Particle Physics and the Universe Proceedings of Nobel Symposium 109 Haga Slott, Enkoping, Sweden, August 2 0 - 2 5 , 1998
Editors
L Bergstrom P. Carlson C. Fransson
Physica Scripta The Royal Swedish Academy of Sciences World Scientific
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Particle Physics and the Universe Proceedings of Nobel Symposium 109 Haga Slott, Enkoping, Sweden, August 2 0 - 2 5 , 1998
Editors
L. Bergstrbm P. Carlson C. Fransson
Recognized by the European Physical Society
0&h KUNGL i J K l VETENSKAPSAKADEMIEN THE ROYALSWEDISH ACADEMY OF SCIENCES
IJkS* World Scientific » s vvona Dciemmc H
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LondorrHongKong
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The contents of this volume were also published as Vol. T85 of Physica Scripta.
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Physica Scripta, Vol. T85, 2000
Contents Committees
4
List of participants
5
Preface
7
Remembering David N. Schramm. MichaelS. Turner
9
Review of Big Bang Nucleosynthesis and Primordial Abundances. David Tytler, John M. O'Meara, Nao Suzuki and Dan Lubin
12
Cosmology with Clusters of Galaxies. Neta A. Bahcall
32
Determination of Cosmological Parameters. Wendy L Freedman
37
The Acceleration of the Universe: Measurements of Cosmological Parameters from Type la Supernovae. A. Goobar, S. Per/mutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, D. £ Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Fi/ippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg and W. J. Couch Bias is Complicated. Max Tegmark and Benjamin C. Bromley Solar Neutrinos: an Overview. J. N. Bahcall Radiochemical Solar Neutrino Experiments and Implications. T. A. Kirsten
47 59 63 71
Evidence for Neutrino Oscillation Observed in Super-Kamiokande. Y. Totsuka
82
Neutrino Oscillations. Eligio Lisi
91
Primary Cosmic Rays, Antiprotons and Atmospheric Neutrinos. T. K. Gaisser
100
High Energy Cosmic Neutrinos. Steven W. Barwick
106
High Energy Cosmic-Rays and Neutrinos from Cosmological Gamma-Ray Burst Fireballs. E/iWaxman . . .
117
Supernova Neutrinos. Adam Burrows and Timothy Young
127
From the Cosmological Microwave Background to Large-Scale Structure. Joseph Silk and Eric Gawiser...
132
Discovery of the Cosmic Microwave Background. D. T. Wilkinson and P. J. £ Peebles
136
Extracting Cosmology from the Cosmic Microwave Background Radiation. DavidN. Spergel
142
Imaging the Sunyaev-Zel'dovich Effect. J. £ Carlstrom, M. K. Joy, L. Grego, G. P. Holder, W. L. Ho/zapfel, J. J. Mohr, S. Patel and E. D. Reese Starlight in the Universe. Piero Madau The Development of Large Scale Cosmic Structure: A Theoretician's Approach. Jeremiah P. Ostriker . . . .
148 156 164
Inflationary Cosmology. Andrei Linde
168
Quintessence and the Missing Energy Problem. Paul J. Steinhardt
177
Ultra High Energy Cosmic Rays - a n Enigma. A. A. Watson
183
Acceleration of Ultra High Energy Cosmic Rays. R. D. Blandford
191
Particle Astrophysics with High Energy Photons. T. C. Weekes
195
Dark Matter and Dark Energy in the Universe. Michael S. Turner
210
Particle Candidates for Dark Matter. John Ellis
221
Early-Universe Issues: Seeds of Perturbations and Birth of Dark Matter. Edward W. Kolb
231
String Cosmology and the Beginning-of-Time Myth. G. Veneziano
246
A Search for Galactic Dark Matter. M. Spiro, Eric Aubourg and Nathalie Palanque-Delabrouille
254
Dark Matter Tomography. J. A. Tyson
259
Status of Models for Gamma Ray Bursts. Martin J. Rees
267
Physica Scripta. Vol. T85, 4, 2000
COMMITTEES
International advisory committee: G. Altarelli J. Bahcall R. Blandford J. Cronin T. Gaisser M. Rees
B. Sadoulet J. Silk J. Taylor Y. Totsuka M. Turner
Local organizing committee: L. Bergstrom P. Carlson T. Francke C. Fransson
Physica Scripta TOO
A. Goobar B. Gustafsson H. Rubinstein
© Physica Scripta 2000
Physica Scripta.Vol. T85, 5, 2000
List of Participant) Hakan Snellman RIT, Stockholm
[email protected] Jenni Adams Uppsala University
[email protected] Tom Gaisser Bartol Research Institute
[email protected] Guido Altarelli CERN guido.
