pre-main sequence stars or intrabinary flares – see, among others, Skinner et al. (1997) and Montmerle et al. (2000). 12.11. Observations of stellar X-ray flares Table 4 summarizes properties of a list of stellar X-ray events that have been modeled with one of the above approaches in the literature (I have added a few selected published flares for which modeling is not available but for which good temperature and EM measurements have been given). Further flares on pre-main sequence stars have been discussed by Imanishi et al. (2003). Some flares have reported durations of several days (Graffagnino et al. 1995; Kürster and Schmitt 1996; see also Ayres et al. 1999, 2001a), some show X-ray luminosities up to 1033 erg s−1 (e.g., Preibisch et al. 1995; Tsuboi et al. 1998), and some show temperatures in excess of 100 MK (Tsuboi et al. 1998; Güdel et al. 1999; Favata and Schmitt 1999). A number of extreme flares were already reported from the pre-Einstein era, with RS CVn binaries recognized as their origin (Pye and McHardy 1983). Unusual shapes of flares have frequently been reported, such as flares with slow rise and rapid decay (Haisch et al. 1987), flares with secondary peaks or separate reheating events during the primary decay (White et al. 1986; Katsova et al. 1999; Güdel et al. 2004), flares with double-exponential decays (Cully et al. 1993; Osten and Brown 1999; Favata et al. 2000a; Reale et al. 2004, see Fig. 25), flat-topped flare light-curves (Agrawal et al. 1986b; Osten and Brown 1999; Raassen et al. 2003b, see Fig. 25), flares with very long rise times (Tagliaferri et al. 1991), or flares in which the temperature stays essentially constant during the decay phase (Graffagnino et al. 1995). 12.12. Flare temperatures When the flare energy release evaporates plasma into the corona, heating and cooling effects compete simultaneously, depending on the density and temperature profiles in a given flare. It is therefore quite surprising to find a broad correlation between peak temperature Tp and peak emission measure EMp , as illustrated in Fig. 26 for the sample reported in Table 4.5 A regression fit gives (for 66 entries) 5 If ranges are given in the table, the geometric mean of the minimum and maximum was taken;

upper or lower limits were treated as measured values.

31.54 (30.95) 32.18

(32.56) 34.64 (32.59)

34.18

32.11 32.91 32.20 32.08 32.40 33.40

33.10 35.46 33.20 31.56 33.63 34.0 33.70 35.78–35.90 35.78–35.90 34.00 33.46

34.00

34.95

30.48 29.30 30.2 29.48

31.18

28.95 29.40 28.85 29.26 29.28 29.51

29.80 (30.92) 29.91 28.90 29.65 30.67 30.90 32.00 32.00 (≈ 30.4) 29.48

31.23

31.04

31.32

c log EX (erg)

27.87 28.59

28.08 28.30

Prox Cen " " Prox Cen Prox Cen " EQ Peg EQ Peg EQ Peg EV Lac EV Lac EV Lac " AD Leo AD Leo AD Leo AD Leo AD Leo AD Leo AD Leo AD Leo AT Mic AU Mic Gl 644 YZ CMi YY Gem YY Gem Castor AB Dor AB Dor AB Dor CC Eri " EQ1839.6+8002 " Gl 355 "

E E E E X X E Ex Ex H R A A A A A R R E EU EU Ex EU Ex E X Ex Ex B B X R R G G R R

log LbX (erg s−1 )

Stara

54.1

54.0

52.1 52.7 52.4 52.3 51.9 52.0 52.3 52.3 52.7 53.0 52.5 51.3 52.1 53.3 53.7 54.7 54.6 52.7 52.6

53.3 51.7 53.3 53.3 52.2 53.9

51.1 51.3

51.0 51.0

log EMd (cm−3 )

52

100

20 25 38 35 12 12 13 < 32 39 ... 50 20 40 64 48 109 110 33 28

44 26 42 (20) ... 73

17 25

20 27

e Tmax (106 K)

10100

629

1800 35000 950 600 960 3900 300-600 3840 3420 3850 (9500)

570 1180 3500 680 8040 5400

2400 1800 2400 < 1300 ∼ 38400 1800

1300 1200 1400-4400

1750

τf (s)

D D C ... D C C C 2R D D D C D

H 2R D D 2R H 2R D ... D Q Q C C C C C C C FH FH ...

modelg 10.70–11.11 12.00 11.18 11.26 11.48–11.70 12.30 12.78 11.30 ... 11.60–12.00 10.48 11.78 11.30–12.30 >11.70 12.53 12.04 12.30 >11.18 11.48 10.60 11.64 ... 10.70 11.90 11.15 11.8 ... 12.54 11.73–12.20 11.49–11.95 11.41 10.0–11.1 11.04–11.1 12.41 11.60–12.23 11.30 11.11

log nhe,max (cm−3 ) 9.65 9.15 9.78 9.30 10.23 ≈ 9.80 9.61 10.11 ... 9.70 11.58 10.50 9.92 < 9.80 9.42 9.65 9.41 < 10.03 9.92 9.68 9.54 ... 10.54–10.85 9.90 10.00 9.10 ... 9.71 10.34 10.49 10.20 9.95–10.10 ... 9.23–9.92 9.50–10.10 10.72 10.80

log (scale)i (cm)

Table 4. Flare interpretation: Summary of results

Reale et al. (1988) Poletto et al. (1988); Haisch et al. (1983) Byrne and McKay (1989) Haisch et al. (1980, 1981) Güdel et al. (2004) Reale et al. (2004) Poletto et al. (1988) Haisch et al. (1987) Pallavicini et al. (1990a) Ambruster et al. (1984) Schmitt (1994) Favata et al. (2000a) Favata et al. (2000a) Favata et al. (2000b) Favata et al. (2000b) Favata et al. (2000b) Reale and Micela (1998); Favata et al. (2000b) Favata et al. (2000b) Favata et al. (2000b) Cully et al. (1997) Cully et al. (1997) Pallavicini et al. (1990a) Katsova et al. (1999) Doyle et al. (1988a) Kahler et al. (1982) Stelzer et al. (2002) Pallavicini et al. (1990a) Pallavicini et al. (1990b) Maggio et al. (2000) Maggio et al. (2000) Güdel et al. (2001b) Pan and Jordan (1995) Pan and Jordan (1995) Pan et al. (1997) Pan et al. (1997) Covino et al. (2001) Covino et al. (2001)

Reference

154 M. Güdel

33.30 (34.90) (33.99) (33.67) 34.38 34.30 ... 37.00 > 35.20 ∼ 34.43 35.26 > 37.00 35.48 (36.30) > 36.70 ∼ 36.89

33.70 36.85 35.00 35.00 (35.34) 37.15

37.15

32.23 > 34.48 ∼ 35.08 > 37.00 37.00

36.60

37.70 36.78

30.00 31.20 30.69 30.21 30.97 30.78 ... 32.30 31.04 30.41 (≈ 32) 32.30 31.78 32.15 32.00 32.15

30.85 32.20 31.20 31.15 31.00 32.48

31.85

29.48 > 31 ∼ 31.58 32.23 33.00

32.70

33.26 32.30

Ex R X X Ex E X R Ex A G G G A B R R Ex R Ex Ex G B B R R R E R A A A R R R A A

π 1 UMa H II 1516 H II 1032 H II 1100 σ 2 CrB σ 2 CrB HR 1099 AR Lac II Peg II Peg II Peg UX Ari UX Ari UX Ari UX Ari HU Vir " XY UMa Algol Algol " Algol Algol " CF Tuc " β Boo HD 27130 HD283572 V773 Tau V773 Tau " LkHα 92 " P1724 YLW15 "

c log EX (erg)


Stara

(56.3) 54.8 55.2

55.7

52.0 53.5–54.0 54.6 55.2 55.7

55.0

53.3-.8 55.0 54.0 54.0 54.1 55.1

52.9 54.3 53.5 53.1 53.8 53.5 54.2 55.0 53.9 53.3 54.5 54.9 54.1 54.8 54.9 55.2

log EMd (cm−3 )

≈ 30 65

43

7800 5600 32000 31000

540 2500 12000 45000 8200

> 17 ∼ 50 30–75 42 115

45

≈ 1000 30400 4350 7000 22000 64000 49600 ≈ 80000

≈ 47000 67600

1000 5000 2000 2900 1700 ≈ 2000 ... 11000 40000 10000 2081

τf (s)

... ≈ 100 78 60 67 140

30 25 23.5 15.4 95 25 36 88 44 36 65 85 105 120 ≈ 100 ≈ 60

e Tmax (106 K)

Table 4. (continued)

D Q C C D D ... Q D Q D D D 2R 2R 2R Q D Q Q D Q Q C Q 2R D D C RM D C D C D Q C

modelg

11.87 11.11 11.70 11.70 11.78 11.95 ... 11.23 < 10.4 ∼ 10.90 11.88 9.3–10.3 11.23 11.0–12.0 10.78–11.00 ... 10.32 11.48–12.0 ≈ 11.7 12.00 11.48 10.70 10.52 10.3-10.48 ≥ 9.95 ≤ 11.6 11.92 11.60 11.45–11.92 ≥ 11.3 11.48 11.72–12.20 11.18 11.68–12.15 10.48 10.70 10.11–10.58

log nhe,max (cm−3 ) 9.86 < 10.98 10.06 9.88 10.17 10.04 ... 10.90 > 11 ∼ 10.90 10.46 ... ... 11.0–11.7 11.28–11.48 11.3–11.6 11.72 10.4–11.1 11.22 10.71 10.3–10.7 ≈ 11.28 ≈ 11.84 11.72 > 11.50 ... 9.62 10.2 10.5 ≤ 11.18 11.10 10.68 ≥ 10.9 10.36 ... 11.49 11.47

log (scale)i (cm) Landini et al. (1986) Gagné et al. (1995a) Briggs and Pye (2003) Briggs and Pye (2003) van den Oord et al. (1988) Agrawal et al. (1986b) Audard et al. (2001a) Ottmann and Schmitt (1994) Tagliaferri et al. (1991) Mewe et al. (1997) Doyle et al. (1991, 1992b) Tsuru et al. (1989) Tsuru et al. (1989) Güdel et al. (1999) Franciosini et al. (2001) Endl et al. (1997) Endl et al. (1997) Jeffries and Bedford (1990) Ottmann and Schmitt (1996) van den Oord and Mewe (1989) White et al. (1986) Stern et al. (1992a) Favata and Schmitt (1999) Favata and Schmitt (1999) Kürster and Schmitt (1996) Kürster and Schmitt (1996) Hünsch and Reimers (1995) Stern et al. (1983) Favata et al. (2001) Skinner et al. (1997) Tsuboi et al. (1998) Favata et al. (2001) Preibisch et al. (1993) Favata et al. (2001) Preibisch et al. (1995) Tsuboi et al. (2000) Favata et al. (2001)

Reference

X-ray astronomy of stellar coronae 155

54.5 54.5 53.6 55.5 55.8 54.0 55.3 54.8-55.1 55.5 47-49 49-50

log EMd (cm−3 ) 137 45 70 80 70 80 75 23 78 10–30 10–30

e Tmax (106 K)

... 8000 20000 6000 7000 6100 12000 6300 56400 1000 10000

τf (s)

Table 4. (continued)

... D D D D D D D D ... ...

modelg ... 11.30 11.00 11.70 11.48 11.51 11.00 10.48–10.78 10.64 11–12 10–11

log nhe,max (cm−3 ) ... 11.40 ... ... ... 11.10 11.00 11.00 11.4 8–9 10

log (scale)i (cm) Imanishi et al. (2001a) Kamata et al. (1997) Tsuboi et al. (2000) Tsuboi et al. (2000) Tsuboi et al. (2000) Kamata et al. (1997) Ozawa et al. (1999) Montmerle et al. (1983) Hamaguchi et al. (2000) Landini et al. (1986) Landini et al. (1986)

Reference

Notes. Values in parentheses are derived from parameters explicitly given by the authors. If no object name is given, observation is the same as next above. Note that spectral energy ranges may

35.60 35.30 36.78 37.11 35.08 (36.60) > 35.90 > 37.43 ∼ 29–31 32

(erg)

c log EX

Hünsch and Reimers (1995), and further references therein.

h Logarithm of peak electron density. i Loop lengths and semi-lengths as given by some authors were converted to (semi-circular) loop heights. j For solar characteristics, see also Montmerle et al. (1983), Stern et al. (1983), Landini et al. (1986), White et al. (1986), van den Oord et al. (1988), Jeffries and Bedford (1990), Pallavicini et al. (1990a),

rotational modulation; FH = evaporation model after Fisher and Hawley (1990).

a Code after star name gives observing satellite; A = ASCA, B = BeppoSAX, E = Einstein, EU = EUVE, Ex = EXOSAT, G = Ginga, H = HEAO 1, R = ROSAT, X = XMM-Newton. b Logarithm of peak X-ray luminosity. c Logarithm of total X-radiated energy. d Logarithm of peak emission measure. e Maximum temperature. f E-folding decay time of luminosity. g Model interpretation: D = estimates from flare decay; Q = quasi-static cooling; C = heating/cooling model after Reale et al. (1997); 2R = two-ribbon model; H = hydrodynamic simulation; RM =

vary.

32.2 (31.70) (31.00) (33.00) (33.26) 31.40 32.54 32.00 > 32.69 ∼ 26–27 27–28

YLW 16A EL29 R CrA SR 24 ROXs31 ROXA 2 SSV 63 ROX 20 MWC 297 Sun, compactj Sun, 2-Rj

A A A A A A A E A – –


Stara

156 M. Güdel


157

14 12

c/s

10 8 6 4 2

AT Mic, XMM−Newton

0 51833.05

51833.10

51833.15 51833.20 MJD [d]

51833.25

51833.30

Fig. 25. Four largely different examples of stellar flares. Top: A very large flare on EV Lac, showing a rapid rise and a long double-exponential decay (figure courtesy of F. Favata, after Favata et al. 2000a, observations with ASCA GIS.) – Middle: Modest, flat-topped flare on AT Mic (from Raassen et al. 2003b, observations with XMM-Newton EPIC). Bottom left: Sequence of very slowly decaying flares on the giant β Cet (figure courtesy of R. Osten, after Ayres et al. 2001a, observations with EUVE). Bottom right: Rapid rise and very slow decay of a flare on the RS CVn binary σ Gem (figure courtesy of R. Osten, observations with EUVE)

158

M. Güdel

Peak emission measure (cm−3)

56

54

52

50

1

10 Peak temperature (MK)

100

Fig. 26. Peak temperatures and EMs of the flares listed in Table 4. Key to the symbols: Filled circles: XMM-Newton observations. Open circles: ASCA or BeppoSAX observations. Small diamonds: observations from other satellites. The solid line shows a regression fit (58). Triangles represent non-flaring parameters of the G star sample from Güdel et al. (1997a) and Güdel et al. (1998), referring to the hotter plasma component in 2-T spectral fits to ROSAT data

EMp ∝ Tp4.30±0.35 .

(58)

The correlation overall indicates that larger flares are hotter. A similar relation was reported previously for solar flares (Feldman et al. 1995), with a suggestion that it extends to selected large stellar flares. Although the trend shown in Fig. 26 does not smoothly connect to the Feldman et al. solar-flare relation (theirs being lower in EM or hotter for a given EM, see also Fig. 27), their stellar loci agree with ours. Various selection effects or data analysis biases related to limited S/N ratios and detector energy resolution may prohibit an accurate comparison of the two relations. Also, Feldman et al. (1995) measured the temperature at the time when the EM reached its peak, whereas Table 4 reports the maximum temperature that often occurs slightly before the EM peak. Consideration of this effect could only increase the disagreement. A handful of stellar flares for which the temperature was determined precisely at the EM peak yield the same slope as given in (58). On the other hand, the correlation is reminiscent of the T − LX correlation for the “non-flaring” coronal stars in Fig. 10 at cooler temperatures. This same sample is plotted as triangles in Fig. 26, again only for the hotter plasma component (data from Güdel et al. 1997a). The stars follow approximately the same slope as the flares, albeit at cooler temperatures, and for a given temperature, the EM is higher. This trend may suggest that flares systematically contribute to the hot plasma component, although we have not temporally averaged the flare temperature and EM for this simple comparison. For this

log(Emission Measure [cm−3 ]


159

58

5G

56

15 G

50 G 150 G

54 52

12

10 cm

50 48 46

10

10 cm 8

10 cm

44 106

107

108

Temperature [K] Fig. 27. Theoretical EM-T relations based on the reconnection model by Shibata and Yokoyama, showing lines of constant loop length L and lines of constant magnetic field strength B. Hatched areas are loci reported for solar flares, and other symbols refer to individual stellar flares in starforming regions (figure courtesy of K. Shibata and T. Yokoyama, after Shibata and Yokoyama 2002)

model, we would require that the coronal emission of more luminous stars is dominated by larger and hotter flares. If flares are distributed in energy as described in Sect. 13.5, then a larger number of flares will generate both a higher luminosity and a shift to higher average temperatures indeed. Shibata and Yokoyama (1999) and Shibata and Yokoyama (2002) interpreted the EM-T relation as presented by Feldman et al. (1995) based on their MHD flare scaling laws (54). The observed loci of the flares require loop magnetic field strengths similar to solar flare values (B ≈ 10 − 150 G) but the loop lengths must increase toward larger flares. This is seen in Fig. 27 where lines of constant L and B are plotted for this flare model. The same applies to the flares in Fig. 26; typical loop lengths would then be L ≈ 1011 cm. 12.13. Flare densities The density of a flaring plasma is of fundamental importance because it determines the time scales of radiation and of several plasma-physical instabilities. For spatially unresolved observations, densities can be inferred either indirectly from a flare decay analysis (see Sect. 12.4–12.7) or directly by measuring density-sensitive line ratios as described in Sect. 10. Good examples from solar studies are relatively rare. McKenzie et al. (1980) presented O vii He-like triplets (Sect. 10.2) observed during a large solar flare and found

160

M. Güdel

f/ i ratios around unity close to the flare peak, implying densities of up to 2×1011 cm−3 . Much shorter flares were discussed by Doschek et al. (1981); in those cases, the densities reached peaks around (10 − 20) × 1011 cm−3 as measured from O vii, but this occurred during the flare rise, while electron densities of a few times 1011 cm−3 were derived during the flare peak. The estimated masses and volumes, on the other hand, steadily increased. For the more relevant hot temperatures, line ratio diagnostics based on Fe xxi, Fe xxii, or (He-like) Fe xxv have been employed. Doschek et al. (1981) and references therein reported densities derived from Fe xxv (T > 10 MK) that are similar to those measured from O vii. Phillips et al. (1996) inferred very high densities of 1013 cm−3 from Fe xxii about one minute after the Ca xix flare peak, and ne ≈ (2 − 3) × 1012 cm−3 from Fe xxi five minutes later. Landi et al. (2003) recently used various density diagnostics for a modest solar limb flare. From Fe xxi lines, they derived densities of up to 3 × 1012 cm−3 , but there are conflicting measurements for lower ionization stages that reveal much lower densities, comparable to pre-flare values (see also further references in their paper). If the density values at ≈ 107 K are real, then pressure equilibrium cannot be assumed for flaring loops; a possible explanation involves spatially separate volumes for the O vii and the Fe xxi–xxv emitting plasmas.

17:00

Time (UT) 18:00

17:30

18:30

1013

80

a Count rate (s−1)

Electron density (cm−3)

1012

60 3 1

1011

40 2

4 X−Rays

1010

20 Q

U Band x 0.15 109

photon flux (arbitrary units)

0

Q

21.5

1

22.0 22.5 21.5

2

3

22.0 22.5 21.5 22.0 22.5 21.5 wavelength (Å)

4

22.0 22.5 21.5

22.0 22.5

Fig. 28. Flare on Proxima Centauri, observed with XMM-Newton. The top panel shows the X-ray light curve and the much shorter U band flare (around 17 UT). The bottom panel shows the O vii He-like triplets observed during various time intervals of the flare. The locations of the r, i, and f lines are marked by vertical lines. The resulting electron densities are given in the top panel by the crosses, where the horizontal arm lengths indicate the time intervals over which the data were integrated, and the right axis gives the logarithmic scale (after Güdel et al. 2002a, 2004)


161

Stellar flare density measurements are in a rather infant state as they require high signal-to-noise ratios over the short time of a flare, and good contrast against the steady stellar emission. A large flare on Proxima Centauri provided first evidence for significant density variations as derived from the He-like O vii triplet (and more tentatively, from Ne ix; Güdel et al. 2002a, 2004, Fig. 28). The densities rapidly increased from ne < 1010 cm−3 to ≈ 4 × 1011 cm−3 at flare peak, then again rapidly decayed to ≈ 2 × 1010 cm−3 , to increase again during a secondary peak, followed by a gradual decay. The instantaneous mass involved in the cool, O vii emitting source was estimated at ≈ 1015 g, resulting in similar (instantaneous) potential and thermal energies in the cool plasma, both of which are much smaller than the total radiated X-ray energy. It is probable that the cool plasma is continuously replenished by the large amount of material that is initially heated to higher temperatures and subsequently cools to O vii forming temperatures and below. The measured densities agree well with estimates from hydrodynamic simulations (Reale et al. 2004). A marginal signature of a density increase was also recorded in O vii during a modest flare on YY Gem (Stelzer et al. 2002), and in Mg xi during a flare on σ 2 CrB although the density stayed similarly high outside the flare (Osten et al. 2003). Further marginal indications for increased densities during flares were reported for AD Leo (van den Besselaar et al. 2003), AT Mic (Raassen et al. 2003b), and AU Mic (Magee et al. 2003). Measurements from Fe line ratios in the EUV have been hampered by the apparently rather large quiescent densities that already reach values expected for flares (see Sect. 10.1). They therefore generally show little evidence for density increases during flares (Osten and Brown 1999). Monsignori Fossi et al. (1996) inferred ne up to 1.5 × 1013 cm−3 from from the Fe xxi λ142.2/λ128.7 flux ratio during a giant flare on AU Mic although the detection is again marginal. Sanz-Forcada et al. (2001) and SanzForcada et al. (2002) found slightly higher densities during flares on λ And, HR 1099, and σ Gem based on Fe xxi compared to quiescence (log ne ≈ 12.9 vs. 12.1 in λ And), but again all values are extremely high. 12.14. Correlation with UV and optical flares Optical continuum flares (“white light flares”), often observed in the Johnson U band, are tracers of the impulsive phase of the flare. The emission is presumably due to enhanced continuum emission after chromospheric heating, possibly following electron impact (e.g., Hawley et al. 1995). In the chromospheric evaporation scenario, U band bursts are expected to occur during the rise phase of soft X-ray flares (Sect. 12.16). Early examples were reported by Kahler et al. (1982), de Jager et al. (1986), and de Jager et al. (1989) for flares on YZ CMi, BY Dra, and UV Cet, respectively. The total optical energy output is approximately 0.1–1 times the X-ray output, a range that has been confirmed by many other observations, including solar data (Kahler et al. 1982 and references therein). The flare amplitudes and radiated energies appear to be correlated in the X-ray and UV ranges (Mitra-Kraev et al. 2004). Occasionally, very good correlations are found between soft X-ray and Hα flares. The total energy emitted in Hα amounts to approximately 5% of the soft X-ray losses (Doyle et al. 1988a) but may, in exceptional cases, reach order unity (Kahler et al. 1982). The physical causes of this correlation were discussed by Butler (1993); direct

162

M. Güdel

photoionization of chromospheric material by coronal soft X-rays is problematic because the Hα ribbons seen on the Sun are narrowly confined to the magnetic footpoints, and the correlation is not necessarily detailed in time. A more likely explanation involves the same electrons that also induce the continuum white light flare in the chromosphere, as discussed above. In some cases, however, optical and X-ray flares may be uncorrelated. Haisch et al. (1981) described an X-ray flare without an accompanying signal in the optical or the UV. Vice versa, Doyle et al. (1986) and Doyle et al. (1988b) reported Hγ and U band flares on YZ CMi with no indication of a simultaneous response in soft X-rays. They suggested that the heating occurred in low-lying loops in the transition region that did not reach coronal levels; alternatively, absorption of the X-rays by cold overlying material is a possibility, or heating by proton beams that are more efficient at inhibiting chromospheric evaporation.

12.15. Correlation with radio flares Similar to the case of U band flares, we expect that non-thermal radio events, produced by accelerated particles, precede X-ray flares. Reports on such correlations have been rather mixed. Kundu et al. (1988) described a poor correlation between X-ray events and radio flares observed during an EXOSAT-VLA joint survey program of dMe stars, although there may be contemporaneous flaring in the two wavelength regions (see also Kahler et al. 1982). Since this program was carried out at relatively long radio wavelengths (6 cm and 20 cm), the observed radio bursts were probably produced by a coherent emission process that requires relatively few electrons in an unstable energy distribution. We cannot expect a one-to-one correspondence in time for those cases. A special diagnostic case of correlated behavior can be observed for gyrosynchrotron radio flares at higher radio frequencies – see below.

12.16. The “Neupert Effect” Radio gyrosynchrotron, hard X-ray, and optical emissions are induced on time scales of the electron propagation (seconds), and therefore essentially develop proportionally to the influx of high-energy particles if long-term trapping does not occur. On the other hand, the cooling time of a thermal plasma in an extended coronal loop is governed by radiation and conduction with typical time scales of several minutes to hours. The X-ray radiation therefore develops roughly proportionally to the accumulating thermal coronal energy6 . To first order thus, for the radio (R), optical (O), and hard X-ray (HXR) luminosities, d LR,O,HXR (t) ∝ LX (t), (59) dt 6 We ignore the detailed evolution of the flare temperature and the density and thus the EM; the

evolution of T and ne may even be coupled, see Sect. 12.6; strictly speaking, in (59) one should refer to the thermal energy in the hot plasma rather than to the X-ray luminosity which may not be proportional to the former (see Güdel et al. 1996).


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a relation that has first been formulated for solar radio and X-ray flares (Neupert 1968) and that has become known as the “Neupert Effect”. It is a good diagnostic for the chromospheric evaporation process and has been well observed on the Sun in most impulsive and many gradual flares (Dennis and Zarro 1993). The search for stellar equivalents has been more challenging. Hawley et al. (1995) observed the dMe star AD Leo in the EUV (as a proxy for X-rays) and in the optical during extremely long gradual flares. Despite the long time scales and considerable time gaps in the EUV observations, the presence of the Neupert relation (59) was demonstrated (in its integrated form). Güdel et al. (1996) observed the similar dMe binary UV Cet during several shorter flares in X-rays and at radio wavelengths. A Neupert dependence between the light curves was clearly evident and was found to be very similar to the behavior of some gradual solar flares. Furthermore, the ratio between the energy losses in the two energy bands was derived to be similar to the corresponding luminosity ratio “in quiescence”. Similar results apply to RS CVn binaries: Osten et al. (2004) reported the Neupert effect in X-ray, EUV, and radio observations of HR 1099, again with radiative X-ray/radio energy ratios that are close to quiescent conditions. An example linking X-rays with white-light emission was presented by Güdel et al. (2002a) in observations obtained with XMM-Newton. The flare is illustrated in Fig. 28. Equation (59) is closely followed by the two light curves during the early part of the flare. The same temporal behavior was identified in a sequence of small flares during the same observation, suggesting that a considerable fraction of the low-level radiation is induced by temporally overlapping episodes of chromospheric evaporation. Although the relative timing provides important support for the evaporation model, the absolute energy content in the fast electrons must also be sufficient to evaporate and heat the observed plasma. Given the uncertain nature of the optical white-light flares, the energy content of the high-energy particles is difficult to assess. The situation is somewhat better at radio wavelengths although the spectral modeling of the non-thermal electron population is usually rather incomplete and order-of-magnitude. During a pair of gradual soft X-ray flares observed on the RS CVn binary σ Gem (Güdel et al. 2002b), (59) was again followed very closely, suggesting that electrons are capable of heating plasma over extended periods. The total injected electron energy was found to equal or possibly largely exceed the associated X-ray losses albeit with large margins of uncertainty. Essentially all of the released energy could therefore initially be contained in the fast electrons. Similar timing between radio and X-ray flare events is seen in previously published light curves, although the Neupert effect was not discussed. Notable examples include flares described by Vilhu et al. (1988), Stern et al. (1992b), Brown et al. (1998), and Ayres et al. (2001b). If optical emission is taken as a proxy for the radio emission, further examples can be found in Doyle et al. (1988b), Kahler et al. (1982), de Jager et al. (1986), and de Jager et al. (1989). The Neupert effect is observed neither in each solar flare (50% of solar gradual flares show a different behavior; Dennis and Zarro 1993), nor in each stellar flare. Stellar counter-examples include an impulsive optical flare with following gradual radio emission (van den Oord et al. 1996), gyrosynchrotron emission that peaks after the soft X-rays (Osten et al. 2000), an X-ray depression during strong radio flaring

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(Güdel et al. 1998), or the absence of any X-ray response during radio flares (Fox et al. 1994; Franciosini et al. 1999).

12.17. Non-thermal hard X-rays? In solar flares, non-thermal hard X-rays begin to dominate the spectrum beyond 15– 20 keV. Typically, these spectral components are power laws since the electron distributions in energy are power laws (Brown 1971). An ultimate test of the flare evaporation scenario in large flares on magnetically active stars would consist in the detection of non-thermal hard X-ray components during the soft X-ray flare rise. Observations with Ginga up to ≈ 20 keV initially seemed to suggest the presence of such emission in quiescence (Doyle et al. 1992a) although Doyle et al. (1992b) showed that an unrealistically large number of electrons, and therefore an unrealistically large rate of energy release, would be involved. A continuous emission measure distribution with a tail up to very 8 high temperatures, T > ∼ 10 K, can explain the data self-consistently, in agreement with previous arguments given by Tsuru et al. (1989). Up to the present day, no compelling evidence has been reported for non-thermal X-rays from stellar coronae. The Phoswich Detector System (PDS) instrument on board BeppoSAX was sensitive enough to detect photons up to 50–100 keV during large stellar flares, but all recorded spectra could be modeled sufficiently well with thermal plasma components. Examples include flares on UX Ari (Franciosini et al. 2001), AR Lac (Rodonò et al. 1999), Algol (Favata and Schmitt 1999), and AB Dor (Pallavicini 2001). The case of UX Ari is shown in Fig. 29. Although the PDS signal was strongest just

Fig. 29. X-ray spectra taken during a large flare on UX Ari by three detectors on board BeppoSAX. The histogram represents a fit based on thermal plasma components; it describes the data acceptably well up to about 40 keV (figure courtesy of E. Franciosini, after Franciosini et al. 2001)


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before the early peak phase of the flare when non-thermal contributions are indeed expected, this is also the phase when the hottest plasma is formed, so that the light curves make no strong argument in favor of non-thermal emission either. The same applies to observations of giant flares on AB Dor (Pallavicini 2001). An interesting suggestion for non-thermal contributions was put forward by Vilhu et al. (1993): the small equivalent width of the Fe K line at 6.7 keV during flares on AB Dor could be due to a continuum level that is enhanced by an additional non-thermal (power-law) component. The principal uncertainty is the location of a lower cut-off in the electron distribution and consequently the turnover in the non-thermal spectral contribution. Model calculations predict that this view is tenable only if the magnetic fields are weaker than 50 G (Vilhu et al. 1993). The elusive non-thermal X-ray components are a classic case for the absence of evidence not giving any evidence of absence: to the contrary, the very efficient production of non-thermal radio emission in many of these active coronae both during flares and during (putative) “quiescence” is clear proof that large numbers of high-energy electrons are present in active coronae. We need more sensitive detectors to trace their radiative signatures, which will hold unparalleled information on the primary energy release in stellar coronae.

13. The statistics of flares The study of coronal structure confronts us with several problems that are difficult to explain by scaling of solar coronal structure: i) Characteristic coronal temperatures increase with increasing magnetic activity (Sect. 9.5). ii) Characteristic coronal densities are typically higher in active than in inactive stars (Sect. 10), and pressures in hot loops can be exceedingly high (Sect. 11.2.2). iii) The maximum stellar X-ray luminosities exceed the levels expected from complete coverage of the surface with solar-like active regions by up to an order of magnitude (Sect. 11.4). iv) Radio observations reveal a persistent population of non-thermal high-energy electrons in magnetically active stars even if the lifetime of such a population should only be tens of minutes to about an hour under ideal trapping conditions in coronal loops (Güdel 2002) and perhaps much less due to efficient scattering of electrons into the chromosphere (Kundu et al. 1987). Several of these features are reminiscent of flaring, as are some structural elements in stellar coronae. If flares are important for any of the above stellar coronal properties indeed, then we must consider the effects of frequent flares that may be unresolved in our observations but that may make up part, if not all, of the “quiescent” emission.

13.1. Correlations between quiescent and flare emissions In 1985, three papers (Doyle and Butler 1985; Skumanich 1985; Whitehouse 1985) reported an unexpected, linear correlation between the time-averaged power from optical flares and the low-level, “quiescent” X-ray luminosity. This correlation could suggest that the mechanism that produces the optical flares also heats the plasma, that is, the quasi-steady, slowly varying X-ray emission may be the product of stochastic flaring. Pearce et al. (1992) showed that over the entire solar magnetic cycle, the monthly average

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soft X-ray luminosity scales in detail and linearly with the rate of detected Hα flares, again supporting a picture in which a continuous distribution of flares at least contributes to the overall coronal heating. This is echoed in the observation that stellar “quiescent” luminosity correlates approximately linearly with the rate of X-ray flares (above some lower energy threshold; Audard et al. 2000, Fig. 33a below). Güdel and Benz (1993) discussed a global relation between non-thermal radio luminosities of active stars and their “quiescent” X-ray luminosities. Since the short lifetime of MeV electrons in coronal magnetic fields implies frequent acceleration, a possible explanation again involves stochastic flares: the flare-accelerated electrons could themselves act as the heating agents via chromospheric evaporation. The smoking gun came with the observation that the total radio and X-ray outputs of solar flares follow the same correlation (Benz and Güdel 1994). Similarly, Haisch et al. (1990a) found that the ratio between energy losses in coronal X-rays and in the chromospheric Mg ii lines is the same in flares and in quiescence. This also applies if UV-filter observations are used instead of Mg ii fluxes (Mitra-Kraev et al. 2004). Finally, Mathioudakis and Doyle (1990) reported a tight correlation between LX and Hγ luminosity that it the same for flares and for “quiescence”. These observations point to an intimate relation between flares and the overall coronal emission.

13.2. Short-term coronal X-ray variability Further suggestive evidence for a connection between steady emission and coronal flares has come from the study of light curves. A strong correlation between Hγ flare flux and simultaneous low-level X-ray flux in dMe stars suggests that a large number of flare-like events are always present (Butler et al. 1986). Continuous low-level variability due to flares has been frequently reported for active M dwarfs in particular, but also for earliertype dwarfs (Pollock et al. 1991; Vilhu et al. 1993; Kürster et al. 1997; Mathioudakis and Mullan 1999; Gagné et al. 1999). Evidence has also been reported for giants, including stars close to saturation (Haisch and Schmitt 1994; Ayres et al. 2001a; Fig. 25) and hybrid stars (Kashyap et al. 1994). Montmerle et al. (1983) estimated from light curves that 50% of the observed X-ray emission in young stars in the ρ Oph star-forming region is due to relatively strong flares. Maggio et al. (2000) found low-level variability in the very active AB Dor at a level of 20–25% which they suggested to be due to ongoing low-level flaring (see similar conclusions by Stern et al. 1992b). When variability is studied for different plasma components, it is the hotter plasma that predominantly varies, while the cooler component is steady (Giampapa et al. 1996). An obvious suggestion is therefore that the high-temperature coronal component in active stars is the result of ongoing flaring.

13.3. Stochastic variability – what is “quiescent emission”? The problem has been attacked in several dedicated statistical studies. While Ambruster et al. (1987) found significant continuous variability on time scales of several minutes in an Einstein sample of M dwarfs, Collura et al. (1988) concluded, from a similar investigation based on EXOSAT data, that the low-level episodes are truly “quiescent”. Pallavicini et al. (1990a) found that approximately half of all investigated EXOSAT


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light curves show some residual variability, while the other half are constant. However, such statements can only be made within the limitations of the available sensitivity that also limits the ability to resolve fluctuations in time. Schmitt and Rosso (1988) and McGale et al. (1995) discussed and simulated in detail to what extent flares can be statistically detected in light curves as a function of the quiescent count rate, the relative flare amplitude, and the decay time. The essence is that a statistically significant number of counts must be collected during the finite time of a flare in order to define sufficient contrast against the “quiescent” background – otherwise the light curve is deemed constant. Higher sensitivity became available with ROSAT, and the picture indeed began to change. Almost all ROSAT X-ray light curves of M stars are statistically variable on short ( < ∼ 1 day) time scales (Marino et al. 2000); this applies to a lesser extent to F-K dwarfs (Marino et al. 2003b). More specifically, the light curve luminosity distribution evaluated over time scales of hours to days is very similar to the equivalent distribution derived for solar flares, which suggests that the overall stellar light curves of dM stars are variable in the same way as a statistical sample of solar flares (Marino et al. 2000). Such variability may thus dominate flux level differences in snapshot observations taken several months apart (Kashyap and Drake 1999). The EUVE satellite, while not being very sensitive, secured many observations from long monitoring programs that lasted up to 44 days. Some of these light curves reveal an astonishing level of continuous variability in main-sequence stars (Audard et al. 2000; Güdel et al. 2003a; Fig. 30), in RS CVn binaries (Osten and Brown 1999; Sanz-Forcada et al. 2002; Fig. 25), and in giants (Ayres et al. 2001a; Fig. 25). Some of those data were used to investigate statistical properties of the flare energy distribution (see Sect. 13.5). With the advent of the much increased sensitivity offered by XMM-Newton and Chandra, weaker flares were uncovered, and they occur – expectedly – at higher rates. Güdel et al. (2002a, 2004) presented sensitive X-ray light curves of Proxima Centauri in which no time intervals longer than a few tens of minutes could be described as constant

Fig. 30. A long light curve of the dMe star AD Leo, obtained by the DS instrument on EUVE. Most of the discernible variability is due to flares (after Güdel et al. 2003a)

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Chandra LETGS 0th order UV Ceti B

ct s−1

1.00

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0.01 52239.80

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MJD [d]

Fig. 31. Light curve of UV Ceti B, observed with the Chandra LETGS/HRC during about 1 day. Note the logarithmic flux axis (figure courtesy of M. Audard, after Audard et al. 2003b)

within the given sensitivity limit. Incidentally, this star was deemed constant outside obvious flares in the much less sensitive EXOSAT study by Pallavicini et al. (1990a). Frequent faint, flare-like X-ray fluctuations in this observation were often accompanied – in fact slightly preceded – by U band bursts, the latter being a signature of the initial bombardment of the chromosphere by high-energy electrons as discussed in Sect. 12.16. Audard et al. (2003b) estimated that no more than 30%, and probably much less, of the long-term average X-ray emission of UV Cet can be attributed to any sort of steady emission, even outside obvious, large flares. On the contrary, almost the entire light curve is resolved into frequent, stochastically occurring flares of various amplitudes (Fig. 31). Many further observations from the new observatories reveal almost continual flaring (Stelzer et al. 2002; Stelzer and Burwitz 2003; van den Besselaar et al. 2003; Raassen et al. 2003b). For active binaries, Osten et al. (2002) found that the flux distributions of the low-level emission significantly deviate from the Poisson distributions expected from a constant source, once again pointing to continual variability. 13.4. The solar analogy If variability is found in stellar light curves, its characteristic time scale is typically at least 3–5 minutes and often longer than 10 minutes (Ambruster et al. 1987; Pallavicini et al. 1990a; Güdel et al. 2002a). This motivated several authors to interpret low-level variability as being due to slow reconfigurations of active regions and emerging flux rather than due to stochastic flaring. The latter was expected to reveal itself in the form of short-term fluctuations, recalling the concept of “microflaring” in the solar corona. There is, however, a widespread misconception that should briefly be discussed. A popular opinion has it that larger flares last longer, and that microvariability in stars should therefore express itself in short-term flickering. This view is not entirely correct. Statistical studies of solar flares usually do not find clear evidence for a dependence between flare duration and flare amplitude over quite wide a range in energy (Pearce and


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Harrison 1988; Feldman et al. 1997; Shimizu 1995). The distributions are dominated by the scatter in the duration, with durations ranging from 1 to 20 minutes even in the domain of quite small solar events. Aschwanden et al. (2000b) investigated scaling laws from solar nanoflares to large flares, covering 9 orders of magnitude in energy. They reported that the radiative and conductive time scales do not depend on the flare size. Güdel et al. (2003a) inspected the brightest flares in a long-duration EUV observation of AD Leo, again finding no trend. The latter authors also studied the sample of selected large flares from different stars reported by Pallavicini et al. (1990a); although a weak trend was found if four orders of magnitude in energy were included (τ ∝ E 0.25 ), the scatter again dominated, and it is unclear what form of selection bias was introduced given that the sample consists only of well-detected bright flares (for the same reason, I refrain from performing statistics with the flares in Table 4; both the decay times and the total energies are subject to selection bias). In fact, the claim that light curves are strictly bi-modal, separating detected flares from truly quiescent episodes, is tantamount to requiring that the peak flux of each flare must exceed a certain fraction of the “quiescent” emission level; since this level varies over at least 6 orders of magnitude in cool stars, the most luminous stars would be bound to produce only flares that exceed the largest solar events by many orders of magnitude, biased such that they are detected by available detectors. This view is not supported by solar observations: the solar flare rate increases steeply toward lower radiative energies, with no evidence (yet) for a lower threshold (e.g., Krucker and Benz 1998). Figure 32 shows an example of a GOES light curve in the 1.5-12 keV range, purposely selected during an extremely active period in November 2003. While the GOES band is harder than typical bands used for stellar observations, it more clearly reveals the level of the underlying variability (a typical detector used for stellar observations would see much less contrast). If the solar analogy has any merit in interpreting stellar coronal X-rays, then low-level emission in stars that do show flares cannot be truly quiescent, that is, constant or slowly varying exclusively due to long-term evolution of active regions, or due to rotational modulation. A measure of flare rates is therefore not meaningful unless

Fig. 32. GOES full-disk solar X-ray light curve, observed in the 1.5–12 keV band in November 2003. The abscissa gives time after 2003 November 1, 7:12 UT in days

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it refers to flares above a given luminosity or energy threshold. This is – emphatically – not to say that steady emission is absent. However, once we accept the solar analogy as a working principle, the question is not so much about the presence of large numbers of flares, but to what extent they contribute to the overall X-ray emission from coronae.

13.5. The flare-energy distribution The suggestion that stochastically occurring flares may be largely responsible for coronal heating is known as the “microflare” or “nanoflare” hypothesis in solar physics (Parker 1988). Observationally, it is supported by evidence for the presence of numerous smallscale flare events occurring in the solar corona at any time (e.g., Lin et al. 1984). Their distribution in energy is a power law, dN = kE −α dE

(60)

where dN is the number of flares per unit time with a total energy in the interval [E, E + dE], and k is a constant. If α ≥ 2, then the energy integration (for a given time interval) diverges for Emin → 0, that is, by extrapolating the power law to sufficiently small flare energies, any energy release power can be attained. This is not the case for α < 2. Solar studies have repeatedly resulted in α values of 1.6 − 1.8 for ordinary solar flares (Crosby et al. 1993), but some recent studies of low-level flaring suggest α = 2.0 − 2.6 (Krucker and Benz 1998; Parnell and Jupp 2000). Relevant stellar studies have been rare (see Table 5). Early investigations lumped several stars together to produce meaningful statistics. A set of M dwarf flares observed with EXOSAT resulted in α ≈ 1.5 (Collura et al. 1988), and similarly, the comprehensive study by Pallavicini et al. (1990a) of an EXOSAT survey of M dwarfs implied α ≈ 1.7. Osten and Brown (1999) used EUVE data to perform a similar investigation of flares on RS CVn-type binaries, and again by lumping stellar samples together they inferred α ≈ 1.6. However, several biases may affect statistical flare studies, all related to the illdetermined problem of flare identification in stellar observations. First, detecting flares Table 5. Stellar radiative flare-energy distributions Star sample

Photon energies [keV]

log (Flare energies)a

α

References

M dwarfs M dwarfs RS CVn binaries Two G dwarfs F-M dwarfs Three M dwarfs AD Leo AD Leo

0.05–2 0.05–2 EUV EUV EUV EUV EUV and 0.1–10 EUV

30.6 − 33.2 30.5 − 34.0 32.9 − 34.6 33.5 − 34.8 30.6 − 35.0 29.0 − 33.7 31.1 − 33.7 31.1 − 33.7

1.52±0.08 1.7±0.1 1.6 2.0–2.2 1.8–2.3 2.2–2.7 2.0–2.5 2.3 ± 0.1

Collura et al. (1988) Pallavicini et al. (1990a) Osten and Brown (1999) Audard et al. (1999) Audard et al. (2000) Kashyap et al. (2002) Güdel et al. (2003a) Arzner and Güdel (2004)

a Total flare-radiated X-ray energies used for the analysis (in ergs).

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Number of flares per day of energy > E

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1

1032 1033 Total X−radiated energy E [0.01−10 keV] in ergs

Fig. 33. Left: The rate of flares above a threshold of 1032 erg in total radiated X-ray energy is plotted against the low-level luminosity for several stars, together with a regression fit. Right: Flare energy distribution for AD Leo, using a flare identification algorithm for an observation with EUVE (both figures courtesy of M. Audard, after Audard et al. 2000)

in light curves is a problem of contrast. Poisson counting statistics increases the detection threshold for flares on top of a higher continuous emission level. The low-energy end of the distribution of detected flares is therefore ill-defined and is underrepresented. Further, large flares can inhibit the detection of the more numerous weak flares during an appreciable fraction of the observing time. And lastly, the detection threshold also depends on stellar distance; by lumping stars together, the low-energy end of the distribution becomes invariably too shallow. To avoid biases of this kind, Audard et al. (1999) and Audard et al. (2000) applied a flare search algorithm to EUVE light curves of individual active main-sequence stars, taking into account flare superpositions and various binning to recognize weak flares, and performing the analysis on individual light curves. Their results indicate a predominance of relatively steep power laws including α ≥ 2 (an example is shown in Fig. 33b). Full forward modeling of a superposition of stochastic flares was applied to EUV and X-ray light curves by Kashyap et al. (2002) and Güdel et al. (2003a) based on Monte Carlo simulations, and by Arzner and Güdel (2004) based on an analytical formulation.7 The results of these investigations are in full agreement, converging to α ≈ 2.0 − 2.5 for M dwarfs (Table 5). If the power-law flare energy distribution extends by about 1–2 orders of magnitude below the actual detection limit in the light curves, then the entire emission could be explained by stochastic flares. The coronal heating process in magnetically active stars would – in this extreme limit – be one solely due to timedependent heating by flares, or, in other words, the X-ray corona would be an entirely hydrodynamic phenomenon rather than an ensemble of hydrostatic loops.

7 Note that the distribution of measured fluxes does not describe the flare amplitude distribution. The problem of inverting the former to obtain the latter was analytically solved by Arzner and Güdel (2004).

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13.6. Observables of stochastic flaring In order for stochastic flaring to be an acceptable coronal heating mechanism, it should explain a number of X-ray observables. Flares develop characteristically in EM and T (fast rise to peak, slow decay). Therefore, the superposition of a statistical ensemble of flares produces a characteristic time-averaged DEM. For simple flare decay laws, the resulting DEM is analytically given by (14) that fits observed, steeply rising DEMs excellently (Güdel et al. 2003a). An extension of the Kopp and Poletto (1993) formalism can be used numerically to find approximations of a DEM that results by time-averaging the EM(T , t) of a population of cooling, stochastic flares drawn from a distribution with a prescribed α; these DEMs show two characteristic maxima, the cooler one being induced by the large rate of small flares, and the hotter one being due to the few large flares with high temperature and EM, somewhat similar to double-peaked DEMs that were derived from observations; in this interpretation, the higher rate of larger flares in more active stars shifts the EM to higher temperatures, as has been found in evolutionary sequences of solar analogs (Güdel et al. 1997a; Güdel 1997; Skinner and Walter 1998). As for the light curves, the superposition of stochastically occurring flares produces an apparently steady baseline emission level that is constantly present and that may be mistaken for a truly quiescent component (Kopp and Poletto 1993), in particular for large α values in (60). Figure 34 shows simulations of superimposed flares drawn from

Flare amplitude depth = 10

2•1027

2•1027

1•1027

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0 0

Proxima Centauri, XMM−Newton

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luminosity (erg s−1)


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0 0

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4•1029 Flare amplitude depth = 1000

YY Gem, XMM−Newton

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1•1029 1•1029

0 0

1•104

2•104 time (s)

3•104

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0 0

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Fig. 34. X-ray light curves. Left panels: Synthetic light curves from superimposed flares; largest to smallest amplitude = 10 (upper) and 1000 (lower plot). No truly quiescent emission has been added. A giant flare on Proxima Centauri (Güdel et al. 2002a) has been used as a shape template, shown filled in the lower plot for the maximum amplitude contributing to the light curve. Right panels: Observed X-ray light curves for comparison. Proxima Centauri (upper plot, Güdel et al. 2004) and YY Gem (lower plot, including eclipse; after Güdel et al. 2001a)


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a power-law distribution with α = 2.2, compared with observations. No truly steady emission has been added. The large flare observed on Proxima Centauri (Güdel et al. 2004) was used as a shape template from which all flares in the simulation were scaled. The first example uses flare energies spread over a factor of ten only, the second uses three orders of magnitude. In the latter case, the light curve has smoothed out to an extent that it is dominated by “quiescent” emission. This effect is stronger for larger α. The individual peaks are merely the peaks of the most energetic flares in the ensemble. For small (dM) stars, the available stellar area may in fact constrain the energy range of stochastic flares because flaring active regions may cover a significant fraction of the surface, which limits the number of simultaneous flares (see upper example in Fig. 34, e.g., Proxima Centauri) and thus makes lower-mass stars statistically more variable. Finally, spectroscopic density measurements of a time-integrated, stochastically flaring corona should yield values equivalent to the densities derived from time-integrating the spectrum of a large flare. There is suggestive evidence in support of this. While large stellar X-ray flares achieve peak electron densities of several times 1011 cm−3 , the time-integrated X-ray spectrum of the Proxima Centauri flare described by Güdel et al. (2002a, 2004) (Fig. 28) yields a characteristic density of log ne ≈ 10.5 ± 0.25 derived from O vii triplet, which compares favorably with densities in magnetically active MS stars during low-level emission (Ness et al. 2001, 2002a, Sect. 10.2).

14. X-ray absorption features and prominences X-ray spectra are sensitive to photoelectric absorption by cooler foreground gas. The absorption column is a powerful diagnostic for the amount of cool circumstellar gas although little can be said about its distribution along the line of sight. X-ray attenuation by the interstellar medium is generally weak for field stars within a few 100 pc, but it becomes very prominent for deeply embedded stars in star formation regions, or stars that are surrounded by thick accretion disks. However, anomalous absorption is sometimes also recorded in more solar-like, nearby stars, in particular during large flares. The observed column densities may vary by typically a factor of two on short time scales. Examples were presented by Haisch et al. (1983) for Proxima Cen, Ottmann and Schmitt (1996) for Algol, and by Ottmann and Schmitt (1994) for AR Lac. Much larger absorption column densities have occasionally been measured, up to 4 × 1022 cm−2 in a flare on V733 Tau (Tsuboi et al. 1998) and 3 × 1021 cm−2 in the course of a large flare on Algol (Favata and Schmitt 1999). The cause of this anomalous absorption is not clear. From the solar analogy, it is possible that prominences related with the flare region pass in front of the X-ray source and temporarily shadow part of it. Coronal mass ejections sometimes accompany solar flares. If the material cools sufficiently rapidly by radiation and expansion, it may also attenuate the X-rays. The detection of ejected mass is of some relevance in binaries. In systems like Algol, the mass may flow onto the binary companion or form a temporary accretion disk around it (Stern et al. 1992a). This could explain why excess absorption has been found also during low-level emission episodes in several Algol-type binaries (Singh et al. 1995). In rapidly rotating single stars, increased amounts of hydrogen may condense out of large cooling loops that grow unstable near their apexes, a suggestion that has

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found direct support in optical observations of AB Dor (e.g., Collier Cameron 1988; Donati 1999).

15. Resonance scattering and the optical depth of stellar coronae When studies of the initial spectra from the EUVE satellite encountered unexpectedly low line-to-continuum ratios (e.g., Mewe et al. 1995), line suppression by optical depth effects due to resonant scattering in stellar coronae surfaced as one possible explanation (Schrijver et al. 1994). Although we nowadays attribute these anomalies mostly to abundance anomalies and to an excess “pseudo”-continuum from weak lines, a search for non-zero optical depths in coronae is worthwhile because it may be used as another tool to study coronal structure. Non-negligible optical depths would also affect our interpretation of stellar coronal X-ray spectra for which we usually assume that the corona is entirely optically thin. Resonant scattering requires optical depths in the line centers of τ > ∼ 1. The latter is essentially proportional to ne /T 1/2 (Mewe et al. 1995). For static coronal loops, this implies τ ∝ T 3/2 (Schrijver et al. 1994; e.g., along a loop or for a sample of nested loops in a coronal volume). Numerical values for τ are given in Schrijver et al. (1994) and Mewe et al. (1995) for several EUV lines. If the optical depth in a line is significant in a coronal environment, then the absorbed photon will be re-emitted (“scattered”) prior to collisional de-excitation. Continuum photons, on the other hand, are much less likely to be scattered. The effects of resonant line scattering into and out of the line of sight, however, cancel in a homogeneous source, but the stellar surface that absorbs down-going photons breaks the symmetry: The line-to-continuum ratio is reduced if the emitting volume is smaller than the scattering volume and lies closer to the stellar surface (Schrijver et al. 1994; Mewe et al. 1995). This situation is fulfilled in a corona since the scattering efficiency decreases only with ne while the emissivity decreases more rapidly, ∝ n2e . Schrijver et al. (1994) predicted suppression of the line fluxes by up to a factor of two in the most extreme cases. A number of applications to EUVE spectra from stars at different activity levels have been given by Schrijver et al. (1995). The authors concluded that significant optical depths may be present in particular in inactive stars such as α Cen and Procyon. The scattering layer would most probably be an extended hot envelope or a stellar wind. This interpretation was subsequently challenged, however, by Schmitt et al. (1996a) in a detailed study of the EUV continuum and a comparison of flux levels in the ROSAT spectral range. They attributed the anomalously low line-to-continuum ratios to an excess EUV continuum that builds up from the superposition of many weak lines that are not tabulated in present-day codes. In the X-ray range, the usually strong Ne-like Fe xvii lines provide excellent diagnostics. The Fe xvii λ15.01 line is often chosen for its large oscillator strength. Its flux is compared with the fluxes of Fe xvii lines with low oscillator strengths such as those at 15.26 Å and at 16.78 Å. There is considerable uncertainty in the atomic physics, however, that has equally affected interpretation of solar data. While Schmelz et al. (1997) and Saba et al. (1999) found evidence for optical depth effects in the Fe xvii λ15.01 line, recent laboratory measurements of the corresponding flux ratios differ significantly from


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previous theoretical calculations (Brown et al. 1998, 2001; Laming et al. 2000). New calculations have recently been presented by, for example, Doron and Behar (2002). Stellar coronal optical depths have become accessible in the X-ray range with Chandra and XMM-Newton. No significant optical depth effects were found for Fe xvii λ15.01 for a restricted initial sample of stars such as Capella and Procyon (Brinkman et al. 2000; Ness et al. 2001; Mewe et al. 2001; Phillips et al. 2001). Ness et al. (2001) calculated upper limits to optical depths based on measured EM and electron densities, assuming homogeneous sources. They found no significant optical depths although none of these stars is very active. Huenemoerder et al. (2001), Ness et al. (2002b) and Audard et al. (2003a) extended the Fe xvii diagnostics to the high end of magnetic activity, viz. II Peg, Algol and a sample of RS CVn binaries, respectively, but again reported no evidence for optical depth effects. The problem was comprehensively studied by Ness et al. (2003a) in a survey of 26 stellar coronae observed with XMM-Newton and Chandra across all levels of activity. They again used the Fe xvii λ15.27/λ15.01 and λ16.78/λ15.01 diagnostics as well as the ratios between the resonance and the forbidden lines in He-like line triplets of O vii and Ne ix. Many line ratios are at variance with solar measurements and with calculated predictions, but the latter themselves are uncertain (see above). The interesting point is, however, that the flux ratios are similar for all stars except for those with the very coolest coronae for which line blends are suspected to bias the flux measurements. Ness et al. (2003a) concluded that optical depth effects are absent on all stars at least in the relevant temperature regime, rather than requiring non-zero but identical optical depth in such variety of stellar coronae. These conclusions also extend to line ratios in Lyα series (e.g., Lyα:Lyβ for O viii, Ne x, or Si xiv, Huenemoerder et al. 2001; Osten et al. 2003). Related effects were previously considered, but also questioned, for the Fe K complex at 6.7–7 keV in intermediate-resolution observations (Tsuru et al. 1989; Stern et al. 1992a; Singh et al. 1996a). Lastly, Güdel et al. (2004) measured Fe xvii flux ratios during a strong flare on Proxima Centauri but again found neither discrepant values nor a time evolution that would contradict an optically thin assumption. To conclude, then, it appears that no X-ray optical depth effects have unambiguously been detected in any stellar corona investigated so far, notwithstanding the large range of geometries, temperatures, and densities likely to be involved in stars across the spectrum of activity, including large flares. Further checks of individual cases or of large flares remain worthwhile, however, given the potential diagnostic power of resonant scattering effects.8

16. The elemental composition of stellar coronae It is quite well established that the solar corona and the solar wind show an elemental composition at variance with the composition of the solar photosphere. Whatever the reason for the discrepancy, our interest in understanding element abundances in stellar coronae is twofold: Observationally, because they shape the X-ray spectra from which we 8 Note added in proof: A recent report by Testa et al. (2004, ApJ, 609, L79) indicates evidence

of resonance scattering in Lyα/Lyβ line-flux ratios of O viii and Ne x in the RS CVn binaries II Peg and IM Peg. The inferred path lengths vary between 2 × 10−4 R∗ and 4 × 10−2 R∗ .

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derive basic coronal parameters; and physically, because abundance anomalies reflect diffusion processes and element fractionation mechanisms in the chromosphere and transition region, and possibly the physics of mass transport into the corona.

16.1. Solar coronal abundances: A brief summary Measurements of the composition of the solar corona have revealed what is commonly known as the “First Ionization Potential (FIP) Effect”: Essentially, elements with a FIP above ≈ 10 eV (e.g., C, N, O, Ne, Ar) show photospheric abundance ratios with respect to hydrogen, while elements with a smaller FIP (e.g., Si, Mg, Ca, Fe) are overabundant by a factor of a few. This picture was comprehensively summarized in the extensive work by Meyer (1985a,b) who showed that the same FIP effect is also present in the solar wind, in solar energetic particles, and – quite surprisingly – in cosmic rays.9 The latter finding immediately suggested that the seeds of cosmic rays may perhaps be ejected by active stellar coronae that are subject to a similar, solar-like abundance anomaly. An extension of the currently accepted picture was given by Feldman (1992) who discussed abundance anomalies in various solar features, pointing out that the degree of the FIP anomaly varies from feature to feature. I refer the interested stellar reader to the extensive solar literature on the solar FIP effect, and in particular to a review of solar FIP models by Hénoux (1995), overviews presented by Jordan et al. (1998) and in the papers by Drake et al. (1995b) and Laming et al. (1995). I only briefly summarize a few principal points. Current thinking is that a fractionation process, probably involving electric and/or magnetic fields or pressure gradients, occurs at chromospheric levels where low-FIP elements are predominantly ionized and high-FIP elements are predominantly neutral. Ions and neutrals are then affected differently by electric and magnetic fields. A successful model for the FIP effect will eventually have to explain why and how low-FIP elements are transported into the corona at an enhanced rate. The FIP effect is most pronounced in relatively evolved solar coronal features such as old loops, but also in magnetically open regions. In contrast, young, compact active regions and newly emerged structures reveal photospheric composition. The latter mixture is also most evident in flares, which suggests that new material is brought up from photospheric/chromospheric layers that has not been subject to fractionation. Notable exceptions exist, such as Ca-rich flares (Sylwester et al. 1984), and Ne-rich flares (Schmelz 1993). In the light of the diverse FIP anomalies in the solar corona, stellar observations should obviously be compared with Sun-as-a-star data. To this end, Laming et al. (1995) have studied the FIP anomaly by making use of full-disk solar spectra. While they confirmed the presence of an overall coronal enrichment of low-FIP elements by factors of about 3–4, they somewhat surprisingly reported an absence of a FIP bias at subcoronal temperatures (< 1 MK). They suggested that the strength of the FIP effect is in fact 9 I note in passing that Meyer normalized the abundances such that the low-FIP element abun-

dances were photospheric and the high-FIP abundances depleted, whereas present-day wisdom has the high-FIP elements at photospheric levels, and the low-FIP elements enriched in the corona (Feldman 1992).


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a function of altitude, with the lower-temperature emission being dominated by the supergranulation network that shows photospheric abundances. 16.2. Stellar coronal abundances: The pre-XMM-Newton/Chandra view Early X-ray observatories typically lacked the spectral resolution required to make solid statements about coronal abundances. Some indications of possible depletions of Fe were reported during very strong flares, as will be summarized in Sect. 16.6. Also, some early medium-resolution spectra apparently required “anomalous abundances” for a successful model fit (Walter et al. 1978b; Swank et al. 1981). Despite these initial developments, element abundances became a non-issue as the available detectors simply did not permit their unambiguous determination. It was customary to adopt a coronal composition equal to the solar photospheric mixture. The basis for this assumption is that most stars in the solar neighborhood belong to Population I, and for these stars we expect a near-solar composition, even if the Sun is a somewhat metal-rich star. On the other hand, the known FIP bias of the solar corona should be more of a concern when interpreting stellar spectra, but the large variations in the solar coronal composition would have made any “standard coronal abundance” tabulation quite arbitrary. As we now know, adopting such a coronal standard would have been useless. When ASCA introduced routine medium-resolution X-ray spectroscopy based on CCD technology with a resolving power of R ≈ 10 − 30, and EUVE allowed for wellresolved EUV line spectroscopy with R ≈ 300, some classes of magnetically active stars started to show perplexing abundance features that were neither comparable with those of the solar corona nor compatible with any pattern expected from the photospheric composition (which is often not well determined either). The only way to reconcile thermal models with the observed CCD spectra was to introduce depleted abundances in particular of Mg, Si, and Fe but also of other elements (White et al. 1994; N. White 1996; Antunes et al. 1994; Gotthelf et al. 1994; S. Drake et al. 1994a; S. Drake 1996; Singh et al. 1995, 1996a; Mewe et al. 1996; Kaastra et al. 1996). Abundances of Fe as low as 10–30% of the solar photospheric value were regularly reported. Little in the way of systematic trends was present for the various other elements (S. Drake 1996; Kaastra et al. 1996). Some observations with ASCA indicated the presence of a “relative” FIP effect because the high-FIP elements were more depleted than the low-FIP elements while all abundances were subsolar, but the evidence was marginal and was not followed by Fe (S. Drake et al. 1994a; Tagliaferri et al. 1997; Güdel et al. 1997a for Mg). Generally, metal depletion was found to be strongest in the most active stars (Singh et al. 1995, 1999; S. Drake 1996). EUVE confirmed the considerable metal depletion for magnetically active stars based on unexpectedly low Fe line-to-continuum ratios (Stern et al. 1995a). Extreme cases such as CF Tuc showed almost no Fe lines, requiring Fe abundances as low as 10% solar (Schmitt et al. 1996d). Further examples of significant metal depletion were reported by Rucinski et al. (1995) and Mewe et al. (1997). EUVE spectra, however, also revealed a solar-like FIP-related bias, but this was found exclusively for weakly or intermediately active stars such as α Cen (Drake et al. 1997), Eri (Laming et al. 1996) and ξ Boo A (Laming and Drake 1999; Drake and Kashyap 2001). Mewe et al. (1998a) found further indications for a FIP effect in α Cen also from

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ASCA observations, but no magnetically active stars were ever reported with a similar coronal composition. Cosmic rays thus no longer appeared to be related to active stars as far as the abundance mix was concerned (Drake et al. 1995b). A peculiarity was found for the inactive Procyon, namely identical coronal and photospheric compositions (Drake et al. 1995a,b). A possible cause of this anomaly among anomalies is that the supergranulation network, assumed to be of photospheric composition as in the solar case, reaches to higher temperatures. As discussed in Sect. 9.3, the X-ray spectroscopic abundance determination is strongly tangled with the derivation of the DEM, and the caveats and debates described there apply here. The problem is particularly serious in low-resolution X-ray spectra, as discussed by Singh et al. (1999) and Favata et al. (1997a). Despite a decent capability of CCD detectors to recover temperatures and EMs, some caveats apply to the abundance determination in particular if the considered spectral ranges are too restricted. The state of the field remained unsatisfactory, and the lack of systematics made much of the physical interpretation quite ambiguous. 16.3. Stellar coronal abundances: New developments with XMM-Newton and Chandra At least some clarification came with the advent of high-resolution X-ray grating spectroscopy. Early observations of HR 1099 and AB Dor with the XMM-Newton Reflection Grating Spectrometer uncovered a new, systematic FIP-related bias in magnetically active stars: in contrast to the solar case, low-FIP abundances are systematically depleted with respect to high-FIP elements (Brinkman et al. 2001; Güdel et al. 2001b; Audard et al. 2001a; Fig. 35), a trend that has been coined the “inverse FIP effect” (IFIP). As a consequence of this anomaly, the ratio between the abundances of Ne (highest FIP) and Fe (low FIP) is unusually large, of order 10, compared to solar photospheric conditions.

Fig. 35. Inverse FIP effect in the corona of HR 1099. The coronal element abundance ratios with respect to oxygen and normalized to the solar photospheric ratios are plotted as a function of the FIP of the respective element (after Brinkman et al. 2001)


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These trends have been widely confirmed for many active stars and from the various gratings available on XMM-Newton or Chandra (e.g., Drake et al. 2001; Huenemoerder et al. 2001, 2003; Raassen et al. 2003b; van den Besselaar et al. 2003, to name a few). With respect to the hydrogen abundance, most elements in active stars remain, however, depleted (Güdel et al. 2001a,b; Audard et al. 2001a), and this agrees with the overall findings reported previously from low-resolution spectroscopy. Strong Ne enhancements can be seen, in retrospect, also in many low-resolution data discussed in the earlier literature, and the IFIP trend has now also been traced into the pre-main sequence domain by Imanishi et al. (2002). When stellar spectra covering a wide range of magnetic activity are compared, only highly active stars show the presence of an IFIP pattern. In intermediately active stars, flat abundance distributions are recovered (Audard et al. 2003a). The abundances revert to a normal, solar-type FIP anomaly for stars at activity levels of log LX /Lbol < ∼ −4 (Güdel et al. 2002c; Telleschi et al. 2004, Fig. 36). Whenever the IFIP pattern is present, all abundances appear to be sub-solar, but the Fe/H abundance ratio gradually rises with decreasing coronal activity. The transition from an IFIP to a solar-like FIP abundance pattern and from very low Fe abundances to mild depletion seems to coincide with i) the transition from coronae with a prominent hot (T > ∼ 10 MK) component to cooler coronae, and ii) with the transition from prominent non-thermal radio emission to the absence thereof (Güdel et al. 2002c). In order to illustrate the above trends more comprehensively, Table 6 summarizes a few important parameters from recent abundance determinations based on high-resolution spectroscopy. The table gives absolute Fe abundances, ratios of the high-FIP elements O and Ne with respect to Fe, and the ratios between the two low-FIP element abundances of Mg and Fe and between the two high-FIP element abundances of Ne and O. Direct comparison of reported abundances should generally be treated with caution because various solar photospheric standards have been adopted. As far as possible, I

Fig. 36. Coronal abundance determination for solar analogs. Left: 47 Cas, a very active nearZAMS star; right: χ 1 Ori, an intermediately active solar analog. Abundances are given relative to Fe, and refer to solar photospheric abundances as given by Anders and Grevesse (1989) and Grevesse and Sauval (1999). Filled circles refer to determinations that used selected line fluxes of Fe for the DEM reconstruction; open circles show values found from a full spectral fit (figures courtesy of A. Telleschi, after Telleschi et al. 2004)

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M. Güdel Table 6. Element abundancesa from high-resolution spectroscopy

Star

Ib

T¯

Fe

Ne/Fe

O/Fe

Mg/Fe

Reference

Procyon Procyon Procyon α Cen A α Cen B Prox Cen Eri χ 1 Ori κ 1 Cet π 1 UMa AD Leo AD Leo Capella Capella Capella YY Gem σ 2 CrB EK Dra AT Mic 47 Cas AB Dor AB Dor V851 Cen λ And λ And VY Ari Algol HR 1099 HR 1099 HR 1099 HR 1099 AR Lac UX Ari II Peg

L L R L L R L R R R R L R R L R H R R R R R R H R R L H R R R H R H

1.4 1.45 1.8 1.5 1.8 3.7 4.0 4.4 4.5 4.5 5.8 6.1 5.0 6.5 6.5 7.6 9 9.1 9.2 10.6 10.0 11.4 11 11 13.2 11.3 12 13 14 14.4 14.8 15 15.1 16

0.66 0.98 1.1 1.36 1.43 0.51 0.74 0.87 1.18 0.81 0.34 0.39 0.92 0.84 1.0 0.21 0.46 0.72 0.30 0.50 0.40 0.33 0.56 0.37 0.2 0.18 0.25 0.30 ... 0.22 0.20 0.74 0.14 0.15

1.5 1.08 1.04 0.37 0.38 1.6 1.35 0.73 0.95 0.62 2.5 3.43 0.64 0.50 0.5 3.62 1.40 1.01 4.8 1.68 4.8 3.04 5.5 2.23 5.3 7.0 2.61 10 15.6 4.2 6.6 2.16 13.4 14.9

1.0 0.37 0.68 0.3 0.23 0.6 0.53 0.33 0.39 0.32 1.21 1.64 0.32 0.50 0.48 1.42 0.55 0.51 3.2 0.70 2.23 1.22 1.76 1.35 1.75 2.2 0.99 3.0 3.9 1.55 2.75 0.81 4.0 7.4

1.1 1.66 ... 1.01 1.12 2.1 0.95 1.12 1.94 1.24 1.13 0.6 1.22 1.08 0.91 0.81 0.99 1.54 1.4 2.21 0.95 0.83 1.6 1.56 2.95 1.83 1.37 2.5 3.7 0.45 0.9 0.95 2.21 2.7

Raassen et al. (2002) Sanz-Forcada et al. (2004) Raassen et al. (2002) Raassen et al. (2003a) Raassen et al. (2003a) Güdel et al. (2004) Sanz-Forcada et al. (2004) Telleschi et al. (2004)c Telleschi et al. (2004)c Telleschi et al. (2004)c van den Besselaar et al. (2003) van den Besselaar et al. (2003) Audard et al. (2003a) Audard et al. (2001b) Argiroffi et al. (2003) Güdel et al. (2001a) Osten et al. (2003) Telleschi et al. (2004)c Raassen et al. (2003b) Telleschi et al. (2004)c Sanz-Forcada et al. (2003) Güdel et al. (2001b) Sanz-Forcada et al. (2004) Sanz-Forcada et al. (2004) Audard et al. (2003a) Audard et al. (2003a) Schmitt and Ness (2004) Drake et al. (2001) Brinkman et al. (2001) Audard et al. (2001a) Audard et al. (2003a) Huenemoerder et al. (2003) Audard et al. (2003a) Huenemoerder et al. (2001)

aAll abundance relative to solar photospheric values: Anders and Grevesse (1989)

except for Fe: Grevesse and Sauval (1999) b Instrument: R = XMM-Newton RGS; H = Chandra HETGS; L = Chandra LETGS c Based on their method 2 using the SPEX database

transformed the abundances to refer to the solar values of Anders and Grevesse (1989) except for Fe, for which I adopted the value given by Grevesse and Sauval (1999). No attempt has been made to quote error estimates. Errors are extremely difficult to assess and include systematics from calibration problems and from the inversion method, and most importantly uncertainties in the atomic parameter tabulations. It is unlikely that any measurement represents its “true” value within better than 20%. The average coro-


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Ne/Fe

Abundance ratio

Abundance

10

1.0

1

Fe Ne

0.1 0

5 10 Average temperature (MK)

0

15

10.0

15


15

10.0 Mg/Fe O/Ne

O/Fe

Abundance ratio

Abundance ratio


1.0

0.1

1.0

0.1

0


15

0

Fig. 37. Abundances as a function of the average coronal temperature from high-resolution spectroscopy with XMM-Newton and Chandra. Top left: Abundances of Fe (filled circles) and Ne (open circles), relative to solar photospheric values for the sample reported in Table 6. Top right: Similar, but the ratio between the Fe and Ne abundance is shown. Lower left: Similar, for the Mg/Fe (filled) and O/Ne ratios (open circles). Lower right: Similar, for the O/Fe ratio. Lines connect points referring to the same star analyzed by different authors, or based on different observations

nal temperature was estimated either from the logarithmic EMD, EM(log T ), or was calculated as the EM-weighted mean of log T in the case of numerically listed EMDs or results from multi-T fits. Figure 37 shows the relevant trends. Clearly, the low-FIP elements (Mg, Fe) vary in concert, and so do the high-FIP elements (O, Ne). But the absolute Fe abundance significantly drops with increasing activity, and the Ne/Fe ratio sharply increases as a consequence. The trend for O/Fe is very similar, with ratios that are lower by typically a factor of two. The transition from the FIP to the IFIP pattern for O/Fe occurs at average temperatures of about 7–10 MK.10 10 The trends are independent of the spectral inversion method used to determine the abundances

and the EMD; 17 spectra were fitted as a whole, while 17 spectra were analyzed with various iterative inversion methods using extracted line fluxes; both subsamples show identical trends.

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16.4. Systematic uncertainties The abundance results presently available from high-resolution spectroscopy refer to data from different detectors, and various methods have been used to analyze the spectra. Some systematic deviations are found when we compare the reported abundance values (see Table 6). This comes as no surprise if we recall the discussion in Sect. 9.3 on the various difficulties inherent in the spectral inversion problem. Nevertheless, the situation is not as bad as it might appear, in particular once we review the actual needs for a physical model interpretation. I discuss examples from the recent literature, including some results from medium-resolution observations. Capella has been a favorite target for case studies given its very high signal-to-noise spectra available from various satellites. Despite some discrepancies, the abundances derived from ASCA, EUVE (Brickhouse et al. 2000), BeppoSAX (Favata et al. 1997c), XMM-Newton (Audard et al. 2001b), and Chandra (Mewe et al. 2001) agree satisfactorily: Fe and Mg are close to solar photospheric values (see Sect. 16.5 below). Several analyses have been presented for the RS CVn binary HR 1099 (for example by Brinkman et al. 2001; Audard et al. 2001a; Drake et al. 2001; Audard et al. 2003a). Although systematic differences are found between the derived abundances, different atomic databases (APEC, SPEX, HULLAC) and different instruments or instrument combinations (e.g., RGS+EPIC MOS on XMM-Newton, or HETGS on Chandra) were used during various stages of coronal activity (and at various stages of early instrument calibration efforts), making any detailed comparison suspect. For example, Audard et al. (2003a) showed conflicting results from two analyses that differ exclusively by their using different atomic databases. The overall trends, however, show gratifying agreement, also for several further magnetically active binaries. All results indicate low Fe (0.2–0.3 times solar photospheric for HR 1099), a high Ne/Fe abundance ratio (≈ 10), a high Mg/Fe abundance ratio (≈ 2 in several active stars), and an overall trend for increasing abundances with increasing FIP. The same conclusions were reported by Schmitt and Ness (2004) for an analysis of the Algol spectrum based on different reconstruction methods, the main uncertainty being due to large systematic errors in the atomic physics parameters. Telleschi et al. (2004) systematically studied element abundances and EMDs for solar analogs at various activity levels, applying approaches that involve either spectral fits of sections of the spectra, or iterative reconstructions based on selected emission line fluxes. The two iteration methods yielded nearly identical abundances (Fig. 36). A more fundamental problem was recognized in an unbiased determination of line fluxes in the presence of line blends, and in the use of different spectroscopic databases. Expectedly, there is less agreement between results from high-resolution data and analyses that make use of low- or medium-resolution observations (from, e.g., ASCA or BeppoSAX), but several trends are noteworthy. First, high Ne/Fe abundance ratios are in fact found in a number of reports based on ASCA observations, even if the agreement is not always convincing. The following ratios have again been converted to the Anders and Grevesse (1989) and Grevesse and Sauval (1999) solar photospheric abundances (see also Table 6): For II Peg, Ne/Fe = 4.5 (ASCA, Mewe et al. 1997) vs. 15 (Chandra, Huenemoerder et al. 2001); for AR Lac, 3.4 (ASCA, White et al. 1994) vs. 2.2 (Chandra, Huenemoerder et al. 2003); for λ And, 3.4 (ASCA, Ortolani et al. 1997) vs. 4.0–5.3 (XMM-Newton, Audard et al. 2003a) and 2.2 (Chandra, Sanz-Forcada et al. 2004); for


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HR 1099, 5.9 (ASCA, Osten et al. 2004) vs. 4.2–10 (Chandra, Audard et al. 2001a, 2003a; Drake et al. 2001); for Algol, 1.4–2.3 (ASCA, Antunes et al. 1994) vs. 2.6 (Chandra, Schmitt and Ness 2004). Similar trends apply to the Mg/Fe ratios: For II Peg, Mg/Fe = 1.2 (ASCA, Mewe et al. 1997) vs. 2.7 (Chandra, Huenemoerder et al. 2001); for AR Lac, 1.0–1.4 (ASCA, White et al. 1994; Kaastra et al. 1996) vs. 0.95 (Chandra, Huenemoerder et al. 2003); for λ And, 1.2–2.2 (ASCA, Ortolani et al. 1997) vs. 2.5–3.0 (XMM-Newton, Audard et al. 2003a) and 1.6 (Chandra, Sanz-Forcada et al. 2004); for HR 1099, 1.6 (ASCA, Osten et al. 2004) vs. 0.45–2.5 (Chandra, Audard et al. 2001a, 2003a; Drake et al. 2001); for Algol, 0.8–1.2 (ASCA, Antunes et al. 1994) vs. 1.4 (Chandra, Schmitt and Ness 2004). The discrepancies are more severe and systematic for several other elements given the strong blending in low-resolution data (see, e.g., discussion in Huenemoerder et al. 2003). In general, abundance ratios are more stable than absolute abundances that require a good measurement of the continuum level. This, in turn, requires an accurate reconstruction of the DEM. But what are we to make out of the residual uncertainties and discrepancies in abundance ratios from the interpretation of high-resolution data? It is perhaps important to recall the situation in the solar corona. There, abundances change spatially, and also in time as a given coronal structure ages (Feldman 1992; Jordan et al. 1998). As a further consequence, abundances are likely to vary with temperature across the corona. Second, the DEM represents a complex mixture of quiet plasma, evolving active regions, bright spots, and flares at many luminosity levels. A “best-fit” parameter derived from a spectrum therefore represents a sample mean related to a statistical distribution of the respective physical parameter. Whatever error ranges are reported, they inevitably refer to this sample mean whereas the actual spread across the physically distinct sources in a stellar corona remains presently unknown. A sound physical interpretation will have to address abundance ratios in specific coronal sources. In this context, excessive accuracy may well be meaningless for observational studies even if atomic physics problems were absent – the essence for further physical interpretation are trends such as those shown in Fig. 37. 16.5. Coronal and photospheric abundances All coronal plasma ultimately derives from the respective stellar photosphere. Strictly speaking, therefore, we should define abundance ratios with respect to the underlying photospheric abundances. Unfortunately, these are all too often poorly known, or unknown altogether. Photospheric metallicities, Zphot , have been reported for a number of RS CVn binaries (see, among others, Randich et al. 1993, 1994; the latter authors, however, cautioned against the strict use of their measurements as true metallicity indicators). Unexpectedly, at least for population I stars, many of these systems turn out to be rather metal poor. If the coronal abundances are compared with these photospheric metallicities, the putative coronal underabundances may disappear entirely. This seems to be the case for Capella (Favata et al. 1997c; Brickhouse et al. 2000). Similarly, White et al. (1994) reported comparable coronal and photospheric abundances for the RS CVn binary AR Lac, and Favata et al. (1997b) found the coronal metallicity of VY Ari (0.4 times solar) to be in the midst of measured photospheric metallicities of RS CVn binaries as

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a class. Ortolani et al. (1997) measured, from low-resolution ROSAT data, a coronal metallicity, Zcor , in λ And that is nearly consistent with the stellar photospheric level, although ASCA data indicated lower metallicity, and several discrepant sets of photospheric abundances have been published (see Audard et al. 2003a). The trend agrees with abundance ratios being the same in the corona and in the photosphere of this star (Audard et al. 2003a). The RS CVn binary CF Tuc has revealed particularly low coronal metal abundances of 0.1 times solar photospheric values (Schmitt et al. 1996d; Kürster and Schmitt 1996), but again this finding is accompanied by low measured photospheric abundances (Randich et al. 1993). The same appears to apply to the RS CVn/BY Dra binaries TY Pyx (Zcor ≈ 0.5 − 0.7, Zphot ≈ 0.63, Franciosini et al. 2003; Randich et al. 1993) and HD 9770 (Zcor ≈ 0.5 − 0.6, Zphot ≈ 0.30 − 0.35, Tagliaferri et al. 1999). Although S. Drake et al. (1994a) found that the spectrum of the giant β Cet cannot be fitted even when assuming the known photospheric abundances, Maggio et al. (1998) reported rough agreement between photospheric (90% confidence ranges for Si: 1.4–3.2, Fe: 0.7–2.5 times solar) and coronal abundances (Si: 0.9 [90%: 0.3–2.4], Fe: 0.7 [90%: 0.5–2] times solar), albeit with large uncertainties. But new complications have surfaced. Ottmann et al. (1998) critically reviewed previous photospheric abundance determinations and revisited the problem using a sophisticated spectroscopic approach to derive all relevant stellar parameters self-consistently. They challenged reports of very low photospheric metallicities in otherwise normal stars, finding at best mild underabundances (e.g., 40–60% solar Mg, Si, and Fe values for II Peg and λ And), and metal abundances very close to solar for young, nearby solar analogs (κ 1 Cet and π 1 UMa). An application of the technique to a solar spectrum returned the correct solar values. These more solar-like values seem closer to what should be expected for nearby, young or intermediately old population I stars (Feltzing et al. 2001). The apparent photospheric underabundances in active stars may be feigned by chromospheric filling-in of the relevant lines and due to photometric bias from large dark-spot areas, an explanation that Randich et al. also put forward to explain their significantly differing abundances for the two components in some active binaries. In the light of these reports, several authors returned to recover significantly depleted coronal abundances also relative to the respective photospheres. An illustrative example is HR 1099. Recent coronal abundance determinations for this star converge to subsolar values in particular for Fe (between 0.2–0.3, Audard et al. 2001a, 2003a; Drake et al. 2001), and these values seem to superficially agree with an Fe abundance of ≈ 0.25 measured for the photosphere (Randich et al. 1994). On the other hand, Strassmeier and Bartus (2000) and Savanov and Tuominen (1991) reported photospheric Fe abundances of, respectively, 0.6–0.8 and 1.0 times solar, which would be in agreement with values expected from the age of this system (Drake 2003a), thus arguing in favor of a real depletion of the coronal Fe. Similarly, Covino et al. (2000) found Zcor ≈ 0.2 for II Peg (Mewe et al. 1997 even give Fe/H ≈ 0.1), whereas the photosphere is 3 times richer in metals (Zphot = 0.6 according to Ottmann et al. 1998). And Huenemoerder et al. (2001) reported a coronal Fe abundance four times below photospheric for II Peg, and various abundances are found at 60% of the photospheric values in AR Lac (Huenemoerder et al. 2003). Particularly interesting test samples are nearby, young solar analogs for which reliable photospheric abundances have been reported, not too surprisingly being consistent


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with solar photospheric values (e.g., Mg, Si, and Fe given by Ottmann et al. 1998 for κ 1 Cet and π 1 UMa; several elements [Al, Ca, Fe, Ni] reported by Vilhu et al. 1987 for AB Dor; further values listed by Cayrel de Strobel et al. 2001 and references therein also for χ 1 Ori; with several individual elements being close to solar, large discrepancies appear rather unlikely for other elements). A corresponding coronal X-ray study based on XMM-Newton spectroscopy, however, indicated significant overall metal depletion on the one hand, where the Fe depletion is stronger for higher activity levels, and a relative FIP bias on the other hand; the latter changes from “normal” to “inverse” with increasing activity level. Both trends disagree with photospheric patterns (Güdel et al. 2002c; Telleschi et al. 2004). Other important test cases are stars that reveal strong, undisputed photospheric deviations from the solar abundance pattern. “Super-metal rich” stars are stars with measured photospheric Fe abundances [Fe/H]≥ 0.2 (logarithmic, relative to the solar photosphere). Maggio et al. (1999) observed two extreme cases with [Fe/H]= 0.25 (30 Ari B) and [Fe/H]= 0.305 (η Boo). Surprisingly, not only were the relative coronal abundances [Mg/Fe], [Si/Fe], and [O/Fe] found to be close to the abundances of otherwise similar field stars with near-solar composition, but the absolute coronal [Fe/H] abundance was also derived to be near-solar. The authors suspected a number of artefacts related to low-resolution CCD spectroscopy, however. At the opposite end, namely in metal-poor Population II stars, the simple lack of metals available in the stellar material should reflect strongly in the coronal emission. A striking case was presented by Fleming and Tagliaferri (1996): The binary HD 89499 with [Fe/H] = –2.1 shows X-ray spectra that are essentially line-free, that is, they are dominated by bremsstrahlung. Because the emissivity of such plasma is much lower than the emissivity of a plasma with solar composition, the material can efficiently be heated to higher temperatures, and indeed all plasma is detected at T ≈ 25 MK, with no significant amounts of cooler material. There are nevertheless important examples of stars that show no indication of coronal metal depletion also in the light of new photospheric abundance measurements. Drake and Kashyap (2001) found a slight enhancement of coronal vs. photospheric abundances in the intermediately active ξ Boo A, in agreement with a measured solar-like FIP effect. A trend for smaller metal deficiencies toward less active stars has been noted earlier (Singh et al. 1995), and the least active stars such as Procyon (Drake et al. 1995b; Raassen et al. 2002) and α Cen generally show solar-like metallicities, with the additional possibility of a solar-type FIP effect (Drake et al. 1997; Mewe et al. 1998a,b; Raassen et al. 2003a). The very active late-F star HD 35850 with measured solar photospheric Fe abundance also requires near-solar or only slightly subsolar abundances (Gagné et al. 1999) although there is disagreement with the analysis given by Tagliaferri et al. (1997). A few further examples with near-photospheric composition were discussed by Sanz-Forcada et al. (2004). The above discussion amply illustrates the inconclusive and unsatisfactory present observational status of the field. The easy access to coronal abundance diagnostics makes further, comprehensive photospheric abundance determinations very desirable.

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16.6. Flare metal abundances Abundances may change in particular in flares because the evaporation process brings new photospheric or chromospheric material into the corona. Peculiar effects have also been noted in some solar flares, as described in Sect. 16.1. There was some early evidence for enhanced or depleted Fe abundances in large stellar flares, mostly on the basis of the line-to-continuum ratio for the Fe Kα line at 6.7 keV. Stern et al. (1992a) found an equivalent width of only 25% of the expected value in a flare on Algol, possibly indicating a corresponding Fe underabundance. A similar effect was noted by Tsuru et al. (1989). In both cases, suppression due to resonance scattering was discussed as an alternative explanation. Doyle et al. (1992a) reported a very low Fe abundance (33% solar) during a large flare on II Peg. Ottmann and Schmitt (1996) noticed an increase of the coronal metallicity from 0.2 to 0.8Z during a giant flare on Algol observed by ROSAT in the 0.1–2.4 keV range, although the low spectral resolution makes such measurements problematic, for example if the dominant plasma found in simple spectral fits is far from the relevant maximum line formation temperatures. White et al. (1986), on the other hand, concluded for a flare on Algol that the Fe abundance was within 20% of the solar photospheric value. Further reports of unusual equivalent widths of the Fe Kα line have been reported by Doyle et al. (1991), Tsuru et al. (1992), and Vilhu et al. (1993). Higher-resolution broad-band spectra permitted measurements of other individual elements and more complicated thermal structures. Güdel et al. (1999), Osten et al. (2000) and Audard et al. (2001a) investigated the temporal evolution of several abundances during large, gradual flares on RS CVn binaries. They all found increases of low-FIP element abundances (e.g., of Fe, Si, Mg) during the flare maximum, and a rapid decay back to pre-flare values during the later phases of the flare. In contrast, a large flare on Proxima Centauri revealed no FIP-related abundance evolution although all abundances appeared to be elevated in proportion during a narrow interval around the flare peak (Güdel et al. 2004). Similarly, Osten et al. (2003) found an increase of the Fe abundance during a flare on σ 2 CrB by a factor of two, while the other elements increased accordingly, with no systematic trend related to the FIP. Another, albeit less detailed, approach involves the monitoring of the “global” metallicity Zcor , i.e., abundances are assumed a priori to vary in proportion. The metallicity is then predominantly driven by Fe, in particular if the Fe Kα complex at 6.7 keV is accessible. Mewe et al. (1997), Tsuboi et al. (1998), Favata and Schmitt (1999), Favata et al. (2000a), Güdel et al. (2001b), Covino et al. (2001), and Osten et al. (2002) noted peak enhancements of Zcor by factors of about 3–4 during flares on II Peg, V773 Tau, Algol, EV Lac, AB Dor, Gl 355, and EI Eri, respectively. In contrast, Maggio et al. (2000) and Franciosini et al. (2001) reported the absence of a significant metallicity enhancement in flares on AB Dor and UX Ari, respectively, although the upper limits were still consistent with enrichment factors of ≈ 3. Despite some variations of the theme, it seems to be certain that flares can change the elemental composition of the plasma, and the trend is toward increasing metallicity in flares on active stars that otherwise show metal-depleted coronae. Some ideas for models will be discussed in the next section.


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16.7. Theoretical models for abundance anomalies It has proven particularly difficult to interpret the abundance anomalies in stellar coronae. This should come as no surprise given that the situation is not all that different for the solar corona, despite the abundance of sophisticated but competing models (Hénoux 1995). I briefly list a few suggestions that, however, all require further elaboration; another recent summary has been given by Drake (2003b). Stratification of the atmosphere. Mewe et al. (1997) proposed that the abundance features observed in active stars are due to the different scale heights of different ions in a hydrostatic coronal loop, depending on mass and charge. As a result, the ion distribution in a magnetic loop is inhomogeneous and the line-to-continuum ratio depends on the scale height of a specific ion. After flares, the settling to equilibrium distributions is expected to occur on time scales of hours. This model cannot, however, explain the high Ne abundances in active stars because of the mass dependence of the proposed stratification: Ne has a mass intermediate between O and Mg! Coronal equilibrium. All determinations of element abundances strongly rely on the assumption of collisional equilibrium. The thermalization time is usually short enough to justify this assumption. If the observed coronal emission is, however, driven by a sequence of small flares (Sect. 13.6) then a number of further conditions would have to apply, which are difficult to assess. Whether such effects could change the measured abundances is currently unknown (see also the discussion in Huenemoerder et al. 2003). “Anomalous flares”. High Ne abundances are occasionally seen on the Sun during “Ne rich” flares (Schmelz 1993). Shemi (1991) argued that the high photoionization cross section of Ne makes it prone to efficient ionization by X-ray irradiation of the chromosphere during flares, thus making Ne behave like a low-FIP element in the solar corona. While this model explains the Ne enrichment, it does not address the apparent underabundance of the low-FIP element Fe. Evaporation. The peak metallicities observed in large flares seem to be bounded by Z < ∼ Z . Assuming that most population I stars in the solar neighborhood have photospheric abundances similar to the Sun, then the coronal abundance increase suggests that new chromospheric/photospheric material is supplied to the corona, most likely by the chromospheric evaporation process (Ottmann and Schmitt 1996; Mewe et al. 1997; Güdel et al. 1999). The selective low-FIP element enhancement during some large flares (Güdel et al. 1999; Osten et al. 2000; Audard et al. 2001a) is further compatible with a chromospheric evaporation model presented by Wang (1996) in which the evaporation induces upward drifts of electrons and protons. These particles then efficiently drag chromospheric ions (i.e., preferentially low-FIP elements) in an ambipolar diffusion process, while they leave neutral (preferentially high-FIP) elements behind. Stellar evolution. Schmitt and Ness (2002) found N/C abundance ratios that are enhanced by factors of up to 40 in Algol and in a sample of (sub-)giants. They attributed this anomaly to an enrichment of N from mass transfer in Algol, and from dredge-up of N in the evolving giants. This has been quantitatively worked out in the context of mass loss evolution and convective dredge-up by Drake (2003a) for Algol. The N enrichment and C depletion then essentially come from nuclear processing through the CN cycle in the secondary star, followed by strong mass loss from the outer convection zone and dredge-up of N enriched material.

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He enrichment. An increased abundance of He relative to H due to some fractionation process in the chromosphere would increase the continuum level and therefore decrease the line-to-continuum ratios, thus leading to an apparent underabundance of the metals (Drake 1998). Helium enhancements by factors of a few are required, however (Rodonò et al. 1999), up to levels where He would be the most abundant element of the plasma (Covino et al. 2000). FIP-related trends are not explained by this model. Non-thermal emission. I mention here another possibility that may lower all abundances in general, and in particular the Fe abundance if measured from the Fe K complex at 6.7 keV. If the continuum level is enhanced by an additional power-law component due to impact of non-thermal electrons in the chromosphere, then the equivalent width of the line is below predictions, simulating a “depleted Fe abundance” (Vilhu et al. 1993). Observationally, quite high signal-to-noise ratios and good spectral resolution may be required to rule out non-thermal contributions. Such a “non-thermal” model is interesting because appreciable suppression of the overall metallicity is found particularly in stars that are strong non-thermal radio emitters (Güdel et al. 2002c). There is another coincidence between the appearance of non-thermal electrons and element abundance anomalies. The change from an inverse-FIP bias to a normal solartype FIP effect occurs at quite high activity levels, close to the empirical saturation limit for main-sequence stars (Güdel et al. 2002c). At the same time, non-thermal radio emission drops sharply (much more rapidly than the X-rays). If electrons continuously propagate into the chromosphere at a modest rate without inducing strong evaporation, then a downward-pointing electric field should build up. This field should tend to trap chromospheric ions, i.e., predominantly the low-FIP elements, at low levels while neutrals, i.e., predominantly high-FIP elements, are free to drift into the corona. As radio emission disappears in lower-activity stars, the low-FIP element suppression disappears, and a solar-type FIP effect may build up, for whatever physical reasons, in analogy to the solar case.

17. X-ray emission in the context of stellar evolution X-ray emission offers easy access to stellar evolution studies because magnetic activity is governed by various stellar parameters such as convection zone depth and rotation that change gradually as a star evolves. Evolutionary studies have been based either on nearby, modestly-sized but well-defined samples of stars or on large statistical samples from open clusters. I will first describe some principal results from the first approach and then concentrate on open cluster studies.

17.1. Main-sequence stars The X-ray luminosity of field F-G stars clearly decays monotonically with age. Studies of young open clusters (Sect. 17.5) indicate a slow decay during the initial few 100 Myr of a solar-like star, with LX scaling approximately like the inverse of the age (Patten and Simon 1996). In contrast, somewhat older field stars show a steep decay toward higher ages. For nearby F-G main-sequence stars for which approximate ages have been derived mostly from their surface Li abundance, moving group membership, or rotation (once


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sufficiently converged toward a mass-dependent value), the X-ray luminosity decays like LX ≈ (3 ± 1) × 1028 t −1.5±0.3 [erg s−1 ] (61) where the age t is given in Gyr (Maggio et al. 1987; Güdel et al. 1997a). The same trend is found in open clusters (see Sect. 17.5 and Fig. 41 below). It is quite certain that this decay law reflects the slowing of the rotation rate with age rather than some intrinsic dynamo ageing (Hempelmann et al. 1995). It must therefore derive directly from the combination of the rotation-age relationship (e.g., Soderblom et al. 1993) and the rotation-activity dependence (Sect. 5). As the star ages and its overall luminosity decreases, the EM distribution shifts to cooler temperatures, with a rapid decrease in particular of the hot plasma component – see Fig. 38 (and Sect. 9.4 and 9.5). A possible cause of the temperature decrease are the less efficient coronal magnetic interactions in less active stars given their lower magnetic filling factors, and consequently a less efficient heating, or a lower rate of flares that produce high-temperature plasma (Güdel et al. 1997a; Güdel 1997). It is reassuring that the Sun and its near-twin, α Cen A, behave very much alike, both in terms of coronal temperature and LX (Mewe et al. 1995, 1998a; Drake et al. 1997). The similarity between α Cen A and the Sun in spectral type, rotation period and age provides a convenient approximation to the “Sun as a star” (Golub et al. 1982; Ayres

solar analogs

Temperature (MK)

10

ROSAT higher T XMM, EM weighted mean T Sun (min-max)

1 0.1

1 Age (Gyr)

10

Fig. 38. Decay of coronal temperature with age for solar-type stars. The temperatures of the hotter component in the G star sample of Güdel et al. (1997a) and Güdel et al. (1998) are shown (filled circles). Solar data are from Peres et al. (2000) and illustrate the range from activity minimum to maximum (triangles). The open circles represent the EM-weighted logarithmic average of T as calculated from EMDs (Telleschi et al. 2004) or from multi-T spectral fits (for α Cen at t = 5 Gyr, Raassen et al. 2003a)

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et al. 1982). Seen from this perspective, the full-disk DEM has cooled to a distribution between 1–5 MK with a peak at 3 MK (Mewe et al. 1998a; Raassen et al. 2003a), representative of a star in which a mixture of active regions, quiet regions, and coronal holes prevail (Orlando et al. 2000; Peres et al. 2000, see Sect. 11.4). When we move to lower-mass stars, the picture changes gradually. A progressively larger fraction of stars is found at relatively high activity levels toward lower masses, in particular among M dwarfs. This is a consequence of the smaller spin-down rate for less massive stars (Fleming et al. 1988, 1995; Giampapa et al. 1996): low-mass stars stay active for a longer time. This may be related to a different dynamo being in operation in late M dwarfs where the radiative core is small or absent altogether (Giampapa et al. 1996). The more rapid spin-down of more massive dwarfs is, in turn, illustrated by the paucity of extremely active G and early K stars in the immediate solar vicinity; the nearest examples are found at distances of 15–30 pc with ages of no more than ≈ 100 Myr (e.g., the K0 V rapid rotator AB Dor [Vilhu et al. 1993] or the young solar analogs EK Dra [Güdel et al. 1995] and 47 Cas B [Güdel et al. 1998]). For M dwarfs, we find a clear ageing trend only when we look at much larger age ranges: their X-ray luminosity significantly decays in concert with their metallicity from young to old disk population stars (Fleming et al. 1995; metallicity generally decreases with increasing population age). This trend continues toward the oldest, halo population M dwarfs that reveal significantly softer X-ray spectra than young and old disk stars (Micela et al. 1997a; see also Barbera et al. 1993).

17.2. Giants The giant and supergiant area of the HRD is more complicated because evolutionary tracks are running close to each other and partly overlap. An overview of the relevant area is shown in Fig. 39. As cool stars evolve from the main sequence to the giant branch, the deepening of the convection zone may temporarily increase the coronal magnetic activity level (Maggio et al. 1990). In general, however, the X-ray activity of stars with masses < ∼ 1.5M further decreases as they move redward in the HRD (Pizzolato et al. 2000) because these stars begin their evolution toward the giant branch as slow rotators on the main sequence, and the increasing radius further slows their rotation rate. The evolution of magnetic activity is different for more massive stars because they start their evolution off the MS as rapidly rotating O, B, and A stars. As convection suddenly sets in, a dynamo begins to operate in the stellar interior, and a magnetized wind starts braking the star in the region of early G-type giants and supergiants (Hünsch and Schröder 1996; Schröder et al. 1998). These “first crossing stars” develop maximum 31 −1 X-ray activity among G giants (LX < ∼ 10 erg s , Maggio et al. 1990; Micela et al. 1992; Scelsi et al. 2004). The break in rotation period is located significantly blueward of the location where X-rays weaken (Gondoin et al. 1987). This is because the convection zone deepens and, possibly, differential rotation strengthens as the star evolves redward; both trends help strengthen the dynamo against the slowing rotation (Gondoin 1999; Pizzolato et al. 2000). As a consequence, one finds no unique rotation-activity relation for the complete ensemble of giants, and some of the more rapidly rotating late giants keep extreme activity levels in X-rays (Gondoin et al. 2002; Gondoin 2003a,b,c, 2004b).