[email protected] Ariel Goobar Stockholm University
[email protected] John Bahcall IAS, Princeton
[email protected] Bengt Gustafsson Uppsala University
[email protected] Neta Bahcall Princeton University
[email protected] Alan Guth MIT
[email protected] Steve Barwick UC Irvine
[email protected] Per Olof Hulth Stockholm University
[email protected] Lars Bergstrom Stockholm University
[email protected] Cecilia Jarlskog Lund Institute of Technology
[email protected] Claes-Ingvar Bjornsson Stockholm University
[email protected] Till Kirsten MPI Heidelberg
[email protected] Roger Blandford Caltech
[email protected] Rocky Kolb Fermilab
[email protected] Yoji Totsuka University of Tokyo
[email protected] Adam Burrows Arizona University
[email protected] Andrei Linde Stanford University
[email protected] Michael Turner University of Chicago
[email protected] Per Carlson RET, Stockholm
[email protected] Eligio Lisi University of Bari
[email protected] John Carlstrom University of Chicago
[email protected] Piero Madau STScI
[email protected] Jim Cronin University of Chicago
[email protected] Jeremiah Ostriker Princeton University
[email protected] Ulf Danielsson Uppsala University
[email protected] Jim Peebles Princeton University
[email protected] John Ellis CERN
[email protected] Martin Rees University of Cambridge
[email protected] Tom Francke RIT, Stockholm
[email protected] Hector Rubinstein Uppsala University
[email protected] Claes Fransson Stockholm University
[email protected] Bernard Sadoulet UC Berkeley
[email protected] Wendy Freedman Carnegie Observatory
[email protected] Joe Silk UC Berkeley
[email protected] © Physica Scripta 2000
David Spergel Princeton University
[email protected] Michel Spiro Saclay SPIRO @ hep. saclay.cea. fr Paul Steinhardt University of Pennsylvania
[email protected] Roland Svensson Stockholm University
[email protected] Max Tegmark IAS, Princeton
[email protected] Tony Tyson Lucent Technologies
[email protected] David Tytler UC San Diego
[email protected] Gabriele Veneziano CERN gabriele.
[email protected] Alan Watson Leeds University
[email protected] Eli Waxman Weizmann Institute
[email protected] Trevor Weekes Whipple Observatory
[email protected] David Wilkinson Princeton University
[email protected] Physica Scripta T85
Physica Scripta.Vol. T85, 7, 2000
PREFACE It is generally felt in the cosmology and particle astrophysics community that we have just entered an era which later can only be looked back upon as a golden age. Thanks to the rapid technical development with powerful new telescopes and other detectors taken into operation at an impressive rate, and an accompanying advancement of theoretical ideas, the picture of the past, present and future Universe is getting ever clearer. Some of the most exciting new findings and expected future developments were discussed at the 109th Nobel Symposium "Particle Physics and the Universe". The meeting took place in the historical setting of Haga Slott, some 100 km west of Stockholm. This is a 16th-century castle which has been transformed into a modern conference site, not least known for its beautiful surroundings and awarded cuisine. The setting turned out to be ideal for the kind of informal discussions and exchange of ideas which consitute the main purpose of Nobel Symposia. Also the scheduled talks, with ample time for discussions, turned out to be just as stimulating as we could ever have hoped. Certainly, as organizers we were extremely pleased with the Symposium, and we deduce from the many signs of appreciations from the participants that this was a general consensus. It is our firm hope and conviction that this volume, containing the written Proceedings of the Symposium, will convey some of the enthusiasm and intellectual excitement that was so clearly felt on location. We sincerely thank the speakers for contributing such excellent written versions of their contributions to the Symposium. We were deeply shocked to learn about the tragic accidental death of one of our most respected colleagues in the field, David Schramm, some months before the Symposium. In his sadly felt absence, we were grateful to Michael Turner for making a special contribution commemorating some of Schramm's most influential work in cosmology and particle astrophysics. The topics covered at the Symposium, and reported