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Fig. 39. Main features of the giant HRD. The hatched region schematically illustrates the Hertzsprung gap area, while the gray oval region marks the area of the “clump stars”. The polygonal region in the upper right corner shows the approximate range of the cool-wind stars. The original dividing line is the lower left hand edge of this area. Individual circles mark the loci of “hybrid” stars. Evolutionary tracks are given for a variety of masses (figure courtesy of T. Ayres, after Ayres 2004)

Only at B − V > ∼ 0.9 − 1 do we find a gradual decrease of LX , up to B − V ≈ 1.1 (≈ K1 III). Toward later spectral types, X-ray emission drops to very low values. The X-ray emission of early F giants and subgiants is deficient with respect to transition region line fluxes (Simon and Drake 1989; Ayres et al. 1995, 1998; Fig. 5). Simon and Drake (1989) therefore argued in favor of acoustic coronal heating for the warmer stars that show no appreciable magnetic braking by a wind, and solar-like magnetic heating for the cooler stars in which magnetic braking is effective. In contrast, Ayres et al. (1998) proposed very extended (L ≈ R∗ ) coronal loops with long (≈ 1 day) filling durations and cooling times that favor a redistribution of the energy into the transition region where it is efficiently radiated. Such loops may be remnants of global magnetospheres as proposed in different contexts for hotter MS stars, coexisting with a growing solar-type corona that is generated by a dynamo in the deepening convection zone. The systematic behavior is less clear in supergiants given their smaller number statistics; the outstanding early-type example among single Hertzsprung gap supergiants is α Car that shows an appreciable LX despite its shallow convection zone (F0 II, log LX = 29.8, Maggio et al. 1990). As giants evolve, and at least the less massive examples undergo a He-flash, they gather in the “clump” region of the HRD, at roughly 0.95 ≤ B − V ≤ 1.2 (K giants,

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see Fig. 39). Again, many of these sources are detected in X-rays, albeit at relatively weak levels, with LX of a few times 1027 erg s−1 (Schröder et al. 1998). Strong flaring activity before and after the He-flash testifies to the ability of the dynamo to survive the internal reconfiguration (Schröder et al. 1998; Ayres et al. 1999, 2001a). In this context, the Capella binary is particularly interesting since it contains a primary clump giant (G8 III) and a presumably co-eval Hertzsprung gap star (G1 III) of about equal mass (≈ 2.6M ). The Fe xxi λ1354 line shows considerable variability on timescales of several years in the clump giant, but not in the Hertzsprung gap star (Johnson et al. 2002; Linsky et al. 1998). The former authors suggested that long-term variability, for example induced by dynamo cycles, occurs only in the clump phase where a deep convection zone has built up. Another example is the quadruplet of the nearly co-eval Hyades giants (γ , δ, , and θ 1 Tau). The four stars are found at very similar locations in the HRD, but show a spread in LX over orders of magnitude (Micela et al. 1988; Stern et al. 1992c). A possible explanation is, apart from contributions by companions, that the high-activity stars are first crossers while the others have already evolved to the clump area (Collura et al. 1993). 17.3. Dividing lines From ultraviolet observations of chromospheric and transition region lines in giants, Linsky and Haisch (1979) proposed a dividing line in the giant and supergiant area of the HRD roughly at V–R = 0.7–0.8, separating stars with chromospheres and hot transition regions to the left from stars that exhibit exclusively chromospheric lines, to the right. A steep gradient in transition region fluxes is found when one moves from spectral type G towards the dividing line, located roughly between K2 III and G Ib (Haisch et al. 1990c). The absence of warm material in the later-type stars suggested an absence of coronal material as well, which was soon confirmed based on Einstein observations (Ayres et al. 1981a; Haisch and Simon 1982; Maggio et al. 1990). ROSAT observations deepened this conclusion, converging to a more “perpendicular” dividing line at spectral type ≈ K3 between luminosity classes II–IV (Haisch et al. 1991b). The dividing line roughly corresponds to the “onset” of massive cool winds toward M giants and supergiants (Reimers et al. 1996). This coincidence may be a consequence of the cooler stars carrying predominantly open magnetic field lines that produce stellar winds somewhat similar to solar coronal holes (Linsky and Haisch 1979). Plasma that resides in open magnetic regions is necessarily cool in such stars because the escape temperature is much smaller than on the Sun, and this leads to small Alfvén-speed scale heights and thus to strong winds via Alfvén-wave reflection (Rosner et al. 1991). Why cooler stars should show predominantly open field lines is unexplained. A shift from an αω dynamo to a turbulent dynamo in cooler stars (Gondoin et al. 1987; Gondoin 1999) could possibly change the magnetic field structure. An α 2 dynamo that relies on convection close to the surface but not on rotation may indeed be a favorable option given the slow rotation of red giants (Ayres et al. 2003a). In this case, one expects that smaller-scale loops are generated, and this has two consequences (e.g., Rosner et al. 1995; Schrijver and Haisch 1996): First, the larger thermal pressure in low-lying hot loops will open them up if the magnetic field strength


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is not sufficiently high, thus draining the available energy into a stellar wind. Second, Antiochos et al. (1986) proposed that the low gravity of the cooler and therefore, larger stars to the right of the dividing line allows for new static cool loop solutions with T < 105 K and small heights (after Martens and Kuin 1982; Antiochos and Noci 1986), while hot X-ray loops with heights less than the (large!) pressure scale height at 105 K grow unstable and are therefore not radiating. In this model, then, the hot magnetic corona is replaced by a cooler but extended transition region. Any hot material detected from stars to the right of the dividing line or from “hybrid stars” (see below) may entirely be due to short-term flaring (Kashyap et al. 1994). The above two instabilities apply to warmer stars as well: Because the magnetic loop size is restricted by the convection zone depth which is small for F stars, there is a regime in that spectral range where the above arguments apply similarly, i.e., hot coronae will become unstable (Schrijver and Haisch 1996). Even if a magnetically confined X-ray corona is present in giants, its X-ray emission may be efficiently absorbed by the stellar wind so that the dearth of coronal emission in M giants may only be apparent (Maggio et al. 1990). Since several non-coronal giants have been found to maintain transition regions up to 105 K, Ayres et al. (1997) proposed that coronal loops are in fact submerged in the cool chromospheric and CO layers and are thus absorbed. The reason for an extended, not magnetically trapped chromosphere is rooted in the 40-fold larger pressure scale height on red giants such as Arcturus compared to the Sun. The model of “buried” coronae would again be aided if the dynamo in these stars favored short, low-lying loops (Rosner et al. 1995). This view has gained strong support from the recent detection of very weak X-ray emission from the K1 III giant Arcturus, with LX ≈ 1.5 × 1025 erg s−1 (Ayres et al. 2003a); Arcturus was previously thought to be X-ray dark (Ayres et al. 1981a, 1991). Ayres et al. (2003a) also reported the presence of transition region lines that are absorbed by overlying cooler material that acts like a “cool absorber”. Hünsch and Schröder (1996) compared the dividing line with evolutionary models and concluded that it is actually nearly parallel to the evolutionary tracks in the giant domain. They suggested that the drop of X-ray activity toward cooler stars is gradual and is a direct function of mass. In this picture, the coolest M giants with masses < ∼ 2M and ages around 109 yr are X-ray faint simply because they had spun down on the MS before and are thus no longer able to drive a dynamo (Ayres et al. 1981b; Haisch and Simon 1982; Hünsch and Schröder 1996; Schröder et al. 1998) while the warmer giants, descendants of M > 2M main-sequence stars, have retained more angular momentum. 17.4. Hybrid stars The situation is somewhat less clear for evolved supergiants and bright giants (luminosity class II) given the small statistics at hand, but there is now evidence against a clear dividing line in this region of the HRD (Reimers et al. 1996). While the wind dividing line sharply bends to the left in the HRD as most bright giants and supergiants show strong winds (Fig. 39), the so-called “hybrid stars” are formally right of a vertical dividing line extended from the giant region, but they show indications both of cool winds and ≈ 105 K transition region material (Hartmann et al. 1980). After first X-ray detections (Brown et al. 1991; Haisch et al. 1992), it soon became evident that X-ray emitting hybrids

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are common across the regime of bright giants and supergiants of luminosity class I–II (Reimers and Schmitt 1992; Reimers et al. 1996; Hünsch et al. 1996). The co-existence of hot coronae and cool winds in hybrids renders them pivotal for understanding the physics of stellar atmospheres in this region of the HRD. The X-ray luminosities of hybrids are relatively modest, with LX = 1027 −1030 erg s−1 (Reimers et al. 1996; Ayres 2004); like other luminosity-class II stars, they are X-ray deficient compared to giants or main-sequence stars (Ayres et al. 1995; Reimers et al. 1996; Ayres 2004; Fig. 5), but at the same time they show very high coronal temperatures. The X-ray deficiency syndrome of supergiants is probably the same as that of F-type giants and subgiants (Simon and Drake 1989, Sect. 17.2). Indeed, the transformation from X-ray deficient to “solar-like” stars occurs at progressively later spectral types as one moves to higher luminosity classes, eventually encompassing almost the complete cool half of the supergiant HRD (Ayres et al. 1995). The co-existence of winds and coronae may be the result of the very rapid evolution of hybrid stars: The X-ray emission may compete with cool-wind production as the dynamo activity persists. In the picture of Hünsch and Schröder (1996), then, hybrids are X-ray sources because their masses are > 2M , i.e., they start out as fast rotators on the main-sequence and keep their dynamo while developing strong winds. The X-ray dividing line defined by spun-down low-mass stars does simply not reach up to these luminosity classes.

17.5. Evolution of X-ray emission in open stellar clusters 17.5.1. Overview Open clusters have become instrumental for the study of stellar coronae and their longterm evolution for several reasons: i) They provide large samples of nearly co-eval stars spread over a broad mass range that encompasses all types of cool MS stars and possibly brown dwarfs, in the statistical proportion dictated by the processes of star formation; ii) their ages are rather well known from their distribution on the HRD; ii) their surface chemical composition is very likely to be constant across the stellar sample. Open clusters are therefore ideal objects with which to test theories of stellar evolution and, in particular, systematic dependences between rotation, activity, and age. While some of the issues have already been covered in the section on rotation (Sect. 5), the present section emphasizes specific evolutionary effects and sample studies made with open clusters. Table 7 summarizes open cluster studies in the literature, also listing – if available – median X-ray luminosities for the spectral classes F, G, K, and M. The colors were not defined identically by all authors, but the large spread of LX and the statistical uncertainties will make this a rather negligible problem. Also included are clusters in star-forming regions. Because these stars are not yet on the main sequence, comparing them with MS clusters based on color may be misleading. For the sake of definition, I have lumped together all T Tau stars from such samples in the “K star” column unless more explicit information was available. Several of the given ages (mostly from the Lausanne open cluster database) must be treated as tentative. Figure 40 shows the distribution of LX and LX /Lbol as a function of B − V for the Pleiades (age ≈ 100 Myr) and the Hyades (age ≈ 700 − 800 Myr). The older


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Table 7. Open cluster studies: Luminosities and bibliography Cluster

Age (Myr) F

NGC 1333 ρ Oph Serpens NGC 2264 Orion NGC 2024 Taurus WTTS ChaI WTTS IC 348 R CrA Upper Sco-Cen η Cha TW Hya Tucanae IC 2602 NGC 2547 IC 4665 IC 2391 α Per NGC 2451 B NGC 2451 A Blanco 1 NGC 2422 Pleiades NGC 2516 Stock 2 NGC 1039 Ursa Major NGC 6475 NGC 3532 NGC 6633 Coma Ber IC 4756 NGC 6940 Praesepe Hyades NGC 752 IC 4651 M67 NGC 188

∼ 75 Myr to a few 100 Myr for K stars, while M dwarfs remain at high activity levels for much longer (Patten and Simon 1996; James and Jeffries 1997, Fig. 40). Incidentally, the distribution of LX levels may then be relatively flat across a wide range of B − V in the age period between the Pleiades and the Hyades. At the same time, the LX /Lbol ratio systematically increases toward larger B − V (Fig. 40). At the age of α Per or the Pleiades, G, K, and M dwarfs still all reach up to the saturation limit (Hodgkin et al. 1995; Prosser et al. 1996; Randich et al. 1996a; Micela et al. 1999a), while at the ages of the Hyades, this is true only for late-K and M dwarfs (Reid et al. 1995; Stern et al. 1995b). The break point at which saturation is reached thus moves to progressively larger B − V as the cluster ages. The different braking histories lead to different characteristic decays of the X-ray luminosities for various spectral ranges, as illustrated in Fig. 41. The error bars refer to the ±1σ spread read off the luminosity functions published in the literature. They are only approximate and are probably dominated by uncertainties from small-number statistics. As we see from Fig. 41, the LX of all spectral classes decays beyond 100 Myr although this decay is clearly slowest for M dwarfs. As a cluster reaches the Hyades’ age (≈ 700 − 800 Myr), the rotation periods of both G and K dwarfs have mostly converged to relatively low values with little spread, and the LX values are consequently also expected to have dropped significantly below the saturation limit, with small statistical spread, while M dwarfs are now in a regime of rapid braking, increasing their scatter in LX as they settle at lower rotation rates (Micela et al. 1988; Stern et al. 1992c, 1994, 1995b). The overall trend agrees nicely with the decay law found from field stars, as is illustrated for the G star panel where the field stars from Fig. 38 are overplotted as filled circles. This scenario is alternatively illustrated by X-ray luminosity functions for various spectral ranges; the sample median and the spread of X-ray luminosities as a


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Fig. 41. The evolution of the median X-ray luminosities of F, G, K, and M stars derived from various open clusters (from Table 7: ρ Oph, NGC 2264, Orion, Taurus, Cha I, IC 348, TW Hya, Tucanae, IC 2602, IC 2391, α Per, Blanco 1, NGC 2451 A, NGC 2422, Pleiades, NGC 2516, Coma Ber, Praesepe, and Hyades). The error bars give the approximate 1σ scatter (if available from the literature). The panel for G stars also includes the field G stars shown in Fig. 38 (filled circles). The TTS samples from star-forming regions are lumped together in the K star panel, except for the Taurus region for which G, K, and M stars are given separately. The ages of the star-forming regions are only characteristic averages as they are typically spread between 0.1–10 Myr

function of spectral type can then be followed as a function of age (e.g., Micela et al. 1990), as shown in Fig. 42. At this point, we recognize the close interrelationship between the activity-age relationship discussed here (see also Sect. 17.1 and (61)), the temperature-activity relation introduced in Sect. 9.5 (Fig. 10, (16)), and the temperature-age relation (Sect. 17.1, Fig. 38). They are all an expression of the coupling between coronal activity and the rotation-induced internal dynamo. 17.5.3. Binaries A different scenario seems to apply to late-type binary stars even if they are not tidally locked. Pye et al. (1994) and Stern et al. (1995b) found components in K- and M-type binaries (but not F- and G-type binaries) in the Hyades to be overluminous by an order of magnitude when compared to single stars. The explanation for this effect is unclear but could involve a less rapid braking in the PMS stage as the circumstellar disks were

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disrupted, thus producing very rapid rotators that have still not spun down at the age of the Hyades (Pye et al. 1994). A reanalysis by Stelzer and Neuhäuser (2001), however, questioned a significant difference between singles and binaries. 17.5.4. Co-eval clusters Intercomparisons between clusters of the same age have greatly helped confirm the above evolutionary picture. Similar trends for LX and LX /Lbol are generally found for co-eval clusters (e.g., Giampapa et al. 1998). A notable exception was discussed by Randich and Schmitt (1995), Randich et al. (1996b), and Barrado Y Navascués et al. (1998) who compared the nearly co-eval Hyades, Coma Berenices, and Praesepe clusters, finding significant LX deficiencies in the latter cluster but agreement between the former two. The cause of the discrepancy is not clear, but could be related to the recent finding that Praesepe shows a spatial segregation of activity levels, which may be the result of a merger of two non-coeval clusters (Franciosini et al. 2004 and references therein). Similar discrepant cases include Stock 2 (Sciortino et al. 2000) and possibly IC 4756 (Randich et al. 1998), NGC 3532 (Franciosini et al. 2000), and NGC 6633 (Briggs et al. 2000; Harmer et al. 2001). Another important influence may come from different metallicities in clusters. Jeffries et al. (1997), Harnden et al. (2001), Sciortino et al. (2001), and Damiani et al. (2003) compared NGC 2516 with the slightly younger Pleiades and found F stars to be more luminous and G/K stars less luminous in the former. Jeffries et al. (1997) suspected that the rotational history of the F stars is different owing to different convective turnover times given NGC 2516’s lower metallicity. This explanation, however, seems to be ruled out by recent spectroscopy that indicates solar metallicity for this cluster. Slightly different rotation period distributions may be present for G and K stars perhaps due to a small age difference (see Damiani et al. 2003 and references therein). A metallicity-


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related effect on X-ray radiation has also been discussed for the metal-rich cluster Blanco 1 that reveals an X-ray excess for M dwarfs (Micela et al. 1999b; Pillitteri et al. 2003). 17.5.5. Toward older clusters An extension of cluster studies toward higher ages suffers both from the small number of clusters that are still bound, thus implying larger typical distances, and from the low X-ray luminosities of old main-sequence stars. Only close binaries that are kept in rapid rotation by tidal forces, or giants have typically been detected in such clusters, with no less interesting results (e.g., Belloni and Verbunt 1996, Belloni and Tagliaferri 1997, and Belloni et al. 1998 for binaries in NGC 752, NGC 6940, and M 67, respectively; see Table 7). 17.5.6. Toward younger clusters Clusters significantly younger than α Per connect to pre-main-sequence (PMS) evolution and the phase of circumstellar-disk dispersal. For example, Jeffries and Tolley (1998) found the X-ray luminosities of all G and K stars in the young (14 Myr; ≈ 35 Myr according to other sources) cluster NGC 2547 to be a factor of two below the saturation limit of LX /Lbol ≈ 10−3 , suggesting that all stars have rotation periods > 3 d. Possibly, their circumstellar disks have only recently, at an unusually late point in time, been dispersed and the stars have not yet spun up from the disk-controlled slow rotation. The preceding evolution of disk environments is thus obviously of pivotal importance for cluster development, as we will discuss in the next section.

18. X-ray coronae and star formation Modern theory of star formation together with results from comprehensive observing programs have converged to a picture in which a forming low-mass star evolves through various stages with progressive clearing of a contracting circumstellar envelope. In its “class 0” stage (according to the mm/infrared classification scheme), the majority of the future mass of the star still resides in the contracting molecular envelope. “Class I” protostars have essentially accreted their final mass while still being deeply embedded in an envelope and surrounded by a thick circumstellar disk. Jets and outflows may be driven by these optically invisible “infrared stars”. Once the envelope is dispersed, the stars enter their “classical T Tauri” stage (CTTS, usually belonging to class II) with excess Hα line emission if they are still surrounded by a massive circumstellar disk; the latter results in an infrared excess. “Weak-lined T Tauri stars” (also “naked T Tauri stars”, Walter 1986; usually with class III characteristics) have lost most of their disk and are dominated by photospheric light (Walter et al. 1988). Consequently, X-ray emission from these latter stars has unequivocally been attributed to solar-like coronal activity (Feigelson and DeCampli 1981; Feigelson and Kriss 1981, 1989; Walter and Kuhi 1984; Walter et al. 1988), an assertion that is less clear for earlier PMS classes. Arguments in favor of solar-like coronal activity in all TTS include i) typical electron temperatures of order 107 K that require magnetic confinement, ii) a “solar-like” correlation with chromospheric emission, iii) the presence of

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flares, and iv) rotation-activity relations that are similar to those in more evolved active stars (e.g., Feigelson and DeCampli 1981; Walter and Kuhi 1984; Walter et al. 1988; Bouvier 1990; Damiani and Micela 1995). The solar analogy may, on the other hand, not hold for the emission excess of optical lines in CTTS; this excess is uncorrelated with X-rays (Bouvier 1990) but that seems to relate to the accretion process. Because this review is primarily concerned with coronal X-rays that are – in the widest sense – solar-like, the discussions in the following sections are confined to lowmass stars in nearby star-forming regions. For a broader view of X-rays in the starformation process, I refer the reader to the review by Feigelson and Montmerle (1999) and references therein.

18.1. T Tauri stars 18.1.1. Overview Because most of the low-mass CTTS and WTTS are fully convective, there has been a special interest in their X-ray behavior and in their rotation-activity relations. Quite some debate has unfolded on whether CTTS and WTTS belong to the same parent population if their X-ray luminosities are compared. CTTS have been found to be, on average, less luminous than WTTS in particular in Taurus (Strom and Strom 1994; Damiani et al. 1995; Neuhäuser et al. 1995a; Stelzer and Neuhäuser 2001), but other authors have found the two samples to be indistinguishable in various other star-forming regions (Feigelson and Kriss 1989; Feigelson et al. 1993; Strom et al. 1990; Casanova et al. 1995; Lawson et al. 1996; Grosso et al. 2000; Flaccomio et al. 2000; Preibisch and Zinnecker 2001, 2002; Feigelson et al. 2002a; Getman et al. 2002, but see contradicting result for Orion by Flaccomio et al. 2003b). It is plausible that WTTS are stronger X-ray sources than CTTS because the latters’ X-ray emission could be absorbed by an overlying wind (Walter and Kuhi 1981, see also Stassun et al. 2004), their coronal activity could somehow be inhibited by the process of mass accretion onto the stellar surface (Damiani and Micela 1995), or because WTTS produce more efficient dynamos given their generally higher measured rotation rates (Neuhäuser et al. 1995a), although most PMS are in the saturation regime (Flaccomio et al. 2003b). However, there are also a number of arguments against any intrinsic Xray difference between WTTS and CTTS. CTTS are usually identified optically, while WTTS are inconspicuous at those wavelengths but are typically selected from X-ray surveys (Feigelson et al. 1987) where many of them stand out given their rapid rotation, hence their bias toward strong X-rays (Feigelson and Kriss 1989; Preibisch et al. 1996). Several authors (Gagné and Caillault 1994; Damiani et al. 1995; Preibisch and Zinnecker 2001, 2002; Getman et al. 2002; Feigelson et al. 2002a, 2003) also tested X-ray activity against infrared excess, but no distinction was found between the two classes, suggesting that the observed X-ray emission does not directly relate to the presence of massive disks. This issue has seen some, albeit still not full, clarification with recent work by Flaccomio et al. (2003a,b,d) who studied various ranges of stellar mass. It probably does matter whether stars are distinguished by an indicator for the presence of a disk (such as their IR classification) or by an indicator of active accretion (e.g., Hα emission). There is no one-to-one correspondence between these indicators (see also Preibisch and


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Fig. 43. The Orion Nebula Cluster as seen in X-rays by Chandra. North is up (Feigelson et al. 2002a)

Zinnecker 2002). The debate remains open; Flaccomio et al.’s work seems to suggest that either indicator points at CTTS being less X-ray luminous than WTTS in a given mass range, at least for the considered star-forming clusters. Stassun et al. (2004) argued, from a reconsideration of the Orion X-ray samples, that the suppression of X-ray luminosity in a subsample of stars, accompanied by increased hardness, is in fact only apparent and is due to the increased attenuation of softer photons by magnetospheric accretion columns in actively accreting stars. 18.1.2. X-ray luminosity and age Spectroscopic evidence and EM distributions in TTS point to an analogy to young solar analogs. It appears that both the EM and the hot temperatures are progressively more enhanced as one moves from the ZAMS into the pre-main sequence regime of CTTS (Fig. 44, Skinner and Walter 1998). The overall X-ray levels of pre-main sequence TTS also fit into the general picture of declining X-ray activity with increasing age (Walter et al. 1988; Feigelson and Kriss 1989; Feigelson et al. 1993; Gagné and Caillault 1994; Gagné et al. 1995b; Damiani et al. 1995; Stelzer and Neuhäuser 2001, Figs. 41, 42), although this effect is not directly – or not only – coupled with rotation. While WTTS

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Fig. 44. Comparison of EMDs of the CTTS SU Aur (solid histogram) and the ZAMS solar analog EK Dra (dashed histogram; figure courtesy of S. Skinner, after Skinner and Walter 1998)

may spin up toward the main sequence and reach X-ray saturation, they at the same time contract and decrease in Lbol ; the X-ray luminosity then peaks around an age of 1 Myr and subsequently slowly decays (Neuhäuser et al. 1995a; Damiani and Micela 1995; Feigelson et al. 2003; Flaccomio et al. 2003c) whereas LX /Lbol remains saturated for all TTS during their descent along the Hayashi track (Flaccomio et al. 2003b,a). It is important to mention that CTTS and WTTS properties do not provide reliable age indicators per se. CTTS and WTTS in a star-forming region may have the same age while disk/envelope dispersal histories were different, although WTTS do tend to dominate the final pre-main sequence episodes (see, e.g., Walter et al. 1988; Feigelson et al. 1993; Lawson et al. 1996; Alcalá et al. 1997; Stelzer and Neuhäuser 2001). 18.1.3. X-ray luminosity, saturation, and rotation Rotation may therefore be a more pivotal parameter. In this context, activity-rotation relationships are particularly interesting because the rotation history is strongly coupled with the presence of accretion disks, probably by magnetic coupling. CTTS generally rotate slowly, with rotation periods typically of P ≈ 4 − 8 days; only once the stars have lost their massive inner accretion disks will the star spin up to rotation periods of typically one to a few days (Bouvier et al. 1993). Many T Tau stars, in particular WTTS, are therefore in the saturation regime (Bouvier 1990; Strom et al. 1990; Strom and Strom 1994; Gagné and Caillault 1994; Gagné et al. 1995b; Casanova et al. 1995; Flaccomio et al. 2000). While often quoted as supportive of the same type of magnetic activity as in normal stars, this result is, at hindsight, rather surprising because PMS have no significant, stable nuclear energy source. The saturation level therefore does not seem to relate to the total nuclear energy production.


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A normal rotation dependence of LX can be found as well, in particular in the Taurus sample. In this case, excellent agreement is found with the behavior of more evolved stars, again suggesting that essentially the same type of magnetic dynamo and coronal activity are at work (Bouvier 1990; Damiani and Micela 1995; Neuhäuser et al. 1995a; Stelzer and Neuhäuser 2001). However, in other star-forming regions, such as the Orion Nebula Cluster, LX appears to be independent of Prot up to quite long periods of 30 d, the stars essentially all residing in a saturated regime despite considerable scatter in LX /Lbol . Feigelson et al. (2003) discussed these results in terms of various dynamo theories. On the other hand, Flaccomio et al. (2003c) have studied rotation and convection for various PMS age ranges. Convection zone parameters indicate that most PMS stars should indeed be in the saturation regime, as observed, for example, in the Orion Nebula Cluster. The interesting point is, however, that the very youngest stars show a suppressed “saturation” level, by as much as an order of magnitude (e.g., LX /Lbol ≈ 10−4 for Orion and ρ Oph, Feigelson et al. 2003; Skinner et al. 2003; Grosso et al. 2000). Whereas Feigelson et al. (2003) hypothesized that a less efficient distributed dynamo is in effect, Flaccomio et al. (2003c) speculated that the disk is somehow inhibiting strong coronal activity during the first few Myr, which then led them to find a characteristic (inner-) disk dispersal time of 1–2 Myr. 18.1.4. The widely dispersed “field WTTS” samples The easy identification of WTTS in X-ray surveys has led to a rather controversial issue related to the dispersal of star-formation clusters and TTS evolution. In general, the location of TTS relative to the cloud cores provides interesting insight into the star formation history in and around a molecular cloud. Feigelson et al. (1987), Walter et al. (1988), Feigelson and Kriss (1989), and Strom et al. (1990) were first to point to a rather large overpopulation of WTTS in Taurus by factors of 2 to 10 compared with CTTS, probably constituting the long-sought post-T Tau population evolving toward the ZAMS. An estimated WTTS/CTTS ratio of order 10 is then consistent with a disk dispersal time of a few Myr (Neuhäuser et al. 1995c; Feigelson 1996). If star formation is cut off in time, the ratios may even be higher; Walter et al. (1994) found a ratio of 40 in Upper Sco-Cen where star formation has ceased about 2 Myr ago. Nevertheless, it came as quite a surprise when further associated WTTS were discovered tens of degrees away from the Taurus, Chamaeleon, Orion, and Lupus molecular clouds (Walter et al. 1988; Neuhäuser et al. 1995b; Sterzik et al. 1995; Wichmann et al. 1996; Alcalá et al. 1995, 1997; Krautter et al. 1997). They show no spatial correlation with the present molecular clouds, which suggests that they have either drifted away from their place of formation (Neuhäuser et al. 1995b), or that they are the products of star formation in now dispersed molecular clouds (Walter et al. 1988) or local high-velocity, turbulent cloudlets (Feigelson 1996). The latter explanation is attractive because some of the samples are as young as 106 yr despite their large distance from the (present-day) “parent cloud” (Alcalá et al. 1997). However, the evolutionary stage of these samples has been the subject of considerable debate. On the one hand, Neuhäuser et al. (1997) estimated their ages at typically ≤ 30 Myr, including a moderately-sized population of widely distributed ZAMS G stars.

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On the other hand, Micela et al. (1993), Briceño et al. (1997), and Briceño et al. (1999) used star-count models, statistics of X-ray detected M dwarfs, and Li measurements to argue that the dispersed WTTS do not relate to the “missing post-T Tau stars” but mostly have a larger, near-ZAMS age of 20 − 100 Myr. This would agree with the nearZAMS status of X-ray selected field stars reported by Micela et al. (1997b) that were, however, not drawn from the sample in question. Such an age population would also solve the problem of the “missing” ZAMS population that is expected from standard star formation models. A likely explanation for the potential misclassification of young field stars as WTTS may relate to the use of low-resolution spectroscopy for Li measurements (Briceño et al. 1997; Favata et al. 1997d; Micela et al. 1997b; Martín and Magazzù 1999). If this revised age classification is correct, then, however, the problem with the “missing post-T Tau” stars at younger ages of 2 − 10 Myr reopens. Covino et al. (1997), Alcalá et al. (1998), and Alcalá et al. (2000) reconsidered and discussed this issue for the Chamaeleon and the Orion regions, arriving at intermediate conclusions. The distributed “WTTS” population appears to consist of at least 50% genuinely young (< 5 Myr) WTTS somewhat concentrated toward the molecular clouds, plus a smaller, widely distributed population of unrelated older, possibly near-ZAMS field stars. There is little evidence for a genuine post-T Tau population, indicating that the star formation process in a given cloud occurs on time scales < 10 Myr and is not continuous, as assumed in some of the population models (see also discussion in Favata et al. 1997d and the counter-arguments in Feigelson 1996). The entire issue remains under debate; see, for example, Alcalá et al. (2000) and references therein for a recent assessment discussing Li abundance, the location of the stars on the HRD, and their spatial distribution. An argument supporting an intermediate age of a few 107 yrs for these stars at the interface between PMS and ZAMS may be their large-scale spatial correlation with the young Gould Belt structure which also contains several star formation regions in the solar vicinity (Krautter et al. 1997; Wichmann et al. 1997). The ages of many foreground Orion “WTTS” are indeed compatible with this hypothesis (Alcalá et al. 1998) – see Sect. 19. 18.1.5. Flares X-ray flares have given clear evidence for underlying magnetic fields not only in WTTS (Walter and Kuhi 1984) but also in CTTS (Feigelson and DeCampli 1981; Walter and Kuhi 1984). They strongly support the presence of solar-like closed coronae in the broadest sense. From an energetics point of view, they play a very important role: As much as half of the emitted X-ray energy, if not more, may be due to strong flares (Montmerle et al. 1983), and many TTS are nearly continuously variable probably also owing to flares (Mamajek et al. 2000; Feigelson et al. 2002a; Preibisch and Zinnecker 2002; Skinner et al. 2003). Examples with extreme luminosities and temperatures up to 100 MK have been reported (Feigelson and DeCampli 1981; Montmerle et al. 1983; Preibisch et al. 1995; Skinner et al. 1997; Tsuboi et al. 1998, 2000; Imanishi et al. 2002, see Sect. 12). Stelzer et al. (2000) systematically studied flares in TTS, comparing them with flares in the Pleiades and the Hyades clusters. They found that TTS flares tend to reach higher luminosities and temperatures than their main-sequence equivalents, and


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the flare rate above a given limit is also higher. The most extreme flares are found on CTTS, a possible hint at star-disk magnetic interactions during flares although this is at variance with suggestions made by Montmerle et al. (2000) (Sect. 18.2.2). The high activity level found for CTTS is echoed by the work of Skinner et al. (2003) who noted a large variability fraction among the hottest and most absorbed sources in NGC 2024. 18.1.6. The circumstellar environment The high-energy emission related to the luminous X-rays may have considerable impact on the circumstellar environment and on the entire surrounding molecular clouds because it changes the ionization balance and induces chemical reactions in molecular material (Montmerle et al. 1983; Casanova et al. 1995; Kastner et al. 1999). Recently, Feigelson et al. (2002b) speculated that the elevated rate of large flares in young solar analogs in the Orion Nebula Cluster may be applicable to the young Sun. The increased activity may possibly explain the production of chondrules by flash-melting and isotopic anomalies in meteorites by high proton fluxes. 18.1.7. Accretion-driven X-ray emission? An entirely different model for X-ray production in CTTS was put forward by Kastner et al. (2002) based on observations of the CTTS TW Hya. This star has been conspicuous by producing luminous radiation with LX = 2 × 1030 erg s−1 which is, however, very soft, with a best-fit temperature of T ≈ 3 MK (Hoff et al. 1998; Kastner et al. 1999). While unusual for active coronal sources, the temperature is compatible with shockinduced X-ray emission at the base of magnetically funneled accretion flows. Explicit density measurements using He-like triplets of O vii and Ne ix indeed suggest very high densities of ne = 1012 − 1013 cm−3 , densities that are not seen at these temperatures in any coronal source. Stelzer and Schmitt (2004) have supported this view and further argued that the low C and Fe abundances relate to their being grain-forming elements, that is, C and Fe have condensed out in the circumstellar disk or cloud. In the light of similarly extreme abundance anomalies in other stars (Sect. 16), this model necessarily remains tentative at this time. The role of accretion columns for the X-ray production has further been discussed by Stassun et al. (2004). They found that actively accreting stars in the Orion Nebula Cluster on average show less luminous but also harder X-ray emission than non-accreting stars, suggesting that accretion columns may attenuate the X-rays while the intrinsic X-ray emission is similar in both samples, i.e., not related to accretion but to rotation. A timedependent effect of this sort has possibly been seen in the CTTS XZ Tau (Favata et al. 2003). To what extent TW Hya is an exception presently remains open. 18.2. Protostars 18.2.1. Overview X-rays from embedded (“infrared”) protostars are strongly attenuated and require access to relatively hard photons. The protostellar survey by Carkner et al. (1998) listed only about a dozen X-ray class I protostars detected at that time, with luminosities of order

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Fig. 45. He-like Ne ix (left) and O vii triplets (right) of the nearby CTTS TW Hya observed by XMM-Newton. The forbidden lines at 13.7 Å and 22.1 Å, respectively, are largely suppressed, indicating high electron densities (figures courtesy of B. Stelzer, after Stelzer and Schmitt 2004)

1030 erg s−1 , and no class 0 objects. First tentative evidence for heavily absorbed hard emission was reported for ρ Oph (Koyama et al. 1994; Casanova et al. 1995), followed by several unambiguous detections of very hard class I sources with temperatures of up to 7 keV in the R CrA cloud (Koyama et al. 1996; Neuhäuser and Preibisch 1997), ρ Oph (Kamata et al. 1997; Grosso 2001), Orion (Ozawa et al. 1999), Taurus (Skinner et al. 1997, see also Carkner et al. 1998), NGC 1333 (Preibisch 1997b; Preibisch et al. 1998), and Serpens (Preibisch 1998). Their luminosities apparently correspond to classical “saturation” (LX /Lbol ≈ 10−3 , Ozawa et al. 1999), but extreme levels of LX ≈ (6 − 18) × 1032 erg s−1 have been reported (Preibisch 1998). Class I protostars have now become accessible in larger numbers thanks to Chandra’s and XMM-Newton’s hard-band sensitivity (Imanishi et al. 2001a; Preibisch and Zinnecker 2001, 2002; Preibisch 2003b; Getman et al. 2002). Their measured characteristic temperatures are very high, of order 20–40 MK (Tsujimoto et al. 2002; Imanishi et al. 2001a). Some of these values may, however, be biased by strongly absorbed (“missing”) softer components in particular in spectra with limited signal-to-noise ratios. It is correspondingly difficult to characterize the LX values in traditional soft X-ray bands for comparison with other stellar sources. 18.2.2. Flares and magnetic fields Direct evidence for magnetic processes and perhaps truly coronal emission came with the detection of flares. Many of these events are exceedingly large, with total soft X-ray energies of up to ≈ 1037 erg (Table 4; Koyama et al. 1996; Kamata et al. 1997; Grosso et al. 1997; Ozawa et al. 1999; Imanishi et al. 2001a, and Preibisch 2003a). Imanishi et al. (2003) conducted a systematic comparative analysis of flares from class I–III stars. They interpreted rise times, decay times and temperatures within the framework of MHD models (Shibata and Yokoyama 2002, Sect. 12.9, Fig. 27). The magnetic fields tend to become stronger toward the typically hotter class I flaring sources. Such flares


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Fig. 46. Triple X-ray flare on the protostar YLW 15, observed with ASCA (figure courtesy of N. Grosso, after Montmerle et al. 2000)

realistically require large volumes, in fact to an extent that star-disk magnetic fields become a possibility for the flaring region (Grosso et al. 1997 for YLW 15 in ρ Oph). Tsuboi et al. (2000) reported on quasi-periodic flare events in YLW 15 that occurred three times in sequence, separated by about 1 day (Fig. 46). If magnetic fields indeed connect the star with the inner border of the circumstellar disk, then they may periodically ignite flares each time the field lines have become sufficiently stretched due to the difference in rotation rates of the star and the disk (Fig. 47). This scenario was computed by Hayashi et al. (1996); their MHD simulations showed extensive episodic heating and large plasmoids detaching from the star-disk magnetic fields. Montmerle et al. (2000) expanded this view qualitatively to suggest that star-disk magnetic flares should be common in protostars through winding-up star-disk magnetic fields because stellar and inner-disk rotation rates have not synchronized at that age. But because the same fields will eventually brake the star to disk-synchronized rotation in TTS, the large star-disk flares should then cease to occur, and the X-ray activity becomes related exclusively to the stellar corona. 18.2.3. The stellar environment X-ray emission in protostars and strong flaring in particular may have far-reaching consequences for the evolution of the stars themselves, but also for the environment in which planets form. First, X-rays efficiently ionize the molecular environment, which may lead to modifications in the accretion rate, for example via the magnetic Balbus-

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Fig. 47. Sketch illustrating a star-disk magnetic-field model in which field lines wind up and reconnect (line labeled ‘5’) because the star rotates faster than the inner edge of the disk (figure courtesy of T. Montmerle, after Montmerle et al. 2000)

Hawley instability (see Montmerle et al. 2000 for a discussion). While X-ray flares may thus induce accretion events, the latter will tend to quench strong magnetic activity, in turn decreasing disk ionization. The effect of flare irradiation of disks may indeed have been seen explicitly: Imanishi et al. (2001a) detected, during a giant flare in YLW 16A (in the ρ Oph dark cloud), strong Fe fluorescence line at 6.4 keV that is possibly induced by X-ray irradiation of a circumstellar disk (Fig. 48; see also Koyama et al. 1996). Second, strong, frequent flares and disk ionization may also be of fundamental importance for the generation of jets (Hayashi et al. 1996), spallation reactions in solids in the circumstellar disk, and the formation of planets, a subject beyond the scope of the present review (see, e.g., Feigelson and Montmerle 1999; Feigelson et al. 2002b, and the extensive review of this subject by Glassgold et al. 2000). 18.2.4. “Class 0” objects Knowing that stars are already extremely active at the deeply embedded class I stage, the interest in the magnetic behavior of class 0 objects is obvious, but the strong photoelectric absorption makes detection experiments extremely challenging. Tsuboi et al. (2001) reported a possible detection of a class 0 object in Orion, with properties surprisingly similar to more evolved class I–III objects, such as an X-ray luminosity of LX ≈ 2 × 1030 erg s−1 , but additional detections and confirmations are badly needed. Specific searches have, so far, given a null result (T. Montmerle 2004, private communication).


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Fig. 48. Chandra CCD spectrum of the protostar YLW 16A observed during a large flare. The spectral line feature at 6.7 keV refers to the Fe xxv complex, whereas the line at 6.4 keV is a fluorescent line of cold Fe (figure courtesy of K. Imanishi, after Imanishi et al. 2001a)

18.3. Young brown dwarfs Brown dwarfs (BD) were first detected as faint X-ray sources in star forming regions such as Cha I, Taurus, and ρ Oph (Neuhäuser and Comerón 1998; Neuhäuser et al. 1999; Comerón et al. 2000). They correspond to spectral types beyond M6 at this age. The list of X-ray detections of BDs and candidates is now rapidly growing thanks to sensitive observations with Chandra and XMM-Newton. Considerable numbers have been reported from the Orion Nebula Cluster (Garmire et al. 2000; Feigelson et al. 2002a; Flaccomio et al. 2003b), ρ Oph (Neuhäuser et al. 1999; Imanishi et al. 2001b), IC 348 (Preibisch and Zinnecker 2001, 2002), Taurus (Mokler and Stelzer 2002; Neuhäuser et al. 1999 using ROSAT), and the σ Ori cluster (Mokler and Stelzer 2002). The latter authors and Tsuboi et al. (2003) provided a summary of all measurements and put the Xray properties in a wider context. Although alternative origins of the X-rays are possible such as primordial magnetic fields or star-disk fields (see Comerón et al. 2000), all Xray properties suggest thermal emission from a solar-like corona. Specifically, LX is typically found to follow the saturation law (LX /Lbol ≈ 10−4 − 10−3 ) of more massive stars, implying a general decrease toward later spectral types, without any evident break. In absolute terms, LX reaches up to a few times 1028 erg s−1 . Young BDs reveal coronal temperatures typically exceeding 1 keV, similar to TTS. A number of these objects have also been found to flare (Imanishi et al. 2001b; Feigelson et al. 2002a). It is only beyond 107 yr that the X-ray emission from BDs decays (see also Sect. 4.3) – again seemingly similar to main-sequence stars (Fig. 49). No thorough study of relations between accretion disk signatures and X-rays is available at this time. For ρ Oph, Imanishi et al. (2001b) found no relation between LX and K band luminosity excess. However, Tsuboi et al. (2003) suggested that the lack of X-ray detections among stars with very large Hα equivalent widths indicates, as in CTTS, increased accretion at the cost of strong X-ray emission.

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Fig. 49. X-ray characteristics of brown dwarfs as a function of age. Top panel: log LX /Lbol ; bottom panel: characteristic electron temperature. Key to the symbols: open squares: Orion Nebula Cluster; triangles: ρ Oph; filled squares: IC 348.All observations were obtained by Chandra (figure courtesy of Y. Tsuboi, after Tsuboi et al. 2003)

The similar behavior of young BDs and TTS is perhaps not entirely surprising, whatever the internal dynamo mechanism is. At this young age, both classes of stars are descending the Hayashi track, are fully convective, have surface temperatures like cool main-sequence dwarfs, and derive most of their energy from gravitational contraction, while they lack a significant central nuclear energy source. Young BDs are not yet aware of their fate to fail as stars.


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19. Young populations in the solar neighborhood Stellar coronae have also proven practical in investigations of (nearby) galactic structure. Large statistical samples of stellar X-ray sources are interesting to compare with galactic population models, for example to uncover “excess populations” of active stars or to assess the stellar contribution to the apparently diffuse galactic soft X-ray background. Sophisticated models take into account the statistical galactic distribution of stellar populations (in terms of scale heights, space densities, etc.) as a function of their color, evolutionary status, and binarity, together with effects of extinction (Favata et al. 1992; Guillout et al. 1996). I will only touch upon this field and mention some of the recent key results. When observations of large samples were compared with predictions from galactic population models, an excess of nearby “yellow” (F, G, K) stars was found (Favata et al. 1988). Later investigations interpreted them as predominantly young (< 1 Gyr), nearZAMS main-sequence stars (Sciortino et al. 1995). RS CVn binaries may contribute as well, but their number is not sufficient to account for the observed excess (Favata et al. 1995a,b). A young population is also conspicuous in the ROSAT All-Sky Survey, providing evidence for a considerable number of such stars in the solar neighborhood. Population studies have further been used to derive constraints on the stellar birthrate. Micela et al. (1993) found that the observed source counts are compatible with a nearly constant galactic stellar birthrate and exclude a rapid decline during the first few Gyr of the galaxy’s life. Guillout et al. (1998a) and Guillout et al. (1998b) undertook a large correlation study between the ROSAT All-Sky Survey and the Tycho Catalog. They found rather compelling evidence for a concentration of luminous and therefore probably young stars along a great circle on the sky that corresponds to the Gould Belt. This local galactic, disk-like structure in the solar vicinity spans over a few hundred parsec and comprises a number of the prominent nearby star-forming regions. The detected population of X-ray stars appears to correspond to the low-mass population of this structure. 20. Long-term variability and stellar magnetic cycles Records of sunspot numbers back over several hundred years show a near-cyclic modulation that has turned out to be a central challenge for dynamo theories. The magnetic activity period between two successive spot maxima of approximately 11 years expresses itself most beautifully in soft X-rays, more so than in any longer wavelength range (see Fig. 1). The X-ray luminosity variation between maximum and minimum has been quoted variably as ranging between a factor of about ten (Aschwanden 1994; Acton 1996) as measured by Yohkoh and GOES, to factors of 20–200 (Kreplin 1970) as measured with SOLRAD, although the spectral bandpasses clearly matter as well for a closer comparison. Converted to the ROSAT bandpass, Hempelmann et al. (1996) estimated variations by a factor of 10, whereas Ayres et al. (1996) found a somewhat more modest factor of 4 as extrapolated from far-UV data. The Mount Wilson HK project (Baliunas et al. 1995) has collected a continuous data stream of the chromospheric H&K line flux diagnostic for many stars over several decades. This stupendous observing project has now clearly demonstrated that many

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stars show magnetic activity cycles somewhat similar to the Sun’s. A subset of stars appear to lack such cycles, however, and very active stars tend to exhibit an irregular rather than a cyclic mode of variability (Hempelmann et al. 1996). The sensitive response of the coronal luminosity to changes in the surface magnetic field should make us believe that cycles are easily seen in X-ray active stars. Surprisingly, evidence is still tentative at the time of writing. Magnetic X-ray cycles have eluded detection because no appropriate program has been carried out for sufficiently long periods; however, there may also be interesting physical reasons for a lack of detections. Two strategies toward detecting X-ray cycles have been followed, the first observing young open clusters or field stars with various satellites to obtain statistical information on long-term variability, and the second approach concentrating on dedicated long-term “monitoring” of select field stars. 20.1. Clusters and field star samples Many open clusters or field star samples were observed by Einstein, EXOSAT, and ROSAT, and they obtain new visits again with XMM-Newton and Chandra. One of the principal results of comparative studies over time scales of 10 years has in fact been a suspicious absence of strong long-term variability. Most of these observing programs reported variations of no more than a factor of two for the large majority of stars. Such results apply to samples of active field dMe stars (Pallavicini et al. 1990a), dM dwarfs (Marino et al. 2000), dF–dK stars (Marino et al. 2002), volume-limited samples of nearby stars (Schmitt et al. 1995; Fleming et al. 1995), old disk and halo stars (Micela et al. 1997a), RS CVn binaries (Dempsey et al. 1993a), T Tau stars (Sciortino et al. 1998; Gagné and Caillault 1994; Gagné et al. 1995b; Grosso et al. 2000) and, most notably, open clusters such as the Pleiades (Gagné et al. 1995a; Micela et al. 1996; Marino et al. 2003b) and the Hyades (Stern et al. 1994, 1995b). Much of the observed variability is statistically consistent with shorter-term flare-like fluctuations or variability due to slow changes in active regions (Ambruster et al. 1987). In some cases, there is a modest excess of long-term over short-term variations (e.g., Gagné et al. 1995a for the Pleiades, Marino et al. 2002 for F-K field stars) but the evidence remains marginal. These investigations were put on a solid statistical footing by comparing short-term with long-term variability of a large sample of active binaries (Kashyap and Drake 1999). Again, most of the variability was identified to occur on time scales < ∼ 2 yr although there is marginal evidence for excess variability on longer terms (see also Marino et al. 2000). The latter could then be attributed to cyclic variability although the ratio of maximum to minimum luminosity would be bounded by a factor of 4, much less than in the case of the Sun. Overall, such results may be taken as evidence for the operation of a distributed dynamo producing relatively unmodulated small-scale magnetic fields (Kashyap and Drake 1999; J. Drake et al. 1996). If this is the case, then it would support a model in which not only the latest M dwarfs, but also earlier-type magnetically active stars are prone to a turbulent dynamo (Weiss 1993). The long-term variability in stellar coronae was further quantified with a large ROSAT sample of observations by Micela and Marino (2003). They modeled the ≈ 10 yr X-ray light curve collected from Yohkoh full-disk observations (Fig. 1) by transforming it to the ROSAT bandpass. Samples of stellar snapshot observations can then be compared


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with the distribution of the solar amplitude variations for a given time separation. In the solar case, statistical variation within a factor of two is due to short-term variability, while another factor of three to four is contributed by the solar cycle. Turning to the stellar sample, the authors concluded that there is some likelihood for inactive stars to have magnetic X-ray cycles somewhat similar to the Sun’s, whereas the most active stars tend to be less variable on long time scales. Hempelmann et al. (1996) attacked the problem by measuring surface flux FX for a number of stars with known Ca H&K activity cycles. They then compared the excess flux with predictions from a rotation-activity relation based on the known Ca H&K cycle phase, finding tentative indications that the X-ray flux varies in concert with Ca along the cycle, but again, the significance is low.