in this volume (with the exception of the talk by B. Sadoulet), include the physics of the early Universe (string cosmology, inflation, nucleosynthesis, dark matter relics) and ultra-high energy processes (gamma ray bursts, AGNs, particles above 100 EeV). A particular emphasis is also put on neutrino physics and astrophysics, with the evidence for non-zero neutrino masses emerging from both solar neutrinos and atmospheric neutrinos covered in great depth. Another field with interesting new results concerns the basic cosmological parameters, where both traditional methods and the potential of new ones like deep supernova surveys and acoustic peak detections in the cosmic microwave background are thoroughly discussed. Various aspects of the dark matter problem, such as gravitational lensing estimates of galaxy masses, cluster evolution and hot cluster electron distorsions of the thermal microwave background spectrum are discussed, as are particle physics candidates of dark matter and methods to detect them. Cosmic rays of matter and antimatter are included as a topic as is the problem of the enigmatic dark energy of the vacuum. We want to express our thanks to the Nobel Foundation and its Symposium Committee for funding the Symposium. The staff of Haga Slott were extremely friendly and helpful, and we also wish to thank a number of graduate students in Stockholm, in particular David Bergstrom, Mirko Boezio, Edvard Mortsell and Piero Ullio, for acting as scientific secretaries at the sessions. Lars Bergstrom Per Carlson Claes Fransson Editors
© Physica Scripta 2000
Physica Scripta T85
Physica Scripta.Vol. T85, 9-11, 2000
Remembering David N. Schramm October 25, 1945 - December 19, 1997 Michael S. Turner Departments of Astronomy & Astrophysics and of Physics, Enrico Fermi Institute, The University of Chicago, Chicago, IL 60637-1433, USA NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510-0500, USA Received April 28, 1999; accepted August 2, 1999
PACS Ref: 01.60.+q
Eight months ago David Schramm died doing one of things he loved most - flying his airplane, known as Big-bang Aviation. He was to have been at this meeting doing something that he loved even more - going to scientific meetings to talk about the latest results and to renew friendships. Our Nobel Symposium celebrates the beginning of a Golden Age in particle astrophysics and cosmology. It is very sad indeed that David won't be here among his friends talking about all the exciting results in a field that he, more than any other individual, helped to create and shape. The organizers asked me to talk about David's contributions to particle astrophysics and cosmology. Not an easy task. David was one of the most influential and productive astrophysicists of his generation. His contributions were manifold - nucleocosmochronology, supernova collapse and neutrinos, big-bang nucleosynthesis, neutrino cosmology, the r-process, solar neutrinos, particle dark matter, gamma-ray bursts, structure formation, topological defects, ultra-high energy cosmic rays, astrophysical and cosmological constraints to particle physics, the first paper on quintessence, and on and on. I have decided to summarize David's contributions with his three favorite transparencies. The first is from the paper he wrote in 1974 with Gott, Gunn and Tinsley [1]. This paper announced his arrival on the cosmology scene. Using big-bang nucleosynthesis (BBN), measurements of the universal matter density and deceleration parameter, and determinations of the age of the Universe they constrained Ho and QQ. It was a widely quoted paper and pioneered a new style, the bringing together of a variety measurements - not just astronomical - to constrain our world model. Gott et al. concluded that we live in an open Universe with a Hubble constant of around 60km/s/Mpc and a density parameter of around 0.1. Not too far from the truth. A key assumption in this paper, one which David would later falsify, was that all matter exists in the form of baryons. He did so by showing that the lower limit to the amount of matter exceeds the BBN upper bound to the amount of ordinary matter. Figure 1 is the modern version of the Gott et al. diagram. In addition to constraining HQ and QQ, it now makes the case for nonbaryonic dark matter. While David was not the first to study BBN, he was the one who honed it into the powerful probe of cosmology and particle physics that it is today. The first success of BBN was in explaining the large primeval abundance of 4 He. David called it the 'go - no go' test of the hot big-bang model. He was among the first to push beyond 4 He and © Physica Scripta 2000
David Schramm
to realize the potential of deuterium as a "baryometer" [2]. He and his collaborators (sometimes called the Chicago Mafia) then brought 7Li and 3 He into the fold. The power of using all four light elements together to test the hot big-bang framework has made BBN one of the cornerstones of the standard cosmology, and David deserves the credit it. The second Figure shows the last BBN concordance diagram he made and hoped that anyone would. Let me explain. The broad concordance band in Fig. 2 dates to a Science paper he and I wrote with Craig Copi in 1995 [3]. David pioneered the concept of the concordance interval - a range for the baryon density within which the predicted abundances of all four light elements are consistent with the observations. The existence of such a range not only was evidence for the validity of the big-bang framework, but also a determination of the baryon density itself. The measurement of the primeval deuterium abundance realized a long time dream of David's: using deuterium by Tytler and Buries to precisely pin down the baryon Physica Scripta T85
10
Michael S. Turner
o.ooi
io""32
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i o "''
c i
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io~ 3 0
10
29
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Fig. 2. Summary of the big-bang production of the light elements (4He is mass fraction; others are number relative to hydrogen). The widths of the Fig. 1. An updated version of thefigurethat originally appeared in Gott etal. curves indicate the 2 5 x 10" 5 , and the third (0130^1021) is inconsistent with D / H > 6.7 x 10~5. Hence D / H is low in these three places. Several quasars allow high D / H , but in all cases this can be explained by contamination by H, which we discuss more below, because it is controversial.
4.1. ISM D/H Observations of D in the ISM are reviewed by Lemoine et al. [73]. The first measurement in the ISM, D / H = 1.4 + 0.2 xl0~ 5 , using Lyman absorption lines observed with the Copernicus satellite [74], have been confirmed with superior HST spectra. A major program by Linsky et al. [75,76] has given a secure value of D / H = 1.6 ± 0.1 x 10~5 for local ISM (< 20 pc). Some measurements have indicated variation, and especially low D / H , in the local and more distant ISM towards a few stars [55,73]. Vidal-Madjar and Gry [55] concluded that the different lines of sight gave different D / H , but those early data may have been inadequate to quantify complex velocity structure [77]. Variation is expected, but at a low level, from different amounts of stellar processing and infall of IGM gas, which leaves differing D / H if the gas is not mixed in a large volume. Lemoine et al. [78] suggested variation of D / H towards G191-B2B, while Vidal-Madjar et al. [79] described the variation as real, however new STIS spectra do not confirm this, and give the usual D / H value. The STIS spectra [80] show a simpler velocity structure, and a lower flux at the D velocity, perhaps because of difficulties with the background subtraction in the GHRS spectra. Hebrandef a/. [81] report the possibility of low D / H < 1.6 x l O - 5 towards Sirius A, B. The only other instance of unusually low D / H from recent data is D / H = 0.74+g\l x l 0 ~ 5 (90%) towards the star 5 Ori [82]. We would much like to see improved data on this star, because a new instrument was used, the signal to noise is very low, and the velocity distribution of the D had to be taken from the N I line, rather than from the H I. Possible variations in D / H in the local ISM have no obvious connections to the D / H towards quasars, where the absorbing clouds are 100 times larger, in the outer halos young of galaxies rather than in the dense disk today, © Physica Scripta 2000