20.2. Case studies Obviously, dedicated long-term programs are in order to obtain more sensitive results on cyclic behavior. First tentative evidence from such a program was reported by Dorren et al. (1995). The star under scrutiny, EK Draconis, is a Pleiades-age solar analog near Xray saturation and is therefore not the type of star for which we expect regular cycles. The evidence for the latter is, however, clear and compelling, with a cycle period of about ten years in optical photometry (measuring the spot coverage) and partly in Ca ii and Mg ii lines (Dorren and Guinan 1994; Dorren et al. 1995). This cycle has now been followed over two full periods (Güdel et al. 2003c). The star has obtained regular coverage with Xray satellites for over ten years. Initial results were presented in Dorren et al. (1995). The attempt to detect an X-ray cycle is illustrated in Fig. 50. While there is a suggestive anticorrelation between X-ray flux and photospheric brightness where the star is brightest at its activity minimum, the evidence must be considered as tentative. The snapshots were partly obtained with different detectors, and the variation is rather modest, i.e., within a factor of two, illustrating the challenges of such observing programs. A more recent report by Hempelmann et al. (2003) indicated a correlation between X-ray luminosity and the Ca H&K S index for the two inactive stars 61 Cyg A and B. Both show chromospheric modulations on time scales of about 10 years, one being regular and the other irregular, and the X-ray fluxes vary in concert during the 4 1/2 years of coverage. A gradual X-ray modulation was also seen during a time span 2.5 years in HD 81809, although there seems to be a phase shift by about 1 year with respect to the Ca cycle (Favata et al. 2004). The evidence in these three examples, while promising, should again be regarded as preliminary given that only 30–50% of the cycle has been covered, and the variations in 61 Cyg are – so far – again within a factor of only ≈ 2. 21. Outlook Stellar coronal X-ray astronomy enters its fourth decade now, with no lack of wonderful instrumentation available to pursue its goals. Its – so far – short history started with feeble detections of exotic sources in the pioneering seventies; the eighties consolidated our view of X-ray coronae and brought them into a perspective of stellar evolution within which we have placed our Sun. The nineties saw rapid progress with increased

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Fig. 50. Illustration of a tentative identification of a magnetic cycle in the corona of EK Dra (G0 V) during one full photospheric magnetic cycle period (about 10 yr). The upper panel gives brightness offset, maximum brightness referring to smallest starspot coverage. The lower panel shows X-ray luminosity measurements (figure courtesy of E. Guinan)

sensitivities and routine access to spectroscopy, permitting the systematic study of numerous physical processes. And finally, the present decade has brought high-resolution X-ray spectroscopy and high-resolution X-ray imaging, paving the way to deep studies of coronal structure, heating, and evolution. Where should we go from here? Challenging questions wait to be answered. The following summary of important issues and recommendations represents my current view: How are coronae heated? The most fundamental question of our subject has started with the very recognition of the presence of hot plasma around the Sun – and it remains unanswered! The subject has not been reviewed in this paper because it is a predominantly solar and plasma-theoretical issue. However, stellar astronomy can shed more light on the problem by making use of what has been called the “solar-stellar connection”: through observations of systematic trends over a wide parameter range, while we assume that the basic physical processes remain the same in all stellar systems and the Sun. Stars offer access to plasmas as hot as 100 MK. Coronae are observed across a range of stellar gravities, magnetic field strengths, convection zone depths, and rotation periods. The systematic studies of stellar X-ray activity across the HRD have played a key role in the arguments for or against acoustic heating. High-resolution spectroscopy offers new possibilities by studying abundances and the form of DEMs, both being the result of heating processes occurring across the face of a star. The new satellites help us address these issues more systematically. How are coronae structured? The new, refined observational facilities enhance our diagnostic capabilities that will lead to conclusive insights into the structure of magnet-


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ically confined coronae, magnetic field generation and distribution, and eventually will help us to locate and identify the dynamo mechanism. It is still unclear whether in certain stars αω or α 2 dynamos are in operation. Structure information may provide the necessary boundary conditions as has been discussed in this review, for example in the context of giants. To understand the global structure of a magnetic corona, however, we have to start recognizing structure distribution. Many spectroscopically determined observables such as “density”, “temperature”, “abundance”, or “opacity” are the product of radiation from a plethora of coronal features that are, in fact, distributed in these parameters. Our X-ray spectra provide only a highly degenerate view of a true corona, with many possible realizations for one given observation. The use of painstakingly and accurately determined singular spectroscopic parameters may produce entirely misleading results in our modeling efforts; a value for a density or an element abundance derived from simple line-flux ratios may not reflect the physical conditions of the magnetic features we aim to understand. If we are to succeed in meaningfully describing entire stellar coronae based on spectroscopic data in the future, we must cope with the challenge of modeling statistical distributions of physical parameters across various coronal features. Additionally, new coronal structure reconstruction methods such as X-ray Doppler imaging, to mention at least one, hold promise to gain complementary insight into this problem. What is the physics behind flares?Although the detailed plasma physical mechanisms of flares can probably only be studied on the Sun, stellar flares offer access to quite extreme situations that may provide important boundary conditions for flare theories. Many characteristics of stellar coronae also suggest contributions of flares. Flare-like processes may be a fundamental mechanism to heat astrophysical plasmas in general. The underlying physical mechanisms certainly deserve more, in-depth observational and theoretical studies. How does magnetic activity evolve? Although a rough outline of rotation-age-activity relations has been established, many details remain unclear. How is magnetic activity controlled at early stages of evolution? Where are the magnetic fields generated in protostars or their environments, and where and how is magnetic energy released? Do circumstellar accretion disks influence it? Is the accretion process itself important for the generation or suppression of X-ray activity? Do star-disk magnetic fields contribute significantly to X-ray emission? Do they regulate the rotational history of a star that defines the starting conditions for stars settling on the main sequence? How do magnetic fields and coronal X-rays interact with the stellar environment? It has become clear that X-rays and magnetic fields do not only weakly interact with surrounding planets via a stellar wind and some magnetospheric processes; in young stellar systems, the high levels of X-ray emission may directly alter accretion disk properties by ionization, possibly controlling accretion events and governing, together with associated ultraviolet radiation, the disk and envelope chemistry. Magnetic fields may play a fundamental role in redistributing matter or in making accretion disks unstable. Coronal research turns into “interplanetary research” when dealing with forming young stellar systems. Many of these aspects are being addressed by present-day observations and theory. But we need to take bolder steps as well, in particular in terms of more sophisticated instrumentation. X-ray spectroscopy is still at an infant stage, essentially separating emission lines but hardly resolving their profiles. With a resolving power exceeding

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≈ 3000, rotational broadening, turbulent motions, or bulk plasma motions (e.g., during flares) could become routinely detectable in many stellar sources. “Doppler imaging” then would start really imaging stellar coronae, possibly even for different temperatures, thus producing a 3-D thermal structure model of a stellar corona. The required resolving powers are within reach of current detector technology, for example in the cryogenic domain. An ultimate goal will be producing spatially resolved images of nearby coronal stars through X-ray interferometric techniques, i.e., the equivalent of what radio astronomy has achieved through very long baseline interferometry. Instead of using a baseline of the Earth’s diameter as in conventional radio VLBI, two X-ray telescopes separated by 1.5 m would – in principle – reach a resolution of 0.3 milliarcsecond at 20Å, sufficient to resolve the diameter of the corona of α Cen into about 30 resolution elements, a resolution that can be compared with early solar X-ray images. First X-ray interferometric laboratory experiments are indeed promising (Cash et al. 2000). Many of our questions started in the solar system. I consider it a privilege that stellar astronomy is in the position of having an example for close scrutiny nearby. There is hope that further exploiting the solar-stellar connection, i.e., carefully comparing detailed solar studies with investigations of stars, will solve many of the remaining outstanding questions. Acknowledgements. It is a pleasure to thank the editors of this journal, Profs. L. Woltjer and M. C. E. Huber, for inviting me to write this review, and for their thoughtful comments on the manuscript. I am grateful to many of my colleagues for helpful advice, the contributions of figures, and answers to my persistent questions. Kaspar Arzner, Marc Audard, and Kevin Briggs critically commented on the text. I extend special thanks to them and to Stephen Skinner and Ton Raassen for discussions on our subject over the past many years. I owe much to the late Rolf Mewe who was a prolific source of inspiration and motivation in all aspects of coronal physics and spectroscopy. Discussions with Roberto Pallavicini, Antonio Maggio, and Giovanni Peres helped clarify issues on coronal loops. I acknowledge permission from several colleagues to use their previously published figures or data, in particular: Drs. Marc Audard, Tom Ayres, Nancy Brickhouse, Kevin Briggs, Jeremy Drake, Fabio Favata, Eric Feigelson, Thomas Fleming, Elena Franciosini, Mark Giampapa, Nicolas Grosso, Edward Guinan, Kensuke Imanishi, Moira Jardine, Antonietta Marino, Giusi Micela, Thierry Montmerle, Jan-Uwe Ness, Rachel Osten, Ton Raassen, Sofia Randich, Karel Schrijver, Kazunari Shibata, Marek Siarkowski, Stephen Skinner, Beate Stelzer, Alessandra Telleschi, Yohko Tsuboi, and Takaaki Yokoyama. The figures are reproduced with the permission of the publishers. I am particularly indebted to M. Audard, T. Ayres, N. Brickhouse, G. Micela, J.-U. Ness, R. Osten, M. Siarkowski, K. Shibata, A. Telleschi, and T. Yokoyama for their generous help by preparing entirely new figures for the present article, and Doris Lang for her editorial support. Several previously unprocessed and unpublished data sets or related results are shown in this paper, namely from XMM-Newton, Chandra, GOES, Yohkoh, and TRACE. XMM-Newton is an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA). The GOES soft X-ray data shown in Fig. 32 are from the Space Environment Center, Boulder, CO, of the US National Oceanic andAtmospheric Administration (NOAA). The solar X-ray images in Fig. 1 were taken by the Yohkoh mission of ISAS, Japan, which is operated by international collaboration of Japanese, US, and UK scientists under the support of ISAS, NASA, and SERC, respectively. Figs. 14 and 24 were obtained by the Transition Region and Coronal Explorer, TRACE, which is a mission of the Stanford-Lockheed Institute for Space Research (a joint program of the Lockheed-Martin Advanced Technology


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Center’s Solar and Astrophysics Laboratory and Stanford’s Solar Observatories Group), and part of the NASA Small Explorer program. Use was made of the Lausanne open cluster database at http://obswww.unige.ch/webda/, and of the SIMBAD database, operated at CDS, Strasbourg, France. General stellar X-ray astronomy research at PSI has been supported by the Swiss National Science Foundation under projects 2100-049343.96, 20-58827.99, and 20-66875.01.

References L. Acton: in 9th Cambridge Workshop on Cool Stars, Stellar Systens, and the Sun, eds. R. Pallavicini, A.K. Dupree, ASP, San Francsico, p. 45 (1996) P.C.Agrawal, T.H. Markert, G.R. Riegler: MNRAS 213, 761 (1985) P.C. Agrawal, A.R. Rao, G.R. Riegler: MNRAS 219, 777 (1986b) P.C. Agrawal, A.R. Rao, B.V. Sreekantan: MNRAS 219, 225 (1986a) P.C. Agrawal, G.R. Riegler, N.E. White: MNRAS 196, 73P (1981) P.C. Agrawal, J. Vaidya: MNRAS 235, 239 (1988) J.M. Alcalá, C. Chavarría-K., L. Terranegra: A&A 330, 1017 (1998) J.M. Alcalá, E. Covino, G. Torres, M.F. Sterzik, M.J. Pfeiffer, R. Neuhäuser: A&A 353, 186 (2000) J.M. Alcalá, J. Krautter, E. Covino, R. Neuhäuser, J.H.M.M. Schmitt, R. Wichmann: A&A 319, 184 (1997) J.M. Alcalá, J. Krautter, J.H.M.M. Schmitt, E. Covino, R. Wichmann, R. Mundt: A&AS 114, 109 (1995) C.W. Ambruster, S. Sciortino, L. Golub: ApJS 65, 273 (1987) C. Ambruster, W.A. Snyder, K.S. Wood: ApJ 284, 270 (1984) E. Anders, N. Grevesse: Geochim. Cosmochim. Acta 53, 197 (1989) S.K. Antiochos: ApJ 241, 385 (1980) S.K. Antiochos, B.M. Haisch, R.A. Stern: ApJ 307, L55 (1986) S.K. Antiochos, G. Noci: ApJ 301, 440 (1986) S.K. Antiochos, P.A. Sturrock: Solar Phys. 49, (1976) 359 S.K. Antiochos, P.A. Sturrock: ApJ 220, 1137 (1978) A. Antunes, F. Nagase, N.E. White: ApJ 436, L83 (1994) C. Argiroffi, A. Maggio, G. Peres: A&A 404, 1033 (2003) K. Arzner, M. Güdel: ApJ 602, 363 (2004) M. Aschwanden: Sol. Phys. 152, 53 (1994) M.J. Aschwanden, R.W. Nightingale, D. Alexander: ApJ 541, 1059 (2000a) M. Aschwanden, C.J Schrijver: ApJS 142, 269 (2002) M.J. Aschwanden, T.D. Tarbell, R.W. Nightingale, C.J. Schrijver, A. Title, C.C. Kankelborg, P.C.H. Martens, H.P. Warren: ApJ 535, 1047 (2000b) M. Audard, E. Behar, M. Güdel, A.J.J. Raassen, D. Porquet, R. Mewe, C.R. Foley, G.E. Bromage: A&A 365, L329 (2001) M. Audard, M. Güdel, J.J. Drake, V. Kashyap: ApJ 541, 396 (2000) M. Audard, M. Güdel, E.F. Guinan: ApJ 513, L53 (1999) M. Audard, M. Güdel, R. Mewe: A&A 365, L318 (2001a) M. Audard, M. Güdel, S.L. Skinner: ApJ 589, 983 (2003b) M. Audard, M. Güdel, A. Sres, A.J.J. Raassen, R. Mewe: A&A 398, 1137 (2003a) M. Audard, A. Telleschi, M. Güdel, S.L. Skinner, R. Pallavicini, U. Mitra-Kraev: ApJ, in press (2004) T.R. Ayres: ApJ submitted (2004) T.R. Ayres, A. Brown, G.M. Harper: ApJ 598, 610 (2003a) T.R. Ayres, A. Brown, G.M. Harper, P.D. Bennett, J.L. Linsky, K.G. Carpenter, R.D. Robinson: ApJ 491, 876 (1997)

220

M. Güdel

T.R. Ayres, A. Brown, G.M. Harper, R.A. Osten, J.L. Linsky, B.E. Wood, S. Redfield: ApJ 583, 963 (2003b) T.R. Ayres, A. Brown, R.A. Osten, D.P. Huenemoerder, J.J. Drake, N.S. Brickhouse, J.L. Linsky: ApJ 549, 554 (2001b) T.R. Ayres, T.A. Fleming, J.H.M.M. Schmitt: ApJ 376, L45 (1991) T.R. Ayres, T.A. Fleming, T. Simon, B.M. Haisch, A. Brown, D. Lenz, W. Wamsteker, D. de Martino, C. Gonzales, J. Bonnell, J.M. Mas-Hesse, C. Rosso, J.H.M.M. Schmitt, J. Trümpter, W. Voges, J. Pye, R.C. Dempsey, J.L. Linsky, E.F. Guinan, G.M. Harper, C. Jordan, B.M. Montesinos, I. Pagano, M. Rodonò: ApJS 96, 223 (1995) T.R. Ayres, J.L. Linsky: ApJ 241, 279 (1980) T.R. Ayres, J.L. Linsky, G.S. Vaiana, L. Golub, R. Rosner: ApJ 250, 293 (1981a) T.R. Ayres, N.C. Marstad, J.L. Linsky: ApJ 247, 545 (1981b) T.R. Ayres, R.A. Osten, A. Brown: ApJ 526, 445 (1999) T.R. Ayres, R.A. Osten, A. Brown: ApJ 562, L83 (2001a) T.R. Ayres, T. Simon, J.L. Linsky: ApJ 263, 791 (1982) T.R. Ayres, T. Simon, J.R. Stauffer, R.A. Stern, J.P. Pye, A. Brown: ApJ 473, 279 (1996) T.R. Ayres, T. Simon, R.A. Stern, S.A. Drake, B.E. Wood, A. Brown: ApJ 496, 428 (1998) J. Babel, T. Montmerle: A&A 323, 121 (1997) S. Baliunas, R.A. Donahue, W.H. Soon, J.H. Horne, J. Frazer, L. Woodward-Eklund, M. Bradford, L.M. Rao, O.C. Wilson, Q. Zhang, W. Bennett, J. Briggs, S.M. Carroll, D.K. Duncan, D. Figueroa, H.H. Lanning, T. Misch, J. Mueller, R.W. Noyes, D. Poppe, A.C. Porter, C.R. Robinson, J. Russell, J.C. Shelton, T. Soyumer, A.H. Vaughan, J.H. Whitney: ApJ 438, 269 (1995) M. Barbera, F. Bocchino, F. Damiani, G. Micela, S. Sciortino, F. Favata, F.R. Harnden Jr.: A&A 387, 463 (2002) M. Barbera, G. Micela, S. Sciortino, F.R. Harnden Jr., R. Rosner: ApJ 414, 846 (1993) D. Barrado Y Navascués, J.R. Stauffer, S. Randich: ApJ 506, 347 (1998) G. Basri: ApJ 316, 377 (1987) D.K. Bedford, R.D. Jeffries, E.H. Geyer, O. Vilhu: MNRAS 243, 557 (1990) E. Behar, J. Cottam, S.M. Kahn: ApJ 548, 966 (2001) T. Belloni, G. Tagliaferri: A&A 326, 608 (1997) T. Belloni, G. Tagliaferri: A&A 335, 517 (1998) T. Belloni, F. Verbunt: A&A 305, 806 (1996) T. Belloni, F. Verbunt, R.D. Mathieu: A&A 339, 431 (1998b) T. Belloni, F. Verbunt, J.H.M.M. Schmitt: A&A 269, 175 (1993) A.O. Benz, J. Conway, M. Güdel: A&A 331, 596 (1998) A.O. Benz, M. Güdel: A&A 285, 621 (1994) E. Berger: ApJ 572, 503 (2002) T.W. Berghöfer, J.H.M.M. Schmitt, J.P. Cassinelli: A&AS 118, 481 (1996) B.W. Bopp, R.E. Stencel: ApJ 247, L231 (1981) J. Bouvier: AJ 99, 946 (1990) J. Bouvier, S. Cabrit, M. Fernández, E.L. Martín, J.M. Matthews: A&A 272, 176 (1993) S. Bowyer, J.J. Drake, S. Vennes: ARA&A 38, 231 (2000) R.J. Bray, L.E. Cram, C.J. Durrant, R.E. Loughhead: in Plasma Loops in the Solar Corona, Cambridge University Press (1991) C. Briceño, N. Calvet, S. Kenyon, L. Hartmann: AJ 118, 1354 (1999) C. Briceño, L.W. Hartmann, J.R. Stauffer, M. Gagné, R.A. Stern, J.-P. Caillault: AJ 113, 740 (1997) N.S. Brickhouse, A.K. Dupree: ApJ 502, 918 (1998)


221

N.S. Brickhouse, A.K. Dupree, R.J. Edgar, D.A. Liedahl, S.A. Drake, N.E. White, K.P. Singh: ApJ 530, 387 (2000) N.S. Brickhouse, A.K. Dupree, P.R. Young: ApJ 562, L75 (2001) N.S. Brickhouse, J.C. Raymond, B.W. Smith: ApJS 97, 551 (1995) K.R. Briggs, J.P. Pye: MNRAS 345, 714 (2003) K.R. Briggs, J.P. Pye: MNRAS in press (2004) K.R. Briggs, J.P. Pye, R.D., Jeffries, E.J. Totten: MNRAS 319, 826 (2000) A.C. Brinkman, E. Behar, M. Güdel, M. Audard, A.J.F. den Boggende, G. Branduardi-Raymont, J. Cottam, C. Erd, J.W. den Herder, F. Jansen, J.S. Kaastra, S.M. Kahn, R. Mewe, F.B.S. Paerels, J.R. Peterson, A.P. Rasmussen, I. Sakelliou, C. de Vries: A&A 365, L324 (2001) A.C. Brinkman, C.J.T. Gunsing, J.S. Kaastra, R.L.J. van der Meer, R. Mewe, F. Paerels, A.J.J. Raassen, J.J. van Rooijen, H. Bräuninger, W. Burkert, V. Burwitz, G. Hartner, P. Predehl, J.-U. Ness, J.H.M.M. Schmitt, J.J. Drake, O. Johnson, M. Juda, V. Kashyap, S.S. Murray, D. Pease, P. Ratzlaff, B.J. Wargelin: ApJ 530, L111 (2000) A. Brown, S.A. Drake, M.E. Van Steenberg, J.L. Linsky: ApJ 373, 614 (1991) A. Brown, R.A. Osten, S.A. Drake, K.L. Jones, R.A. Stern: in The Hot Universe, IAU Symp 188, eds. K. Koyama, S. Kitamoto, M. Itoh, Kluwer, Dordrecht, p. 215 (1998) G.V. Brown, P. Beiersdorfer, H. Chen, M.H. Chen, K.J. Reed: ApJ 557, L75 (2001) G.V. Brown, P. Beiersdorfer, D.A. Liedahl, K. Widmann, S.M. Kahn: ApJ 502, 1015 (1998) J.C. Brown: Solar Phys. 18, 489 (1971) T.R. Burnight: Phys. Rev. A 76, 165 (1949) C.J. Butler: A&A 272, 507 (1993) C.J. Butler, M. Rodonò, B.H. Foing, B.M. Haisch: Nature 321, 679 (1986) P.B. Byrne, D. McKay: A&A 223, 241 (1989) J.-P. Caillault, D.J. Helfand: ApJ 289, 279 (1985) C.R. Canizares, D.P. Huenemoerder, D.S. Davis, D. Dewey, K.A. Flanagan, J. Houck, T.H. Markert, H.L. Marshall, M.L. Schattenburg, N.S. Schulz, M. Wise, J.J. Drake, N.S. Brickhouse: ApJ 539, L41 (2000) P.J. Cargill: ApJ 422, 381 (1994) L. Carkner, E.D. Feigelson, K. Koyama, T. Montmerle, I.N. Reid: ApJ 464, 286 (1996) L. Carkner, J.A. Kozak, E.D. Feigelson: AJ 116, 1933 (1998) R.W. Carroll, R.G. Cruddace, H. Friedman, E.T. Byram, K. Wood, J. Meekins, D. Yentis, G.H. Share, T.A. Chubb: ApJ 235, L77 (1980) S. Casanova, T. Montmerle, E.D. Feigelson, P. André: ApJ 439, 752 (1995) W. Cash, S. Bowyer, P.A. Charles, M. Lampton, G. Garmire, G. Riegler: ApJ 223, L21 (1978) W. Cash, P. Charles, S. Bowyer, F. Walter, T.R. Ayres, J.L. Linsky: ApJ 231, L137 (1979a) W. Cash, A. Shipley, S. Osterman, M. Joy: Nature 407, 160 (2000) W. Cash, T.P. Snow Jr.: ApJ 263, L59 (1982) W. Cash, T.P. Snow Jr., P. Charles: ApJ 232, L111 (1979b) R.C. Catura, L.W. Acton, H.M. Johnson: ApJ 196, L47 (1975) G. Cayrel de Strobel, C. Soubiran, N. Ralite: A&A 373, 159 (2001) P. Charles, F. Walter, S. Bowyer: Nature 282, 691 (1979) C.-C. Cheng, R. Pallavicini: ApJ 381, 234 (1991) C.S. Choi, T. Dotani: ApJ 492, 761 (1998) A. Ciaravella, A. Maggio, G. Peres: A&A 320, 945 (1997) A. Ciaravella, G. Peres, A. Maggio, S. Serio: A&A 306, 553 (1996) A. Collier Cameron: MNRAS 233, 235 (1988) A. Collier Cameron, D.K. Bedford, S.M. Rucinski, O. Vilhu, N.E. White: MNRAS 231, 131 (1988) A. Collura, A. Maggio, G. Micela, S. Sciortino, F.R. Harnden Jr., R. Rosner: ApJ 416, 204 (1993) A. Collura, L. Pasquini, J.H.M.M. Schmitt: A&A 205, 197 (1988)

222

M. Güdel

F. Comerón, R. Neuhäuser, A.A. Kaas: A&A 359, 269 (2000) E. Covino, J.M. Alcalá, S. Allain, J. Bouvier, L. Terranegra, J. Krautter: A&A 328, 187 (1997) S. Covino, M.R. Panzera, G. Tagliaferri, R. Pallavicini: A&A 371, 973 (2001) S. Covino, G. Tagliaferri, R. Pallavicini, R. Mewe, E. Poretti: A&A 355, 681 (2000) J.D. Craig, J.C. Brown: A&A 49, 239 (1976) N.B. Crosby, M.J. Aschwanden, B.R. Dennis: Solar Phys. 143, 275 (1993) R.G. Cruddace, A.K. Dupree: ApJ 277, 263 (1984) J.L. Culhane, N.E. White, R.A. Shafer, A.N. Parmar: MNRAS 243, 424 (1990) S.L. Cully, G. Fisher, M.J. Abbott, O.H.W. Siegmund: ApJ 435, 449 (1994) S.L. Cully, G.H. Fisher, S.L. Hawley, T. Simon: ApJ 491, 910 (1997) S.L. Cully, O.H.W. Siegmund, P.W. Vedder, J.V. Vallerga: ApJ 414, L49 (1993) J. Dachs, W. Hummel: A&A 312, 818 (1996) F. Damiani, E. Flaccomio, G. Micela, S. Sciortino, F.R. Harnden Jr., S.S. Murray, S.J. Wolk, R.D. Jeffries: ApJ 588, 1009 (2003) F. Damiani, G. Micela: ApJ 446, 341 (1995) F. Damiani, G. Micela, S. Sciortino, F.R. Harnden Jr.: ApJ 446, 331 (1995) K.J. Daniel, J.L. Linsky, M. Gagné: ApJ 578, 486 (2002) C. de Jager, J. Heise, S. Avgoloupis, G. Cutispoto, K. Kieboom, R.B. Herr, M. Landini, A.F. Langerwerf, L.N. Mavridis,A.S. Melkonian, R. Molenaar, B.C. Monsignori-Fossi, H.L. Nations, R. Pallavicini, V. Piirola, M. Rodonò, M.A. Seeds, G.H.J. van den Oord, O. Vilhu, C. Waelkens: A&A 156, 95 (1986) C. de Jager, J. Heise, A.M. van Genderen, B.H. Foing, I.V. Ilyin, D.S. Kilkenny, S. Avgoloupis, L. Mavridis, G. Cutispoto, M. Rodonò, M.A. Seeds, Yuen K. Ng, W. van Driel, X. Rabattu, A.M. Zodi, J.W.S. Vilas Boas, E. Scarlise, R.E. Schaal, P. Kaufmann, C. Waelkens: A&A 211, 157 (1989) R.C. Dempsey, J.L. Linsky, T.A. Fleming, J.H.M.M. Schmitt: ApJS 86, 599 (1993a) R.C. Dempsey, J.L. Linsky, T.A. Fleming, J.H.M.M. Schmitt: ApJ 478, 358 (1997) R.C. Dempsey, J.L. Linsky, J.H.M.M. Schmitt, T.A. Fleming: ApJ 413, 333 (1993b) B.R. Dennis, D.M. Zarro: Solar Phys. 146, 177 (1993) A.K. Dobson, R.R. Radick: ApJ 344, 907 (1989) J.-F. Donati: MNRAS 302, 457 (1999) R. Doron, E. Behar: ApJ 574, 518 (2002) J.D. Dorren, M. Güdel, E.F. Guinan: ApJ 448, 431 (1995) J.D. Dorren, E.F. Guinan: ApJ 428, 805 (1994) G.A. Doschek, U. Feldman, P.B. Landecker, D.L. McKenzie: ApJ 249, 372 (1981) J.F. Dowdy Jr., R.L. Moore, S.T. Wu: Solar Phys. 99, 79 (1985) J.G. Doyle, C.J. Butler: Nature 313, 378 (1985) J.G. Doyle, C.J. Butler, P.B. Byrne, G.H.J. van den Oord: A&A 193, 229 (1988b) J.G. Doyle, C.J. Butler, P.J. Callanan, G. Tagliaferri, R. de la Reza, N.E. White, C.A. Torres, G. Quast: A&A 191, 79 (1988a) J.G. Doyle, C.J. Butler, B.M. Haisch, M. Rodonò: MNRAS 223, 1P (1986) J.G. Doyle, B.J. Kellett, C.J. Butler, P.B. Byrne, J.E. Neff, A. Brown, D. Fox, J.L. Linsky, G.E. Bromage, S. Avgoloupis, L.N. Mavridis, J.H. Seiradakis, M. Mathioudakis, H.M. Murphy, J. Krzesinski, G. Pajdosz, V. Dadonas, J. Sperauskas, F. van Wyk, F. Marang, K. Olah, A. Collier Cameron, E. Antonomoulos, P. Rovithis, H. Rovithis-Livaniou: A&A 96, 351 (1992a) J.G. Doyle, B.J. Kellett, P.B. Byrne, S. Avgoloupis, L.N. Mavridis, J.H. Seiradakis, G.E. Bromage, T. Tsuru, K. Makishima, I.M. McHardy: MNRAS 248, 503 (1991) J.G. Doyle, M. Mathioudakis: A&A 227, 130 (1990) J.G. Doyle, G.H.J. van den Oord, B.J. Kellett: A&A 262, 533 (1992b) J.J. Drake: ApJ 496, L33 (1998)


223

J.J. Drake: ApJ 594, 496 (2003a) J.J. Drake: Adv. Space Res. 32, 945 (2003b) J.J. Drake, N.S. Brickhouse, V. Kashyap, J.M. Laming, D.P. Huenemoerder, R. Smith, B.J. Wargelin: ApJ 548, L81 (2001) J.J. Drake, A. Brown, R.J. Patterer, P.W. Vedder, S. Bowyer, E.F. Guinan: ApJ 421, L43 (1994) J.J. Drake, V. Kashya: ApJ 547, 428 (2001) J.J. Drake, J.M. Laming, K.G. Widing: ApJ 443, 393 (1995b) J.J. Drake, J.M. Laming, K.G. Widing: ApJ 478, 403 (1997) J.J. Drake, J.M. Laming, K.G. Widing, J.H.M.M. Schmitt, B. Haisch, S. Bowyer: Science 267, 1470 (1995a) J.J. Drake, G. Peres, S. Orlando, J.M. Laming, A. Maggio: ApJ 545, 1074 (2000) J.J. Drake, R.A. Stern, G.S. Stringfellow, M. Mathioudakis, J.M. Laming, D.L. Lambert: ApJ 469, 828 (1996) S.A. Drake, in Cosmic Abundances, eds. S.S. Holt, G. Sonneborn, ASP, San Francisco, p. 215 (1996) S.A. Drake, D.C. Abbott, T.S. Bastian, J.H. Bieging, E. Churchwell, G. Dulk, J.L. Linsky: ApJS 322, 902 (1987) S.A. Drake, J.L. Linsky, J.H.M.M. Schmitt, C. Rosso: ApJ 420, 387 (1994b) S.A. Drake, T. Simon, J.L. Linsky: ApJS 71, 905 (1989) S.A. Drake, T. Simon, J.L. Linsky: ApJS 82, 311 (1992) S.A. Drake, K.P. Singh, N.E. White, T. Simon: ApJ 436, L87 (1994a) A.K. Dupree, N.S. Brickhouse, G.A. Doschek, J.C. Green, J.C. Raymond: ApJ 418, L41 (1993) B. Edlén: Z. Astrophys. 22, 30 (1942) M. Endl, K.G. Strassmeier, M. Kürster: A&A 328, 565 (1997) F. Favata, M. Barbera, G. Micela, S. Sciortino: A&A 295, 147 (1995b) F. Favata, G. Giardino, G. Micela, S. Sciortino, F. Damiani: A&A 403, 187 (2003) F. Favata, A. Maggio, G. Peres, S. Sciortino: A&A 326, 1013 (1997a) F. Favata, R. Mewe, N.S. Brickhouse, R. Pallavicini, G. Micela, A.K. Dupree: A&A 324, L37 (1997c) F. Favata, G. Micela: Space Sci. Rev. 108, 577 (2003b) F. Favata, G. Micela, S.L. Baliunas, J.H.M.M. Schmitt, M. Güdel, F.R. Harnden Jr., S. Sciortino, R.A. Stern: A&A 418, L13 (2004) F. Favata, G. Micela, F. Reale: A&A 354, 1021 (2000b) F. Favata, G. Micela, F. Reale: A&A 375, 485 (2001) F. Favata, G. Micela, S. Sciortino: A&A 298, 482 (1995a) F. Favata, G. Micela, S. Sciortino: A&A 326, 647 (1997d) F. Favata, G. Micela, S. Sciortino, G.S. Vaiana: A&A 256, 86 (1992) F. Favata, T. Mineo, A.N. Parmar, G. Cusumano: A&A 324, L41 (1997b) F. Favata, F. Reale, G. Micela, S. Sciortino, A. Maggio, H. Matsumoto: A&A 353, 987 (2000a) F. Favata, R. Rosner, S. Sciortino, G.S. Vaiana: ApJ 324, 1010 (1988) F. Favata, J.H.M.M. Schmitt: A&A 350, 900 (1999) E.D. Feigelson: ApJ 468, 306 (1996) E.D. Feigelson, P. Broos, J.A. Gaffney III, G. Garmire, L.A. Hillenbrand, S.H. Pravdo, L. Townsley, Y. Tsuboi: ApJ 574, 258 (2002a) E.D. Feigelson, S. Casanova, T. Montmerle, J. Guibert: ApJ 416, 623 (1993) E.D. Feigelson, W.M. DeCampli: ApJ 243, L89 (1981) E.D. Feigelson, J.A. Gaffney III, G. Garmire, L.A. Hillenbrand, L. Townsley: ApJ 584, 911 (2003) E.D. Feigelson, G. Garmire, S.H. Pravdo: ApJ 572, 335 (2002b) E.D. Feigelson, J.M. Jackson, R.D. Mathieu, P.C. Myers, F.M. Walter: AJ 94, 1251 (1987) E.D. Feigelson, G.A. Kriss: ApJ 248, L35 (1981)

224

M. Güdel

E.D. Feigelson, G.A. Kriss: ApJ 338, 262 (1989) E.D. Feigelson, T. Montmerle: ARA&A 37, 363 (1999) U. Feldman: Phys. Scripta 46, 202 (1992) U. Feldman, G.A. Doschek, J.A. Klimchuk: ApJ 474, 511 (1997) U. Feldman, J.M. Laming, G.A. Doschek: ApJ 451, L79 (1995) S. Feltzing, J., Holmberg, J.R. Hurley: A&A 377, 911 (2001) G.A. Fisher, S.L. Hawley: ApJ 357, 243 (1990) G.A. Fisher, D.W. Longcope, T.R. Metcalf, A.A. Pevtsov: ApJ 508, 885 (1998) E. Flaccomio, F. Damiani, G. Micela, S. Sciortino, F.R. Harnden Jr., S.S. Murray, S.J. Wolk: ApJ 582, 382 (2003a) E. Flaccomio, F. Damiani, G. Micela, S. Sciortino, F.R. Harnden Jr., S.S. Murray, S.J. Wolk: ApJ 582, 398 (2003b) E. Flaccomio, G. Micela, S. Sciortino: A&A 402, 277 (2003c) E. Flaccomio, G. Micela, S. Sciortino: A&A 397, 611 (2003d) E. Flaccomio, G. Micela, S. Sciortino, F. Damiani, F. Favata, F.R. Harnden Jr., J. Schachter: A&A 355, 651 (2000) E. Flaccomio, G. Micela, S. Sciortino, F. Favata, C. Corbally, A. Tomaney: A&A 345, 521 (1999) T.A. Fleming, M.S. Giampapa, D. Garza: ApJ 594, 982 (2003) T.A. Fleming, M.S. Giampapa, J.H.M.M. Schmitt: ApJ 533, 372 (2000) T.A. Fleming, M.S. Giampapa, J.H.M.M. Schmitt, J.A. Bookbinder: ApJ 410, 387 (1993) T.A. Fleming, I.M. Gioia, T. Maccacaro: ApJ 340, 1011 (1989) T.A. Fleming, J. Liebert, I.M. Gioia, T. Maccacaro: ApJ 331, 958 (1988) T.A. Fleming, J.H.M.M. Schmitt, M.S. Giampapa: ApJ 450, 401 (1995) T.A. Fleming, G. Tagliaferri: ApJ 472, L101 (1996) D.C. Fox, J.L. Linsky, A. Vealé, R.C. Dempsey, A. Brown, J.E. Neff, I. Pagano, M. Rodonò, G.E. Bromage, M. Kürster, J.H.M.M. Schmitt: A&A 284, 91 (1994) E. Franciosini, R. Pallavicini, T. Bastian, F. Chiuderi-Drago, S. Randich, G. Tagliaferri, M. Massi, J. Neidhöfer: in 11th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, eds. R.J. García López, R. Rebolo, M.R. Zapaterio Osorio, ASP, San Francisco, p. 930 (1999) E. Franciosini, R. Pallavicini, G. Tagliaferri: A&A 375, 196 (2001) E. Franciosini, R. Pallavicini, G. Tagliaferri: A&A 399, 279 (2003) E. Franciosini, S. Randich, R. Pallavicini: A&A 357, 139 (2000) E. Franciosini, S. Randich, R. Pallavicini: A&A in press (2004) M. Freyberg, J.H.M.M. Schmitt: A&A 296, L21 (1995) A.H. Gabriel, C. Jordan: MNRAS 145, 241 (1969) M. Gagné, J.-P. Caillault: ApJ 437, 361 (1994) M. Gagné, J.-P. Caillault, J.R. Stauffer: ApJ 450, 217 (1995a) M. Gagné, J.-P. Caillault, J.R. Stauffer: ApJ 445, 280 (1995b) M. Gagné, J.A. Valenti, J.L. Linsky, G. Tagliaferri, S. Covino, M. Güdel: ApJ 515, 423 (1999) G.F. Gahm: ApJ 242, L163 (1980) G. Garmire, E.D. Feigelson, P. Broos, L.A. Hillenbrand, S. Pravdo, L. Townsley, Y. Tsuboi: AJ 120, 1426 (2000) N. Gehrels, E.D. Williams: ApJ 418, L25 (1993) K.V. Getman, E.D. Feigelson, L. Townsley, J. Bally, C.J. Lada, B. Reipurth: ApJ 575, 354 (2002) M.S. Giampapa, L. Golub, G. Peres, S. Serio, G.S. Vaiana: ApJ 289, 203 (1985) M.S. Giampapa, C.F. Prosser, T.A. Fleming: ApJ 501, 624 (1998) M.S. Giampapa, R. Rosner, V. Kashyap, T.A. Fleming, J.H.M.M. Schmitt, J.A. Bookbinder: ApJ 463, 707 (1996) G. Giardino, F. Favata, G. Micela, F. Reale: A&A 669, 679 (2004) P.A. Gilman: ApJS 53, 243 (1983)


225

A.E. Glassgold, E.D. Feigelson, T. Montmerle: in Protostars and Planets IV, eds. V. Mannings, A.P. Boss, S.S. Russell, University of Arizona, Tucson, p. 429 (2000) L. Golub, F.R. Harnden Jr., C.W. Maxson, R. Rosner, G.S. Vaiana, W. Cash Jr., T.P. Snow Jr.: ApJ 271, 264 (1983) L. Golub, F.R. Harnden Jr., R. Pallavicini, R. Rosner, G.S. Vaiana: ApJ 253, 242 (1982) P. Gondoin: A&A 352, 217 (1999) P. Gondoin: A&A 400, 249 (2003a) P. Gondoin: A&A 404, 355 (2003b) P. Gondoin: A&A 409, 263 (2003c) P. Gondoin: A&A 415, 1113 (2004a) P. Gondoin: A&A 413, 1095 (2004b) P. Gondoin, C. Erd, D. Lumb: A&A 383, 919 (2002) P. Gondoin, A. Mangeney, F. Praderie: A&A 174, 187 (1987) E.V. Gotthelf, L. Jalota, K. Mukai, N.E. White: ApJ 436, L91 (1994) V.G. Graffagnino, D. Wonnacott, S. Schaeidt: MNRAS 275, 129 (1995) N. Grevesse, A.J. Sauval: A&A 347, 348 (1999) N.W. Griffiths: ApJ 518, 873 (1999) N.W. Griffiths, C. Jordan: ApJ 497, 883 (1998) N. Grosso: A&A 370, L22 (2001) N. Grosso, T. Montmerle, S. Bontemps, P. André, E.D. Feigelson: A&A 359, 113 (2000) N. Grosso, T. Montmerle, E.D. Feigelson, P. André, S. Casanova, J. Gregorio-Hetem: Nature 387, 56 (1997) W. Grotrian: Naturw 27, 214 (1939) M. Güdel: ApJ 480, L121 (1997) M. Güdel: ARA&A 40, 217 (2002) M. Güdel, K. Arzner, M. Audard, R. Mewe: A&A 403, 155 (2003b) M. Güdel, M. Audard, K. Briggs, F. Haberl, H. Magee, A. Maggio, R. Mewe, R. Pallavicini, J. Pye: A&A 365, L336 (2001b) M. Güdel, M. Audard, V.L. Kashyap, J.J. Drake, E.F. Guinan: ApJ 582, 423 (2003a) M. Güdel, M. Audard, H. Magee, E. Franciosini, N. Grosso, F.A. Cordova, R. Pallavicini, R. Mewe: A&A 365, L344 (2001a) M. Güdel, M. Audard, F. Reale, S.L. Skinner, J.L. Linsky: A&A 416, 713 (2004) M. Güdel, M. Audard, S.L. Skinner, M.I. Horvath: ApJ 580, L73 (2002a) M. Güdel, M. Audard, K.W. Smith, E. Behar, A.J. Beasley, R. Mewe: ApJ 577, 371 (2002b) M. Güdel, M. Audard, K.W. Smith, A. Sres, C., Escoda, R. Wehrli, E.F. Guinan, I. Ribas, A.J. Beasley, R. Mewe, A.J.J. Raassen, E. Behar, H. Magee: in 12th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, eds. T. Ayres, et al., on-line publication at http://origins.colorado.edu/cs12/, (2003c) M. Güdel, M. Audard, A. Sres, R. Wehrli, E. Behar, R. Mewe, A.J.J. Raassen, H.R.M. Magee: in Stellar Coronae in the Chandra and XMM-Newton Era, eds. F. Favata, J.J. Drake, ASP, San Francisco, p. 497 (2002c) M. Güdel, A.O. Benz: ApJ 405, L63 (1993) M. Güdel, A.O. Benz, J.H.M.M. Schmitt, S.L. Skinner: ApJ 471, 1002 (1996) M. Güdel, E.F. Guinan, P.B. Etzel, R. Mewe, J.S. Kaastra, S.L. Skinner: in Tenth Cambridge Workshop on Cool Stars, Stellar Systems and the Sun, eds. R. A. Donahue, J.A. Bookbinder, ASP, San Francisco, p. 1247 (1998) M. Güdel, E.F. Guinan, R. Mewe, J.S. Kaastra, S.L. Skinner: ApJ 479, 416 (1997b) M. Güdel, E.F. Guinan, S.L. Skinner: ApJ 483, 947 (1997a) M. Güdel, J.L. Linsky, A. Brown, F. Nagase: ApJ 511, 405 (1999)

226

M. Güdel

M. Güdel, J.H.M.M. Schmitt: in Röntgenstrahlung from the Universe, eds. H.U. Zimmermann, J.E. Trümper, H. Yorke, MPE, München, p. 35 (1995) M. Güdel, J.H.M.M. Schmitt, A.O. Benz, N.M. Elias II: A&A 301, 201 (1995) M. Güdel, J.H.M.M. Schmitt, J.A. Bookbinder, T.A. Fleming: ApJ 415, 236 (1993) P. Guillout, M. Haywood, C. Motch, A.C. Robin: A&A 316, 89 (1996) P. Guillout, M.F. Sterzik, J.H.M.M. Schmitt, C. Motch, D. Egret, W. Voges, R. Neuhäuser: A&A 334, 540 (1998a) P. Guillout, M.F. Sterzik, J.H.M.M. Schmitt, C. Motch, R. Neuhäuser: A&A 337, 113 (1998b) A.G. Gunn, P.A. Brady, V. Migenes, R.E. Spencer, J.G. Doyle: MNRAS 304, 611 (1999) A.G. Gunn, V. Migenes, J.G. Doyle, R.E. Spencer, M. Mathioudakis: MNRAS 287, 199 (1997) B.M. Haisch, J.A. Bookbinder, A. Maggio, G.S. Vaiana, J.O. Bennett: ApJ 361, 570 (1990c) B.M. Haisch, C.J. Butler, J.G. Doyle, M. Rodonò: A&A 181, 96 (1987) B.M. Haisch, C.J. Butler, B. Foing, M. Rodonò, M.S. Giampapa: A&A 232, 387 (1990a) B. Haisch, J.J. Drake, J.H.M.M. Schmitt: ApJ 421, L39 (1994) B.M. Haisch, J.L. Linsky, P.L. Bornmann, R.E. Stencel, S.K. Antiochos, L. Golub, G.S. Vaiana: ApJ 267, 280 (1983) B.M. Haisch, J.L. Linsky, F.R. Harnden Jr., R. Rosner, F.D. Seward, G.S. Vaiana: ApJ 242, L99 (1980) B.M. Haisch, J.L. Linsky, M. Lampton, F. Paresce, B. Margon, R. Stern: ApJ 213, L119 (1977) B.M. Haisch, J.L. Linsky, O.B. Slee, B.C. Siegman, I. Nikoloff, M. Candy, D. Harwood,A. Verveer, P.J. Quinn, I. Wilson, A.A. Page, P. Higson, F.D. Seward: ApJ 245, 1009 (1981) B. Haisch, J.H.M.M. Schmitt: ApJ 426, 716 (1994) B.M. Haisch, J.H.M.M. Schmitt, M. Rodonò, D.M. Gibson: A&A 230, 419 (1990b) B. Haisch, J.H.M.M. Schmitt, C. Rosso: ApJ 383, L15 (1991b) B. Haisch, J.H.M.M. Schmitt, C. Rosso: ApJ 388, L61 (1992) B.M. Haisch, T. Simon: ApJ 263, 252 (1982) B. Haisch, K.T. Strong, M. Rodonò: ARA&A 29, 275 (1991a) K. Hamaguchi, H. Terada, A. Bamba, K. Koyama: ApJ 532, 1111 (2000) S. Harmer, R.D. Jeffries, E.J. Totten, J.P. Pye: MNRAS 324, 473 (2001) F.R. Harnden Jr., N.R. Adams, F. Damiani, J.J. Drake, N.R. Evans, F. Favata, E. Flaccomio, P. Freeman, R.D. Jeffries, V. Kashyap, G. Micela, B.M. Patten, N. Pizzolato, J.F. Schachter, S. Sciortino, J. Stauffer, S.J. Wolk, M.V. Zombeck: ApJ 547, L141 (2001) F.R. Harnden Jr., D. Fabricant, K. Topka, B.P. Flannery, W.H. Tucker, P. Gorenstein: ApJ 214, 418 (1977) L. Hartmann, A.K. Dupree, J.C. Raymond: ApJ 236, L143 (1980) A. Hatzes: in Stellar Surface Structure – Poster Proceedings, ed. K.G. Strassmeier, University of Vienna, Vienna, p. 90 (1995) S.L. Hawley, G.H. Fisher, T. Simon, S.L. Cully, S.E. Deustua, M. Jablonski, C.M. Johns-Krull, B.R. Pettersen, V. Smith, W.J. Spiesman, J. Valenti: ApJ 453, 464 (1995) M.R. Hayashi, K. Shibata, R. Matsumoto: ApJ 468, L37 (1996) J. Heise, A.C. Brinkman, J. Schrijver, R. Mewe, E.H.B.M. Gronenschild, A.J.F. den Boggende, J. Grindlay: ApJ 202, L73 (1975) A. Hempelmann, J.H.M.M. Schmitt, S.L. Baliunas, R.A. Donahue: A&A 406, L39 (2003) A. Hempelmann, J.H.M.M. Schmitt, M. Schultz, G. Rüdiger, K. St¸epie`n: A&A 294, 515 (1995) A. Hempelmann, J.H.M.M. Schmitt, K. St¸epie`n: A&A 305, 284 (1996) J.-C. Hénoux: Adv. Space Res. 15, 23 (1995) J.S. Hey: Nature 157, 47 (1946) S.T. Hodgkin, R.F. Jameson, I.A. Steele: MNRAS 274, 869 (1995) W. Hoff, T. Henning, W. Pfau: A&A 336, 242 (1998)


227

S.S. Holt, N.E. White, R.H. Becker, E.A. Boldt, R.F. Mushotzky, P.J. Serlemitsos, B.W. Smith: ApJ 234, L65 (1979) H.S. Hudson, L.W. Acton, T. Hirayama, Y. Uchida: PASP 44, L77 (1992) D.P. Huenemoerder, C.R. Canizares, J.J. Drake, J. Sanz-Forcada: ApJ 595, 1131 (2003) D.P. Huenemoerder, C.R. Canizares, N.S. Schulz: ApJ 559, 1135 (2001) M. Hünsch, D. Reimers: A&A 296, 509 (1995) M. Hünsch, J.H.M.M. Schmitt, K.-P. Schröder, D. Reimers: A&A 310, 801 (1996) M. Hünsch, J.H.M.M. Schmitt, M.F. Sterzik, W. Voges: A&AS 135, 319 (1999) M. Hünsch, J.H.M.M. Schmitt, W. Voges: A&AS 127, 251 (1998a) M. Hünsch, J.H.M.M. Schmitt, W. Voges: A&AS 132, 155 (1998b) M. Hünsch, K.-P. Schröder: A&A 309, L51 (1996) M. Hünsch, C. Weidner, J.H.M.M. Schmitt: A&A 402, 571 (2003) G.A.J. Hussain, A.A. van Ballegooijen, M. Jardine, A. Collier Cameron: ApJ 575, 1078 (2002) K. Imanishi, K. Koyama, Y. Tsuboi: ApJ 557, 747 (2001a) K. Imanishi, M. Nakajima, M. Tsujimoto, K. Koyama, Y. Tsuboi: PASJ 55, 653 (2003) K. Imanishi, M. Tsujimoto, K. Koyama: ApJ 563, 361 (2001b) K. Imanishi, M. Tsujimoto, K. Koyama: ApJ 572, 300 (2002) J. Jakimiec, B. Sylwester, J. Sylwester, S. Serio, G. Peres, F. Reale: A&A 253, 269 (1992) D.J. James, M.M. Jardine, R.D. Jeffries, S. Randich, A. Collier Cameron, M. Ferreira: MNRAS 318, 1217 (2000) D.J. James, R.D. Jeffries: MNRAS 291, 252 (1997) M. Jardine: A&A 414, L5 (2004) M. Jardine, A. Collier Cameron, J.-F. Donati: MNRAS 333, 339 (2002a) M. Jardine, K. Wood, A. Collier Cameron, J.-F. Donati, D.H. Mackay: MNRAS 336, 1364 (2002b) M. Jardine, Y.C. Unruh: A&A 346, 883 (1999) R.D. Jeffries: MNRAS 295, 825 (1998) R.D. Jeffries, D.K. Bedford: MNRAS 246, 337 (1990) R.D. Jeffries, M.R. Thurston, J.P. Pye: MNRAS 287, 350 (1997) R.D. Jeffries, A.J. Tolley: MNRAS 300, 331 (1998) E.L.N. Jensen, D.H. Cohen, R. Neuhäuser: AJ 116, 414 (1998) H.M. Johnson: ApJ 243, 234 (1981) H.M. Johnson: ApJ 316, 458 (1987) O. Johnson, J.J. Drake, V. Kashyap, N.S. Brickhouse, A.K. Dupree, P. Freeman, P.R. Young, G.A. Kriss: ApJ 565, L97 (2002) C. Jordan: A&A 86, 355 (1980) C. Jordan, T.R. Ayres, A. Brown, J.L. Linsky, T. Simon: MNRAS 225, 903 (1987) C. Jordan, A. Brown, F.M. Walter, J.L. Linsky: MNRAS 218, 465 (1986) C. Jordan, G.A. Doschek, J.J. Drake, A.B. Galvin, J.C. Raymond: in 10th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, eds. R.A. Donahue, J.A. Bookbinder, ASP, San Francisco, p. 91 (1998) C. Jordan, B. Montesinos: MNRAS 252, 21P (1991) J.S. Kaastra, R. Mewe, D.A. Liedahl, K.P. Singh, N.E. White, S.A. Drake: A&A 314, 547 (1996) S. Kahler, L. Golub, F.R. Harnden Jr., W. Liller, F. Seward, G. Vaiana, B. Lovell, R.J. Davis, R.E. Spencer, D.R. Whitehouse, P.A. Feldman, M.R. Viner, B. Leslie, S.M. Kahn, K.O. Mason, M.M. Davis, C.J. Grannell, R.W. Hobbs, T.J. Schneeberger, S.P. Worden, R.A. Schommer, S.S. Vogt, B.R. Pettersen, G.D. Coleman, J.T. Karpen, M.S. Giampapa, E.K. Hege, V. Pazzani, M. Rodonò, G. Romeo, P.F. Chugainov: ApJ 252, 239 (1982) S.M. Kahn, J.L. Linsky, K.O. Mason, B.M. Haisch, C.S. Bowyer, N.E. White, S.H. Pravdo: ApJ 234, L107 (1979) Y. Kamata, K. Koyama, Y. Tsuboi, S. Yamauchi: PASJ 49, 461 (1997)

228

M. Güdel

V. Kashyap, J.J. Drake: ApJ 524, 988 (1996) V. Kashyap, J.J. Drake: ApJ 503, 450 (1998) V. Kashyap, J.J. Drake: ApJ 524, 988 (1999) V. Kashyap, J.J. Drake, M. Güdel, M. Audard: ApJ 580, 1118 (2002) V. Kashyap, R. Rosner, F.R. Harnden Jr., A. Maggio, G. Micela, S. Sciortino: ApJ 431, 402 (1994) J.H. Kastner, D.P. Huenemoerder, N.S. Schulz, C.R. Canizares, D.A. Weintraub: ApJ 567, 434 (2002) J.H. Kastner, D.P. Huenemoerder, N.S. Schulz, D.A. Weintraub: ApJ 525, 837 (1999) M.M. Katsova, A.Ya. Boiko, M.A. Livshits: A&A 321, 549 (1997) M.M. Katsova, J.J. Drake, M.A. Livshits: ApJ 510, 986 (1999) R.A. Kopp, G. Poletto: Sol. Phys. 93, 351 (1984) R.A. Kopp, G. Poletto: ApJ 418, 496 (1993) T. Kosugi, B.R. Dennis, K. Kai: ApJ 324, 1118 (1988) K. Koyama, K. Hamaguchi, S. Ueno, N. Kobayashi, E.D. Feigelson: PASJ 48, L87 (1996) K. Koyama, Y. Maeda, M. Ozaki, S. Ueno, Y. Kamata, Y. Tawara, S. Skinner, S. Yamauchi: PASJ 46, L125 (1994) J. Krautter, R. Wichmann, J.H.M.M. Schmitt, J.M. Alcalá, R. Neuhäuser, L. Terranegra: A&AS 123, 329 (1997) R.W. Kreplin: Ann. Geophys. 26, 567 (1970) A. Krishnamurthi, C.S. Reynolds, J.L. Linsky, E. Martín, M. Gagné: AJ 121, 337 (2001) S. Krucker, A.O. Benz: ApJ 501, L213 (1998) W.H.-M. Ku, G.A. Chanan: ApJ 234, L59 (1979) W.H.-M. Ku, G. Righini-Cohen, M. Simon: Science 215, 61 (1982) M.R. Kundu, P.D. Jackson, S.M. White, M. Melozzi: ApJ 312, 822 (1987) M.R. Kundu, R. Pallavicini, S.M. White, P.D. Jackson: A&A 195, 159 (1988) M. Kürster, J.H.M.M. Schmitt: A&A 311, 211 (1996) M. Kürster, J.H.M.M. Schmitt, G. Cutispoto, K. Dennerl: A&A 320, 831 (1997) J.M. Laming, J.J. Drake: ApJ 516, 324 (1999) J.M. Laming, J.J. Drake, K.G. Widing: ApJ 443, 416 (1995) J.M. Laming, J.J. Drake, K.G. Widing: ApJ 462, 948 (1996) J.M. Laming, I. Kink, E. Takacs, J.V. Porto, J.D. Gillaspy, E.H. Silver, H.W. Schnopper, S.R. Bandler, N.S. Brickhouse, S.S. Murray, M. Barbera, A.K. Bhatia, G.A. Doschek, N. Madden, D. Landis, J. Beeman, E.E. Haller: ApJ 545, L161 (2000) E. Landi, U. Feldman, D.E. Innes, W. Curdt: ApJ 582, 506 (2003) E. Landi, M. Landini: A&A 340, 265 (1998) M. Landini, B.C. Monsignori Fossi, R. Pallavicini, L. Piro: A&A 157, 217 (1986) W.A. Lawson, E.D. Feigelson, D.P. Huenemoerder: MNRAS 280, 1071 (1996) J.R. Lemen, R. Mewe, C.J. Schrijver, A. Fludra: ApJ 341, 474 (1989) J.K. Lepson, P. Beiersdorfer, G.V. Brown, D.A. Liedahl, S.B. Utter, N.S. Brickhouse, A.K. Dupree, J.S. Kaastra, R. Mewe, S.M. Kahn: ApJ 578, 648 (2002) J. Lim, G.J. Nelson, C. Castro, D. Kilkenny, F. van Wyk: ApJ 388, L27 (1992) J. Lim, S.M. White, S.L. Cully: ApJ 461, 1009 (1996) R.P. Lin, R.A. Schwartz, S.R. Kane, R.M. Pelling, K. Hurley: ApJ 283, 421 (1984) J.L. Linsky: Solar Phys. 100, 333 (1985) J.L. Linsky, B.M. Haisch: ApJ 229, L27 (1979) J.L. Linsky, B.E. Wood, A. Brown, R. Osten: ApJ 492, 767 (1998) L.B. Lucy: AJ 79, 745 (1974) H.R.M. Magee, M. Güdel, M. Audard, R. Mewe: Adv. Space Res. 32, 1149 (2003) A. Maggio, F. Favata, H. Negoro, N.S. Brickhouse, A.K. Dupree: A&A 352, 248 (1999) A. Maggio, F. Favata, G. Peres, S. Sciortino: A&A 330, 139 (1998)


229

A. Maggio, R. Pallavicini, F. Reale, G. Tagliaferri: A&A 356, 627 (2000) A. Maggio, G. Peres: A&A 306, 563 (1996) A. Maggio, G. Peres: A&A 325, 237 (1997) A. Maggio, S. Sciortino, F.R. Harnden Jr.: ApJ 432, 701 (1994) A. Maggio, S. Sciortino, G.S. Vaiana, P. Majer, J.A. Bookbinder, L. Golub, F.R. Harnden Jr., R. Rosner: ApJ 315, 687 (1987) A. Maggio, G.S. Vaiana, B.M. Haisch, R.A. Stern, J. Bookbinder, F.R. Harnden Jr., R. Rosner: ApJ 348, 253 (1990) P. Majer, J.H.M.M. Schmitt, L. Golub, F.R. Harnden Jr., R. Rosner: ApJ 300, 360 (1986) E.E. Mamajek, W.A. Lawson, E.D. Feigelson: ApJ 516, L77 (1999) E.E. Mamajek, W.A. Lawson, E.D. Feigelson: ApJ 544, 356 (2000) A. Mangeney, F. Praderie: A&A 130, 143 (1984) S.P. Maran, R.D. Robinson, S.N. Shore, J.W. Brosius, K.G. Carpenter, B.E. Woodgate, J.L. Linsky, A. Brown, P.B. Byrne, M.R. Kundu, S. White, J.C. Brandt, R.A. Shine, F.M. Walter: ApJ 421, 800 (1994) A. Marino, G. Micela, G. Peres: A&A 353, 177 (2000) A. Marino, G. Micela, G. Peres, G., S. Sciortino: A&A 383, 210 (2002) A. Marino, G. Micela, G. Peres, S. Sciortino: A&A 407, L63 (2003a) A. Marino, G. Micela, G. Peres, S. Sciortino: A&A 406, 629 (2003b) J.T. Mariska, A.G. Emslie, P. Li: ApJ 341, 1067 (1989) P.C.H. Martens, N.P.M. Kuin: A&A 112, 366 (1982) E.L. Martín, A. Magazzù: A&A 342, 173 (1999) M. Mathioudakis, J.G. Doyle: A&A 224, 179 (1989) M. Mathioudakis, J.G. Doyle: A&A 240, 357 (1990) M. Mathioudakis, D.J. Mullan: A&A 342, 524 (1999) G.E. McCluskey Jr., Y. Kondo: PASP 96, 817 (1984) P.A. McGale, J.P. Pye, C.R. Barber, C.G. Page: MNRAS 275, 1232 (1995) P.A. McGale, J.P. Pye, S.T. Hodgkin: MNRAS 280, 627 (1996) D.L. McKenzie, R.M. Broussard, P.N. Landecker, H.R. Rugge, R.M. Young, G.A. Doschek, U. Feldman: ApJ 238, L43 (1980) R. Mewe: A&AR 3, 127 (1991) R. Mewe, S.A. Drake, J.S. Kaastra, C.J. Schrijver, J.J. Drake, M. Güdel, J.H.M.M. Schmitt, K.P. Singh, N.E. White: A&A 339, 545 (1998a) R. Mewe, E.H.B.M. Gronenschild, G.H.J. van den Oord: A&AS 62, 197 (1985) R. Mewe, E.H.B.M. Gronenschild, N.J. Westergaard, J. Heise, F. Seward, T. Chlebowski, N.P.M. Kuin, A.C. Brinkman, J.H. Dijkstra, H.W. Schnopper: ApJ 260, 233 (1982) R. Mewe, M. Güdel, F. Favata, J.S. Kaastra: A&A 340, 216 (1998b) R. Mewe, J. Heise, E.H.B.M. Gronenschild, A.C. Brinkman, J. Schrijver, A.J.F. den Boggende: ApJ 202, L67 (1975) R. Mewe, J.S. Kaastra, C.J. Schrijver, G.H.J. van den Oord, F.J.M. Alkemade: A&A 296, 477 (1995) R. Mewe, J.S. Kaastra, G.H.J. van den Oord, J. Vink, Y. Tawara: A&A 320, 147 (1997) R. Mewe, J.S. Kaastra, S.M. White, R. Pallavicini: A&A 315, 170 (1996) R. Mewe, A.J.J. Raassen, J.J. Drake, J.S. Kaastra, R.L.J. van der Meer, D. Porquet: A&A 368, 888 (2001) R. Mewe, C.J. Schrijver: A&A 169, 178 (1986) J.-P. Meyer: ApJS 57, 151 (1985a) J.-P. Meyer: ApJS 57, 171 (1985b) G. Micela, F. Favata, S. Sciortino: A&A 326, 221 (1997b) G. Micela, A. Maggio, G.S. Vaiana: ApJ 388, 171 (1992)

230

M. Güdel

G. Micela, A. Marino: A&A 404, 637 (2003) G. Micela, J. Pye, S. Sciortino: A&A 320, 865 (1997a) G. Micela, S. Sciortino, F. Favata: ApJ 412, 618 (1993) G. Micela, S. Sciortino, F. Favata, R. Pallavicini, J. Pye: A&A 344, 83 (1999b) G. Micela, S. Sciortino, F.R. Harnden Jr., V. Kashyap, R. Rosner, C.F. Prosser, F. Damiani, J. Stauffer, J.-P. Caillault: A&A 341, 751 (1999a) G. Micela, S. Sciortino, R.D. Jeffries, M.R. Thurston, F. Favata: A&A 357, 909 (2000) G. Micela, S. Sciortino, V. Kashyap, F.R. Harnden Jr., R. Rosner: ApJS 102, 75 (1996) G. Micela, S. Sciortino, S. Serio, G.S. Vaiana, J. Bookbinder, L. Golub, F.R. Harnden Jr., R. Rosner: ApJ 292, 171 (1985) G. Micela, S. Sciortino, G.S. Vaiana, F.R. Harnden Jr., R. Rosner, J.H.M.M. Schmitt: ApJ 348, 557 (1990) G. Micela, S. Sciortino, G.S. Vaiana, J.H.M.M. Schmitt, R.A. Stern, F.R. Harnden Jr., R. Rosner: ApJ 325, 798 (1988) U. Mitra-Kraev, L.K. Harra, M. Güdel, M. Audard, G. Branduardi-Raymont, H.R.M. Kay, R. Mewe, A.J.J. Raassen, L. van Driel-Gesztelyi: A&A submitted (2004) F. Mokler, B. Stelzer: A&A 391, 1025 (2002) B.C. Monsignori Fossi, M. Landini, G. Del Zanna, S. Bowyer: ApJ 466, 427 (1996) T. Montmerle, N. Grosso, Y. Tsuboi, K. Koyama: ApJ 532, 1097 (2000) T. Montmerle, L. Koch-Miramond, E. Falgarone, J.E. Grindlay: ApJ 269, 182 (1983) D.J. Mullan, Q.Q. Cheng: ApJ 420, 392 (1994a) D.J. Mullan, Q.Q. Cheng: ApJ 435, 435 (1994b) D.J. Mullan, T.A. Fleming: ApJ 464, 890 (1996) F. Nagai: Solar Phys. 68, 351 (1980) J.-U. Ness, N.S. Brickhouse, J.J. Drake, D.P. Huenemoerder: ApJ 598, 1277 (2003b) J.-U. Ness, M. Güdel, J.H.M.M. Schmitt, M. Audard, A. Telleschi: A&A in press (2004) J.-U. Ness, R. Mewe, J.H.M.M. Schmitt, A.J.J. Raassen, D. Porquet, J.S. Kaastra, R.L.J. van der Meer, V. Burwitz, P. Predehl: A&A 367, 282 (2001) J.-U. Ness, J.H.M.M. Schmitt, M. Audard, M. Güdel, R. Mewe: A&A 407, 347 (2003a) J.-U. Ness, J.H.M.M. Schmitt, V. Burwitz, R. Mewe, P. Predehl: A&A 387, 1032 (2002b) J.-U. Ness, J.H.M.M. Schmitt, V. Burwitz, R. Mewe, A.J.J. Raassen, R.L.J. van der Meer, P. Predehl, A.C. Brinkman: A&A 394, 911 (2002a) R. Neuhäuser, C. Briceño, F. Comerón, T. Hearty, E.L. Martín, J.H.M.M. Schmitt, B. Stelzer, R. Supper, W. Voges, H. Zinnecker: A&A 343, 883 (1999) R. Neuhäuser, F. Comerón: Science 282, 83 (1998) R. Neuhäuser, T. Preibisch: A&A 322, L37 (1997) R. Neuhäuser, M.F. Sterzik, J.H.M.M. Schmitt, R. Wichmann, J. Krautter: A&A 297, 391 (1995a) R. Neuhäuser, M.F. Sterzik, J.H.M.M. Schmitt, R. Wichmann, J. Krautter: A&A 295, L5 (1995c) R. Neuhäuser, M.F. Sterzik, G. Torres, E.L. Martín: A&A 299, L13 (1995b) R. Neuhäuser, G. Torres, M.F. Sterzik, S. Randich: A&A 325, 647 (1997) W.M. Neupert: ApJ 153, L59 (1968) R.W. Noyes, L.W. Hartmann, S.L. Baliunas, D.K. Duncan, A.N. Vaughan: ApJ 279, 763 (1984) J. Nugent, G. Garmire: ApJ 226, L83 (1978) S. Orlando, G. Peres, F. Reale: ApJ 528, 524 (2000) S. Orlando, G. Peres, F. Reale: ApJ 560, 499 (2001) A. Ortolani, A. Maggio, R. Pallavicini, S. Sciortino, J.J. Drake, S.A. Drake: A&A 325, 664 (1997) R.A. Osten, T.R. Ayres, A. Brown, J.L. Linsky, A. Krishnamurthi: ApJ 582, 1073 (2003) R.A. Osten, A. Brown: ApJ 515, 746 (1999) R.A. Osten, A. Brown, T.R. Ayres, S.A. Drake, E. Franciosini, R. Pallavicini, G. Tagliaferri, R.T. Stewart, S.L. Skinner, J.L. Linsky: ApJS 153, 317 (2004)


231

R.A. Osten, A. Brown, T.R. Ayres, J.L. Linsky, S.A. Drake, M. Gagné, R.A. Stern: ApJ 544, 953 (2000) R.A. Osten, A. Brown, B.E. Wood, P. Brady: ApJS 138, 99 (2002) R. Ottmann: A&A 273, 546 (1993) R. Ottmann: A&A 286, L27 (1994) R. Ottmann, T.A. Fleming, L. Pasquini: A&A 322, 785 (1997) R. Ottmann, M.J. Pfeiffer, T. Gehren: A&A 338, 661 (1998) R. Ottmann, J.H.M.M. Schmitt: A&A 283, 871 (1994) R. Ottmann, J.H.M.M. Schmitt: A&A 307, 813 (1996) R. Ottmann, J.H.M.M. Schmitt, M. Kürster: ApJ 413, 710 (1993) H. Ozawa, F. Nagase, Y. Ueda, T. Dotani, M. Ishida: ApJ 523, L81 (1999) R. Pallavicini: A&AR 1, 177 (1989) R. Pallavicini: in 11th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, eds. R.J. Garcia Lopez, et al., ASP, San Francisco, p. 377 (2001) R. Pallavicini, L. Golub, R. Rosner, G.S. Vaiana, T. Ayres, J.L. Linsky: ApJ 248, 279 (1981) R. Pallavicini, B.C. Monsignori-Fossi, M. Landini, J.H.M.M. Schmitt: A&A 191, 109 (1988) R. Pallavicini, G. Peres, S. Serio, G. Vaiana, L. Acton, J. Leibacher, R. Rosner: ApJ 270, 270 (1983) R. Pallavicini, S. Serio, G.S. Vaiana: ApJ 216, 108 (1977) R. Pallavicini, G. Tagliaferri, A.M.T. Pollock, J.H.M.M. Schmitt, C. Rosso: A&A 227, 483 (1990b) R. Pallavicini, G. Tagliaferri, L. Stella: A&A 228, 403 (1990a) H.C. Pan, C. Jordan: MNRAS 272, 11 (1995) H.C. Pan, C. Jordan, K. Makishima, R.A. Stern, K. Hayashida, M. Inda-Koide: MNRAS 285, 735 (1997) M.R. Panzera, G. Tagliaferri, L. Pasinetti, E. Antonello: A&A 348, 161 (1999) E.N. Parker: ApJ 330, 474 (1988) C.E. Parnell, P.E. Jupp: ApJ 529, 554 (2000) L. Pasquini, J.H.M.M. Schmitt, R. Pallavicini: A&A 226, 225 (1989) B.M. Patten, T. Simon: ApJ 415, L123 (1993) B.M. Patten, T. Simon: ApJS 106, 489 (1996) G. Pearce, R.A. Harrison: A&A, 206, 121 (1988) G. Pearce, R.A. Harrison, B.J.I. Bromage, A.G.M. Pickering: A&A 253, 601 (1992) G. Peres, S. Orlando, F. Reale, R. Rosner: ApJ 563, 1045 (2001) G. Peres, S. Orlando, F. Reale, R. Rosner, H. Hudson: ApJ 528, 537 (2000) G. Peres, F. Reale, S. Serio, R. Pallavicini: ApJ 312, 895 (1987) G. Peres, R. Rosner, S. Serio, G.S. Vaiana: ApJ 252, 791 (1982) M.A.C. Perryman, and the Hipparcos Science Team: The Hipparcos and Tycho Catalogues, ESA report SP-1200, ESA, Noordwijk (1997) A.A. Pevtsov, G.H. Fisher, L.W. Acton, D.W. Longcope, C.M. Johns-Krull, C.C. Kankelborg, T.R. Metcalf: ApJ 598, 1387 (2003) K.J.H. Phillips, A.K. Bhatia, H.E. Mason, D.M. Zarro: ApJ 466, 549 (1996) K.J.H. Phillips, M. Mathioudakis, D.P. Huenemoerder, D.R. Williams, M.E. Phillips, F.P. Keenan: MNRAS 325, 1500 (2001) I. Pillitteri, G. Micela, S. Sciortino, F. Favata: A&A 399, 919 (2003) N. Pizzolato, A. Maggio, G. Micela, S. Sciortino, P. Ventura: A&A 397, 147 (2003) N. Pizzolato, A. Maggio, S. Sciortino: A&A 361, 614 (2000) G.W. Pneuman: Sol. Phys. 78, 229 (1982) G. Poletto, R. Pallavicini, R.A. Kopp: A&A 201, 93 (1988) A.M.T. Pollock, G. Tagliaferri, R. Pallavicini: A&A 241, 541 (1991) D. Porquet, R. Mewe, J. Dubau, A.J.J. Raassen, J.S. Kaastra: A&A 376, 1113 (2001)

232

M. Güdel

S.H. Pravdo, L. Angelini: ApJ 447, 342 (1995) T. Preibisch: A&A 320, 525 (1997a) T. Preibisch: A&A 324, 690 (1997b) T. Preibisch: A&A 338, L25 (1998) T. Preibisch: A&A 401, 543 (2003a) T. Preibisch: A&A 410, 951 (2003b) Th. Preibisch, R. Neuhäuser, J.M. Alcalá: A&A 304, L13 (1995) T. Preibisch, R. Neuhäuser, T. Stanke: A&A 338, 923 (1998) T. Preibisch, H. Zinnecker: AJ 122, 866 (2001) T. Preibisch, H. Zinnecker: AJ 123, 1613 (2002) T. Preibisch, H. Zinnecker, G.H. Herbig: A&A 310, 456 (1996) Th. Preibisch, H. Zinnecker, J.H.M.M. Schmitt: A&A 279, L33 (1993) P. Pre´s, M. Siarkowski, J. Sylwester: MNRAS 275, 43 (1995) C.F. Prosser, S. Randich, J.R. Stauffer, J.H.M.M. Schmitt, T. Simon: AJ 112, 1570 (1996) C.F. Prosser, J.R. Stauffer, J.-P. Caillault, S. Balachandran, R.A. Stern, S. Randich: AJ 110, 1229 (1995) J.P. Pye, S.T. Hodgkin, R.A. Stern, J.R. Stauffer: MNRAS 266, 798 (1994) J.P. Pye, I.M. McHardy: MNRAS 205, 875 (1983) A.J.J. Raassen, R. Mewe, M. Audard, M. Güdel: A&A 411, 509 (2003b) A.J.J. Raassen, R. Mewe, M. Audard, M. Güdel, E. Behar, J.S. Kaastra, R.L.J. van der Meer, C.R. Foley, J.-U. Ness: A&A 389, 228 (2002) A.J.J. Raassen, J.-U. Ness, R. Mewe, R.L.J. van der Meer, V. Burwitz, J.S. Kaastra: A&A 400, 671 (2003a) S. Randich: in Stellar Clusters and Associations: Convection, Rotation, and Dynamos, eds. R. Pallavicini, G. Micela, S. Sciortino, ASP, San Francisco, p. 401 (2000) S. Randich, M.S. Giampapa, R. Pallavicini: A&A 283, 893 (1994) S. Randich, R. Gratton, R. Pallavicini: A&A 273, 194 (1993) S. Randich, J.H.M.M. Schmitt: A&A 298, 115 (1995) S. Randich, J.H.M.M. Schmitt, C. Prosser: A&A 313, 815 (1996b) S. Randich, J.H.M.M. Schmitt, C.F. Prosser, J.R. Stauffer: A&A 300, 134 (1995) S. Randich, J.H.M.M. Schmitt, C.F. Prosser, J.R. Stauffer: A&A 305, 785 (1996a) S. Randich, K.P. Singh, T. Simon, S.A. Drake, J.H.M.M. Schmitt: A&A 337, 372 (1998) J. Raymond, J.G. Doyle: ApJ 247, 686 (1981) F. Reale: in Stellar Coronae in the Chandra and XMM-Newton Era, eds. F. Favata, J.J. Drake, ASP, San Francisco, p. 103 (2002) F. Reale, R. Betta, G. Peres, S. Serio, J. McTiernan: A&A 325, 782 (1997) F. Reale, F. Bocchino, G. Peres: A&A 383, 952 (2002) F. Reale, M. Güdel, G. Peres, M. Audard: A&A 416, 733 (2004) F. Reale, G. Micela: A&A 334, 1028 (1998) F. Reale, G. Peres: A&A 299, 225 (1995) F. Reale, G. Peres, S. Serio, R. Rosner, J.H.M.M. Schmitt: ApJ 328, 256 (1988) F. Reale, S. Serio, G. Peres: A&A 272, 486 (1993) S. Redfield, R.R. Ayres, J.L. Linsky, T.B. Ake, A.K. Dupree, R.D. Robinson, P.R. Young: ApJ 585, 993 (2003) N. Reid, S.L. Hawley, M. Mateo: MNRAS 272, 828 (1995) D. Reimers, M. Hünsch, J.H.M.M. Schmitt, F. Toussaint: A&A 310, 813 (1996) D. Reimers, J.H.M.M. Schmitt: ApJ 392, L55 (1992) T.N. Rengarajan, R.P. Verma: MNRAS 203, 1035 (1983) R.D. Robinson, V.S. Airapetian, S.P. Maran, K.G. Carpenter: ApJ 469, 872 (1996)


233

M. Rodonò, I. Pagano, G. Leto, F. Walter, S. Catalano, G. Cutispoto, G. Umana: A&A 346, 811 (1999) R. Rosner, C.-H. An, Z.E. Musielak, R.L. Moore, S.T. Suess: ApJ 372, L91 (1991) R. Rosner, L., Golub, G.S. Vaiana: ARA&A 23, 413 (1985) R. Rosner, Z.E. Musielak, F. Cattaneo, R.L. Moore, S.T. Suess: ApJ 442, L25 (1995) R. Rosner, W.H. Tucker, G.S. Vaiana: ApJ 220, 643 (1978) = RTV S.M. Rucinski, R. Mewe, J.S. Kaastra, O. Vilhu, S.M. White: ApJ 449, 900 (1995) R.E. Rutledge, G. Basri, E.L. Martín, L. Bildstein: ApJ 538, L141 (2000) R.G.M. Rutten, C.J. Schrijver: A&A 177, 155 (1987) R.G.M. Rutten, C.J. Schrijver, A.F.P. Lemmens, C. Zwaan: A&A 252, 203 (1991) J.L.R. Saba, J.T. Schmelz, A.K. Bhatia, K.T. Strong: ApJ 510, 1064 (1999) J. Sanz-Forcada, N.S. Brickhouse, A.K. Dupree: ApJ 554, 1079 (2001) J. Sanz-Forcada, N.S. Brickhouse, A.K. Dupree: ApJ 570, 799 (2002) J. Sanz-Forcada, F. Favata, G. Micela: A&A 416, 281 (2004) J. Sanz-Forcada, A. Maggio, G. Micela: A&A 408, 1087 (2003) I.S. Savanov, I. Tuominen: in The Sun and Cool Stars: Activity, Magnetism, Dynamos, eds. I. Tuominen, D. Moss, G. Rüdiger, Springer, Berlin, p. 449 (1991) L. Scelsi, A. Maggio, G. Peres, P. Gondoin: A&A 413, 643 (2004) J.T. Schmelz: ApJ 408, 373 (1993) J.T. Schmelz, J.L.R. Saba, J.C. Chauvin, K.T. Strong: ApJ 477, 509 (1997) J.H.M.M. Schmitt: ApJS 90, 735 (1994) J.H.M.M. Schmitt: in Stellar Surface Structure, IAU Sym. 176, eds. K.G. Strassmeier, J.L. Linsky, Kluwer, Dordrecht, p. 85 (1996) J.H.M.M. Schmitt: A&A 318, 215 (1997) J.H.M.M. Schmitt, A. Collura, S. Sciortino, G.S. Vaiana, F.R. Harnden Jr., R. Rosner: ApJ 365, 704 (1990a) J.H.M.M. Schmitt, J.J. Drake, B.M. Haisch, R.A. Stern: ApJ 467, 841 (1996c) J.H.M.M. Schmitt, J.J. Drake, R.A. Stern: ApJ 465, L51 (1996a) J.H.M.M. Schmitt, J.J. Drake, R.A. Stern, B.M. Haisch: ApJ 457, 882 (1996b) J.H.M.M. Schmitt, F. Favata: Nature 401, 44 (1999) J.H.M.M. Schmitt, T.A. Fleming, M.S. Giampapa: ApJ 450, 392 (1995) J.H.M.M. Schmitt, L. Golub, F.R. Harnden Jr., C.W. Maxson, R. Rosner, G.S. Vaiana: ApJ 290, 307 (1985a) J.H.M.M. Schmitt, M. Güdel, P. Predehl: A&A 287, 843 (1994b) J.H.M.M. Schmitt, B.M. Haisch, J.J. Drake: Science 265, 1420 (1994a) J.H.M.M. Schmitt, F.R. Harnden Jr., G. Peres, R. Rosner, S. Serio: ApJ 288, 751 (1985b) J.H.M.M. Schmitt, P. Kahabka, J. Stauffer, A.J.M. Pieters: A&A 277, 114 (1993a) J.H.M.M. Schmitt, M. Kürster: Science 262, 215 (1993) J.H.M.M. Schmitt, C. Liefke: A&A 382, L9 (2002) J.H.M.M. Schmitt, G. Micela, S. Sciortino, G.S. Vaiana, F.R. Harnden Jr., R. Rosner: ApJ 351, 492 (1990b) J.H.M.M. Schmitt, J.-U. Ness: A&A 388, L13 (2002) J.H.M.M. Schmitt, J.-U. Ness: A&A 415, 1099 (2004) J.H.M.M. Schmitt, J.-U. Ness, G. Franco: A&A 412, 849 (2003) J.H.M.M. Schmitt, R. Pallavicini, B.C. Monsignori-Fossi, F.R. Harnden Jr.: A&A 179, 193 (1987) J.H.M.M. Schmitt, C. Rosso: A&A 191, 99 (1988) J.H.M.M. Schmitt, R.A. Stern, J.J. Drake, M. Kürster: ApJ 464, 898 (1996d) J.H.M.M. Schmitt, R. Wichmann: Nature 412, 508 (2001) H.W. Schnopper, J.P. Delvaille, A. Epstein, H. Helmken, S.S. Murray, G. Clark, G. Jernigan, R. Doxsey: ApJ 210, L75 (1976)

234

M. Güdel

C.J. Schrijver: A&A 127, 289 (1983) C.J. Schrijver: A&A 172, 111 (1987) C.J. Schrijver, M.J. Aschwanden: ApJ 566, 1147 (2002) C.J. Schrijver: A&A 269, 446 (1993) C.J. Schrijver, J. Coté, C. Zwaan, S.H. Saar: ApJ 337, 964 (1989a) C.J. Schrijver, A.K. Dobson, R.R. Radick: A&A 258, 432 (1992) C.J. Schrijver, B. Haisch: ApJ 456, L55 (1996) C.J. Schrijver, K.L. Harvey: ApJ 343, 481 (1989) C.J. Schrijver, J.R. Lemen, R. Mewe: ApJ 341, 484 (1989b) C.J. Schrijver, R. Mewe, G.H.J. van den Oord, J.S. Kaastra: A&A 302, 438 (1995) C.J. Schrijver, R. Mewe, F.M. Walter: A&A 138, 258 (1984) C.J. Schrijver, G.H.J. van den Oord, R. Mewe: A&A 289, L23 (1994) K.-P. Schröder, M. Hünsch, J.H.M.M. Schmitt: A&A 335, 591 (1998) S. Sciortino, F. Damiani, F. Favata, G. Micela: A&A 332, 825 (1998) S. Sciortino, F. Favata, G. Micela: A&A 296, 370 (1995) S. Sciortino, A. Maggio, F. Favata, S. Orlando: A&A 342, 502 (1999) S. Sciortino, G. Micela, F. Damiani, E. Flaccomio, K. Briggs, M. Denby, J. Pye, N. Grosso, A.M. Read, P. Gondoin, R.D. Jeffries: A&A (2001) 365, L259 S. Sciortino, G. Micela, F. Favata, A. Spagna, M.G. Lattanzi: A&A 357, 460 (2000) S. Serio, G. Peres, G.S. Vaiana, L. Golub, R. Rosner: ApJ 243, 288 (1981) S. Serio, F. Reale, J. Jakimiec, B. Sylwester, J. Sylwester: A&A 241, 197 (1991) J.S. Shaw, J.-P. Caillault, J.H.M.M. Schmitt: ApJ 461, 951 (1996) A. Shemi: MNRAS 251, 221 (1991) K. Shibata, T. Yokoyama: ApJ 526, L49 (1999) K. Shibata, T. Yokoyama: ApJ 577, 422 (2002) T. Shimizu: PASJ 47, 251 (1995) M. Siarkowski: MNRAS 259, 453 (1992) M. Siarkowski, P. Pre´s, S.A. Drake, N.E. White, K.P. Singh: ApJ 473, 470 (1996) T. Simon: PASP 112, 599 (2000) T. Simon, W. Cash, T.P., Snow Jr.: ApJ 293, 542 (1985) T. Simon, S.A. Drake: ApJ 346, 303 (1989) T. Simon, S.A. Drake: AJ 106, 1660 (1993) T. Simon, S.A. Drake, P.D. Kim: PASP 107, 1034 (1995) T. Simon, W. Landsman: ApJ 380, 200 (1991) T. Simon, W. Landsman: ApJ 483, 435 (1997) T. Simon, B.M. Patten: PASP 110, 283 (1998) K.P. Singh, S.A. Drake, E.V. Gotthelf, N.E. White: ApJ 512, 874 (1999) K.P. Singh, S.A. Drake, N.E. White: ApJ 445, 840 (1995) K.P. Singh, S.A. Drake, N.E. White: AJ 111, 2415 (1996b) K.P. Singh, S.A. Drake, N.E. White, T. Simon: AJ 112, 221 (1996c) K.-P. Singh, S. Slijkhuis, N.J. Westergaard, H.W. Schnopper, Ø. Elgarøy, O. Engvold, P. Joras: MNRAS 224, 481 (1987) K.P. Singh, N.E. White, S.A. Drake: ApJ 456, 766 (1996a) S.L. Skinner, M. Gagné, E. Belzer: ApJ 598, 375 (2003) S.L. Skinner, M. Güdel, M. Audard, K. Smith: ApJ in press (2004) S.L. Skinner, M. Güdel, K. Koyama, S. Yamauchi: ApJ 486, 886 (1997) S.L. Skinner, F.M. Walter: ApJ 509, 761 (1998) S.L. Skinner, S. Yamauchi: ApJ 471, 987 (1996) A. Skumanich: ApJ 171, 565 (1972) A. Skumanich: Aust. J. Phys. 38, 971 (1985)


235

D.R. Soderblom, J.R. Stauffer, K.B. MacGregor, B.F. Jones: ApJ 409, 624 (1993) L. Spitzer: Physics of Fully Ionized Gases, Interscience, New York (1962) K.G. Stassun, D.R. Ardila, M. Barsony, G. Basri, R.D. Mathieu: AJ 127, 3537 (2004) J.R. Stauffer, J.-P. Caillault, M. Gagné, C.F. Prosser, L.W. Hartmann: ApJS 91, 625 (1994) B. Stelzer, V. Burwitz: A&A 402, 719 (2003) B. Stelzer, V. Burwitz, M. Audard, M. Güdel, J.-U. Ness, N. Grosso, R. Neuhäuser, J.H.M.M. Schmitt, P. Predehl, B. Aschenbach: A&A 392, 585 (2002) B. Stelzer, R. Neuhäuser: A&A 361, 581 (2000) B. Stelzer, R. Neuhäuser: A&A 377, 538 (2001) B. Stelzer, R. Neuhäuser, S. Casanova, T. Montmerle: A&A 344, 154 (1999) B. Stelzer, R. Neuhäuser, V. Hambaryan: A&A 356, 949 (2000) B. Stelzer, J.H.M.M. Schmitt: A&A 418, 687 (2004) K. St¸epie`n: A&A 292, 191 (1994) K. St¸epie`n, J.H.M.M. Schmitt, W. Voges: A&A 370, 157 (2001) R.A. Stern, S.K. Antiochos, F.R. Harnden Jr.: ApJ 305, 417 (1986) R.A. Stern, J.R. Lemen, J.H.M.M. Schmitt, J.P. Pye: ApJ 444, L45 (1995a) R.A. Stern, J.H.M.M. Schmitt, P.T. Kahabka: ApJ 448, 683 (1995b) R.A. Stern, J.H.M.M. Schmitt, J.P. Pye, S.T. Hodgkin, J.R. Stauffer, T. Simon: ApJ 427, 808 (1994) R.A. Stern, J.H.M.M. Schmitt, C. Rosso, J.P. Pye, S.T. Hodgkin, J.R. Stauffer: ApJ 399, L159 (1992c) R.A. Stern, Y. Uchida, S. Tsuneta, F. Nagase: ApJ 400, 321 (1992a) R.A. Stern, Y. Uchida, F. Walter, O. Vilhu, D. Hannikainen, A. Brown, A. Vealé, B.M. Haisch: ApJ 391, 760 (1992b) R.A. Stern, J.H. Underwood, S.K. Antiochos: ApJ 264, L55 (1983) R.A. Stern, M.-C. Zolcinski, S.K. Antiochos, J.H. Underwood: ApJ 249, 647 (1981) M.F. Sterzik, J.M. Alcalá, R. Neuhäuser, J.H.M.M. Schmitt: A&A 297, 418 (1995) K.G. Strassmeier, J. Bartus: A&A 354, 537 (2000) K.M. Strom, S.E. Strom: ApJ 424, 237 (1994) K.M. Strom, S.E. Strom, F.P. Wilkin, L. Carrasco, I. Cruz-Gonzalez, E. Recillas, A. Serrano, R.L. Seaman, J.R. Stauffer, D. Dai, J. Sottile: ApJ 362, 168 (1990) P.A. Sturrock, W.W. Dixon, J.A. Klimchuk, S.K. Antiochos: ApJ 356, L31 (1990) J.H. Swank, N.E. White, S.S. Holt, R.H. Becker: ApJ 246, 208 (1981) J. Sylwester, J.R. Lemen, R. Mewe: Nature 310, 665 (1984) B. Sylwester, J. Sylwester, S. Serio, F. Reale, R.D. Bentley, A. Fludra: A&A 267, 586 (1993) G. Tagliaferri, S. Covino, G. Cutispoto, R. Pallavicini: A&A 345, 514 (1999) G. Tagliaferri, S. Covino, T.A. Fleming, M. Gagné, R. Pallavicini, F. Haardt, Y. Uchida: A&A 321, 850 (1997) G. Tagliaferri, J.G. Doyle, P. Giommi: A&A 231, 131 (1990) G. Tagliaferri, N.E. White, J.G. Doyle, J.L. Culhane, B.J.M. Hassall, J.H. Swank: A&A 251, 161 (1991) A. Telleschi, M. Güdel, K. Briggs, M. Audard, J.-U. Ness, S.L. Skinner: ApJ submitted (2004) P. Testa, J.J. Drake, G. Peres: ApJ in press (2004) K. Topka, Y. Avni, L. Golub, P. Gorenstein, F.R. Harnden Jr., R. Rosner, G.S. Vaiana: ApJ 259, 677 (1982) K. Topka, D. Fabricant, F.R. Harnden Jr., P. Gorenstein, R. Rosner: ApJ 229, 661 (1979) Y. Tsuboi, K. Imanishi, K. Koyama, N. Grosso, T. Montmerle: ApJ 532, 1089 (2000) Y. Tsuboi, K. Koyama, K. Hamaguchi, K. Tatematsu, Y. Sekimoto, J. Bally, B. Reipurth: ApJ 554, 734 (2001) Y. Tsuboi, K. Koyama, H. Murakami, M. Hayashi, S. Skinner, S. Ueno: ApJ 503, 894 (1998)

236

M. Güdel

Y. Tsuboi, Y. Maeda, E.D. Feigelson, G.P. Garmire, G. Chartas, K. Mori, S.H. Pravdo: ApJ 587, L51 (2003) M. Tsujimoto, K. Koyama, Y. Tsuboi, M. Goto, N. Kobayashi: ApJ 566, 974 (2002) T. Tsuru, K. Makishima, T. Ohashi, H. Inoue, K. Koyama, M.J.L. Turner, M.A. Marstow, I.M. McHardy, J.P. Pye, H. Tsunemi, S. Kitamoto, A.R. Taylor, R.F. Nelson: PASJ 41, 679 (1989) T. Tsuru, K. Makishima, T. Ohashi, T. Sakao, J.P. Pye, O.R. Williams, M.A. Barstow, S. Takano: MNRAS 255, 192 (1992) Y. Uchida, T. Sakurai: in Activity in Red Dwarf Stars, eds. P.B. Byrne, M. Rodonò, Reidel, Dordrecht, p. 629 (1984) Y. Uchida, T. Sakurai: in Unstable Current Systems and Plasma Instabilities in Astrophysics, eds. M.R. Kundu, G. Holman, Reidel, Dordrecht, p. 287 (1985) Y.C. Unruh, M. Jardine: A&A 321, 177 (1997) G.S Vaiana: in Solar and Stellar Magnetic Fields: Origins and Coronal Effects, ed. J.O. Stenflo, Reidel, Dordrecht, p. 165 (1983) G.S. Vaiana, J.P. Cassinelli, G. Fabbiano, R. Giacconi, L. Golub, P. Gorenstein, B.M. Haisch, F.R. Harnden Jr., H.M. Johnson, J.L. Linsky, C.W. Maxson, R. Mewe, R. Rosner, F. Seward, K. Topka, C. Zwaan: ApJ 245, 163 (1981) G.S. Vaiana, R. Rosner: ARA&A 15, 363 (1978) E.J.M. van den Besselaar, A.J.J. Raassen, R. Mewe, R.L.J. van der Meer, M. Güdel, M. Audard: A&A 411, 587 (2003) G.H.J. van den Oord, J.G. Doyle, M. Rodonò, D.E. Gary, G.W. Henry, P.B. Byrne, J.L. Linsky, B.M. Haisch, I. Pagano, G. Leto: A&A 310, 908 (1996) G.H.J. van den Oord, R. Mewe: A&A 213, 245 (1989) G.H.J. van den Oord, R. Mewe, A.C. Brinkman: A&A 205, 181 (1988) G.H.J. van den Oord, C.J. Schrijver, M. Camphens, R. Mewe, J.S. Kaastra: A&A 326, 1090 (1997) P.W. Vedder, C.R. Canizares: ApJ 270, 666 (1983) R. Ventura, A. Maggio, G. Peres: A&A 334, 188 (1998) J.F. Vesecky, S.K. Antiochos, J.H. Underwood: ApJ 233, 987 (1979) = VAU O. Vilhu: A&A 133, 117 (1984) O. Vilhu, J.-P. Caillault, J. Heise: ApJ 330, 922 (1988) O. Vilhu, A. Collier Cameron, E. Budding, T. Banks, B. Slee, P. Ehrenfreund, B.H. Foing: A&A 278, 467 (1993) O. Vilhu, B. Gustafsson, B. Edvardsson: ApJ 320, 850 (1987) O. Vilhu, J. Heise: ApJ 311, 937 (1986) O. Vilhu, S.M. Rucinski: A&A 127, 5 (1983) O. Vilhu, F.M. Walter: ApJ 321, 958 (1987) F.M. Walter: ApJ 245, 677 (1981) F.M. Walter: ApJ 253, 745 (1982) F.M. Walter: ApJ 274, 794 (1983) F.M. Walter: ApJ 306, 573 (1986) F.M. Walter, S. Bowyer: ApJ 245, 671 (1981) F.M. Walter, A. Brown, R.D. Mathieu, P.C. Myers, F.J. Vrba: AJ 96, 297 (1988) F.M. Walter, W. Cash, P.A. Charles, C.S. Bowyer: ApJ 236, 212 (1980a) F.M. Walter, P. Charles, S. Bowyer: Nature 274, 569 (1978a) F.M. Walter, P. Charles, S. Bowyer: ApJ 225, L119 (1978b) F.M. Walter, P. Charles, S. Bowyer: AJ 83, 1539 (1978c) F.M. Walter, D.M. Gibson, G.S. Basri: ApJ 267, 665 (1983) F.M. Walter, L.V. Kuhi: ApJ 250, 254 (1981) F.M. Walter, L.V. Kuhi: ApJ 284, 194 (1984) F.M. Walter, J.L. Linsky, S. Bowyer, G. Garmire: ApJ 236, L137 (1980b)


237

F.M. Walter, J.L. Linsky, T. Simon, L. Golub, G.S. Vaiana: ApJ 281, 815 (1984) F.M. Walter, F.J. Vrba, R.D. Mathieu, A. Brown, P.C. Myers: AJ 107, 692 (1994) F.M. Walter, F.J. Vrba, S.J. Wolk, R.D. Mathieu, R. Neuhäuser: AJ 114, 1544 (1997) Y.-M. Wang: ApJ 464, L91 (1996) N.O. Weiss: in Physics of Solar and Stellar Coronae, eds. J.L. Linsky, S. Serio, Kluwer, Dordrecht, p. 541 (1993) A.D. Welty, L.W. Ramsey: AJ 108, 299 (1994) N.E. White: in 9th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, eds. R. Pallavicini and A.K. Dupree, ASP, San Francisco, p. 193 (1996) N.E. White, K. Arnaud, C.R. Day, K. Ebisawa, E.V. Gotthelf, K. Mukai, Y. Soong, T. Yaqoob, A. Antunes: PASJ 46, L97 (1994) N.E. White, J.L. Culhane, A.N. Parmar, B.J. Kellett, S. Kahn, G.H.J. van den Oord, J. Kuijpers: ApJ 301, 262 (1986) N.E. White, S.S. Holt, R.H. Becker, E.A. Boldt, P.J. Serlemitsos: ApJ 239, L69 (1980) N.E. White, F.E. Marshall: ApJ 268, L117 (1983) N.E. White, P.W. Sanford, E.J. Weiler: Nature 274, 569 (1978) N.E. White, R.A. Shafer, K. Horne, A.N. Parmar, J.L. Culhane: ApJ 350, 776 (1990) S.M. White, J. Lim, S.M. Rucinski, C. Roberts, D. Kilkenny, S.G. Ryan, P. Prado, M.R. Kundu: in Astrophysics in the Extreme Ultraviolet, eds. S. Bowyer, R.F. Malina, Kluwer, Dordrecht, p. 165 (1996) D.R. Whitehouse: A&A 145, 449 (1985) R. Wichmann, J. Krautter, J.H.M.M. Schmitt, R. Neuhäuser, J.M. Alcalá, H. Zinnecker, R.M. Wagner, R. Mundt, M.F. Sterzik: A&A 312, 439 (1996) R. Wichmann, M. Sterzik, J. Krautter, A. Metanomski, W. Voges: A&A 326, 211 (1997) G.L. Withbroe: Solar Phys. 45, 301 (1975) B.E. Wood, A. Brown, J.L. Linsky, B.J. Kellett, G.E. Bromage, S.T. Hodgkin, J.P. Pye: ApJS 93, 287 (1994) S. Yamauchi, K. Koyama, M. Sakano, K. Okada: PASJ 48, 719 (1996) H. Zinnecker, T. Preibisch: A&A 292, 152 (1994)


THE


Morphology and characteristics of radio pulsars John H. Seiradakis1 , Richard Wielebinski2 1 University of Thessaloniki, Department of Physics, Section of Astrophysics, Astronomy &

Mechanics, 541 24 Thessaloniki, Greece (e-mail: [email protected]) 2 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany

(e-mail: [email protected]) Received 5 December 2003 / Published online 15 April 2004 – © Springer-Verlag 2004

Abstract. This review describes the observational properties of radio pulsars, fast rotating neutron stars, emitting radio waves. After the introduction we give a list of milestones in pulsar research. The following chapters concentrate on pulsar morphology: the characteristic pulsar parameters such as pulse shape, pulsar spectrum, polarization and time dependence. We give information on the evolution of pulsars with frequency since this has a direct connection with the emission heights, as postulated in the radius to frequency mapping (RFM) concept. We deal successively with the properties of normal (slow) pulsars and of millisecond (fast-recycled) pulsars. The final chapters give the distribution characteristics of the presently catalogued 1300 objects. Key words: Radio pulsar morphology: pulse shapes – spectra – polarization – distributions

1. Introduction The first publication [54] announcing the discovery of a new class of objects, soon to be known as pulsars [99,90], appeared in the literature almost exactly 35 years ago. Since then, large strides toward the understanding of pulsars and their radiation have been made. We know that they are fast rotating neutron stars [3,4,118] with masses of the order of 1 M [122,29,151,58,20,149,144,49,57] and strong magnetic field (between 109 and 1014 Gauss [39,15,138,109,2,169]. They are probably born during a Supernova Type II explosion of a (massive) late-type star (Fig. 1). Pulsars emit highly accurate periodic signals (mostly in radio waves), beamed in a cone of radiation, centred around their magnetic axis. These signals reveal the period of rotation of the neutron star, which radiates, like a light-house, once per revolution. The lighthouse effect is caused by the dipolar magnetic field not being aligned with the rotation axis of the neutron star. As a consequence of the magnetic field, pulsar radiation Correspondence to: R. Wielebinski

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J. H. Seiradakis, R. Wielebinski

Fig. 1. Scenario of the birth and evolution of pulsars

is highly polarized. Their period of rotation (P) varies between 1.557 ms (642 Hz) [8] and 8.5 s (0.12 Hz) [168]. As pulsars rotate, they loose energy and their rate of rotation decreases. This period derivative (P˙ ) is an important observational parameter. In 1975 a pulsar in a binary system was discovered [56]. Slow rotating pulsars, with rotation period P ≥ 20 ms and P˙ > 10−18 are considered to be normal pulsars. Pulsars with P < 20 ms and P˙ ≤ 10−18 are called millisecond or recycled pulsars. A full list of 1300 pulsars [105] is available at http://www.atnf.csiro.au/research/pulsar/psrcat/. The period of rotation of normal pulsars increases with time, an observational fact, discovered during the very early history of pulsars [134] and led to the rejection of suggestions that the periodic signals could be due to the orbital period of binary stars. The orbital period of an isolated binary system decreases as it looses energy, whereas the period of a rotating body increases as it looses energy. Millisecond pulsars are considered to be recycled pulsars, spun up by mass transfer (accretion) from a binary companion [1]. In the early history of pulsars, models involving pulsations of white dwarfs and neutron stars were also proposed and quickly rejected. The discovery of the Vela pulsar (PSR 0833-45 – see Table 1) led to the suggestion of pulsar – supernova association. This suggestion was corroborated by the discovery of a pulsar (PSR 0531+21) in the heart of the Crab supernova remnant with a period of 33 milliseconds (see Table 1), which led to the unequivocal association of (radio) pulsars with rotating neutron stars [45]. Subsequent polarimetric observations led to the establishment of the “Rotating Vector Model” [125]. Soon after its discovery, the Crab pulsar was post-detected in earlier (1967, Jun 04) archived X-ray data [37] and soft γ -ray data [38]. To date (excluding non-pulsed detections of neutron stars) 5 normal

Morphology and characteristics of radio pulsars

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Table 1. Pulsar milestones Date

Milestone

Reference

1932, Feb 1934, 1967 1939 1967, Nov 28 1967, Nov 28–1968, Mar 03 1968, Mar 15 1968 1968 1968, Feb 24 1968, Apr 01 1968, Apr 03 1968 1968 1968, Nov 1969 1969 1969 1969 1969 1969, Aug 1974, Jul 02 1975 1982 1991, Sep 15 1992, Oct 19 1998 1998, Nov 05

The discovery of neutron Neutron stars are predicted Neutron stars Equation of State The discovery of pulsars “Pulsar” designation First published “Pulsar” designation Discovery of the Vela pulsar Discovery of the Crab pulsar Dispersion measure measured First polarimetric observation Faraday Rotation measured Gravitational emission proposed Lighthouse model proposed Galactic distribution established Post-detection of pulsar X-rays Post-detection of pulsar γ -rays Scintillation explained Rotating Vector Model proposed Observations of pulsar glitches First emission process proposed Discovery of binary pulsars First complete theory attempted Discovery of millisecond pulsars Detection of extrasolar planets Detection at mm-wavelengths Discovery of magnetars Discovery of the 1000th pulsar

[22,23] [3,121] [119] [54] [14] [154,152] [81] [145,25] [30] [89] [143] [158] [45] [82] [37] [38] [135] [125] [126] [46] [56] [139] [8] [163] [162] [69] [28]

pulsars have been detected in the optical, 17 normal and 6 millisecond pulsars in X-rays and 7 normal pulsars in γ -rays (up to 1025 Hz, covering, thus, the largest frequency range of all known compact species emitting intense radiation in the Universe) (updated information from [13] – W. Becker, private communication). The first (and fastest, up to now) millisecond pulsar, PSR B1937+214 was discovered in 1982 [8]. Ten years later the first planetary system (two planets orbiting PSR B1257+12), outside the solar system, was discovered [163]. The discovery of millisecond and binary pulsars (see Table 1) gave new insight in pulsar research. It was soon realized that the extremely fast rotation of millisecond pulsars could only be explained by transfer of angular momentum from companion stars. The notion of recycling of old and exhausted neutron stars became popular. On the

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other hand binary pulsars were used to check the effects of General Relativity, which successfully survived the new tests. For these particular discoveries the Nobel Price in Physics (see http://www.nobel.se/physics/laureates/) was twice awarded to pulsar researchers: In 1974 it was awarded to Antony Hewish for the discovery of the first pulsar, PRS B1919+21, and in 1993 to Russell A. Hulse and Joseph H. Taylor for the discovery and subsequent work on the physics of the binary pulsar PSR B1913+16. Recently the discovery of a double pulsar system, PSR J0737-3039B (spin period 2.7 sec), PSR J0737-3039A (spin period 22 msec) in a 2.4 hr eccentric orbit was announced [86]. This system will, certainly play a very important role in deciphering the pulsar riddle and in testing physical theories. Meanwhile, a large number of strange and unexpected properties of pulsar emission were observed. Drifting subpulses, mode changing and nulling were among the first such properties to be studied[129]. Extremely narrow pulses [51,76,52] were soon to become an important tool for theoretical investigations and 90◦ polarization jumps (orthogonal modes) imposed restrictions to the existing models. In addition, period glitches were observed, during which the pulsar period decreased by a large amount and then, within a few days, it increased again to its previous value. Glitch properties are used to study the physical structure of neutron stars.

2. Pulsar milestones Before proceeding with the description of the characteristics of pulsar emission, it is worth looking back and paying tribute to the main discoveries concerning pulsars. Table 1 summarises the most important steps in pulsar research, both in observation and theory. It is not always easy to unearth a “first” date or a “first” publication. For example, J. Bell-Burnell has communicated to us her personal view [154] and we have found a report in a March 1968 issue of the Time magazine [152] referring to the first use of the word pulsar. Nevertheless, we believe that still earlier references to the “pulsar” notation may have escaped our search. The list can be expanded to include several other “firsts”. However, we decided to restrict its size to what we consider to be the most important ones.