Review of Big Bang Nucleosynthesis and Primordial Abundances and the influence of stars should be slight because heavy element abundances are 100 to 1000 times smaller. Chengalur, Braun and Burton [83] report D / H = 3.9 ± 1.0 x l O - 5 from the marginal detection of radio emission from the hyper-fine transition of D at 327 MHz (92 cm). This observation was of the ISM in the direction of the Galactic anti-center, where the molecular column density is low, so that most D should be atomic. The D / H is higher than in the local ISM, and similar to the primordial value, as expected, because there has been little stellar processing in this direction. Deuterium has been detected in molecules in the ISM. Some of these results are considered less secure because of fractionation and in low density regions, HD is more readily destroyed by ultraviolet radiation, because its abundance is too low to provide self shielding, making H D / H 2 smaller than D / H . However, Wright et al. [84] deduce D / H = 1.0±0.3x 10~5 from the first detection of the 112 um pure rotation line of HD outside the solar system, towards the dense warm molecular clouds in the Orion bar, where most D is expected to be in H D , so that D / H ~ H D / H 2 . This D / H is low, but not significantly lower than in the local ISM, especially because the H 2 column density was hard to measure. Lubowich et al. [85,86] report D / H = 0.2 ± 1 xlO" 5 from DCN in the Sgr A molecular cloud near the Galactic center, later revised to 0.3xl0~ 5 (private communication 1999). This detection has two important implications. First, there must be a source of D, because all of the gas here should have been inside at least one star, leaving no detectable D. Nucleosynthesis is ruled out because this would enhance the Li and B abundances by orders of magnitude, contrary to observations. Infall of less processed gas seems likely. Second, the low D / H in the Galactic center implies that there is no major source of D, otherwise D / H could be very high. However, this is not completely secure, since we could imagine a fortuitous cancellation between creation and destruction of D. We eagerly anticipate a dramatic improvement in the data on the ISM in the coming years. The FUSE satellite, launched in 1999, will measure the D and H Lyman lines towards thousands of stars and a few quasars, while SOFIA (2002) and FIRST (2007) will measure HD in dense molecular clouds. The new GMAT radio telescope should allow secure detection of D 92 cm emission from the outer Galaxy, while the Square Kilometer Array Interferometer would be able to image this D emission in the outer regions of nearby galaxies; regions with low metal abundances. These data should give the relationship between metal abundance and D / H , and especially determine the fluctuations of D / H at a given metal abundance which will better determine Galactic chemical evolution, and, we hope, allow an accurate prediction of primordial D / H independent of the QSO observations.
4.2. Solar system D/H The D / H in the ISM from which the solar system formed 4.6 Gyr ago can be deduced from the D in the solar system today, since there should be no change in D / H , except in the sun. © Physica Scripta 2000
17
Measurement in the atmosphere of Jupiter will give the pre-solar D / H provided (1) most of Jupiter's mass was accreted directly from the gas phase, and not from icy planetessimals, which, like comets today, have excess D / H by fractionation, and (2) the unknown mechanisms which deplete He in Jupiter's atmosphere do not depend on mass. Mahaffy et al. [87] find D / H = 2 . 6 ± 0 . 7 x l 0 " 5 from the Galileo probe mass spectrometer. Feuchtgruber et al. [88] used infrared spectra of the pure rotational lines of HD at 37.7 urn to measure D / H = 5.5+^ x 10" 5 in Uranus and 6.5+jjX 10" 5 in Neptune, which are both sensibly higher because these planets are known to be primarily composed of ices which have excess D / H . The pre-solar D / H can also be deduced indirectly from the present solar wind, assuming that the pre-solar D was converted into 3 He. The present 3 He/ 4 He ratio is measured and corrected for (1) changes in 3 H e / H and 4 H e / H because of burning in the sun, (2) the changes in isotope ratios in the chromosphere and corona, and (3) the 3 He present in the pre-solar gas. Geiss and Gloeckler [89] reported D / H = 2.1 ± 0 . 5 xl0~ 5 , later revised to 1.94± 0.36xl0" 5 [90]. The present ISM D / H = 1.6± O.lxlO" 5 is lower, as expected, and consistent with Galactic chemical evolution models, which we now mention.