3. Morphology Pulsars present to the observer a most complicated set of time variable phenomena. On the one hand, their period of rotation P varies from 1.5 millisecond up to 8.5 seconds from object to object. On the other, this period increases regularly with time, as the pulsar looses gravitational energy and slows down. The deceleration is expressed quantitatively by the measured P˙ . The youngest (normal) pulsars exhibit usually the largest deceleration and thus they demonstrate the largest P˙ . Quite to the opposite, millisecond pulsars have very low P˙ and are interpreted to be recycled objects, slow, normal pulsars that have been sped up by accretion from a binary counterpart. The deceleration process is not always constant. Some pulsars are known to exhibit glitches, sudden acceleration to higher periods, which are interpreted to be due to crust related “starquakes”.


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Taking into account single pulse intensities and their duration, extremely high brightness temperatures (of the order of 1029 K) are calculated, especially for their low frequency emission. This constrains their radio emission to be coherent (see also [83] and references therein). The intensity of single pulses show enormous intrinsic variations. The situation is even further complicated by the fact that interstellar scintillation introduces an additional fluctuating effect, in particular at lower radio frequencies. However with enough repeated observations the average emitted pulsar flux density can be determined. The addition of a sequence of single pulses leads quickly (usually, after a few hundred pulses) to a stable pulse shape, a signature of the geometry of lighthouse emission mechanism. The pulse shape is a firm characteristic of a pulsar, having anything from one up to nine sub-pulse components. Within the sub-pulse structure a number of phenomena has been observed. Sub-pulse drifting (see above) reveals the emitting beam structure. In addition, the existence of very narrow pulsar micro- and nano-structure [35,52], that are the signs of individual emission regions, has been confirmed. Pulsar radiation is highly polarized in a most complicated way. At low radio frequencies some pulsars are almost 100% linearly polarized. Others have very high and variable circular polarization. The development of polarization with frequency is radically different from all other radio sources. The polarization may be high at low frequencies while dropping rapidly to zero at high frequencies. Possibly this is a hint for a coherent (low frequencies) – incoherent (high frequencies) emission mechanism, an effect corroborated by high frequency pulsar spectra [72].

3.1. Displaying pulses Pulsars are immediately recognised from the periodic nature of their radiation. Pulse sequences (Fig. 2) can be depicted in a much more compact and informative way if their period is accurately known. Then, instead of showing the pulses one-after-theother, they can be displayed one-underneath-the-other. Thus, many more pulses can be conveniently accommodated in a single graph. By ignoring the unpulsed noise either side of the pulses, high time resolution single pulses are readily displayed (Fig. 3 – top). It is evident from Figs. 2 and 3 that individual, single pulses vary greatly in intensity. Most of these variations are intrinsic. Some are due to interstellar scintillation. However, if a large number of single pulses are added together, a very stable profile is obtained (Fig. 3 – bottom). For most pulsars, this integrated profile characterizes uniquely a pulsar at a particular frequency. The stability of pulsar integrated profiles has been thoroughly investigated for a large sample of normal pulsars [53] and some millisecond pulsars [65].

3.2. Integrated pulses In the integrated pulsar profiles distinct components can be identified [140,67]. They are thought to represent coherent physical regions in the magnetosphere of the star. Therefore their properties are of extreme importance for understanding the emission mechanism of pulsars. These components are often blended and their shape and longitudinal location within the pulsar profile is difficult to establish. A large collection of pulse

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Fig. 2. A sequence of 17 single pulses observed simultaneously at 4 frequencies, plotted one after the other. Courtesy of A. Karastergiou

profiles can be found in the European Pulsar Network data archive at http://www.mpifrbonn.mpd.de/div/pulsar/data/. Although there are no rigorous theoretical arguments, usually they can be fitted with gaussian curves, the parameters of which are easily obtained. Experience has shown that pulsar profiles can indeed be reconstructed by a sum of individual gaussian components. This method usually involves some assumptions which can be minimized by reducing the number of degrees of freedom of the gauss–fitting procedure [71,70]. Some gauss–fitted components are shown in Fig. 4. 3.2.1. Normal pulsars (P ≥ 20 ms) Pulse profiles come in a variety of shapes (Fig. 5, 6). In most cases they can be represented by a smooth curve with a single (almost gaussian) component or with two or more components. Soon after the discovery of pulsars, it was realised that their integrated profiles exhibit important morphological differences. In order to explain double profiles, the hollow cone model was proposed in the early seventies [68,6,120]. Triple profiles were explained by the introduction of a central pencil beam and five-component profiles were interpreted by assuming a more complicated beam, comprising of a central beam surrounded by an inner and an outer cone [127,128,130,131]. The number of cones that can be accommodated within the narrow polar cap region, whose radius is bound by the last open magnetic field lines cannot be very large. It is interesting that pulsars exhibiting a single core component, seem to occupy a distinct region in the PP˙ diagram [43] (Fig. 21). On the other hand a patchy beam model was proposed [87], according


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Fig. 3. (Top): A sequence of 100 single pulses from PSR 1133+16 plotted underneath each other (Noise wings are suppressed). (Bottom): By adding the above single pulses, we get the Integrated profile

to which pulsar beams are patchy, with components randomly located within the last open magnetic field lines. This model is based on the fact that single pulses vary in intensity and often they seem to be missing altogether. There have been several attempts to explain the pulsar beam shapes using both theoretical and geometrical arguments [44, 98,42,110]. However, there are still many uncertainties due to the erratic behaviour of pulsar emission and the lack of an accepted model for pulsar radiation. 3.2.2. Millisecond (recycled) pulsars (P < 20 ms) The first millisecond pulsars to be discovered exhibited rather simple profiles. Nowadays about 100 millisecond pulsars have been detected, many of which have complex integrated profiles [75], not dissimilar to the profiles of normal pulsars (Fig. 7). One difference is that millisecond pulsars tend to have wider profiles than normal pulsars.

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Fig. 4. Time-aligned profiles at three frequencies, with gauss-fitted components. Radius to Frequency Mapping (RFM) is obvious in this figure. Left panel: PSR B0355+54. Right panel: PSR B0740-28 [70]

3.2.3. Radius to frequency mapping The frequency development of pulse shapes has led to the concept of a Radius to Frequency Mapping (RFM – Fig. 8), according to which, higher radio frequencies are emitted in the lower reaches of the pulsar magnetosphere (closer to the surface of the star). In order to investigate the RFM concept, time-aligned pulse shapes are needed, that require accurate pulsar timing. Following the standard pulsar model [139] the integrated pulse width is expected to decrease monotonically with frequency (RFM effect). This effect was implicit in earlier work [142] and has been extensively investigated ever since [26,157]. Multi frequency observations of pulsars have confirmed the narrowing of pulse profiles with frequency [79,75]. The effect is adequately demonstrated for both normal and millisecond pulsars in Figs. 4, 9 and 10. 3.2.4. The Crab pulsar from radio frequencies to γ -rays The Crab pulsar (PSR B0531+21) is probably, the best studied pulsar. Soon after its discovery, archival searches led to post detection of pulsed emission at X-rays and γ rays [37,38]. Its “main-pulse – interpulse” integrated profile is unmistakably evident throughout the electromagnetic spectrum (Fig. 11). However, carefully time-aligned profiles [111] reveal slight, but significant, displacement of its high frequency components from its lower (radio) components. This has been interpreted as evidence of two different mechanisms of emission, with the high frequency emission (optical, X-rays, γ -


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Fig. 5. Integrated profiles of pulsars at 1.41 GHz [140]

rays) originating in a region close to the light cylinder. Furthermore, recent investigations [111,63] have revealed that between 4.7 GHz and 8.4 GHz extra components appear in its integrated profile (Fig. 11). These components impose additional difficulties in the investigation of the emission mechanism of this interesting object.

3.3. Single pulses Investigations of single pulses is of utmost importance, showing the variability and spatial structure of the pulsar emission process. Already in the discovery paper [54] and other early papers [30,82,27,32,137] single pulses at low frequencies were studied. Single pulses show a variety of sharp emission structures from millisecond through microsecond down to nanosecond range [27,51,80,52]. Early two-frequency simultaneous

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Fig. 6. Integrated profiles of pulsars at 10.7 GHz [140]

observations suggested that the emission is inherently broad-band [9], i.e. emission is correlated over a wide frequency range. Later observations [16,12,31,64] were made for total intensity only and at most for two simultaneous frequencies. Most of these investigations were then used to determine the bandwidth of the emission. More recently, using many radio telescopes at different frequencies, simultaneously, at up to five frequencies [77] have investigated the single pulse characteristics in detail (see also Fig. 2).

3.4. Millistructure, microstructure, nanostructure The fact that very short time structures are present in single pulses was noted from the very beginning [54] leading to a stringent requirement for theories attempting to explain the origin of pulsar emission. First observation of pulsar millistructure was made soon after their discovery [27]. The limitation was due to signal to noise in the narrow band


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Fig. 7. Integrated profiles of millisecond pulsars at 1.41 GHz. Effelsberg observations, M. Kramer et al. (unpublished)

receiver needed to show such short time structures. A few years later a de-dispersion technique at the frequency of 115.5 MHz revealed time structures as short as 8 µs in PSR 0950+08 [51]. Direct observations at 1420 MHz on PSR 1133+16 [36] resolved structures with time scale of 14 µs. The microstructure was found to be broad-band [136,16]. Periodic structures were observed that seem to be also correlated across a wide frequency range [17]. More recently [80] microstructure investigations were extended up to 4.85 GHz, showing that many pulsar have this emission signature. This result was

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Fig. 8. Radius to Frequency Mapping (RFM). High frequencies are emitted close to the surface of the star. Low frequencies are emitted higher up, where the cone of emission is wider

confirmed in the studies of the Vela pulsar which shows microstructure [76] in most of the pulses. Most recently the time structure studies were taken in to the nanosecond range with observations of giant pulses from the Crab pulsar [52]. Their best time resolution was in fact 2 nanoseconds. This latest observation suggests that the plasma responsible for such emission must be of the order of one meter in size. If the emission is isotropic, these nanosecond pulses must be the brightest transient source in the radio sky.

4. Flux densities The flux density of a radio source and its frequency evolution (its spectrum) are basic information that relate to the emission mechanism. However, one of the problems with flux densities is that pulsars vary on various time scales: (a) due to inherent variations [147] or (b) due to scintillations [94] or (c) due to scattering [84]. For low frequency radio waves of the Milky Way the spectrum of the radio emission could be explained only by the non-thermal (synchrotron) emission process. From the very beginning of pulsar observations it was clear that the spectra of pulsars were very different from all other known radio sources [88,137]. Instead of values of α ∼ – 0.8 ( S = ν α ), as in cosmic radio sources, the observed spectral index of pulsars was α ∼ – 1.5 on average. The spectral index at the highest frequencies was for some objects much higher than this average value. At lower radio frequencies a spectral turn-over was observed. It was known in the earliest papers that pulsars were very weak at higher frequencies posing in fact a great instrumental challenge to study these objects at cm wavelengths.

4.1. Normal pulsars (P ≥ 20 ms) The first spectra of pulsars, using flux density values at three (plus an upper limit at 1.4 GHz) frequencies, were obtained in 1968 [88]. Earlier observations [137], published


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Fig. 9. The development of pulsar integrated profiles with frequency. Note that new components can appear both at high and low frequencies. Courtesy M. Kramer

slightly later, were obtained at five frequencies, four of them simultaneously, giving an average spectrum and spectra of individual (single) pulses of PSR1919+21. The average spectrum was extended to 2.7 GHz and suggested a spectral break with an index of α ∼ – 3.0 above 1.4 GHz. The data collection to determine flux densities of a larger sample of pulsars took many years to complete. While numerous observatories (Arecibo, Jodrell Bank, Green Bank, Parkes) made observations at frequencies of 1.4 GHz and below only the Goldstone facility detected pulsars at 13cm [32]. Observations of the low frequency extension of pulsar spectra were carried out in the Soviet Union [18,19,94] at frequencies as low as 10 MHz. Three pulsars were detected at 8.1 GHz [55]. The suggested existence of a spectral break at high radio frequencies [137] was later confirmed [5]. A major step forward in the measurement of pulsar flux densities at high radio frequencies and hence of pulsar spectra was made by the commissioning of the 100-m Effelsberg radio telescope. Immediately, six pulsars were detected at 2.8 cm wavelength [161]. This telescope continued to set records of the highest frequencies at which pulsars could be studied by reporting detections at 22.7 GHz [10,11] and finally in the mmwavelengths [162,73]. A detection of the pulsar PSR 0355+54 at 3 mm wavelength has also been achieved with the Pico Veleta telescope [116].

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Fig. 10. The development of millisecond pulsars integrated profiles with frequency. Adapted from [75]

The early measurements of flux density of the strongest pulsars had to give way to studies of larger samples, if possible with a wide frequency flux density coverage. An early compendium of pulsar spectra was given for 27 pulsars [141]. Further multifrequency spectra have been presented [7,142]. In both of these papers the spectral breaks of some pulsars at high frequencies were confirmed and in the latter work the frequency evolution of the pulse width was noticed (this eventually led to the Radiusto-Frequency Mapping concept). Low radio frequency observations [92] confirmed the cut-off in pulsar spectra for a number of objects. Subsequently, the flux density of a larger sample of pulsars was measured at several frequencies [140,85,67] and spectra of pulsars were derived [93,153,106] (Fig. 12). From all these publications the conclusion was that the average spectral index is α = −1.8. From our gauss fitted distribution (see below) we have found a similar value, α = −1.75. It is obvious from Fig. 25, that the distribution is fairly wide. Some 10% of all pulsars require a two power law fit in the high frequency range. A small number of pulsars have been recognized with almost flat spectrum (α > –1.0) [106]. In addition pulsar spectra seem to follow the power law down to low frequencies (a few 10s of MHz) with a few exceptions, where a turn-down is observed.


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Fig. 11. The integrated profile of the Crab pulsar from low frequency radio waves to soft gammarays. Note the absence of the main pulse and the peculiar extra components between 4.7 and 8.4 GHz. Courtesy T.H. Hankins

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Fig. 12. Spectra of pulsars detected at 9 mm [160]

4.2. Millisecond pulsars (P < 20 ms) Millisecond pulsars were discovered in 1982 [8] as a result of a search in the direction of radio sources with very steep spectra. The flux density of these objects is very low. This, combined with the effects of interstellar broadening, rendered their detection difficult. Early studies of millisecond pulsars [34,40] suggested that these objects have spectra steeper than slow pulsars. Recently high frequency observations of millisecond pulsars were also made [66,107] in spite of their low flux densities. The spectra of 20 objects were studied at lower radio frequencies in a survey of 280 pulsars [85] in the northern hemisphere. Several southern millisecond pulsars were also studied [153] in a narrow frequency range. A major study of millisecond pulsars [74,167,75] showed that once a


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volume-limited sample is considered, many of the characteristics of slow and fast pulsars (spectrum, pulse shapes, number of sub-pulse components, polarization) are the same. The one distinct difference is found in the luminosity. Slow pulsars are some 10 times more luminous than millisecond pulsars. An investigation of the low frequency turn-over of millisecond pulsars [78,95] revealed that the morphology of millisecond pulsars is very similar to that of normal pulsars but with lower luminosity.

5. Polarisation Soon after the discovery of pulsars [54] their linear polarization was also discovered [89] using the Jodrell Bank Mark I radio telescope. Variations of the intensity from pulse to pulse were detected from orthogonal dipoles connected to a high speed recorder. The linear polarization was found to be surprisingly high even at lower (150 MHz; 408 MHz) radio frequencies. Soon it was realized that considerable circular polarization was also present in pulsar emission [27,24]. The early observations with the Parkes telescope [125] of the pulsar PSR B0833-45 showed a very high degree of linear polarization of the integrated pulse (in fact nearly 100%) and gave arguments for a (magnetized) rotating vector model for pulsars. The observations that followed, e.g. [33,113], showed that the phase-drift of the linear polarization is a common feature in pulsars and, hence, gave support for the rotational model.

5.1. Integrated pulses After these early observations a number of observers embarked on determining the detailed polarization characteristics of larger samples of pulsars. In all these studies all four Stokes parameters were observed since pulsars unlike extra-galactic sources showed high degree of linear and circular polarization. 5.1.1. Normal pulsars (P ≥ 20 ms) In 1971 the results of observations of 21 pulsars, at the frequencies of 410 and 1665 MHz, were published [96] (Fig. 13). Numerous studies of the Crab pulsar in polarization have also been made [21,48,100,112]. In 1971 an important result was observed, showing that pulsar polarization is constant up to some frequency, after which it decreases almost linearly [101]. This was a result not observed in any other radio source and required new interpretation. Major surveys of polarisation characteristics of larger samples of pulsars started with the access to large radio telescopes like the Effelsberg 100-m radio telescope [114,115, 165,166]. The Arecibo telescope was also involved in polarimetric observations [133, 159]. In the southern skies pulsars were studied with the Parkes dish [50,108,103,164, 124,104]. A multi-frequency survey of 300 radio pulsars, at frequencies below 1.6 GHz, has been conducted [47] with the Lovell telescope at Jodrell Bank. The polarization of a large sample of pulsars was subsequently studied at the highest radio frequencies [156,155] up to the frequency of 32 GHz (Fig. 14). Some generalizations about pulsar polarization properties can now be made.

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Fig. 13. Early pulsar polarization [96] showing the frequency dependence

In Fig. 15 we show the polarization evolution with frequency for four characteristic types of pulsars. The pulsar B0355+54 (Fig. 15a) begins with low linear polarization percentage at low radio frequencies, then reaches a maximum (for one component) in the middle range of frequencies and finally falls to low polarization values at the highest frequency so far observed. The phase sweep is linear for the highly polarized component but jumps through 90◦ between components. Circular polarization is low but evolves in a manner similar to the linear polarization. Most pulsars evolve in this manner. The second evolution sequence is shown for pulsar B0521+21 (Fig. 15b). Both components are polarized. The degree of polarization falls at high frequencies and the phase-sweep is S-shaped for both components. In Fig. 15c the polarization evolution of the pulsar B1800-21 is shown. This has the familiar increase and decrease behaviour, but in addition, with a considerable circular polarization component. A more unusual evolution is seen in Fig. 15d for the pulsar B0144+59. The linear polarization decreases with frequency. However its circular polarization keeps increasing up to the highest frequency observed so far.

5.1.2. Millisecond pulsars (P < 20 ms) The discovery of millisecond pulsars [8] did not lead to immediate studies of their polarization. The first reports came in the 90’s [150,117]. This was due to the fact that millisecond pulsars are, on average, an order of magnitude less luminous than normal pulsars and thus require very sensitive polarimeters. A major contribution on millisecond pulsar polarimetry was published in 1998 [167] and more recently in 1999 [146]. The polarization characteristics of millisecond pulsars are similar to those of normal pulsars, namely that the linear polarization falls to high frequencies [167] (Fig. 15).


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Fig. 14. Polarisation development with frequency of the integrated pulses of normal pulsars for the sample of pulsars shown in Fig. 12 [160]

5.2. Single pulses Most of the polarization observations presented so far referred to integrated pulses. However it is the polarization of the single pulse that tells us about constraints that are necessary for the interpretation of their emission mechanism. Early observations [132, 102] gave strong indications that pulsar radiation is highly polarized. Soon after a strange behaviour was also detected, e.g. that orthogonal polarization modes, i.e. abrupt jumps of the position angle by 90◦ in consecutive single pulses are often observed [97,41]. In 1995 a major co-operation project was organized under the auspices of the European Pulsar Network. Various telescopes in Europe (Effelsberg, Jodrell Bank, Bologna, Westerbork, Torun and Pushchino) were used simultaneously to observe pulsars at a number of frequencies. Recently the radio telescopes in Ooty and GMRT (both in India) have joined this network. Each telescope was optimal at some frequency, so that a very

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Angle [deg]

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925 MHz

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d Fig. 15a–d. Characteristic polarization behaviour of pulsars. The dark-shaded area represents linearly polarized power and the light-shaded area circularly polarized power. (a) PSR B0355+54. (b) PSR 0525+21. (c) PSR B1800-21. (d) PSR 0144+59. From [155]


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Fig. 16. The polarization of millisecond pulsars at 1410 MHz from [167]. Four curves are plotted: the total power is shown by the outer curve in arbitrary units. The linear polarization is shown by the dashed curve and the circular polarization by the dotted curve. The linear polarization position angle is plotted on the lower panel in degrees. All curves are plotted against longitude in ms (upper scale) and in degrees (lower scale)

wide frequency coverage was achieved. Many of the telescopes have the capability to observe the full polarization of pulsars as well. The results of this major multi-frequency network have shed new light on the wide band performance of pulsars as emitters [59– 62,77]. The fundamental result, that pulsar radio emission is basically broad-band, was confirmed. This is seen in Fig. 2 where single pulses observed at four widely spaced frequencies are plotted. Observations of full polarization showed even more unusual time sequences. While the total intensities correlated rather well, the polarization deviations were much higher. In particular the circular polarization (usually observed in the conal lobes of a pulse) vary highly from pulse to pulse (Fig. 17). 6. Distributions More than 1500 pulsars have been discovered to date, facilitating the statistical investigation of their distribution in space, period, period derivative and in other parameter spaces. These distributions are by now statistically stable and reliable, not only because of the large number of stars involved in the sample but because they cover a large portion (∼1%) of the pulsar population which is believed to be of the

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Fig. 17. Two examples of individual pulse pairs of PSR B0329+54, observed in full polarization. The dark-shaded area represents linearly polarized power and the light-shaded area circularly polarized power. From [59]

order of 105 pulsars in our Galaxy. The figures presented below were produced using the data for 1300 pulsars available in the recently released ATNF pulsar catalogue (http:www.atnf.csiro.au/research/pulsar/psrcat/) [105]. A few pulsars in the ATNF pulsar catalogue are X-ray pulsars. Among them there are some with long period. They have been included as their properties are very similar to normal radio pulsars.

6.1. Spatial distribution The distribution of pulsars in galactic coordinates is shown in Fig. 18 in Hammer-Aitoff projection. It is obvious that pulsars are strongly grouped along the galactic plane. Millisecond pulsars (many of which are also binary) are more isotropically distributed. This effect is due to their inherent weaker emission, which allows the detection of, primarily, nearby objects.

6.2. Dispersion measure vs. galactic latitude distribution The Dispersion Measure (DM) of pulsars depicts the electron content on the line of sight, between the star and the observer, ne (l) × dl, where ne (l) is the electron density and l is the distance. If the average electron density is known, then the DM is a direct measure of the pulsar distance. From Fig. 19 it is obvious (a) that pulsars are tightly clustered along the galactic plane (galactic latitude, b = 0◦ ) and (b) that the highest DMs are found


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Fig. 18. The distribution of 1395 pulsars in Galactic Coordinates. Normal pulsars are depicted by dots. Binary pulsars have a large circle around them. Pulsars with p < 20 msec are depicted by stars. Binary millisecond pulsars are shown by encircled stars. Figure courtesy of B. Klein

Fig. 19. The distribution of the Dispersion Measure of 1282 pulsars as a function of their Galactic Latitude

on this plane. This is due to the electron density distribution in the Galaxy, which has been modelled by several researchers [91,148]. According to these models, the electron density peaks at the Galactic centre and falls off with a scale height of about 70 parsecs away from the plane. A few pulsars deviate from the smooth 1/e distribution. These objects are known to be located behind dense HII regions, e.g. the Gum Nebula.

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6.3. Period distribution Pulsar periods range from 1.5 ms to about 8.5 s (Fig. 20). This range of values for a physical parameter characterizing one species of objects is too wide to be explained by a common origin. It is widely accepted that ms pulsars are recycled pulsars, spun up by accretion processes, during which they accumulate mass and obtain extra spin (from this mass) from a binary component. This is confirmed by the data of Fig. 18, which show that most millisecond pulsars are in binary systems. The histogram of pulsar periods shows a distinct bimodal distribution. The median of the period distribution of normal pulsars is about 0.65 s, whereas for millisecond pulsars it is 0.0043 s (4.3 ms). There is a characteristic lack of pulsars with period around 20 ms. 6.4. Period derivative (P˙ ) distribution The P˙ distribution of pulsars (not shown, as it is directly connected to Figs. 20 and 21) varies between 10−21 s s−1 to 10−10 s s−1 . Millisecond pulsars exhibit a much slower decay (lengthening) of their period. One of the fastest decaying period pulsars is the Crab pulsar, whose period slows down by 36 ns per day. In general the P˙ distribution of pulsars is very similar to the period distribution. There is a noticeable bimodal distribution. The median of the P˙ distribution of normal pulsars is 2.6 × 10−15 s s−1 , whereas for millisecond pulsars it is of the order of 2 × 10−20 s s−1 ; five orders of magnitude slower period decay. 6.5. Period – period derivative (P˙ ) distribution One of the most important graphical distributions of pulsars is their period (P) – period derivative (P˙ ) distribution (Fig. 21). As expected from Figs. 20 and 22 it shows very

Fig. 20. The period distribution of 1300 pulsars


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Fig. 21. The P – P˙ distribution of 1395 pulsars. Binary pulsars are depicted by encircled dots

clearly the characteristic clustering of normal pulsars (large P, large P˙ ) and of millisecond pulsars (small P, small P˙ ). The vast majority of normal pulsars are isolated single stars. On the contrary, the majority of millisecond pulsars are members of binary star systems. Binary pulsars located between the two clusters will slowly drift toward the millisecond cluster in less than 108 years. Assuming that the decay of pulsar periods is due to their dipole radiation, their characteristic age can be calculated from the very simple expression τchar = 21 PP˙ years. The “dash-dot” lines in Fig. 21 correspond to lines of constant age. The characteristic age of normal pulsars is of the order of 107 years, whereas the age of millisecond pulsars is slightly above 109 years. The Crab pulsar is the isolated pulsar closest to the 103 years line. Following classical electrodynamics theory, √ the surface magnetic field of pulsars is 19 given by the expression B0 = 3.3 × 10 × P P˙ gauss. The “dash” lines in Fig. 21 correspond to lines of constant magnetic field. It is immediately noted that normal pulsars have a surface magnetic field of about 1012 gauss, whereas the surface magnetic field of millisecond pulsars is much lower, of the order of 109 gauss. Finally it should be mentioned that the absence of pulsars in the lower right corner of the diagram is due to the existence of a “death line”, owing to the gradual decaying

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Fig. 22. The Age distribution of 1194 pulsars

of the induced electrical potential of pulsars. Slow pulsars with low magnetic field cannot develop a large enough potential above their magnetic poles for discharges (and therefore radiation) to take place. The absence of millisecond pulsars below about 1010 years indicates that their age cannot exceed the Hubble time (age of the Universe). 6.6. Age distribution The characteristic age (τchar = 21 PP˙ ) distribution of pulsars (Fig. 22) shows the expected bimodal distribution attributed to the different ages of normal pulsars and millisecond pulsars. The median age of normal pulsars is 4.7 × 106 years, whereas the age of millisecond pulsars is of the order of 5 × 109 years. 6.7. Surface magnetic field distribution √ The surface magnetic field (B0 = 3.3 × 1019 × P P˙ ) distribution of normal pulsars is tightly peaked at 1.3 × 1012 gauss, whereas for millisecond pulsars is much lower, of the order of 4 × 108 gauss (Fig. 23). In a few stars the surface magnetic field is larger than 1014 gauss. This is the surface magnetic field of a new class of objects, called magnetars, first detected through their X-ray emission [69]. Magnetars are known to be neutron stars, which do not always emit at radio wavelengths. 6.8. Luminosity distribution The luminosity distribution at 400 MHz of 612 pulsars is depicted in Fig. 24. The mean of the gauss fitted distribution is 115 mJy kpc2 . The luminosity is calculated from the


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Fig. 23. The surface magnetic field distribution of 1194 pulsars

Fig. 24. The luminosity distribution at 408 MHz of 612 pulsars

400 MHz flux density, assuming that the Dispersion Measure is a true measure of the distance of each pulsar. This may lead to an over estimate of the luminosity of pulsars located behind HII regions.

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Fig. 25. The spectral index distribution of 285 pulsars. Data between 400 MHz and 1400 MHz were used

6.9. Spectral index distribution The spectral index distribution between 400 MHz and 1400 MHz of 285 pulsars is shown in Fig. 25. It is a rather wide distribution. The bulk of pulsars demonstrate a spectral index between −3 and 0. The mean of the gauss fitted distribution is −1.75±0.1. Pulsars with flat spectral indices are the ones which should be investigated at high frequencies. Acknowledgements. JHS acknowledges financial support from the Alexander von Humboldt Foundation and the Max-Planck-Gesellschaft during his sabbatical from the University of Thessaloniki. We would like to acknowledge the fact that the publicly available ATNF pulsar catalogue of 1300 objects has given new momentum to pulsar research. We thank Dr. Axel Jessner for comments on an early version of this paper. Figures 18 and 21 were produced by Dr. Bernd Klein (Max-Planck-Institut für Radioastronomie, Bonn). Dr. Michael Kramer provided us with unpublished material which was used in some figures. Finally, we would like to thank an anonymous referee for useful comments.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

M.A. Alpar, A.F. Cheng, M.A. Ruderman, et al.: Nature 300, 728 (1982) J. Arons: Astrophys. J. 408, 160 (1993) W. Baade, F. Zwicky: Proc. Nat. Acad. Sci. 20, 254 (1934) W. Baade, F. Zwicky: Phys. Rev. 46, 76 (1934) D.C. Backer: Astrophys. J. 174, L157 (1972) D.C. Backer: Astrophys. J. 209, 895 (1976) D.C. Backer, J.R. Fisher: Astrophys. J. 189, 137 (1974) D.C. Backer, S.R Kulkarni, C. Heiles, M.M. Davis, W.M. Goss: Nature 300, 615 (1982) N. Bartel, W. Sieber: Astron. Astrophys. 70, 307 (1978) N. Bartel, W. Sieber, R. Wielebinski: Astron. Astrophys. 55, 319 (1977) N. Bartel, W. Sieber, R. Wielebinski: Astron. Astrophys. 68, 361 (1978)


267

12. N. Bartel, W. Sieber, R. Wielebinski, N.S. Kardashev, N.Ia. Nikolaev, M.V. Popov, V.A. Soglasnov, A.D. Kuzmin, T.V. Smirnova: Astron. Astrophys. 93, 85 (1981) 13. W. Becker, B. Aschenbach: X-ray observations of neutron stars and pulsars: First results from XMM-Newton. in Proceedings of the 270. WE-Heraus Seminar on: W. Becker W., H. Lesch, J. Trümper (eds) Neutron stars, Pulsars, and Supernovae. MPE Report 278, 64 (2002) 14. S.J. Bell Burnell: Little green men, white dwarfs or pulsars? http://www.bigear.org/vol1no1/burnell.htm (1979) 15. V.S. Beskin, A.V. Gurevich, Ya.N. Istomin: Physics of pulsar magnetospheres. Cambridge University Press, Cambridge (1986) 16. V. Boriakoff, D.C. Ferguson: Microstructure cross-correlations in pulses observed at frequencies separated by 1 GHz. in: Pulsars: 13 years of research on neutron stars. Proc. IAU Symp. 95, eds. W. Sieber & R. Wielebinski, Reidel, Dordrecht, pp. 191 (1981) 17. V. Boriakoff, D.C. Ferguson, G. Slater: Pulsar microstucture quasiperiodicity, in Pulsars: 13 years of research on neutron stars, Proc. IAU Symp. 95, eds. W. Sieber & R. Wielebinski. Reidel, Dordrecht, pp. 199 (1981) 18. V.N. Brezgunov, V.A. Udaltsov: Astronom. Zh. 48, 14 (1971) 19. Yu.M. Bruck, B.Yu. Ustimenko: Nature Phys. Sci. 242, 58 (1973) 20. P.J. Callanan, P.M. Garnavich, D. Koester: Mon. Not. R. Astr. Soc. 298, 207 (1998) 21. D.B. Campbell, C. Heiles, J.M. Rankin: Nature 225, 527 (1970) 22. J. Chadwick: Proc. Roy. Soc. 136, 692 (1932) 23. J. Chadwick: Nature 129, 312 (1932) 24. R.R. Clark, F.G. Smith: Nature 221, 724 (1969) 25. J.M. Comella, H.D. Craft Jr., R.V.E. Lovelace, J.M. Sutton, G.L. Tyler: Nature 221, 453 (1969) 26. J.M. Cordes: Astrophys. J. 222, 1006 (1978) 27. H.D. Craft, J.M. Comella, F.D. Drake: Nature 218, 1122 (1968) 28. CSIRO Media Release: Parkes Telescope puts 1000 pulsar runs on the board. http://www.csiro.au/news/mediarel/mr1998/mr98259.html (1998) 29. B. Datta, A. Ray: Mon. Not. R. Astr. Soc. 204, 75 (1983) 30. J.G. Davies, P.W. Horton, A.G. Lyne, B.J. Rickett, F.G. Smith: Nature 217, 910 (1968) 31. J.G. Davies, A.G. Lyne, F.G. Smith, V.A. Izvekova, A.D. Kuzmin, Iu.P. Shitov: Mon. Not. R. Astr. Soc. 211: 57 (1984) 32. R.D. Ekers, A.T. Moffet: Nature 220, 756 (1968) 33. R.D. Ekers, A.T. Moffet: Astrophys. J. 158, L1 (1969) 34. W.C. Erickson, M.J. Mahoney: Astrophys. J. 299, L29 (1985) 35. D.C. Ferguson, J.H. Seiradakis: Astron. Astrophys. 64, 27 (1978) 36. D.C. Ferguson, D.A. Graham, B.B. Jones, J.H. Seiradakis, R. Wielebinski: Nature 260, 25 (1976) 37. G.J. Fishman, F.R. Harnden, R.C. Haymes: Astrophys. J. Lett. 156, L107 (1969) 38. G.J. Fishman, F.R. Harnden, W.N Johnson III, R.C. Haymes: Astrophys. J. Lett. 158, L61 (1969) 39. E. Flowers, M.A. Ruderman: Astrophys. J. 215, 302 (1977) 40. R.S. Foster, L. Fairhead, D.C. Backer: Astrophys. J. 378, 687 (1991) 41. R.T. Gangadhara: Astron. Astrophys. 327, 155 (1997) 42. J. Gil, A. Krawczyk: Mon. Not. R. Astr. Soc. 285, 561 (1997) 43. J. Gil, M. Sendyk: Astrophys. J. 541, 351 (1999) 44. J. Gil, J. Kijak, J.H. Seiradakis: Astron. Astrophys. 272, 268 (1993) 45. T. Gold: Nature 218, 731 (1968) 46. P. Goldreich, W.H. Julian: Astrophys. J. 157, 869 (1969) 47. D.M. Gould, A.G. Lyne: 0Mon. Not. R. Astr. Soc. 301, 235 (1998)

268


48. D.A. Graham, A.G. Lyne, F.G. Smith: Nature 225, 526 (1970) 49. P. Haensel, J.L. Zdunik, F. Douchin: Astron. Astrophys. 385, 301 (2002) 50. P.A. Hamilton, P.M. McCulloch, J.G. Ables, M.M. Komesaroff: Mon. Not. R. Astr. Soc. 180, 1 (1977) 51. T.H. Hankins: Astrophys. J. 169, 487 (1971) 52. T.H. Hankins, J.S. Kern, J.C. Weatherell, J.A. Eilek: Nature 422, 141 (2003) 53. D.J. Helfand, R.N. Manchester, J.H. Taylor: Astrophys. J. 198, 661-670 (1975) 54. A. Hewish, S.J. Bell, J.D.H. Pilkington, et al.: Nature 217, 709 (1968) 55. G.R. Huguenin, J.H. Taylor, R.M. Hjellming, C.M. Wade: Nature Phys. Sci. 234, 50 (1971) 56. R.A. Hulse, J.H. Taylor: Astrophys. J. Lett. 195, L51 (1975) 57. P.G. Jonker, M. van der Klis, P.J. Groot: Mon. Not. R. Astr. Soc. 339, 663 (2003) 58. V. Kalogera, G. Baym: Astrophys. J. 470, L61 (1996) 59. A. Karastergiou,A. von Hoensbroech, M. Kramer, D.R. Lorimer,A.G. Lyne, O. Doroshenko, A. Jessner, C. Jordan, R. Wielebinski: Astron. Astrophys. 379, 270 (2001) 60. A. Karastergiou, M. Kramer, S. Johnston, A.G. Lyne, N.D.R. Bhat, Y. Gupta: Astron. Astrophys. 391, 247 (2002) 61. A. Karastergiou, S. Johnston, M. Kramer: Astron. Astrophys. 404, 325 (2003) 62. A. Karastergiou, S. Johnston, D. Mitra, A.G.J. van Leeuwen, R.T. Edwards: Mon. Not. R. Astr. Soc. 344, L69 (2003) 63. A. Karastergiou, A. Jessner, R. Wielebinski: High Frequency Polarimetric Observations of the Crab Pulsar. In Young Neutron Stars and their Environment, Proc. IAU Symp. 218, eds. F. Camilo & B.M. Gaensler, p. 170 (2003) 64. N.S. Kardashev, N.Ya. Nikolaev,A.Yu. Novikov, M.V. Popov,V.A. Soglasnov,A.D. Kuzmin, T.V. Smirnova, W. Sieber, R. Wielebinski: Astron. Astrophys. 163, 114 (1986) 65. V.M. Kaspi, A. Wolszczan: A preliminary analysis of pulse profile stability in PSR 1257+12. In Planets around pulsars, eds. J.A. Philipps, J.E. Thorsett, S.R. Kulkarni, ASP Conf. Ser. 36, Princeton Univ., N.J., pp. 81 (1993) 66. J. Kijak, M. Kramer, R. Wielebinski, A. Jessner: Astron. Astrophys. 318, L63 (1997) 67. J. Kijak, M. Kramer, R. Wielebinski, A. Jessner: Astron. Astrophys. Suppl. Ser. 127, 153 (1998) 68. M.M. Komesaroff: Nature 225, 612 (1970) 69. C. Kouveliotou, S. Dieters, T. Strohmayer, J. van Paradijs, G.J. Fishman, C.A. Meegan, K. Hurley, J. Kommers, I. Smith, D. Frail, T. Murakami: Nature 393, 235 (1998) 70. M. Kramer: Astron. Astrophys. Suppl. Ser. 107, 527 (1994) 71. M. Kramer, R. Wielebinski, A. Jessner, J.A. Gil, J.H. Seiradakis: Astron. Astrophys. Suppl. Ser. 107, 515 (1994) 72. M. Kramer, K.M. Xilouris, A. Jessner, R. Wielebinski, M. Timofeev: Astron. Astrophys. 306, 867 (1996) 73. M. Kramer, A. Jessner, O. Doroshenko, R. Wielebinski: Astrophys. J. 488, 364 (1997) 74. M. Kramer, K.M. Xilouris, D.R. Lorimer, O. Doroshenko, A. Jessner, R. Wielebinski, A. Wolszczan, F. Camilo: Astrophys. J. 501, 270 (1998) 75. M. Kramer, C. Lange, D.R. Lorimer, D.C. Backer, K.M. Xilouris, A. Jessner, R. Wielebinski: Astrophys. J. 526, 957 (1999) 76. M. Kramer, S. Johnston, W. van Straten: Mon. Not. R. Astr. Soc. 334, 523 (2002) 77. M. Kramer, A. Karastergiou, Y. Gupta, N.D.R. Bhat, A.G. Lyne: Astron. Astrophys. 407, 655 (2003) 78. A.D. Kuzmin, B.Ya. Losovsky: Astron. Astrophys. 368, 230 (2001) 79. A.D. Kuzmin, V.A. Izvekova,Yu.P. Shitov, W. Sieber, A. Jessner, R. Wielebinski, A.G. Lyne, F.G. Smith: Astron. Astrophys. Suppl. Ser. 127, 355 (1998) 80. Ch. Lange, M. Kramer, R. Wielebinski, A. Jessner: Astron. Astrophys. 332, 111 (1998) 81. M.I. Large, A.E. Vaughan, B.Y. Mills: Nature 220, 340 (1968)

Morphology and characteristics of radio pulsars 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122.

269

M.I. Large, A.E. Vaughan, R. Wielebinski: Nature 220, 753 (1968) H. Lesch, A. Jessner, M. Kramer, T. Kunzl: Astron. Astrophys. 332, L21 (1998) O. Löhmer, M. Kramer, D. Mitra, A.G. Lorimer, A.G. Lyne: Astrophys. J. 562, L157 (2002) D.R. Lorimer, J.A. Yates, A.G. Lyne, D.M. Gould: Mon. Not. R. Astr. Soc. 273, 411 (1995) A.G. Lyne, M. Burgay, M. Kramer et al.: Science 303, 1153 (2004) A.G. Lyne, R.N. Manchester: Mon. Not. R. Astr. Soc. 234, 477 (1988) A.G. Lyne, B.J. Rickett: Nature 218, 326 (1968) A.G. Lyne, F.G. Smith: Nature 218, 124 (1968) A.G. Lyne, F.G. Smith: Pulsar Astronomy. Cambridge University Press, Cambridge (1990) A.G. Lyne, R.N. Manchester, J.H. Taylor: Mon. Not. R. Astr. Soc. 213, 613 (1985) V.A. Malofeev, I.F. Malov: Sov. Astron. 24, 54 (1980) V.M. Malofeev, J.A. Gil, A. Jessner, I.F. Malov, J.H. Seiradakis, W. Sieber, R. Wielebinski: Astron. Astrophys. 285, 201 (1994) V.A. Malofeev, I.F. Malov, N.V. Shchegoleva: Astron. Rep. 44, 436 (2000) V.M. Malofeev, R. Wielebinski, M. Kramer, A. Jessner, I. Malov, O. Malov, S. Tyul’bashev: Astron. Astrophys. (submitted) (2003) R.N. Manchester: Astrophys. J. Suppl. Ser. 23, 283 (1971) R.N. Manchester: PASA 2, 334 (1975) R.N. Manchester: J. Astrophys. Astron. 295, 280 (1995) R.N. Manchester, J.H. Taylor: Pulsars. Freeman, San Francisco (1977) R.N. Manchester, G.R. Huguenin, J.H. Taylor: Astrophys. J. 174, L19 (1972) R.N. Manchester, J.H. Taylor, G.R. Huguenin: Astrophys. J. 179, L7 (1973) R.N. Manchester, J.H. Taylor, G.R. Huguenin: Astrophys. J. 196, 83 (1975) R.N. Manchester, P.A. Hamilton, P.M. McCulloch: Mon. Not. R. Astr. Soc. 16, 107 (1980) R.N. Manchester, J.L. Han, G.J. Qiao: Mon. Not. R. Astr. Soc. 295, 280 (1998) R.N. Manchester, G.B. Hobbs, A. Teoh, M. Hobbs: Astron. J. (submitted) 2003, presently at http://www.atnf.csiro.au/research/pulsar/psrcat/ O. Maron, J. Kijak, M. Kramer, R. Wielebinski: Astron. Astrophys. Suppl. Ser. 147, 195 (2000) O. Maron, J. Kijak, R. Wielebinski: Astron. Astrophys. 413, L19 (2004) P.M. McCulloch, P.A. Hamilton, R.N. Manchester, J.G. Ables: Mon. Not. R. Astr. Soc. 183, 645 (1978) F.C. Michel: Theory of Pulsar Magnetospheres. Univ. of Chicago Press, Chicago (1991) D. Mitra, A.A. Deshpande: Astron. Astrophys. 346, 906 (1999) D.A. Moffett, T.H. Hankins: Astrophys. J. 468: 779 (1996) D.A. Moffett, T.H. Hankins: Astrophys. J. 522, 1046–1052 (1999) D. Morris, U.J. Schwarz, D.J. Cooke: Astrophys. Lett. 5, 181 (1970) D. Morris, D.A. Graham, W. Sieber, B.B. Jones, J.H. Seiradakis, P. Thomasson: Astron. Astrophys. 73, 46 (1979) D. Morris, D.A. Graham, W. Sieber, N. Bartel, P. Thomasson: Astron. Astrophys. Suppl. Ser. 46, 421-472 (1981) D. Morris, M. Kramer, C. Thum, R. Wielebinski, M. Grewing, J. Penalver, A. Jessner, G. Butin, W. Brunswig: Astron. Astrophys. 322, L17 (1997) J. Navarro, A.G. de Bruyn, D.A. Frail, S.R. Kulkarni, A.G. Lyne: Astrophys. J. 455, L55 (1995) H.-P. Nollert, H. Ruder, H. Herold, U. Kraus: Astron. Astrophys. 208, 153 (1988) J.R. Oppenheimer, G.M. Volkoff: Phys.Rev. 55, 374 (1939) L. Oster, W. Sieber: Astrophys. J. 210, 220 (1976) F. Pacini: Nature 216, 567 (1967) V.R. Pandharipande, D. Pines, R.A. Smith: Astrophys. J. 208, 550 (1976)

270


123. D. Psaltis, J.H. Seiradakis: The peculiar Moding of PSR 1237+25. In 2nd Hellenic astronomical conference : proceedings eds. M. Contadakis et al. Hellenic Astronomical Society, Greece, pp. 316 (1996) 124. G. Qiao, R.N. Manchester, A.G. Lyne, D.M. Gould: Mon. Not. R. Astr. Soc. 274, 572 (1995) 125. V. Radhakrishnanm, D.J. Cooke: Astrophys. Lett. 3, 225 (1969) 126. V. Radhakrishnan, R.N. Manchester: Nature 222, 228 (1969) 127. J.M. Rankin: Astrophys. J. 274, 333 (1983) 128. J.M. Rankin: Astrophys. J. 274, 359 (1983) 129. J.M. Rankin: Astrophys. J. 301, 901 (1986) 130. J.M. Rankin: Astrophys. J. 405, 285 (1993) 131. J.M. Rankin: Astrophys. J. Suppl. Ser. 85, 145 (1993) 132. J.M. Rankin, D.B. Campbell, D.C. Backer: Astrophys. J. 188, 609 (1974) 133. J.M. Rankin, D.R. Stinebring, J.M. Weisberg: Astrophys. J. 346, 869 (1989) 134. D.W. Richards, J.M. Comella: Nature 222, 551 (1969) 135. B.J. Rickett: Nature 221, 158 (1969) 136. B.J. Rickett, T.H. Hankins, J.M. Cordes: Astrophys. J. 201, 425 (1975) 137. B.J. Robinson, B.F.C. Cooper, F.F. Gardner, R. Wielebinski, T.L. Landecker: Nature 218, 1143 (1968) 138. R.W. Romani: Nature 347, 741 (1990) 139. M.A. Ruderman, P.G. Sutherland: Astrophys. J. 196, 51 (1975) 140. J.H. Seiradakis, J.A. Gil, D.A. Graham, A. Jessner, Kramer M., Malofeev V.M., Sieber W., Wielebinski R.: Astron. Astrophys. Suppl. Ser. 111, 205 (1995) 141. W. Sieber: Astron. Astrophys. 28, 237 (1973) 142. W. Sieber, R. Reinecke, R. Wielebinski: Astron. Astrophys. 38, 169 (1975) 143. F.G. Smith: Nature 218, 325 (1968) 144. G. Srinivasan: Astron. Astrophys. Rev. 11, 67 (2002) 145. D. Staelin, E.C. Reifenstein: Science 162, 1481 (1969) 146. I.H. Stairs, S.E. Thorsett, F. Camilo: Astrophys. J. Suppl. Ser. 123, 627 (1999) 147. D.R. Stinebring, T.V. Smirnova, T. Hankins, J.S. Hovis, V.M. Kaspi, J.C. Kempner, E. Myers, D.J. Nice: Astrophys. J. 539, 300 (2000) 148. J.H. Taylor, J.M. Cordes: Astrophys. J. 411, 674 (1993) 149. S.E. Thorsett, D. Chakrabarty: Astrophys. J. 512, 288 (1999) 150. S.E. Thorsett, D.R. Stinebring: Astrophys. J. 361, 644 (1990) 151. S.E. Thorsett, Z. Arzoumanian, M.M. McKinnon, J.H. Taylor: Astrophys. J. 405, L29 (1993) 152. Time 15 March 1968, 36 (1968) 153. M. Toscano, M. Bailes, R.N. Manchester, J.S. Sandhu: Astrophys. J. 506, 863-867 (1998) 154. Unknown: Daily Telegraph Science reporter. 1968. Bell-Burnell S.J., private communication. See also http://www.nap.edu/readingroom/books/obas/contents/authorship.html 155. A. von Hoensbroech: The polarization of pulsar radio emission. Ph.D. Thesis Bonn University, Germany (1999) 156. A. von Hoensbroech, K.M. Xilouris: Astron. Astrophys. S 126, 121 (1997) 157. A. von Hoensbroech, K.M. Xilouris: Astron. Astrophys. 324, 981 (1998) 158. J. Weber: Phys. Rev. Lett. 21, 395 (1968) 159. J.M. Weisberg, J.M. Cordes, S.C. Lundgren, B.R. Dawson, J.T. Despotes, J.J. Morgan, K.A. Weitz, E.C. Zink, D.C. Backer: Astrophys. J. Suppl. Ser. 121, 171 (1999) 160. R. Wielebinski: Characteristics of (normal) pulsars at highest radio frequencies. In 270. WE-Heraeus Seminar on Neutron Stars, Pulsars and Supernova Remnants, eds. W. Becker et al., MPE Report 278, 167 (2002) 161. R. Wielebinski, W. Sieber, D.A. Graham, H. Hesse, R.E Schönhardt: Nature Phys. Sci. 240, 131 (1972) 162. R. Wielebinski, A. Jessner, M. Kramer, J.A. Gil: Astron. Astrophys. 272, L13 (1993)

Morphology and characteristics of radio pulsars 163. 164. 165. 166.