4.3. Galactic chemical evolution of D Numerical models are constructed to follow the evolution of the abundances of the elements in the ISM of our Galaxy. The main parameters of the model include the yields of different stars, the distribution of stellar masses, the star formation rate, and the infall and outflow of gas. These parameters are adjusted to fit many different data. Such Galactic chemical evolution models are especially useful to compare abundances at different epochs, for example, D / H today, in the ISM when the solar system formed, and primordially. In an analysis of a variety of different models, Tosi et al. [91] concluded that the destruction of D in our Galaxy was at most a factor of a few, consistent with low but not high primordial D. They find that all models, which are consistent with all Galactic data, destroy D in the ISM today by less than a factor of three. Such chemical evolution will destroy an insignificant amount of D when metal abundances are as low as seen in the quasar absorbers. Others have designed models which do destroy more D [7,92-94], for example, by cycling most gas through low mass stars and removing the metals made by the accompanying high mass stars from the Galaxy. These models were designed to reduce high primordial D / H , expected from the low Yp values prevalent at that time, to the low ISM values. Tosi et al. [91] describe the generic difficulties with these models. To destroy 90% of the D, 90% of the gas must have been processed in and ejected from stars. These stars would then release more metals than are seen. If the gas is removed (e.g. expelled from the galaxy) to hide the metals, then the ratio of the mass in gas to that in remnants is would be lower than observed. Infall of primordial gas does not help, because this brings in excess D. These models also fail to deplete the D in quasar absorbers, because the stars which deplete the D, by ejecting gas without D, also eject carbon. The low abundance of Physica Scripta T85
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David Tytler, John M. O'Meara, Nao Suzuki and Dan Lubin
carbon in the absorbers limits the destruction of D to < 1 % [52]. 4.4. Questions about D/H Here we review some common questions about D / H in quasar spectra. 4.4.1. Why is saturation of absorption lines important? Wampler [95] suggested that the low D / H value towards Q1937-1009 might be inaccurate because in some cases the H absorption lines have zero flux in their cores; they are saturated. Songaila, Wampler and Cowie [96] suggested that this well known problem might lead to errors in the H column density, but later work, using better data and more detailed analyses [97] has shown that these concerns were not significant, and that the initial result [98] was reliable. Neutral deuterium (DI) is detected in Lyman series absorption lines, which are adjacent to the H I lines. The isotopic shift of 82 km s"1 is easily resolved in high resolution spectra, but it is not enough to move D out of the absorption by the H. The Lyman series lines lie between 1216A and 912A, and can be observed from the ground at redshifts > 2.5. Ideally, many (in the best cases > 20) Lyman lines are observed, to help determine the column density and velocity width (b values, b = \/2 1 [177] it contains most of the baryons. The baryon density is estimated from the total amount of H I absorption, correcting for density fluctuations which change the ionization. The gas is photoionized, recombination times are faster in the denser gas, and hence this gas shows more H I absorption per unit gas. Using the observed ionizing radiation from QSOs, we have a lower limit on the ionizing flux, and hence a lower limit on the ionization of the gas. If the gas is more ionized than this, then we have underestimated the baryon density in the IGM. Three different groups obtained similar results [178-180]: fib> 0.035/zf02. This seems to be a secure lower limit, but not if the IGM is less ionized than assumed, because there is more neutral gas in high density regions, and these were missing from simulations which lack resolution. We do not have similar measurements at lower redshifts, because the space based data are not yet good enough, and the universe has expanded sufficiently that simulations are either too small in volume or lack resolution. Cen and Ostriker [177] have shown that by today, structure formation may have heated most local baryons to temperatures of 105 - 107 K, which are extremely hard to detect [177,181]. 