271

A. Wolszczan, D.A. Frail: Nature 355, 145 (1992) X. Wu, R.N. Manchester, A.G. Lyne, G. Qiao: Mon. Not. R. Astr. Soc. 261, 630 (1993) K.M. Xilouris, J.M. Rankin, J.H. Seiradakis, W. Sieber: Astron. Astrophys. 241, 87 (1991) K.M. Xilouris, J.H. Seiradakis, J. Gil, W. Sieber, R. Wielebinski: Astron. Astrophys. 293, 153 (1995) 167. K.M. Xilouris, M. Kramer, A. Jessner, A. von Hoensbroech, D.R. Lorimer, R. Wielebinski, A. Wolszczan, F. Camilo: Astrophys. J. 501, 286 (1998) 168. M.D. Young, R.N. Manchester, S. Johnston: Nature 400, 848 (1999) 169. B. Zhang, A.K. Harding: Astrophys. J. 535, L51 (2000)


THE


Solar radiative output and its variability: evidence and mechanisms Claus Fröhlich1 , Judith Lean2 1 Physikalisch-Meteorologisches Observatorium Davos, World Radiation Center,

7260 Davos Dorf, Switzerland 2 E.O. Hulburt Center for Space Research, Naval Research Laboratory, Washington,

DC 20375-5320, USA Received 26 August 2004 / Published online 16 November 2004 – © Springer-Verlag 2004

Abstract. Electromagnetic radiation from the Sun is Earth’s primary energy source. Space-based radiometric measurements in the past two decades have begun to establish the nature, magnitude and origins of its variability. An 11-year cycle with peak-topeak amplitude of order 0.1 % is now well established in recent total solar irradiance observations, as are larger variations of order 0.2 % associated with the Sun’s 27-day rotation period. The ultraviolet, visible and infrared spectral regions all participate in these variations, with larger changes at shorter wavelengths. Linkages of solar radiative output variations with solar magnetism are clearly identified.Active regions alter the local radiance, and their wavelength-dependent contrasts relative to the quiet Sun control the relative spectrum of irradiance variability. Solar radiative output also responds to subsurface convection and to eruptive events on the Sun. On the shortest time scales, total irradiance exhibits five minute fluctuations of amplitude ≈ 0.003 %, and can increase to as much as 0.015 % during the very largest solar flares. Unknown is whether multidecadal changes in solar activity produce longer-term irradiance variations larger than observed thus far in the contemporary epoch. Empirical associations with solar activity proxies suggest reduced total solar irradiance during the anomalously low activity in the seventeenth century Maunder Minimum relative to the present. Uncertainties in understanding the physical relationships between direct magnetic modulation of solar radiative output and heliospheric modulation of cosmogenic proxies preclude definitive historical irradiance estimates, as yet. Key words: Sun: irradiance, activity, UV radiation, solar-terrestrial relations Correspondence to: [email protected]

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1. Introduction The radiative output of the Sun was termed the ‘solar constant’ until relatively recently when solar monitoring by satellite experiments revealed that it varies continuously. Commencing with the NIMBUS-7 spacecraft in the late nineteen seventies, the record of solar radiative output now extends without interruption to the present time, and exhibits variations on all time scales – from minutes to decades – accessed thus far. Prior to the advent of space-based observations, astronomers and solar physicists argued that the radiative output of the Sun as a star changed in a substantial way only on evolutionary time scales, and was invariant for all practical purposes such as contemporary terrestrial effects. While it was recognized that the occurrence of sunspots might change the irradiance at the Earth, their effect was considered negligible because they cover at most a few tenths of a percent of the visible solar disk. As well, the results of a half-century of ground-based measurements of the ‘solar constant’ by the Smithsonian Institution were inconclusive, and likely reflected the influence of solar activity related variations on the terrestrial atmosphere. Solar observations made with radiometers in space provided the first unequivocal evidence of solar irradiance variability on time scales from minutes to days and months [144]. The radiometers detected fluctuations that sometimes reached a few tenths of a percent and were associated with the movement of sunspots across the face of the solar disk visible at Earth as the Sun rotated on its axis. Establishing the reality of 11-year cycle-related solar irradiance variations proved more difficult. An overall decrease of the irradiance from the solar activity maximum in 1980 to activity minimum in 1986 was recognized as being of solar origin (rather than instrumental drift) only after the irradiance increased again towards the next solar maximum. Scientific scepticism about the reality of solar radiative output variations, especially on solar-cycle time-scales, derived from the assumption that measurements made with absolute uncertainties of order ±0.3 % precluded the unambiguous detection of true solar variability which a re-analysis of the Smithsonian observations [33, 36] had determined to be of smaller magnitude. But because of their high precision (0.001 % or better) the space-based radiometric measurements demonstrated that most, if not all, of the observed variability was indeed of solar origin. Since then, continuous variations in solar irradiance have been recorded on time scales from minutes, arising from p-mode oscillations and large flares, to the 11-year activity cycle, arising from changing solar activity. The important role of sunspots as a cause of radiative output variability has been quantified, additional bright sources of variability have been identified and speculated, and the spectral nature of the changes estimated. The extent of longer-term, inter-cycle radiative output changes during past centuries has also been speculated, based on cosmogenic isotope archives of solar activity and variations in sun-like stars. However, the record of direct irradiance observations (≈ 25 years) is too short, as yet, to clarify the extent of the changes postulated. 1.1. Definition of solar radiative output Irradiance, S, is the quantity that a solar radiometer observes at the annual mean sun-earth distance of one astronomical unit, R = 1 AU. It is the power of the Sun’s electromag-

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netic radiation received per unit area at the radiometer’s entrance aperture, either in a given wavelength interval dλ at λ, as spectral irradiance F (λ), or integrated over all wavelengths as total irradiance, S = F (λ)dλ. This integral, which is the Sun’s total radiative output in the direction to Earth, is the quantity referred to as the ’solar constant’ for more than a century. Radiometers in the vicinity of the Earth can only record the power radiated from the solar hemisphere projected towards Earth. The power that the Sun radiates from its entire surface, called the solar luminosity, L = 4π R 2 S, has not been observed directly. This would require, for example, measurements made by a large number of space-based radiometers evenly distributed around the Sun. Solar irradiance is composed of the radiance I (λ) emitted from all elements of the solar hemisphere visible to the radiometer according to F (λ) = I (λ)d (1)

where is the solid angle that the solar disk extends at Earth for a given wavelength. Explicitly, 1 R 2 2π f (µ, λ)µdµ (2) F (λ) = I0 (λ) R 0 where I0 is the radiance at the disk center, R is the radius of the Sun at a given wavelength, R the distance from the Sun to the radiometer, and f (µ, λ) is the centerto-limb radiance variation function with µ = cos θ for θ the angle subtended by the emitting surface element from the center of the solar disk. The center-to-limb function f (µ, λ) describes radiance variation across the disk which is mainly due to changes in the path length through the solar atmosphere, but also due to the variation of the angular variation of the radiance. As the Sun’s rotation axis is currently inclined by about 7◦ relative to the ecliptic plane the physical coordinates on the visible solar disk (heliospheric latitude of the center of the disk and the direction of the rotation axis) vary over the course of the year, from the perspective at Earth. With an ascending node around 5th June, the largest inclination with the solar south pole visible is in early March and with the north pole in early September. Thus, a persistent north-south radiance asymmetry such as may arise from different strengths of the activity in the two solar hemispheres, could produce an irradiance modulation with a one-year period.

1.2. Historical investigations of solar activity and radiative output variability Although direct observations of the Sun’s radiative output from space with high radiometric accuracy commenced only in 1978, telescopic observations of the Sun began in 1610 and led to the discovery of sunspots. Solar variability was established when the 11-year sunspot cycle was reported in 1843. Sunspot numbers have been recorded ever since, and reconstructed back to the time of the first observations [61]. Most extensive are the Greenwich Observatory records of sunspots (and also faculae) from 1882 to 1976. As Fig. 1 shows, sunspots provide a record of solar activity that now extends for almost four centuries, documenting large fluctuations in the amplitude of the 11-year cycle (Fig. 1b), and attendant phase changes as well (Fig. 1c).

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Fig. 1. Shown in (a) are variations in the annual mean group sunspot number, Rg , and in (b) and (c) the amplitude and phase of the 11-year cycle, during the past four hundred years. Amplitude and phase in (b) and (c) are determined from demodulation of the time series at a period of the solar cycle. The epochs A, B and C designate the Maunder Minimum, Dalton Minimum and Modern Maximum, respectively

Radiative output – brightness – changes were speculated to occur as a result of solar activity revealed by the sunspot record. Measurements were devised to detect changes in solar irradiance, culminating in the Smithsonian Astrophysical Observatory groundbased program from 1902 to 1957. Changes associated with the Sun’s activity cycle were inferred for both the short-term decrease due to sunspots [2] and the 11-year cycle, shown as a positive correlation between sunspot numbers and the solar constant especially during the strong solar cycle 19 [1,3]. However, the determined amplitudes were nearly an order of magnitude higher than evident in the subsequent space-based record: the measurements failed to unambiguously detect real changes because of interference by the Earth’s atmosphere. As a result, the view that the total radiative output was a constant quantity prevailed until the 1980s, when space-based records became available. (Hufbauer [62] and Hoyt and Schatten [59] provide historical details)


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Fig. 2. Variation of the daily mean (a) total and (b) spectral (160–208 nm) solar irradiance during the last 25 years. The total irradiance record is a composite of observations from multiple spacecraft (PMOD composite). The two primary UV data sets are from the Solar Mesosphere Explorer (SME) and the Upper Atmosphere Research Satellite (UARS)

1.3. Knowledge of contemporary radiative output variability From measurements made during the last 25 years by accurate radiometers in space, solar electromagnetic radiation is now understood to vary at all wavelengths, and on all time scales (e.g., [73]). The spectral irradiance variations F (λ) produce a net change of order 0.1 % in total radiative output, S, during recent 11-year cycles, on which are superimposed larger variations of a few tenths of a percent on shorter time scales. Figure 2 shows plots of daily mean values of the total and UV spectral irradiance time series now available. Spectral irradiance, shown in Fig. 3, and the amplitude of the spectrum variability are both strongly wavelength dependent. In general, the visible, near UV and near IR spectral regions, where the flux of the Sun’s electromagnetic radiation peaks, vary the least – by a few tenths of a percent during the 11-year activity cycle. Significantly more variable is solar radiation at wavelengths both shorter and longer than the peak of the curve – in the ultraviolet (Fig. 2b), X-ray and radio portions of the electromagnetic spectrum. Knowledge of solar spectral irradiance variability is poor except at wavelengths shorter than visible/near UV and longer than IR. This is because relatively reliable long term observations have been possible only at wavelengths for which irradiance variability exceeds a few percent. The percentage level variations of UV radiation emergent from the Sun’s upper photosphere in the band from 160 nm (originating near the temperature minimum regions) to 208 nm (the Al ionization edge) can be seen in Fig. 2b to vary by an order of magnitude more than the total irradiance (Fig. 2a) which emerges from

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lower photospheric layers. Evident in the UV spectrum, as for total irradiance, are variations associated with the 27-day solar rotation, monthly to annual fluctuations, and the prominent 11-year cycle. Unlike the total irradiance for which an uninterrupted record exists since 1978, the UV spectral irradiance record is intermittent in this interval.

1.4. Relevance for models of the sun The Sun and its variability provide unique constraints on models of stellar evolution, which in turn provide scenarios for solar variability on exceedingly long time scales, not accessible by irradiance observations. Luminosity, radius and age, fundamental parameters in standard models of stellar evolution, are known relatively accurately for the Sun, although the transfer of irradiance values to luminosity is complicated. However, stellar evolution models have only very simple atmospheres that lack the dynamo-driven magnetic fields that produce activity in the Sun, so accommodating irradiance cycles is problematic. Furthermore, a luminosity averaged over several 1000 years is more appropriate than a value determined from contemporary observations but this requires knowledge of long-term solar irradiance changes. Even if the transfer from irradiance to luminosity could be performed accurately, and a long-term average determined, the uncertainty in irradiance simulated by these models would be no better than about 0.1 % which cannot adequately constrain solar models. Knowledge of the Sun’s radius can potentially calibrate solar models but changes in the optically observed value, which is normally used, are not known (for a review see, e.g., [107]). Thus far, solar evolution theory only provides evidence for radiative output changes over very long time scales, such as the increase of the luminosity during the last three billion years by about 30 % (e.g., [116]). The standard values used to calibrate current models are: radius R = 6.9599 · 108 m, luminosity L = 3.846 · 1026W (corresponding to a ‘solar constant’ of 1367.6 W m−2 ), age t = 4.65 Gy, and a photospheric metallicity Z/X = 0.0245. Standard models of the Sun itself (see, e.g., [105]) incorporate more physical parameters (opacities and equation of state) and include processes such as microscopic diffusion, penetrative convection and mass loss. At present helioseismology affords the most important constraints for standard solar models, by allowing comparison with a ‘seismic’ model, inverted from observed, highly accurate p-mode frequencies (see, e.g., [130]). New helioseismic results have substantially improved our knowledge of the internal structure and dynamics of the Sun. The deficit of the observed neutrinos, for example, is no longer a problem of understanding stellar evolution, but rather one of the behaviour of the neutrinos. Helioseismology also provides some evidence for solar-cycle related changes at the base of the convection zone, within it and below the surface which may be related to structural changes (see, e.g., [5, 12, 56]). Changes of the Sun’s radius would be a further indication of structural changes, for which the ratio W = (dL/L)/(dR/R) provides important information about the location of the perturbation within the Sun leading to such variations. Determination of W and of possible changes over the solar cycle is the aim of PICARD to be launched in 2008 [129].


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Fig. 3. Shown are the Sun’s spectral irradiance at the top of the Earth’s atmosphere and at the Earth’s surface (0 km). Gases in the Earth’s atmosphere absorb solar radiation, especially in the UV and IR spectrum (e.g., O2 , O3 , H2 O, CO2 )

1.5. Relevance for global change on earth A balance between incoming solar radiation (which peaks in the visible spectrum, Fig. 3), referred to as ‘short-wave’, and outgoing terrestrial radiation (which peaks in the vicinity of 10 µm), referred to as ‘long-wave’, establishes the equilibrium temperature in the vicinity of the Earth’s surface. The spectrum of the Sun’s irradiance at the top of the Earth’s atmosphere is therefore a critical determinant of Earth’s climate (e.g., [100]). Both the solar spectral irradiance variability and the processes that facilitate climate response to solar radiative forcing are strongly wavelength dependent. There is considerable atmospheric absorption in the ultraviolet (UV) and near infrared (IR) spectral regions, which depletes certain spectral regions and produces a solar irradiance spectrum at the Earth’s surface (0 km in Fig. 3) that differs substantially from the unattenuated spectrum. Since the Sun’s electromagnetic radiation is the primary source of energy for the Earth, even small variations in irradiance have the potential to influence Earth’s climate and atmosphere, including the ozone layer (e.g., [22, 50, 76, 110]). Furthermore, the extinction of solar radiation by absorption and scattering in the Earth’s atmosphere, and its reflection by land surfaces and oceans are strongly wavelength dependent, as are the processes through which climate responds to radiative input changes, involving atmospheric constituents such as water vapour and ozone, surface properties such as sea ice and snow cover, and most importantly clouds (e.g., [93]). Reliable knowledge of solar-induced variations is essential for understanding and attribution of anthropogenic influences on Earth’s climate [126] and changes of the ozone layer in the stratosphere (e.g., [47]). This requires the specification of solar spectral irradiance from 0.1 to 100 micron on time scales of years to centuries. Climate model simulations of Earth’s surface temperature response to solar variability in past centuries require as input estimates of historical irradiance. However, on climatological and solar-evolution time scales the irradiance database acquired thus

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far is extremely short. This has motivated the development of variability models that reconstruct past irradiance changes, based on understanding the sources of variability evident in the contemporary database and their relationship to solar activity indices. Most models adopt a speculated (but unproven) long-term component which produces an irradiance increase in the range 0.2 to 0.4 % from the Maunder Minimum to the present maxima (e.g., [28, 58, 74, 87]). In response to such irradiance reconstructions, simulations of climate change in recent centuries suggest solar-related surface temperature changes between 0.2 K [21] and 0.4 K [111, 112], which are unable to account for global warming in the past few decades. The state of the terrestrial upper atmosphere and ionosphere depends crucially on solar irradiance in the extreme ultraviolet spectrum, which varies significantly – by factors of two to an order of magnitude during the solar cycle. These irradiance changes at short wavelengths produce dramatic modulation of temperature and densities of the upper atmosphere (e.g., [73]). But since the contribution to the total radiative output of solar irradiance variations at wavelengths shorter than Ly-α is negligible, this spectral region is not considered here.

2. Properties of solar radiation The Sun emits radiation primarily from the vicinity of its surface. Some 99 % of solar radiative output – that at wavelengths from 275 to 4900 nm – emerges from the photosphere. As Fig. 4 shows, the brightness temperature of the quiet Sun’s surface is 6520 K decreasing to about 4400 K at the top of the photosphere after which the temperature decline with height reverses into the overlying chromosphere. Height is defined here as the radial distance above unit optical depth in the continuum at 500 nm, τ500 = 1. Above the chromosphere, in the transition region and the corona, the temperature increases to a few million degrees as the outer solar atmosphere expands into the heliosphere. Here, the intensity of the emergent high energy (short wavelength) radiation is very weak and contributes only a few mW m−2 to the Sun’s total radiative output of ≈ 1365 W m−2 . 2.1. Spectral distribution Although the spectrum of photospheric radiation appears as a relatively smooth continuum when viewed with moderate spectral resolution, as in Fig. 3, it actually comprises numerous spectral features shown in Fig. 5. Absorption and emission processes of gases in the Sun’s atmosphere – H, He, C, N, O, Mg, Al, Si, Ca and Fe in various states of ionization – produce spectral features with widths typically a few tens of pm. Many spectral features are attributable to hydrogen, the most common component of the Sun’s atmosphere, including prominent emission and absorption lines (e.g., at 121 nm and 656.3 nm, respectively). Likewise, the second most common solar atmosphere constituent, He, produces strong line emission (e.g., at 30.4 nm and 58.4 nm) and absorption (e.g., at 1083 nm). In addition to composition, temperature in the solar atmosphere is a primary determinant of solar spectrum structure. In fact, in the photosphere (heights less than ≈ 525 km)


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Fig. 5. The spectral distribution of the solar irradiance is shown at high resolution for isolated spectral regions corresponding to (a) the Mg h and k, (b) the CaII H and K Fraunhofer lines, and (c) the He I absorption line. In (d) a theoretical spectrum is shown at all wavelengths [69]

and in the chromosphere (heights from ≈ 525 km to ≈ 2100 km) measurements of radiation spectrum intensities are used to infer the solar atmospheric temperature distribution by adjusting the spectrum from radiative transfer calculations to agree with the spatially averaged spectrum of the quiet Sun. The quiet solar spectrum (see, e.g., [7]) has a maximum brightness temperature of about 7500 K at 1.6 µm where the solar atmosphere has minimum opacity (the H− bound-free opacity is zero at this wavelength) and the deepest photospheric layers (≈ −40 km) are accessible as shown in Fig. 6. From this minimum, opacity increases towards shorter wavelengths due to H− bound-free absorption and the Balmer, Al, Si and Lyman edges. Longward, opacity increases due to H− free-free absorption. As opacity increases, the brightness temperature decreases because increas-

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ingly higher layers of the photosphere have lower temperatures. The resulting spectrum is called a continuum because it does not contain any lines (see ‘Continuum’ in Fig. 6). For the quiet Sun a minimum value of about 4450 K is reached at around 150 µm and near 160 nm. At wavelengths λ > 150 µm and λ < 160 nm the brightness temperature increases and the lines in the spectrum are seen in emission rather than absorption. The intensity of the lines are related to the temperature distribution via the formation height of the line (see ‘Formation Height’ in Fig. 6). Radiative transfer models are able to match not only the general properties of the solar spectrum, but also the observed emission near the centers of the Ca II and Mg II lines (Fig. 5) by including non-LTE calculations above the temperature minimum with temperature distributions such as those shown in Fig. 4 (e.g., [29, and references therein]). These atmospheric models are semi-empirical, because the temperature is adapted to reproduce the observed spectral intensities; the law of conservation of energy is not used. Transport of the energy in the chromosphere and corona is not by radiation only, but includes other mechanisms which are not understood sufficiently to be modelled adequately.

2.2. Spatial distribution Solar radiation is not distributed homogeneously on the disk of the Sun viewed from the Earth. The radiance from a spatial element of the solar atmosphere varies from the center of the Sun’s disk to the limb, in different ways at different wavelengths. Superimposed on this center-to-limb variation is a changing distribution of bright and dark emission associated with various solar features, such as sunspots, faculae and network. The solar images in Fig. 7 illustrate the distinct character of active regions in different solar atmospheric regimes and their associations with photospheric magnetic flux. Compact, bright faculae tend to occur in the vicinity of large sunspots, both of which signify regions of enhanced magnetic flux. The magnetic fields in these features alter the temperature and density of the solar atmosphere, and thereby the emitted radiation, in


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Fig. 7. Images of the Sun recorded by the Photometric Solar Precision Telescope (PSPT) in the UV Ca K line and the red continuum are compared with magnetograms from the U.S. National Solar Observatory (NSO). Changes in (a) total and (b) UV solar irradiance (from Fig. 2) are traceable to changes in magnetic features

wavelength-dependent ways. Compact, dark sunspots are the primary magnetic signature in visible and red continuum photospheric images, such as those in Fig. 7. Here the photospheric gas pressure is large enough to balance the magnetic field strength. Higher, in the solar chromosphere, the dominant magnetic features are extended, bright plages, in which magnetic fluxes are smaller than in sunspots. These features are evident in the Ca K images in Fig. 7. Temperature distributions for typical activity-related features are shown in Fig. 4. Compared with the quiet Sun are average network, average plage, facula or bright plage, and sunspot umbra. Sunspots are darker and cooler than the surrounding photosphere at all wavelengths except possibly at the shortest EUV wavelengths [96]. Faculae and plages are generally brighter except possibly at the center of the disk and in the near

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IR [30, 72, 95]. When active features are present in the solar atmosphere, their different temperature distributions and altered radiance change the solar spectrum by an amount proportional to their fractional coverage of the solar surface. Thus the continual eruption, evolution and submergence of magnetic field produces time-dependent temperature and thus radiance inhomogeneities, which subsequently alter solar irradiance. For example, the irradiance time series in Fig. 7 illustrate the decrease in total solar irradiance, but not in UV irradiance, coincident with a large sunspot group present near the central meridian shown in the left column of the images of Fig. 7.

2.3. Solar radiation proxies Different regions of the solar spectrum arise from radiation formed in different solar atmospheric layers. Since magnetic fields produce different conditions of temperature and density in different atmospheric layers, observing the Sun at selected wavelengths or wavelength regions formed over a range of different temperatures provides a tool for detecting and quantifying the impact of solar activity throughout the solar atmosphere, and hence on the emergent radiation at many wavelengths. Particularly useful in this regard are solar emission and absorption line features in which the cores of the lines form above the temperature minimum region (i.e., in the chromosphere). This is the case for the Mg II and Ca II doublets and the He I line shown in the top panels in Fig. 5. When measured as an average over the disk (sun-as-a-star observation), ratios of the core emission relative to the wings of such spectral features yield information about the prevailing global temperature structure pertaining to an area-weighted average of the distributions from specific magnetic features. Quantitative relationships exist among various globally integrated fluxes as a result of the significant spatial correlations of their variability sources, although the spatial scales are altered by the different pressure conditions. In this way, photospheric faculae are identified in addition to plage and enhanced network from indices in the upper photosphere and chromosphere. Figure 8 compares the variations in three different indices of solar activity that have been widely used to infer irradiance variations. The Mg II chromospheric index is the core-to-wing ratio of the Mg II doublet (at 280 nm), shown in Fig. 5a. This index tracks closely the flux variations in the equivalent width of the He I line at 1083 nm and the core of the Ca II K emission at 393 nm (also shown in Fig. 5). Compared in Fig. 8 with the chromospheric Mg II index are the 10.7 cm radio flux, whose fluctuations reflect a combination of chromospheric (longer term) and coronal (short term) influences, and the sunspot number, which is a visually determined, numerical rather than physical index, but the longest available direct indicator of solar activity (Fig. 1).

3. Observational evidence for irradiance variability 3.1. Radiometric measurements of total irradiance from space A first attempt to use electrically calibrated radiometers (ECRs) in space was made on the Mariner VI and VII missions to Mars in 1969 [102, 103] in order to test spacecraft


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Fig. 8. Shown are the time variations of daily values of three solar activity proxies that have been used in various ways to infer solar irradiance variations. The radio flux at 10.7 cm (F10.7 ) in (a) is available since 1947, and primarily reflects brightness changes in the corona, whereas the Mg II index of chromospheric activity in (b) is available only since 1978 and closely simulates changes in global brightness associated with faculae and plages. The sunspot number in c) is a generic indicator of solar activity, available since 1610, as shown in Fig. 1

behaviour under extended exposure to solar radiation. However, the results were unable to distinguish instrumental effects from true solar variability at the few tenths of a percent level (see also [37]). Conclusive evidence for solar irradiance variability was achieved only after ECRs were launched on space platforms to monitor the Sun more or less continuously, that is with the launch of the Earth Radiation Budget experiment on NIMBUS 7 in November 1978. In early 1980 the Solar Maximum Mission satellite (SMM) followed, then the Earth Radiation Budget Experiment (ERBE), the Upper Atmosphere Research Satellite (UARS), the European Retrievable Carrier (EURECA), the Solar and Heliospheric Observatory (SOHO), ACRIMSAT and most recently the Solar Radiation and Climate Experiment (SORCE). Figure 9 compares the various irradiance data sets acquired from these missions. Offsets among the data sets reflect the different radiometric scales of the individual measurements. Since late 1978 at least two inde-

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pendent solar monitors have operated simultaneously in space. Currently operating are radiometers on SOHO, ACRIMSAT and SORCE. The two composite irradiance records also shown in Fig. 9 are compiled from multiple, cross-calibrated independent measurements [38,39,44,142,146]. Both composite records use Nimbus 7 and ACRIM data prior to 1996 but in one time series (designated as the PMOD composite) the VIRGO data from SOHO are used after 1996 [46], whereas the other time series (designated as the ACRIM composite) relies primarily on ACRIM data [146]. Each TSI composite exhibits a prominent 11-year cycle of peak-to-peak amplitude 0.085 % (difference between September 1986 and November 1989 monthly means). Larger fluctuations are evident, and are associated with the Sun’s 27-day rotation on its axis. During epochs of high solar activity these shorter term fluctuations corre-


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spond to irradiance decreases of a few tenths of a percent whereas near solar minimum the decreases are much smaller. According to the PMOD composite irradiance record in Fig. 9b, levels of irradiance during the two minima of 1986 and 1996 are similar. This suggests that TSI does not have a significant long-term trend underlying the 11-year cycle during the last 3 decades. Combining the data sets with different assumptions about their long-term stabilities produces a different composite record in which solar irradiance during 1990 to 1992 increases by 0.04 % as shown in Fig. 9c. Willson [142] and Willson and Mordvinov [146] interpret this change as evidence for secular irradiance changes in addition to the 11-year cycle. An individual radiometer measures irradiance with a typical uncertainty (accuracy) of order 0.2 %, which is insufficient to determine even the change of ≈ 0.1 % that occurs during an 11-year solar activity cycle. Measurement repeatability (precision) is much higher, and adequate for monitoring short-term changes, but retrieving long-term behaviour is more difficult. Careful tracing of the observational databases to each other is crucial. This requires not only cross-calibration of different absolute radiometric scales but also reliable knowledge of the degradation and operating environment (thermal, pointing, etc.) of each individual radiometer in space. Only the ACRIM, VIRGO and SORCE instruments have the ability to determine exposure-dependent sensitivity drifts by on-board comparisons with redundant radiometers that receive less solar exposure. Because of this, the PMOD composite relies primarily on the measurements made by ACRIM I on SMM, ACRIM II on UARS and VIRGO on SOHO. The Nimbus 7 Hickey-Frieden (HF) radiometer observations are used to place ACRIM I and ACRIM II data (which do not overlap in time) on a common radiometric scale, which is then adjusted to the Space Absolute Radiometric Reference (SARR) scale [20]. Figure 10 shows the deviations of the original data from the PMOD composite in Fig. 9 and illustrates the most important corrections applied to the original data. Fröhlich and Lean [44, 45] and Fröhlich [38, 39] provide a detailed description of the corrections, which are summarized in the following. Significant corrections are applied to the NIMBUS 7 HF measurements to account for sensitivity changes at the beginning of the mission (before 1980 and during the spinmode period of SMM) and, more importantly, near the end of the mission from 1990 to 1992. This latter period coincides with the gap between the ACRIM I and II data. A variety of independent studies suggest that the HF radiometer experienced notable sensitivity changes. Comparisons with both the ERBE data [85] and models based on ground based observations [17] indicate two discontinuities of −0.31 and −0.37 W m−2 near 1 October, 1989 and 8 May, 1990, respectively. The second jump is difficult to identify and may reflect the continuation of sensitivity drifts identified by comparison with ACRIM I [41, 46] earlier in the record. The change in the Nimbus 7 sensitivity during the ACRIM I to ACRIM II gap is determined as −617 ± 50 ppm (≈ 0.06 %). In the PMOD composite construction, the corrected HF data are then used to adjust ACRIM II measurements to the scale of the ACRIM I measurements and the original ACRIM II data are shifted by +2149±33 ppm. The only correction made toACRIM I data is during 1980 when a time-allocation of the degradation different from that published by Willson and Hudson [145] is applied (as described in [44]). This correction is evident in Fig. 10 as a small linear decrease of ACRIM I data relative to the PMOD composite.

288


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Deviation (%)

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Fig. 10. Shown are differences of the PMOD total solar irradiance composite to the original data sets. Smooth lines indicate that the radiometer is the basis for the composite and if coincident with zero that only an overall scale shift has been applied (ACRIM I after 1984, ACRIM II and VIRGO). The largest corrections are applied to the HF record, as summarized in the text. For the ACRIM I record in 1980 the original correction published by Willson and Hudson [145] was revised slightly, as described in [44]. Also shown are ratios of the ACRIM composite [142,146] to the PMOD composite. It is evident in these ratios that the primary difference between the PMOD and ACRIM composites is due to the omission in the ACRIM composite of the HF correction during the gap between the ACRIM-I and II data sets in the period from 1990–1992 2000

Difference relative to ERBS [Wm−2]

3

Days (Epoch Jan 0, 1980) 4000 6000

8000

PMOD Composite Slope: 50 ± 15 µWm−2d−1

2 1 0 −1 −2 3

Slope: 85 ± 68 µWm−2d−1

Difference: 0.02 Wm−2

ACRIM Composite Slope: −18 ± 21 µWm−2d−1

2 1 0 −1 −2

Slope: 137 ±100 µWm−2d−1

Difference: −0.55 Wm−2

84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 Year

Fig. 11. Shown are the ratios of the PMOD and ACRIM composite TSI records to the independent ERBS observations. The main difference is localized in the gap between the ACRIM I and ACRIM II missions. It is unlikely that ERBE instrumental effects can explain these differences as Willson and Mordvinov [146] suggest, since this would require an episodic sensitivity change confined only to this period


289

The VIRGO radiometers used in the PMOD composite are also corrected for long-term sensitivity changes, related to their solar exposure (for details see, e.g., [39]. The ACRIM composite1 shown in Fig. 9c differs from the PMOD composite2 primarily because in the former the Nimbus 7 HF data are used without any corrections to place ACRIM I and ACRIM II data on a common radiometric scale. This is confirmed in Fig. 11 where comparison of the two different composites with the independent ERBE data reveals distinct differences mainly in the 1990 to 1992 period, i.e., during the gap between the ACRIM I and ACRIM II data sets. Since the ERBE radiometer has had minimal solar exposure (equivalent to about 2 days during its 17 years of operation) its sensitivity drifts are expected to be small. The increase of 18.2 ppm/year seen in Fig. 11 relative to the PMOD composite amounts to a total change over the 17 years of 310 ppm, or an increase of about 150 ppm per exposure day. This increase may be analogous to the sensitivity increase observed in the PMO6V radiometers early in the mission, which are about 70 ppm per exposure day. Neither the PMOD composite nor the ERBE data supports the claim of Willson and Mordvinov [146] that the ERBE radiometer has degraded primarily during 1990 – 1992 (a speculated consequence of high solar activity levels), nor that solar irradiance has undergone significant secular changes in recent decades. The slope of the ratio to the PMOD and ERBE TSI time series suggests that the uncertainty of the long-term behaviour of the composite TSI is about ±60 ppm per decade. Alternatively, the uncertainty is estimated as ±92 ppm by adding the uncertainties related to the tracing of ACRIM II to I together with the HF corrections. Thus, any change of TSI between the two recent solar minima can be regarded as zero with a high level of confidence.

3.2. Characterization of TSI variability in the frequency domain Fourier-transforming the TSI time series produces the power spectrum shown in Fig. 12, which characterizes total solar irradiance variance in the frequency domain. The power spectrum of the daily values (using the PMOD composite), shown as the red line in Fig. 12, extends to 5.8 µHz, the Nyquist frequency for 1-day sampling, and has an inherent frequency resolution of 1.3 nHz, afforded by the length of the time series of nearly 24 years (more than 8700 days). To better characterize the solar cycle peak, the plotted spectrum is 3 times over-sampled and yields a peak-to-peak amplitude of 670 ppm at 9.89 years for solar cycles 21–23. The two peaks in the power spectrum near a 1-year period (peak-to-peak amplitude of 126 ppm at 1.09 year and 81 ppm at 0.96 year) are only marginally significant. VIRGO data with 1-minute sampling allow an extension of the TSI power spectrum to higher frequencies, where significant power is evident near 5 minutes. Since VIRGO 1 The ACRIM composite and the ACRIM I, II and III data sets are available from

http://www.acrim.com/Data%20Products.htm. 2 The PMOD composite and VIRGO TSI are available from http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant and http://www.pmodwrc.ch/pmod.php?topic=tsi/virgo/proj_space_virgo as daily values and in the case ofVIRGO also as hourly values.VIRGO version 6_000_0401 is used for the PMOD composite in Fig. 9b.

290


10000.00

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Power [ppm2/µHz]

106

104 5−minute Oscillations

102

11−year Period

100 TSI Composite (26_00_0312) VIRGO TSI (6_000_0312) 2000.8−2002.2 VIRGO TSI (6_000_0312) 1996.1−1997.5

0.001

0.010

0.100

1.000 10.000 Frequency [µHz]

100.000

1000.000

Fig. 12. Shown is the power spectrum of the composite record of daily total solar irradiance for the period from 1978 until 2002 (red). To illustrate the solar cycle variability in the frequency domain, the power spectra of data from VIRGO during solar minimum (Feb. 1996–Aug. 1997) are compared to that of solar maximum (Oct. 2000–Feb. 2002). The solar cycle influence is evident in the differences in power at low frequencies

data now cover more than half a solar cycle, they allow quantification of activity related irradiance changes in the frequency domain from the 5-minute oscillations to periods up to 1000 days. In Fig. 12 the power spectrum for the period 2000.8 – 2002.2 corresponds to high solar activity while that for 1996.1–1997.5 to solar activity minimum. The two power spectra overlap at the highest frequencies but begin to deviate in the region of supergranulation; the difference gradually increases towards lower frequencies reaching more than an order of magnitude in the vicinity of the nominal 27-day rotational period (see also Fig. 17). In addition to the two distinct peaks at 11 and 1 year, and the peaks of the solar oscillations in the 5-minute range, the power spectrum in Fig. 12 displays turning edges due to characteristic time scales or frequencies where the constant power at low frequency starts to decrease (often termed as 3-db points). The following characteristic time scales are identified with their approximate turning points and average (for minimum and maximum activity) exponent of slopes (slope in double logarithmic scale): 27-day rotational period (≈ 0.68 µHz): −3.3, supergranulation (≈ 6.2 µHz): −1.3, mesogranulation (≈ 56 µHz): −0.4, and granulation (≈ 825 µHz): −1.2. 3.3. Spectroradiometry from space Space-based observations of solar spectral irradiance have concentrated primarily on measurements at UV wavelengths. The terrestrial atmosphere absorbs solar radiation at these wavelengths (see Fig. 3), and knowledge of its variability is sought to understand stratospheric and ozone fluctuations. Heath and Thekaekara [55] summarize the database


291

Fig. 13. Shown are space-based observations of solar UV spectral irradiance in selected broad bands at (a) 160 to 208 nm, (b) 208 to 220 nm, and (c) 250 to 400 nm, indicating UV irradiance increases in phase with the solar activity cycle (see also Fig. 2 which includes also a plot of the UV irradiance in the range 160 to 208 nm)

of the early measurements from space, in which instrumental effects obscured true variability. Currently the longest and most reliable data are the measurements made by the Solar Stellar Irradiance Comparison Experiment (SOLSTICE) and the Solar Ultraviolet Spectral Irradiance Monitor (SUSIM) on UARS, since October 1991 [24]. Prior to UARS, the Solar Mesosphere Explorer (SME) monitored the UV irradiance with lesser accuracy and precision. The UARS and SME data, examples of which are shown in Fig. 13, suggest solar cycle irradiance changes of 20 %, 8 % and 3 % near 140, 200 and 250 nm, respectively [81, 113, 115]. Figure 14 shows current understanding of solar spectral irradiance variability during the 11-year solar cycle in terms of percentage changes relative to the irradiance, and also as energy changes. Rotational modulation of spectral irradiance is superimposed on the solar cycle variations at all wavelengths, in phase with solar activity in the UV spectrum, transitioning at wavelengths from 300 to 400 nm to TSI-type anti-phase fluctuations at visible and infrared wavelengths. Although the spectral irradiance energy changes sum to produce the TSI changes in Fig. 2, the actual energy changes in the spectrum are not well constrained. The variability amplitudes in the UV spectrum shown in Fig. 14 are derived from UARS observations [81] but the spectrum changes shown at wavelengths longward of 400 nm are theoretical estimates [124, 132].

292


Fig. 14. The spectrum variations that cause the changes in total solar irradiance are shown in (a) as ratios of spectra at high and low solar activity, respectively (FMAX ) and (FMIN ), and in (b) as their difference in energy units. The variability amplitudes in the UV spectrum are derived from UARS observations [81] and the changes for wavelengths longward of 400 nm are theoretical estimates [124, 132]

Solar UV spectral irradiance monitors, such as those flown on UARS and SME, utilize various combinations of filters, gratings and mirrors to select, disperse and focus the solar spectrum into sub-nanometer resolution. Photomultipliers or photodiode detectors record the dispersed spectrum. Both SOLSTICE and SUSIM on UARS (and also SOLSTICE on SORCE) have absolute uncertainties approaching ±6 %, depending on wavelength. Differences between the SOLSTICE and SUSIM spectral irradiances, such as in Fig. 13, are within these uncertainties for 5 nm bands. SME irradiances have larger uncertainties, of order ±15 %, and are shown in Fig. 2 scaled to match the UARS irradiance scale. As with total irradiance radiometers, exposure to solar radiation can alter the overall sensitivity of UV spectroradiometers by changing the transmittance and reflectance of optical surfaces. SOLSTICE and SUSIM on the UARS aim to achieve long-term repeatability of a few percent by incorporating in-flight sensitivity tracking to correct their signals for instrumental drifts. SOLSTICE accomplishes these corrections by regular comparisons with signals from a collection of bright blue stars. SUSIM uses deuterium lamps and redundant optical elements to quantitatively estimate the impact of exposure-related degradation on its multiple optical surfaces. [148] describe validations and comparisons of SOLSTICE and SUSIM observations. Observations of solar cycle spectral irradiance variability at visible and infrared wavelengths are lacking because, until the launch of the SORCE mission in 2003, spacebased spectroradiometers had neither the sensitivity nor long-term stability necessary for the detection of variations on time-scale of the solar cycle or longer. Real variability

Solar radiative output and its variability: evidence and mechanisms 1996

1997

1998

1999

2000

2001

2002

293 2003

0

Deviation of Detrended Solar Irradiance (ppm)

−1000 −2000 −3000 500 0 −500 −1000 −1500 −2000 −2500 1000 0 −1000 −2000 −3000 −4000

a) VIRGO TSI

0.1%

b) SPMA 862nm

0.1%

c) SPMA 500nm

0.1%

d) SPMA 402nm

0.1%

0 −2000 −4000 0

500

1000 1500 2000 Epoch January 0, 1996

2500

Fig. 15. Time series from SOHO/VIRGO of detrended TSI (a) and the three channels of filterradiometers (b–d) show coherent modulation with increasing amplitude during epochs of higher solar activity 1000.00

100.00 1−year Period

10.00

Period (days) 1.00

0.10

0.01

27−day Period

Power [ppm2/µHz]

106

104 5−minute Oscillations

102

100 SPM−RED SPM−GREEN SPM−BLUE

0.01

0.10

1.00

10.00 Frequency [µHz]

100.00

1000.00

Fig. 16. Shown are power spectra of the detrended spectral irradiance data measured by the SOHO/VIRGO filterradiometer channels from 1996 until December 2003

in the solar visible and infrared spectrum has nevertheless been detected on shorter time scales from observations by filter radiometers on Nimbus 7 [81], on EURECA by the SOVA2 SPM [19] and on SOHO by the VIRGO SPM channels in three 5-nm bands, centered at 402 nm, 500 nm and 862 nm [42]. The latter data show modulation up to periods of about one year in detrended solar irradiances [40]. The variations are compared in Fig. 15 with TSI variations, with all data sets detrended by subtracting

294


polynomials of the same degree. Variability, which can be reliably assessed at periods 1 year, decreases in the visible spectrum with increasing wavelength, from 465 ppm near 400 nm to 170 ppm near 800 nm. This may be compared with the TSI variance of 185 ppm for the same period of time. This decrease is qualitatively consistent with the theoretical estimates from [124, 132] (Fig. 14) which show that solar cycle variability amplitudes in the visible part of the spectrum also decrease with increasing wavelength. The power spectra of the three VIRGO channels shown in Fig. 16 are qualitatively similar to that of TSI in Fig. 12. Spectra for active and quiet Sun are compared in Fig. 17 together with the corresponding ratio for TSI. The most interesting feature in Fig. 17 is the dip at the 27-day period which indicates that the rotational modulation is only weekly dependent on the level of solar activity. Towards higher frequencies the ratio first increases until a maximum at about 10 days, then decreases to a constant value slightly above one for periods shorter than a few hours. The different behaviour of the visible (green) and near UV (blue) channels at periods longer than the rotational period probably reflects the detrending method, and may not be of solar origin. Note that the ratios at frequencies above 200 µHz, in the region of the granulation and mesogranulation, are unexpectedly different from unity, with values of 1.15, 1.19, 1.18 for the red, green and blue channels and 1.21 for TSI, respectively. Figure 18 shows the relative contributions to TSI variability of spectral irradiance in the three different VIRGO wavelength bands, as determined from multivariate frequency analysis (see, e.g., [64, Chapters 5.6f, 8.4f]). In the frequency range from 0.29 to 1.65 µHz (periods of 7 to 40 days) the explained variance reaches 97 % with a share between the colours of 12, 25 and 60 % for the infrared (red), visible (green) and near UV (blue) channels, respectively. It is interesting to note that for the same range the red and blue channel are more or less in phase with TSI whereas the green channel lags by about 30 degrees [40]. 3.4. Limitations of present solar monitoring capability The cluster of recently-measured total solar irradiance values near 1365.5 W m2 , evident in Fig. 9 by the lower spread in the absolute scale of observations since about 1990, suggests that the accuracy of TSI measurements has improved significantly relative to the measurements made 20 years earlier. In spite of this apparent improvement, the problem of absolute accuracy remains an important issue, as does the determination of the long-term measurement stability (see, e.g., [106]). In particular, preliminary SORCE TSI measurements [71] are about 4 W m−2 lower [65] than the values of the PMOD composite which is referred to SARR [20]. This difference exceeds the combined stated uncertainties, for reasons unresolved as yet. A demonstrated capability for radiometric accuracies at least a factor of 10 better than currently possible is urgently needed to establish a benchmark for future solar irradiance monitoring. In lieu of this, overlap by successive radiometers remains essential for cross tracking of radiometer calibrations to achieve the needed long-term precision. For this reason, producing a reliable long-term composite record requires at least two independent experiments simultaneously in space. Although more than one space-based TSI instrument is planned during the next few years, this may not be the case in the extended future. For the spectral irradiance at near UV, visible and near IR wavelengths,


1000.00

100.00

10.00

Period (days) 1.00

295

0.10

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TSI SPM−RED SPM−GREEN SPM−BLUE

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1

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5−minute Oscillations

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0.10

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10.00 Frequency [µHz]

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1000.00

Fig. 17. Ratio of the active (2000.8–2002.2) to quite (1996.1–1997.5) power spectra of TSI and the detrended channels of filterradiometers (data sets from SOHO/VIRGO). The reason for the different behaviour of the green and blue channel from that of TSI and the red channel is probably due to instrumental effects not removed during the period of solar minimum. The ratio at high frequencies (> 200 µHz, as indicated by the horizontal lines) amounts to 1.15, 1.19, 1.18 and 1.21 for TSI, the red, green and blue channels, respectively Period (days) 100

10 27−day

13−day period

Power (ppm2µHz−1)

105

104

Red Green Blue

0.1

1.0 Frequency (µHz)

Fig. 18. Shown are results from a multi-variate frequency analysis of VIRGO’s three spectral irradiance (SPM) channels relative to total solar irradiance (TSI). The top curve is the power of TSI and the shaded areas indicate that part explained by the spectral irradiance in each of the three different spectral bands

296


Fig. 19. Variations in the Sun’s gross and net magnetic flux are shown during the epoch of spacebased irradiance measurements in the lower diagram. The time series are obtained from the unsigned sum and signed sum, respectively, of magnetic flux in images made by the National Solar Observatory, such as those shown for three different periods in the upper panel. In these magnetograms, light and dark areas signify regions of opposite polarity

the situation in terms of long-term stability is even less satisfactory. New, accurate inflight techniques for assessing the long-term instrumental changes are needed. Hopefully, the novel approaches now being utilized by instruments on the SORCE mission [52,71, 114,147] will produce spectral irradiance time series with significantly higher long-term repeatability than has been achieved thus far.

4. Sources of irradiance variability Solar radiative output undergoes distinct, wavelength-dependent variability with amplitudes and time scales that relate closely to the level of the Sun’s activity. Solar activity, initially detected in sunspot observations in the mid nineteenth century (Fig. 1), is now known to originate in a cycle of magnetic flux driven by a dynamo seated near the bottom of the convection zone, at ≈ 0.7R (e.g., [25]). This flux produces a variety of features, such as sunspots, faculae and plages (Fig. 7), and coronal holes, and instigates numerous solar phenomena, including irradiance and solar wind fluctuations, flares and coronal mass ejections. During times of high solar activity substantially more magnetic flux pervades the solar atmosphere than during quiet conditions at solar minima. Figure 19 shows the


297

Fig. 20. Shown are scatter plots of daily mean solar irradiance, from Fig. 2, with total (net and absolute) magnetic flux, from Fig. 19. In the upper panel, the scatter plots of total irradiance and magnetic flux illustrate a distinctly non-linear relationship. UV irradiances (160–208 nm) have a more linear relationship with magnetic flux, as the scatter plot in the lower panel demonstrates

variations in magnetic flux during recent 11-year cycles, as disk-averages of both the absolute and signed quantities. But although the solar magnetic cycle is the ultimate driver of irradiance variations, the scatter plots in Fig. 20 show that solar irradiance correlates poorly with the net and disk-averaged magnetic flux; with a correlation coefficient of 0.43 for unsigned flux and 0.21 for signed flux versus TSI, only 18 and 4 % of the variance is explained. Changes in specific magnetic features, rather than in the netor disk-averaged magnetic flux, relate better to irradiance variability. Magnetic fields in the solar atmosphere produce at least two types of features that cause significant variations in solar irradiance. These features are evident in the solar images in Fig. 7. Sunspots, which are cooler (see Fig. 4) and darker than the surrounding solar atmosphere, are evident in the red continuum images. Faculae, which are hotter (see Fig. 4) and brighter, are seen primarily on the limb of visible-light images; the Ca K images reveal their overlying chromospheric counterparts, the plages. Sunspots and faculae, respectively, deplete and enhance local solar radiance, thereby altering the net radiation projected in the direction of the Earth, i.e., the irradiance. Since sunspots and faculae typically occur on the Sun together, a competition of their relative strengths, which are strongly wavelength-dependent, determines solar irradiance variability. For example, while sunspots produce significant depletions in the visible and infrared spectrum, evident by the reduced total solar irradiance near 1999.6 in the time series in Fig. 7a, they have minimal effect in the UV spectrum, where no depletion of UV irradiance in Fig. 7b occurs at that time. Modulation by sunspot darkening causes prominent reductions in total solar irradiance on time scales of solar rotation. TSI brightening associated with the largest, contiguous facular regions (those associated with chromospheric plages) also occurs, but with notably smaller amplitudes than the sunspot-related reductions. The net effect


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21 22 23

0.6 0.4 0.2 0.0 −4 −3 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2 Wm−2 Wm−2 Wm−2 Wm−2

Fig. 21. Histograms of TSI values are shown for different phases of solar cycles 21–23. The histograms are averaged over the following periods: maxima of cycle 21: 1979.2 . . . 1982.0, cycle 22: 1989.3 . . . 1992.1, and cycle 23: 2000.0 . . . 2003.1; descending part of cycle 21: 1982.0 . . . 1985.3, cycle 22: 1992.1 . . . 1995.3, and cycle 23: 2003.1 . . . 2003.9; minima of cycle 21/22: 1985.3 . . . 1987.4, and cycle 22/23: 1995.3 . . . 1997.6; ascending part of cycle 22: 1987.4 . . . 1989.3, and cycle 23: 1997.6 . . . 2000.0.

of these two competing variability sources explains why, on average, periodograms of TSI lack significant power near the rotational modulation period [34] and suggest a reason why rotational modulation is not strongly dependent on solar activity (Fig. 17). In the UV spectrum (below 300 nm), however, rotational modulation arises primarily from the influence of facular features which are comparatively much brighter than sunspots are dark at UV wavelengths: UV irradiance time series have significant power near the rotational modulation period [80]. Enhanced emission from bright magnetic features that have smaller spatial scales than the largest contiguous faculae and are more dispersed on the solar disk (typically tracing the boarders of the chromospheric network) contribute additional variability to both total and UV irradiance during the solar cycle [29, 35, 79]. Other sources of solar cycle irradiance variability are also postulated, such as a change in photospheric temperature [49, 67]. Whether ‘non-facular’ variations result from, or are independent of, solar magnetic features (e.g., thermal shadows, active network) is not yet clarified. Distributions of daily TSI values, such as those shown in Fig. 21, help quantify the relative influences of magnetic features. As sunspots and faculae, respectively, decrease and increase the irradiance, each influences the distribution on opposites sides of its maximum, called the mode, in a distinct way. Figure 21 shows the mean distributions for maximum, decreasing, minimum and ascending phases of the solar cycle. As expected, except during solar minimum the distributions are asymmetric, with an extended tail of lower values, especially during times of higher activity, associated with sunspots. The distributions in Fig. 21 can help characterize the mean influence of sunspots and faculae at different solar cycle phases. They show, for example, that the ratio of the sunspot and facular effects changes during the solar cycle. The average ratio is 1.77 ± 0.58 according to the mean of the negative and positive differences to the mode. The standard deviation of the ratio is mainly determined by changes over the solar cycle with a maximum ratio of 2.24 during the descending part and a minimum of 1.18 during solar minima.


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Days (Epoch Jan 0, 1980) 2000 4000 6000

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Fig. 22. Models of total solar irradiance variability that combine the influences of sunspot darkening and facular brightening can account for a significant fraction of the observed variance in the total solar irradiance composite record. Shown in (a) is the facular influence PF together with PFl determined as the lower envelope of PF . Shown in (b) is PFs , PFl and −PS , and in (c) the net effect on total solar irradiance of the combined sunspot and facular changes (all calibrated by linear regression against the PMOD composite)

5. Empirical models of magnetic sources of irradiance variability Information about the two primary sources of irradiance variability, sunspots and faculae (associated with both plages and active network), is available from a variety of solar observations which enable the quantitative modelling of irradiance variability independently of direct measurements. The daily facular brightening, PF , and sunspot darkening, PS , time series shown in the upper panel of Fig. 22 since 1976 are two indices that are used widely for this purpose. The facular brightening index is a composite of directly measured flux ratios of emission from the center of Fraunhofer features, primarily the MgII h & k index, (e.g., Figs. 5 and 8) relative to emission in the line wings [23,83,138]. White light solar images that record the locations and areas of sunspots, such as in Fig. 7, provide the primary inputs for the sunspot darkening index.

5.1. Sunspots Sunspot darkening, the fractional change in irradiance caused by sunspots, is calculated explicitly (in this case for total irradiance) as PS =

S/SQ =

µAWDC (CS − 1) 1 0

R(µ) R(µ)µdµ

(3)

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Fig. 23. The contrasts of (a) bright faculae and (b) dark sunspots are shown as functions of wavelength from the UV to the IR spectral regions. The contrasts are ratios of the radiance of these features to that of the background photosphere, determined from theoretical calculations with the radiative transfer code ATLAS9 from [68] by [131] and limited observations [4]

where S is the reduction in irradiance relative to the quiet Sun, SQ , for a sunspot of area AWDC (in fractions of the solar hemisphere) at location µ in heliocentric coordinates. CS is the sunspot’s contrast (ratio of spot emission to the background quiet photosphere) and R(µ) is the center-to-limb variation function which is assumed to be the same for the quiet photosphere and the spot. The summation is over all spots on the solar disk at a specific time, and utilizes bolometric contrast and center-to-limb functions (Eddington limb darkening R(µ) = (3µ + 2)/5) appropriate for modelling total solar irradiance variations. Ground-based white light images made from 1882 to 1976 by the Greenwich Observatory, and most recently by the U.S. Air Force operational Solar Observation Optical Network (SOON) sites 3 supply the basic time-dependent information about sunspot areas and locations. Greenwich sunspot areas are reported to be 20 % larger than SOON sunspot areas [27]. The time series shown in Fig. 22b, is the energy reduction in total radiative output caused by sunspot darkening, PS , calculated from SOON sunspot data and calibrated by linear regression against the PMOD composite. Sunspots in reality comprise a very dark central umbra and a less dark surrounding penumbra but present versions of PS do not include this distinction because the SOON data lack sufficient information about these specific sunspot features. Sunspots also have wavelength-dependent contrasts. As Fig. 23 shows, they are factors of 3 to 5 darker in the UV spectrum than in the IR spectrum. The bolometric sunspot contrast takes this into account by weighting the contrast spectrum (e.g., Fig. 23) with the solar spectrum 3 The observations of the sunspot regions are available from the National Geophysical Data Cen-

ter (NGDC) operated by the National Oceanographic and Atmospheric Administration (NOAA) at Boulder, Colorado, http://www.ngdc.noaa.gov/stp/SOLAR/ftpsunspotregions.html.


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(e.g., Fig. 3). However, the spectral dependence of sunspot contrast has not been well determined, as indicated by the differences between the observational and theoretical estimates in Fig. 23.

5.2. Faculae The explicit calculation of a facular index, PF , analogous to PS is also possible [79] but more difficult because faculae have lower contrasts in the visible spectrum and more fragmented areas than sunspots. In solar images made in the core of Ca and other Fraunhofer lines (e.g., Fig. 7) the emission is preferentially enhanced in chromospheric plage and bright network that overlie photospheric faculae. Ca images therefore provide information about facular areas and locations from which to construct facular brightening indices [53, 79]. Faculae can also be identified in magnetograms (e.g., [66]). Facular indices derived from feature quantification in solar images are difficult to produce over extended periods of time because of the lack of a long-term database of appropriately calibrated images. Furthermore, physical characteristics of faculae and plages such as their center-to-limb variations and contrasts are less well known than for sunspots. This motivates the use of alternative facular indices such as the Mg-II index, which consists of the ratio of the core and wing fluxes and minimizes the influence of instrumental drifts. The line cores originate in the chromosphere where bright features have greater contrast than their photospheric counterparts (a factor of 2 versus a few percent for an active region), and the flux measurements automatically integrate emission over the full disk. One disadvantage is that chromospheric and photospheric radiances can have different center-to-limb dependence of emission and contrast.

5.3. Models of contemporary irradiance variability Empirical models of solar irradiance variability over multiple time scales utilize as inputs the sunspot darkening and facular brightening indices, PS and PF , combined in different proportions for total versus spectral irradiance at different wavelengths. Historical reconstructions may utilize an additional third index of postulated long-term variability. The models are constructed differently depending on whether or not direct irradiance observations are available to establish the relative contributions of sunspots and faculae at the wavelengths of interest, over the time scales of interest. Models of contemporary total and UV spectral irradiance variability, for which adequate observational databases exist, are developed in one of two ways. Either the PF and PS time series are regressed together against the observed irradiance, S or F (λ), or the observations are first corrected for sunspot effects then the residual time series, S − PS or F (λ) − PS (λ), is linearly regressed against PF [44, 74, 81]. Both approaches yield an expression of the form S(t) ∝ atot PS (t) + btot PF (t) for total solar irradiance or F (λ, t) ∝ aλ PS (t) + bλ PF (t) for spectral irradiance at time t and wavelength λ. Thus, in empirical irradiance variability models the indices PS (t) and PF (t) contain time dependent information about the sources of the irradiance variability and the (time-independent) coefficients aλ,tot and bλ,tot adjust the relative contributions of these sources for radiation at different wavelengths, or for total irradiance. In practice, the

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observations may or may not be detrended prior to the regression, depending on the confidence (or lack of) in their long-term stability (e.g., [81]). A model that has two components – sunspot darkening, PS , and facular brightening, PF (Fig. 22) – explains 77.2 % of the variance of the total solar irradiance composite record. A further refinement consists of separating the facular component into shorterand longer-term parts, PFs and PFl . The component PFl is determined as a smoothed lower envelope of PF , as shown in Fig. 22a, and PFs = PF − PFl . Multiple regression against the three indices yields some improvement in the model’s reproduction of short-term total irradiance variations, and explains 78.6 % of the variance. This approach better accommodates possible differences in the short and long-term sources of irradiance variability. The fact that the coefficients determined with the three-component model are notably different for the short and long-term facular proxy may indicate differences in the physical sources that produce the longer-term irradiance variations, presumably associated with bright network inside and outside the active regions. Direct observations

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from MDI/SOHO of the fractional disk areas of bright features and their contrast as a function of the magnetic field [98,99] indicate that this difference may just be due to the fact that the translation from MgII index to TSI depends on the specific contrast, C/B, of the network and faculae and not on C. The comparison in Fig. 24 with the PMOD composite TSI record of the threecomponent model (calibrated over the full period from 1978 to 2003) shows that the model reproduces the observed gross temporal features [40]. However, during activity maxima the modelled sunspot and facular signals show about 25 % higher amplitudes than the deviations from the mode (Fig. 21) recognizes. A more detailed analysis shows that during the descending phases and minima of the activity cycle only the sunspots determined from the model differ, whereas during the ascending parts both methods give similar results. These differences can be explained partly by some direct compensation of darkening by spots and simultaneous brightening by faculae, but may also arise from changes of the spot contrast during the cycle as observed by [90] which the model does not include. Bi-variate spectral analysis clarifies the frequency dependence of the variance in the observed total irradiance explained by the three-component model. Figure 25 shows that for periods from 13 to 1200 days the mean coherence squared is 0.73 which means that the model explains 73 % of the variance. At some periods the coherence is very low, most prominently near the 27-day rotational period, but also near 575, 206 and 141 days. The comparison in Figure 25 illustrates that the model based on daily sunspots and facular indices can only explain the main features of the actual irradiance variations, but not all details of the variability.

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During the solar cycle, there is a close correlation of the irradiance brightness source with p-mode oscillation modes in the Sun. Figure 26 shows that the solar cycle changes in p-mode frequencies clearly track the residual time series of total solar irradiance corrected for sunspot influences, i.e., the long-term brightening component of irradiance variability. This empirical association may afford a more physical approach for interpreting TSI variability, since these low-degree p-mode oscillations are global in nature and reflect sub-surface processes. However, the mechanisms responsible for this high correlation between the low-degree p-mode frequencies and the facular irradiance signal are not yet understood theoretically, other than by stating that both are related to magnetic field changes. A theoretical explanation for the frequency changes suggests, however, a correlation with opposite sign to that which is observed (e.g., [9]). At UV wavelengths, empirical models have been developed in a similar way by regression of the sunspot and facular indices against observations [81] and from facular indices determined directly from Ca-K images [79,149]. Figure 27 compares models and observations in three UV bands. The models generally reproduce observed variability better at shorter wavelengths where the changes are larger and less affected by instrument long-term instabilities. For example, a model developed from regression of the PS and PFs +PFl indices in Fig. 22 with detrended SOLSTICE data correlates better with the data at 200 nm (0.88) than at 250 nm (0.7). As Fig. 27 illustrates, there is overall agreement between the model and observations, especially for shorter UV wavelengths on rotational modulation time scales, although less variance is explained than for total irradiance. Wavelength-dependent instrumental drifts may remain in the observations, whose longterm stabilities are still being revised. As well, in the spectral region 250 to 400 nm the precision and stability of the UARS instruments (a few percent) likely exceeds the true


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Fig. 27. Empirical models constructed from combinations of the facular brightening and sunspot darkening indices in Fig. 21 are compared with observations in three UV bands during the solar cycle, on the left, and solar rotation, on the right. In each case, the absolute levels of the various observations have been adjusted to match those of the model.

irradiance variability. This motivated the development of SORCE’s new approach for measuring solar spectral irradiance longward of 300 nm by using a prism and miniature electrical-substitution radiometer, rather than a grating and photomultiplier [52]. Models of solar irradiance variability at wavelengths longer than 400 nm, for which adequate observational databases are lacking, also utilize the sunspot darkening and facular brightening indices in Fig. 22 but rely on theoretical calculation [132] to provide information about their relative roles, as quantified by the coefficients aλ and bλ . The wavelength dependencies of the contrasts of faculae and sunspots, shown in Fig. 23, determine appropriate combinations of PS and PF for reproducing irradiance variabilities at different wavelengths. This approach, described by Lean (2000), produced the estimates of solar cycle spectral irradiance variability at wavelengths longer than 400 nm, shown in Fig. 14. Future validation of spectral irradiance variability models at wavelength longward of 300 nm will be possible with SORCE observations. Initial results already suggest that model revisions are needed; in particular, the SORCE observations do not support facular contrasts as dark in the infrared spectrum as those shown in Fig. 23 [30].

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6. Past and future irradiance variations Knowledge of irradiance variations on much longer time scales than the few decades of direct observations are needed, for example to aid in the interpretation of past climate change. This knowledge must be inferred from indicators and proxy records of solar activity. The sunspot numbers since 1610, shown in Fig. 1, are the longest record of solar activity based on actual solar observations (see, e.g., [61]), and capture the Maunder Minimum epoch of anomalously low activity in the seventeenth century. Information extracted from observations of the terrestrial environment provide indirect evidence of solar activity. These proxies include the aa index of geomagnetic activity since 1882 [91] and the 14 C and 10 Be cosmogenic isotopes archived in tree-rings and ice-cores, respectively, over past millennia [11, 13]. Reconstructing past solar irradiance from sunspot numbers, geomagnetic activity or cosmogenic isotopes is a challenging task. The most crucial aspect is establishing whether – or not – longer-term irradiance variability is present in addition to the known 11-year cycle. Long-term trends in the aa index and the cosmogenic isotopes, together with the range of variability in sun-like stars [8], suggest that the Sun is capable of a broader range of activity than witnessed during recent solar cycles. This implies the existence of one or more long-term irradiance variability components which models of historical irradiance have attempted to incorporate. But recent studies [48,51] refute the initial evidence from sun-like stars of a Maunder-Minimum-type behaviour as demonstrated by the bi-modal distribution of [8]. It seems that the lowest activity level of sun-like stars better corresponds to the brightness level of the minimum between the two distributions, rather than to the peak of the lower mode. Independent studies also raise the possibility of long-term instrumental drifts in the aa index [127], and question the assumption of a linear relationship between heliospheric-modulated proxies and solar irradiance [82]. 6.1. Evidence for long-term solar activity changes That solar activity evolves with time is evident in the sunspot group number, Rg , shown in Fig. 1. The amplitude of the 11-year activity cycle has varied by two orders of magnitude over the past 400 years, while the phase of the cycle has ranged from 8 to 15 years. Solar cycles with lower amplitudes tend to last longer, but the amplitude (Fig. 1b) and length (Fig. 1c) of solar cycles are only loosely related (correlation coefficient of −0.34). This suggests the behaviour of a non-linear oscillator (e.g., [94]) but the true origin of solar activity and the sunspot cycle is uncertain. Waxing and waning sunspot numbers during the past four centuries, evident in Fig. 1, indicate fluctuations in solar activity that are undoubtedly accompanied by variations in many solar phenomena, including radiative output. When sunspot numbers are high, not only are there more, and larger, dark sunspots present on the Sun, but bright features (faculae, plages) are also larger and more frequent. High sunspot numbers correspond to increased gross magnetic flux (Fig. 19) and related solar indices, including the fluxes of the Ca, Mg and He chromospheric indices and the 10.7 cm radio emission (Fig. 8). Although the sunspot number is a numerical, rather than geophysical, proxy of solar activity, it tracks these indices rather closely: for example, the correlation coefficient


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Fig. 28. Cosmogenic isotopes stored in tree-rings (14 C) and ice-cores (10 Be) provide indirect information about solar activity. The residence time of 10 Be in the climate system is sufficiently small that solar-induced changes are evident during the 11-year solar activity cycle (solid line), and are seen to track concurrent solar-induced changes in the aa index of geomagnetic activity (symbols) and sunspot numbers (shaded). In both the 10 Be and aa indices, the 11-year cycles are superimposed on a significant overall drift in the first half of the twentieth century that is not seen in sunspot numbers at solar minima

of daily sunspot numbers and 10.7 cm fluxes (shown in Fig. 8 since 1980) is 0.94 for daily non-zero values between 1947 and 2003. Hence, the combination of the number of groups g and the number of individual spots n, Rz = 10g + n, that Wolf devised for the definition of the Zürich sunspot number is more representative for solar activity in general than of spots per se [60, and references therein]. The aa geomagnetic index and the 10 Be cosmogenic isotope record likewise indicate the inconstancy of the Sun’s 11-year activity cycle, as Fig. 28 illustrates during the past century. The aa index is recorded by magnetometers at antipodal locations on Earth (to mitigate the effect of the Earth’s magnetic field) and it’s variations reflect the impact of the solar wind (speed and density) and heliosphere (interplanetary magnetic field) on the magnetosphere [108,125]. The cosmogenic isotopes are the products of galactic cosmic ray interactions with gases in the Earth’s atmosphere. Levels of cosmic ray fluxes are reduced during times of high solar activity because enhanced open flux from the Sun impedes their motion through the heliosphere and reduces the number that reaches the Earth. As with geomagnetic activity, cosmic ray fluxes reflect heliospheric variability, including the solar wind structure, strength of the interplanetary magnetic field, and the tilt angle of the heliospheric current sheet [15, 104]. Cosmogenic isotopes are the primary proxy of solar activity prior to about 1600. As Fig. 29 shows, their anti-correlation with sunspot numbers, evident in Fig. 28 during the 11-year cycle, persists during the past millennium, including an increase in the Maunder Minimum and other similar solar activity minima [10,13]. Both the 14 C and 10 Be records exhibit common cycles that are apparently solar-related (reflecting that the Sun is the common source of their production) with periods near 90 years, called the Gleissberg cycle, and near 205 years, in addition to the 11-year cycle [97]. Attempts to reconstruct sunspot numbers prior to 1600 yield ambiguous results. The extrapolation of cycles identified by spectral decomposition of the sunspot record itself indicates solar activity in the Medieval Maximum (1140–1200) only slightly less than

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Fig. 29. Shown are the records of cosmogenic isotope fluctuations in tree-rings and ice-cores associated with solar activity during the past millennium. The long-term trends in the cosmogenic isotopes track the envelope of sunspot number amplitudes

in the present Modern Maximum (1900–2000) [109]. In contrast, an inversion of the 10 Be suggests that the Sun has been unusually active since the 1940s, relative to the past millennium [133,134]. Both approaches agree, however, that sunspot numbers between 1400 and 1700 were reduced significantly relative to current levels as a consequence of the Spörer and Maunder minima (Fig. 29). There are also conflicting interpretations of the various solar proxies in Figs. 28 and 29 in terms of long-term variations in solar magnetic flux. By analyzing the aa index to isolate the solar sources of its variability [89] infer a doubling of the Sun’s coronal magnetic field strength since 1900, and a 40 % increase since 1964 (see also [86]). In contrast the last two cycles of solar magnetic field data show no secular trend in photospheric flux in the immediate past [6]. Furthermore, it is the open coronal flux, not the total flux, that extends into the heliosphere and controls geomagnetic activity and cosmic ray fluxes [6, 15, 135]. According to simulations of the transport and evolution of emerging bipolar magnetic regions on the Sun’s surface (which are the sources of active regions and sunspots), and the spreading of magnetic flux into interplanetary space, secular trends in open magnetic flux need not necessarily infer equivalent secular trends in total magnetic flux, i.e., in solar activity [82, 135]. The simulations suggest that increasing solar cycle amplitudes, such as seen in sunspot number cycles from 1900 to 1950, can indeed cause an accumulation of open flux and a long-term secular trend, and hence cause a drift in cosmogenic isotopes and geomagnetic activity. However, the total magnetic flux (of which only 10 % extends into the heliosphere) does not exhibit a concurrent secular trend. Contrary claims, that 10 Be is a good proxy for the total surface magnetic fields, arise from studies that postulate ephemeral region sources of magnetic flux (parameterized by solar cycle length) in addition to the larger bipolar magnetic regions associated with active regions parameterized by sunspot numbers [122, 123]. Evidence for long-term changes in ephemeral regions is, however, uncertain. Although postulated to vary in a significant way on long-term scales from a comparison of current solar activity with the distribution of Ca brightness in sun-like stars [32,139]


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did not detect in Ca K solar images long-term changes in the network, where ephemeral regions mainly reside. And a reassessment of the stellar data has been unable to recover the original bimodal separation of (lower) Ca emission in non-cycling stars compared with (higher) emission in cycling stars [51]. In their interpretation of the original bimodal distribution from [8, 139] had inferred solar Ca K levels during the Maunder Minimum that matched the stellar Ca levels of the non-cycling stars at the peak of the lower bi-modal distribution. It is interesting to note that [139] found that a Sun with all the magnetic network removed from the present minima would lie approximately at the minimum between the two distribution, which is now thought to better indicate the lowest possible activity level that sun-like stars may reach [48,51]. Additional reduction in the basal emission from the centers of the network cells must be hypothesized in order to achieve the lower brightness levels of non-cycling stars [139]. Speculated long-term variability mechanisms in addition to changes in the area of ephemeral regions include fluctuations in facular brightness, in solar diameter [119] and in sub-surface convective strength [58].

6.2. The Maunder Minimum Whereas many sunspots are present during contemporary solar maxima (e.g., 1980, 1990), they were less prevalent in the centuries before 1900. During the 17th-century Maunder Minimum, from 1645 to 1715, sunspots were absent from the disk entirely for long periods [26]. This is the only such episode of a spot-less Sun in the available sunspot record. A less severe and less prolonged episode of reduced solar activity, the Dalton Minimum, occurred near 1800 (Figs. 1, 29). During past millennia, series of Maunder-like solar activity minima punctuate the Sun’s activity, as indicated by cosmogenic isotopes. The Spörer Minimum can be seen in Fig. 29 to immediately precede the Maunder Minimum; other similar minima are evident episodically during the past 10,000 year record of 14 C (e.g., around 800 BC). Conceptually, the excess cosmogenic isotopes in the Maunder and other solar minima relative to the present is associated with reduced and less structured heliospheric magnetic fields. However, [136] suggest that with the reduced solar activity the modulation of the interplanetary magnetic field derived from the open flux associated with the very low sunspot numbers is too small to account for the significant fluctuations of 10 Be during the Maunder Minimum [14], including apparent cyclicity. Ephemeral regions are, once again, postulated, as an additional source of open flux to explain why 10 Be levels fluctuated during the seventeenth century [123]. An adequate physical understanding of the solar processes (from the interior dynamo to the extended heliosphere) that simultaneously altered cosmogenic isotopes and sunspot numbers during the Maunder Minimum remains to be achieved. There are also concerns about a possible climate influence on cosmogenic isotopes, which may compromise their fidelity as indicators of pure solar activity. Climate change affects the deposition of cosmogenic isotopes in their respective archives, and may contribute additional variations to that imposed by solar-induced production (e.g., [70,92]), especially during times of negligible manifestations of solar activity.

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Fig. 30. Shown in (a) are variations in the total solar irradiance arising from changes in solar activity during the 11-year solar cycle. The time series is determined from the correlation of the annual means of observed total solar irradiance and sunspot numbers. The historical irradiance reconstructions shown in (b) all assume the existence of a longer term source of irradiance variability, in addition to the 11-year cycle. Their different long-term trends reflect different assumptions about the irradiance reduction during the Maunder Minimum relative to the present. For comparison, the absolute scales of the various reconstructions have been adjusted by constant offsets to agree during the contemporary epoch

6.3. Long-term irradiance reconstructions Direct, instrumental measurements of solar irradiance from satellite measurements, although available for only the past 25 years, indicate that solar irradiance (Fig. 2) is increased when sunspot numbers (Fig. 8) are high. The direct correlation of annual mean total solar irradiance and sunspot number allows estimates of solar irradiance cycles directly from the long-term sunspot record in Fig. 1. Such a reconstruction is shown in the upper panel of Fig. 30, and indicates that contemporary irradiance cycles are the largest of the past 400 years. When reconstructed from a linear transformation of sunspot numbers, irradiance levels during the Maunder Minimum are estimated to be similar to those of current cycle minima [73, 118]. But high sunspot numbers actually correspond to increased sunspot darkening and increased facular brightening (Fig. 22), both of which alter solar irradiance, but in opposite ways. The approach of modelling contemporary total solar irradiance variations using sunspot and facular proxies has also been adopted for reconstructing longer term irradiance variations. Sunspot darkening is determined since the 1880s from Greenwich Observatory white light solar observations, and is assumed to be zero during the Maun-


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der Minimum. Estimating a facular index prior to 1975 is, however, problematic. The irradiance reconstructions shown in Fig. 30b all postulate a source of long-term irradiance variability on multi-decadal to centennial time scales, based on circumstantial evidence from geomagnetic activity [88], cosmogenic isotopes [120], variations in sunlike stars [74, 75] and changes in interior solar structure implied by evolving sunspot umbral and penumbral ratios [58]. A facular index is then developed from, for example, the smoothed amplitude of the 11-year Rg cycle [74,75,120] or its instantaneous period (i.e., cycle length [58,120]) with the amplitude scaled to match circumstantial evidence. As Fig. 1 shows, the temporal structure of these two quantities are rather different from each other. The most recent irradiance reconstructions utilize both the sunspot amplitude and the cycle length, to parameterize, the sunspot and active region irradiance sources, respectively, and the assumed ephemeral region changes [87, 121]. Lean et al. [77] estimated the level of irradiance during the Maunder Minimum to be 2.7 W m−2 below present minima, corresponding to non-cycling stars at the peak of the lower mode of the bi-modal distribution. As a result of a revised transfer of the stellar Ca HK to solar Ca K values by Lean [74] this reduction was determined to be 2.2 W m−2 . They also estimated a reduction of 1.5 W m−2 for a non-magnetic Sun. This value was obtained from knowledge of the network contrast and fractional disk coverage in the contemporary Sun, and is independent of the brightness distribution of sun-like stars. It is interesting to note that it is very close to a recent determination from MDI/SOHO data by [31] of 1.7 ± 0.1 W m−2 . Which of the time series in Fig. 30 better represents actual irradiance variability is unknown. The primary uncertainty is whether the secular changes that the models assume actually occur [146], or not [32, 82]. Nor is the extant contemporary database of sufficient duration to adequately judge the various approaches. The comparisons in Fig. 31 show that the historical reconstructions deviate from each other prior to 1980, which is when actual observations were just commencing. Lack of a clear physical relationship between the 14 C and 10 Be cosmogenic isotopes and irradiance variability is a critical impediment to improved understanding of long-term irradiance variability. Whereas the sources of irradiance variability are magnetic active regions near the surface of the Sun, cosmogenic isotopes variations occur because the extended solar atmosphere in interplanetary space modulates the flux of galactic cosmic rays that reaches the Earth’s atmosphere [10, 137]. The recent simulations of magnetic flux transport on the Sun, suggesting the lack of a linear relationship between total and open flux (and hence irradiance and the interplanetary magnetic field) are preliminary, and raise additional questions about the role or meridional transport and the extrapolation of surface magnetic fields to the corona and heliosphere that require further study. Even assuming secular irradiance changes to be present, most estimates of solar irradiance variability over the past thousand or so years indicate amplitude changes of 2 to 3 tenths of a percent on time scales of a few hundred years. Like the solar cycle changes, long-term irradiance variations, if they exist, can be expected to have significant spectral dependence. The reconstructions of selected broad spectral bands shown in Fig. 32 present scenarios in which solar spectral irradiance is determined as F (λ, t) ∝ aλ PS (t) + bλ PF (t) + cλ IL (t) where IL is the smoothed sunspot group number from Fig. 1, and cλ accounts for the wavelength-dependent amplitude of the long-term component. The long-term component is scaled such that it produces an

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Fig. 31. The reconstructions of historical total solar irradiance shown in Fig. 30b are compared with annual means of the observational composite time series. It is important to note that this is a crucial test for the validity of a reconstruction: failure to reproduce the present three irradiance cycles indicates an incorrect parameterization of some sort

irradiance change from 1650 to 1986 approximately equal to the solar cycle variation in the facular component of the variability. Also shown, for comparison, are reconstructions of the 11-year activity cycle alone, i.e., with cλ = 0. 6.4. Future irradiance scenarios Levels of future solar activity cycles are routinely predicted using two techniques that estimate sunspot numbers and 10.7 cm fluxes. The statistical regression technique employs the sunspot record to quantify average properties and mean behaviour patterns [54]. The geophysical precursor technique recognizes the extended nature of the solar cycle and uses geophysical indices during descending and minima phases to predict subsequent maxima [128]. An alternative precursor approach invokes solar dynamo theory to forecast cycle maxima from the strength of the Sun’s polar fields at minima [117]. Future levels of the Sun’s irradiance corresponding to predicted cycles of the 10.7 cm flux, shown in Fig. 33, are estimated from a parameterization of annual total solar irradiance and 10.7 cm radio flux. The observational irradiance database is too short for the detection or understanding of long-term solar irradiance trends that may affect future solar radiative output but speculations are possible by assuming that historical irradiance reconstructions during the past 350 years (e.g., Fig. 30b) sample the plausible range. With this assumption, maximum total irradiance trends are ±0.4 W m−2 per decade [78]. The dashed lines in Fig. 33 indicate these trend limits. The fact that current levels of solar activity are at overall high levels, according to both the sunspot numbers and cosmogenic isotopes, may imply that future solar irradiance values will not be significantly higher than seen in the contemporary database. A projection of future solar activity based on spectral synthesis of the cosmogenic isotope record confirms that solar activity is presently peaking, and in 2100 will reach levels comparable to those in 1990 [18]. Projections of combined 11-, 88- and 208-year solar cycles also suggest that overall solar activity will increase in the near future, but only


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Fig. 32. Model estimates of long-term variability in the total solar irradiance and in three spectral bands in the UV, visible and IR. In these calculations, the adopted amplitude of the long-term facular component is approximately equal to its contemporary solar cycle amplitude. Reconstructions of 11-year cycles alone are also shown

Fig. 33. Shown are projected total solar irradiance variations obtained from predictions of the 10.7 cm flux in future solar cycles made by [117]. The dashed lines indicate the range of plausible trends assuming the maximum rate of change of the [74] historical irradiance in Fig. 30

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until 2030, followed by decreasing activity until 2090 [63]. In contrast, a numerical model of solar irradiance variability which combines cycles related to the fundamental 11 year cycle by powers of 2 predicts an irradiance decrease of 0.05 % during the next two decades [101]. A lack of physical understanding how dynamo-driven solar activity produces the competing effects of sunspot blocking and facular brightening, cautions against future predictions, even of 11-year cycle amplitudes. 7. Conclusions Knowledge and understanding of solar radiative output and its variability has advanced rapidly in the space era. Crucial for this advance is the observational record of total solar irradiance (TSI), monitored continuously since late 1978 by electrically calibrated radiometers on several overlapping space missions. The observations provide definitive evidence that the Sun is about 0.1 % brighter during recent maxima than during minima of the 11-year activity cycles. Although the question of a contemporary long-term trend of TSI is still under discussion, there are strong arguments in support of constant radiative output levels during the last two solar activity minima. Knowledge and understanding of the spectral irradiance variations that compose the total are far less certain, primarily because of the lack of sufficient long-term observations with the needed accuracy and spectral coverage. While irradiance variability is relatively well known at wavelengths below about 300 nm, where it exceeds that of TSI by large factors (up to orders of magnitude), concomitant advances in understanding of the variations in most of the spectrum await new measurements such as those recently commenced by next-generation instrumentation on the SORCE spacecraft. Initial results demonstrate unequivocally the variability of solar spectral irradiance at all wavelengths, not just in the UV spectrum. Clearly evident in the more than 25-year long record of daily values of a composite TSI record, constructed from the individual observations, are the prominent roles of dark sunspots and bright faculae (in active regions and the surrounding network) as sources of irradiance variability. Empirical models confirm this understanding; combining the sunspot darkening index, PS , and PF , an index for the brightening due to faculae and network (such as the Mg II index), accounts for nearly 80 % of the observed variance of total solar irradiance during the 11-year solar activity cycle. Allowing for the wavelength dependence of the contrasts of sunspots and faculae provides a first order description of spectral irradiance variations, currently limited by poor knowledge of facular contrasts especially in the near infrared spectrum. The empirical models support the zero-trend hypothesis of contemporary irradiance, thereby constraining mechanisms of such a trend, should they exist, to other than those magnetic features responsible for the 11-year irradiance cycle. Because relationships between solar irradiance and solar activity are, thus far, largely empirical, their implications for long-term variability are uncertain. Robust understanding of solar irradiance variability ultimately requires that the various solar activity indices and proxies be physically derived from solar magnetic fields. On longer time-scales, possible mechanisms must be validated and detected in the instrumental record, separately from non-solar influence. A dynamo at the base of the convection zone governs the emergence, reorganization and transport of magnetic activity that produces the waxing and waning of surface magnetic fields, and the resultant dark sunspots, bright faculae


315

and network that modulate solar irradiance. Thus, a complete physical specification of irradiance variations involves processes below the solar surface as well as in the solar atmosphere. Rapid progress in understanding the interior of the Sun also occurred during the space era as a result of helioseismology and its impact on major improvements of the standard solar model, such as more accurate opacities and a better equation of state. But the physical understanding and characterization of structures in the solar atmosphere, from the photosphere out to the corona, and their impacts on radiative outputs, is less advanced. Radiative transfer calculations which formulate our understanding of radiative output in the direction of the Earth – that is, the irradiance – are based on temperature distributions with height which match the observations. Self-consistent theoretical calculations are still not possible mainly due to the lacking understanding of the details of the energy transport. Knowledge of solar irradiance variability prior to the space era is rudimentary, as demonstrated by the range of values for total solar irradiance prescribed for the seventeenth century Maunder Minimum. Postulating an irradiance reduction below that of contemporary solar minima requires the identification of mechanisms in addition to the sunspot and faculae fluctuations that produce the 11-year cycle. One scenario is the removal of the bright faculae that compose the “quiet” network surrounding supergranular cells, even in contemporary solar minimum. Such a removal is estimated to reduce total solar irradiance by about 1.5 W m−2 , or slightly more than 0.1 % below current solar minimum levels. Larger-amplitude irradiance reductions require additional mechanisms, such as the overall dimming of the basal emission from cell centers, or changes in radius or interior structure. However, quantitative knowledge of such speculated mechanisms is lacking. Inferences made from long-term trends in cosmogenic isotope proxies suffer from the inability, thus far, to quantify the physical relationships between closed magnetic flux that relates to irradiance, versus the open flux that pervades the heliosphere and modulates the galactic cosmic rays that produce the cosmogenic solar activity proxies. Determining whether – or not – and why, solar irradiance varies on long time scales will require considerable additional research and understanding, and much longer irradiance time series. Acknowledgements. Continued support of solar irradiance research at PMOD/WRC by the Swiss National Science Foundation is greatly acknowledged, including support of C. Fröhlich’s contributions to this review. NASA and The Office of Naval Research supported the contributions of J. Lean (including NASA UARS, LWS and SORCE grants). Very much appreciated are the efforts of the many observers and instrumentalists who produced the data sources that this review utilizes, and the NOAA NGDC which archives many of the datasets. Included are unpublished data from VIRGO on SOHO, a cooperative ESA/NASA mission and from ACRIM III on ACRIM-Sat. During the preparation of this review, C. Fröhlich and J. Lean have benefited from many helpful discussions with the solar irradiance community, including R. B. Lee, R. C. Willson, G. J. Rottman and O. R. White.

316


References 1. C.G. Abbot: Smithsonian Misc.Coll. 117, 1 (1952) 2. C.G. Abbot: Smithsonian Misc.Coll. 146, 1 (1963) 3. L.B. Aldrich, W.H. Hoover: Annals of the Astrophysical Observatory of the Smithsonian Institution, vol. 7, chap.7: Statistical Studies of the Solar-Constant Record, pp. 165–168. Smithsonian Institution, Washington, DC, USA (1954) 4. C.W. Allen: Astrophysical Quantities. Athlone, London, 3rd edn (1981) 5. H.M. Antia, S. Basu, F. Hill, R. Howe, R.W. Komm, J. Schou: MNRAS 327, 1029 (2001) 6. C.N. Arge, E. Hildner, V.J. Pizzo, J.W. Harvey: J. Geophys. Res. 107, 1319 (2002) 7. E.H. Avrett: Modelling solar variability – synthetic models. In: J. Pap, C. Fröhlich, R. Ulrich (eds) Proceedings of the SOLERS22 Workshop, Sacramento Peak, June 1996, pp. 449–469. Kluwer, Dordrecht, The Netherlands (1998) 8. S. Baliunas, R. Jastrow: Nature 348, 520 (1990) 9. N.J. Balmforth, D.O. Gough, W.J. Merryfield: MNRAS 278, 437 (1996) 10. E. Bard, G. Raisbeck, P. Yiou, J. Jouzel: Tellus B 52, 985 (2000) 11. E. Bard, G.M. Raisbeck, F. Yiou, J. Jouzel: Earth and Planetary Science Letters 150, 453 (1997) 12. S. Basu: What does helioseismology tell us about solar cycle related structural changes in the sun? In: A. Wilson (ed.) SOHO-11: From Solar Minimum to Maximum, pp. 7–14. SP-508, ESA Publ. Division, ESTEC, Norrdwijk, The Netherlands (2002) 13. J. Beer: Space Sci. Rev. 94, 53 (2000) 14. J. Beer, S.M. Tobias, N.O. Weiss: Sol. Phys. 181, 237 (1998) 15. H.V. Cane, G. Wibberenz, I.G. Richardson, T.T. von Rosenvinge: Geophys. Res. Lett. 26, 565 (1999) 16. W.J. Chaplin, Y. Elsworth, G.R. Isaak, B.A. Miller, R. New: MNRAS 352, 1102 (2004) 17. G.A. Chapman, A.M. Cookson, J.J. Dobias: J. Geophys. Res. 101, 13541 (1996) 18. M.A. Clilverd, E. Clarke, H. Rishbeth, T.D. G. Clark, T. Ulich: Astronomy and Geophysics 44, 20 (2003) 19. D. Crommelynck, V. Domingo, A. Fichot, C. Fröhlich, B. Penelle, J. Romero, Ch. Wehrli: Metrologia 30, 375 (1993) 20. D. Crommelynck, A. Fichot, R.B. Lee III, J. Romero: Adv. Space Res. 16, 17 (1995) 21. T.J. Crowley: Science 289, 270 (2000) 22. U. Cubasch, R. Voss: Space Sci. Rev. 94, 185 (2000) 23. G. de Toma, O.R. White, B.G. Knapp, G.J. Rottman, T.N. Woods: Mg II core-to-wing index: Comparison of SBUV2 and SOLSTICE time series. J. Geophys. Res. 102, 2597 (1997) 24. A.E. Dessler, M.D. Burrage, J.-U. Grooss, J.R. Holton, J.L. Lean, S.T. Massie, M.R. Schoeberl, A.R. Douglass, C.H. Jackman: Reviews of Geophysics 36, 183 (1998) 25. M. Dikpati, P. Charbonneau: ApJ 518, 508 (1999) 26. J.A. Eddy: Science 192, 1189 (1976) 27. M. Fligge, S.K. Solanki: Sol. Phys. 173, 427 (1997) 28. M. Fligge, S.K. Solanki: Geophys. Res. Lett. 27, 2157 (2000) 29. J. Fontenla, O.R. White, P.A. Fox, E.H. Avrett, R.L. Kurucz: ApJ 518, 480 (1999) 30. J.M. Fontenla, J. Harder, G. Rottman, T. Woods, G.M. Lawrence, S. Davis: ApJ 605, L85 (2004) 31. S.S. Foster: Reconstruction of Solar Irradiance Variations for use in Studies of Global Climate Change: Application of Recent SOHO Observations with Historic Data from the Greenwich Observatory. PhD thesis, University of Southhampton, Faculty of Science, School of Pysics and Astronomy (2004) 32. P. Foukal L. Milano: Geophys. Res. Lett. 28, 883 (2001) 33. P. Foukal, J. Vernazza: ApJ 234, 707 (1979)

Solar radiative output and its variability: evidence and mechanisms 34. 35. 36. 37. 38. 39. 40.

41.

42.

43. 44. 45.

46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66.

317

P.V. Foukal, J. Lean: ApJ 302, 826 (1986) P.V. Foukal, J. Lean: ApJ 328, 347 (1988) P.V. Foukal, P.E. Mack, J.E. Vernazza: ApJ 215, 952 (1977) C. Fröhlich: Contemporary measures of the solar constant. In: O.R. White (ed.) The Solar Output and its Variation, pp. 93–109 (1977) C. Fröhlich: Space Sci. Rev. 94, 15 (2000) C. Fröhlich: Metrologia 40, 60 (2003) C. Fröhlich: Solar Irradiance Variations. In: Proc. ISCS 2003: Solar Variability as an Input to the Earth’s Environment. SP-535, ESA Publ. Division, ESTEC, Norrdwijk, The Netherlands (2003) C. Fröhlich: Solar Irradiance Variability. In: Geophysical Monograph 141: Solar Variability and its Effect on Climate, chap. 2: Solar Energy Flux Variations, pp. 97–110. American Geophysical Union, Washington DC, USA (2004) C. Fröhlich, B. Andersen, T. Appourchaux, G. Berthomieu, D.A. Crommelynck, V. Domingo, A. Fichot, W. Finsterle, M.F. Gómez, D.O. Gough, A. Jiménez, T. Leifsen, M. Lombaerts, J.M. Pap, J. Provost, T. Roca Cortés, J. Romero, H. Roth, T. Sekii, U. Telljohann, T. Toutain, C. Wehrli: Sol. Phys. 170, 1 (1997) C. Fröhlich, D. Crommelynck, C. Wehrli, M. Anklin, S. Dewitte, A. Fichot, W. Finsterle, A. Jiménez, A. Chevalier, H.J. Roth: Sol. Phys. 175, 267 (1997) C. Fröhlich, J. Lean: Geophys. Res. Lett. 25, 4380 (1998) C. Fröhlich, J. Lean: Total solar irradiance variations: The construction of a composite and its comparison with models. In: F.L. Deubner, J. Christensen-Dalsgaard, D. Kurtz, (eds) IAU Symposium 185: New Eyes to See Inside the Sun and Stars, pp. 89–102. Kluwer, Dordrecht, The Netherlands (1998) C. Fröhlich, J. Lean: Astron. Nachr. 323, 203 (2002) M.A. Geller, S.P. Smyshlyaev: Geophys. Res. Lett. 29, 2048 (2002) M.S. Giampapa, J.C. Hall, R.R. Radick, S.L. Baliunas: AAS/Solar Physics Division Meeting 34 (2003) D.F. Gray, W.C. Livingston: ApJ 474, 802 (1997) J.D. Haigh: Phil. Trans. Roy. Soc. A 361, 95 (2003) J.C. Hall, G.W. Lockwood: American Astronomical Society Meeting 204 (2004) Abstract 03.02 J. Harder, G.M. Lawrence, G. Rottman, T. Woods: Metrologia 37, 415 (2000) K.L. Harvey, O.R. White: Astron. Soc. Pacific Conf. Ser. 140, 247 (1998) D.H. Hathaway, R.M. Wilson, E.J. Reichmann: J. Geophys. Res. 104. 22375 (1999) ˚ In O.R. White, D.F. Heath, M.P. Thekaekara: The solar spectrum between 1200 and 3000 A. editor, The Solar Output and its Variation, pp. 193 (1977) R. Howe, J. Christensen-Dalsgaard, F. Hill, R.W. Komm, R.M. Larsen, J. Schou, M.J. Thompson, J. Toomre: Science 287, 2456 (2000) D.V. Hoyt, H.L. Kyle, J.R. Hickey, R.H. Maschhoff: J. Geophys. Res. 97, 51 (1992) D.V. Hoyt, K.H. Schatten: J. Geophys. Res. 98, 18895 (1993) D.V. Hoyt, K.H. Schatten: The Role of the Sun in Climate Change. Oxford University Press, Oxford GB (1997) D.V. Hoyt, K.H. Schatten: Sol. Phys. 181, 491 (1998) D.V. Hoyt, K.H. Schatten, E. Nesme-Ribes: Geophys. Res. Lett. 21, 2067 (1994) K. Hufbauer: Exploring the Sun. The Johns Hopkins University Press, Baltimore (1991) J.L. Jirikowic, P.E. Damon: Climatic Change 26, 309 (1994) L.H. Koopmans: The Spectral Analysis of Time Series. Academic Press, London, GB (1974) G.A. Kopp, G. Lawrence, G. Rottman: What is theAccuracy of the Total Irradiance Monitor? AGU Fall Meeting Abstracts (2003) Abstract SH31C-C7 N.A. Krivova, S.K. Solanki, M. Fligge, Y.C. Unruh: A&A 399, L1 (2003)

318


67. J.R. Kuhn, K.G. Libbrecht: ApJ 381, L35 (1991) 68. R.L. Kurucz: New opacity calculations. In: L. Crivellari, I. Hubeny, D.G. Hummer (eds) Stellar Atmospheres: Beyond Classical Models, pp. 441–448. NATOASI Ser. C 341, Kluwer, Dordrecht, The Netherlands (1991) 69. R.L. Kurucz: The solar spectrum. In: A.N. Cox, W.C. Livingston, M.S. Matthews (eds) Solar interior and atmosphere, pp. 663–669. University of Arizona Press, Tucson, AZ, USA (1991) 70. D. Lal: Geophys. Res. Lett. 14, 785 (1987) 71. G.M. Lawrence, G. Rottman, J. Harder, T. Woods: Metrologia, 37, 407 (2000) 72. J.K. Lawrence, G.A. Chapman, A.D. Herzog: ApJ 324, 1184 (1988) 73. J. Lean: ARA&A 35, 33 (1997) 74. J. Lean: Geophys. Res. Lett. 27, 2425 (2000) 75. J. Lean, J. Beer, R. Bradley: Geophys. Res. Lett. 22, 3195 (1995) 76. J. Lean, D. Rind: Science 292, 234 (2001) 77. J. Lean, A. Skumanich, O. White: Geophys. Res. Lett. 19, 1595 (1992) 78. J.L. Lean: Geophys. Res. Lett. 28, 4119 (2001) 79. J.L. Lean, J. Cook, W. Marquette, A. Johannesson: ApJ 492, 390 (1998) 80. J.L. Lean, T.P. Repoff: J. Geophys. Res. 92, 5555 (1987) 81. J.L. Lean, G.J. Rottman, H.L. Kyle, T.N. Woods, J.R. Hickey, L.C. Puga: J. Geophys. Res. 102, 29939 (1997) 82. J.L. Lean, Y.-M. Wang, N.R. Sheeley: Geophys. Res. Lett. 29, 2224 (2002) 83. J.L. Lean, O.R. White, W.C. Livingston, J.M. Picone: J. Geophys. Res. 106, 10645 (2001) 84. R.B. Lee III, B.R. Barkstrom, R.D. Cess: Appl. Opt. 26, 3090 (1987) 85. R.B. Lee III, M.A. Gibson, R.S. Wilson, S. Thomas: J. Geophys. Res. 100, 1667 (1995) 86. M. Lockwood: J. Geophys. Res. 106, 16021 (2001) 87. M. Lockwood: Solar outputs, their variations and their effects on earth. In: M. Güdel, I. Rüedi, W. Schmutz (eds) Saas-Fee Advanced Courses, Number 32: The Sun, Solar Analogs and the Climate. Springer-Verlag, Heidelberg, Germany (2004) (in press) 88. M. Lockwood, R. Stamper: Geophys. Res. Lett. 26, 2461 (1999) 89. M. Lockwood, R. Stamper, M.N. Wild: Nature 399, 437 (1999) 90. P. Maltby, E.H. Avrett, M. Carlsson, O. Kjeldseth-Moe, R.L. Kurucz, R. Loeser: ApJ 306, 284 (1986) 91. P.N. Mayaud: J. Geophys. Res. 77, 6870 (1972) 92. K.G. McCracken: J. Geophys. Res. 109, A04101 (2004) 93. G.A. Meehl, W.M. Washington, T.M. L. Wigley, J.M. Arblaster, A. Dai: Journal of Climate 16, 426 (2003) 94. P.D. Mininni, D.O. Gomez, G.B. Mindlin: Sol. Phys. 208, 167 (2002) 95. T. Moran, P. Foukal, D. Rabin: Sol. Phys. 142, 35 (1992) 96. R.W. Noyes, J.C. Raymond, J.G. Doyle, A.E. Kingston: ApJ 297, 805 (1985) 97. M.G. Ogurtsov, Y.A. Nagovitsyn, G.E. Kocharov, H. Jungner: Sol. Phys. 211, 371 (2002) 98. A. Ortiz, S.K. Solanki, V. Domingo, M. Fligge, B. Sanahuja: A&A 388, 1036 (2002) 99. A. Ortiz Carbonell: Solar Irradiance Variations Induced by Faculae and small Magnetic Elements in the Photosphere. PhD thesis, Unversitat de Barcelona, Departament d’Astronomia i Metrologia (2003) 100. J.P. Peixoto, A.H. Oort: Physics of Climate. American Institute of Physics (AIP), New York (1992) 101. C.A. Perry, K.J. Hsu: PNAS 97, 12433 (2000) 102. J.A. Plamondon: JPL Space Prog. Summary 37–59, 162 (1969) 103. J.A. Plamondon, J.M. Kendall, Sr.: JPL Space Prog. Summary 37-35, 66 (1965) 104. M.S. Potgieter, R.A. Burger, S.E.S. Ferreira: Space Science Reviews 97, 295 (2001) 105. J. Provost, G. Berthomieu, Morel P.: A&A 353, 775 (2000)


319

106. T.J. Quinn, C. Fröhlich: Nature 401, 841 (1999) 107. E. Ribes, B. Beardsley, T.M. Brown, P. Delache, F. Laclare, J.R. Kuhn, N.V. Leister: The variability of the solar diameter. In: C. Sonnet, M.S. Giampapa, and M.S. Matthews (eds) Sun in Time, pp. 59–97 (1991) 108. I.G. Richardson, E.W. Cliver, H.V. Cane: J. Geophys. Res. 105(A8), 18203 (2000) 109. N.R. Rigozo, E. Echer, L.E. A. Vieira, D.J. R. Nordemann: Sol. Phys. 203, 179 (2001) 110. D. Rind: Science 296, 673 (2002) 111. D. Rind, J. Lean, R. Healy: J. Geophys. Res. 104, 1973 (1999) 112. D. Rind, D. Shindell, J. Perlwitz, J. Lerner, P. Lonergan, J. Lean, C. McLinden: Journal of Climate 17, 906 (2004) 113. G. Rottman: Space Sci. Rev. 94, 83 (2000) 114. G. Rottman, G. Mount, G. Lawrence, T. Woods, J. Harder, S. Tournois: Metrologia 35, 707 (1998) 115. G. Rottman, L. Floyd, R. Viereck: Measurement of the Solar Ultraviolet Irradiance. In: J.M. Pap, P. Fox (eds) Geophysical Monograph 141: Solar Variability and its Effect on Climate, chapter 2: Solar Energy Flux Variations, pp. 111–126. American Geophysical Union, Washington DC, USA (2004) 116. I.-J. Sackmann, A.I. Boothroyd: ApJ 583, 1024 (2003) 117. K. Schatten, D.J. Myers, S. Sofia: Geophys. Res. Lett. 23, 605 (1996) 118. K.H. Schatten, J.A. Orosz: A solar constant model for sun-climate studies: 1600-2000AD. In: Climate Impact of Solar Variability, pp. 175–180 (1990) 119. S. Sofia, P. Fox: Climate Change 30, 1 (1994) 120. S.K. Solanki, M. Fligge: Geophys. Res. Lett. 26, 2465 (1999) 121. S.K. Solanki, N.A. Krivova, M. Schüssler, M. Fligge: A&A 396, 1029 (2002) 122. S.K. Solanki, M. Schüssler, M. Fligge: Nature 408, 445 (2000) 123. S.K. Solanki, M. Schüssler, M. Fligge: A&A 383: 706 (2002) 124. S.K. Solanki, Y.C. Unruh: A&A 329, 747 (1998) 125. R. Stamper, M. Lockwood, M.N. Wild, T.D. G. Clark: J. Geophys. Res. 104, 28325 (1999) 126. P.A. Stott, S.F. B. Tett, G.S. Jones, M.R. Allen, J.F. B. Mitchell, G.J. Jenkins: Science 290, 2133 (2000) 127. L. Svalgaard, E.W. Cliver, P. Le Sager: Advances in Space Research 34, 436 (2004) 128. R.J. Thompson: Sol. Phys. 148, 383 (1993) 129. G. Thuillier M. Meissonnier: Picard Mission. In: SF2A-2002: Semaine de l’Astrophysique Francaise (2002) 130. S. Turck-Chièze, S. Couvidat, A.G. Kosovichev, A.H. Gabriel, G. Berthomieu, A.S. Brun, J. Christensen-Dalsgaard, R.A. García, D.O. Gough, J. Provost, T. Roca-Cortes, I.W. Roxburgh, R.K. Ulrich: ApJ 555, L69 (2001) 131. Y.C. Unruh, S.K. Solanki, M. Fligge. A&A 345, 635 (1999) 132. Y.C. Unruh, S.K. Solanki, M. Fligge: Space Sci. Rev. 94, 145 (2000) 133. I.G. Usoskin, K. Mursula, S. Solanki, M. Schüssler, K. Alanko: A&A 413, 745 (2004) 134. I.G. Usoskin, S.K. Solanki, M. Schüssler, K. Mursula, K. Alanko: Physical Review Letters 91, 211101 (2003) 135. Y.-M. Wang, J. Lean, N.R. Sheeley: Geophys. Res. Lett. 27, 505 (2000) 136. Y.-M. Wang, N.R. Sheeley: ApJ 591, 1248 (2003) 137. W.R. Webber, P.R. Higbie: J. Geophys. Res. 108, (2003) 138. O.R. White, W.C. Livingston, S.L. Keil: Astro. Soc. Pac. Conf. Ser. 140, 293 (1998) 139. O.R. White, A. Skumanich, J. Lean, W.C. Livingston, S.L. Keil: Publications of the Astronomical Society of the Pacific 104, 1139 (1992) 140. R.C. Willson: Space Sci. Rev. 38, 203 (1984) 141. R.C. Willson: Irradiance observations from SMM, UARS and ATLAS experiments. In: J. Pap, C. Fröhlich, H.S. Hudson, and S. Solanki (eds) The Sun as a Variable Star, Solar and Stellar Irradiance Variations, pp. 54–62 (1994)

320


142. R.C. Willson: Science 277, 1963 (1997) 143. R.C. Willson: ACRIM II and ACRIM III data products (version 10/10/01). http://www.acrim.com/ in the directory Data%20Products.htm (2001) 144. R.C. Willson, S. Gulkis, M. Janssen, H.S. Hudson, G.A. Chapman: Science 211, 700 (1981) 145. R.C. Willson, H.S. Hudson: Nature 351, 42 (1991) 146. R.C. Willson, A.V. Mordvinov: Geophys. Res. Lett. 30, 1199 (2003) 147. T.N. Woods, F.G. Eparvier, J. Fontenla, J. Harder, G. Kopp, W.E. McClintock, G. Rottman, B. Smiley, M. Snow: Geophys. Res. Lett. 31, L10802 (2004) 148. T.N. Woods, D.K. Prinz, G.J. Rottman, J. London, P.C. Crane, R.P. Cebula, E. Hilsenrath, G.E. Brueckner, M.D. Andrews, O.R. White, M.E. Vanhoosier, L.E. Floyd, L.C. Herring, B.G. Knapp, C.K. Pankratz, et al.: J. Geophys. Res. 101, 9541 (1996) 149. J.R. Worden, O.R. White, T.N. Woods: ApJ 496, 998 (1998)

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