11.2. Clusters of galaxies Clusters of galaxies provide an estimate of the baryon density because most of the gas which they contain is hot and hence visible. The baryons in gas were heated up to 8 keV through fast collisions as the clusters assembled. The mass of gas in a cluster can be estimated from the observed X-ray emission, or from the scattering of CMB photons in the Sunyaev-Zel'dovich (SZ) effect. Other baryons in stars, stellar remnants and cool gas contribute about 6% to the total baryon mass. The cosmological baryon density is obtained from the ratio of the baryonic mass to the total gravitating mass [182]. Numerical simulations show that the value of this ratio in the clusters will be similar to the cosmological average, because the clusters are so large and massive, but slightly smaller, because shock heating makes baryons more extended than dark matter [183,184]. The total mass of a cluster, Mu can be estimated from the velocity dispersion of the galaxies, from the X-ray emission, or from the weak lensing of background galaxies. We then use fib/ fim ~ Mb/M t . The baryon fraction in clusters in the last factor is about O.lO/z^1 (SZ effect: [185]), or 0 . 0 5 O.Uh~*/2 (X-ray: [186]), or 0.11^ 0 3 / 2 (X-ray: [187,188]). Using fim= 0.3 ± 0.2 from a variety of methods [189], we get fib~ 0.03, with factor of two errors. These fib estimates count only observed baryons. 11.3. Local dark baryonic matter The baryon density estimated in the Lya forest at z ~ 3 and in local clusters of galaxies are both similar to the that from Physica Scripta T85
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David Tytler, John M. O'Meara, Nao Suzuki and Dan Lubin
SBBN using low D / H . This implies that there is little dark baryonic matter in the universe [190]. This result seems conceptually secure, since there is little opportunity to remove baryons from the IGM at z < 3 or to hide them in dense objects without making stars which we would see [191], and the clusters are believed to be representative of the contents of the universe as a whole today. However, the numerical estimates involved are not yet accurate enough to rule out a significant density (e.g. 0.5 Qb) of baryonic MACHOS. 11.4. Simulations of the formation of Galaxies Ostriker (private communication) notes that the Qb can be constrained to a factor of two of that derived from SBBN using low D / H by the requirement that these baryons make galaxies. Semi-analytic models can also address the distribution of baryons in temperature and the total required to make observed structures (Frenk and Baugh, personal communication). 11.5. CMB The baryon density can be obtained from the amplitude of the fluctuations on the sky of the temperature of the CMB. The baryons in the IGM at z ~ 1300 scattered the CMB photons. The amplitude of the fluctuations is a measure of Qbh2, and other parameters. Published data favor large Qb, with large errors, however dramatic improvements are imminent, and future constraints may approach or exceed the accuracy of Qb from SBBN [192,193]. 12. The achievements of BBN Standard Big Bang Nucleosynthesis (SBBN) is a major success because the theory is well understood, close connections have developed between theory and observation, and observations are becoming more reliable. The early attempts to include physics in the mathematical model of the expanding universe lead to an understanding of the creation of the elements and the development of standard big bang theory, including the predictions of the CMB. The general success of SBBN is based on the robustness of the theory, and the resulting predictions of the abundances of the light nuclei. The abundances of 4 He, 7 Li and D can be explained with a single value for the free parameter n, and the implied Qb agrees with other estimates. This agreement is used to limit physics beyond that in SBBN, including alternative theories of gravity, inhomogeneous baryon density, extra particles which were relativistic during BBN, and decays of particles after BBN. After decades of detailed study, no compelling major departures from SBBN have been found, and few departures are allowed. Using SBBN predictions and measured abundances, we obtain the best estimates for the cosmological parameters r\ and Qb. The abundances of D, 4 He and 7 Li have all been measured in gas where there has been little stellar processing. In all three cases, the observed abundance are near to the primordial value remaining after SBBN. The D / H measured toward QSOs has the advantage of simplicity: D is not made after BBN, there are no known ways to destroy D in the QSO absorbers, and D / H can be extracted directly from the ultraviolet spectra, without corrections. There are now three Physica Scripta T85
cases of low D / H which seem secure. There remains the possibility that D / H is high in other absorbers seen towards other QSOs, but such high D must be very rare because no secure cases have been found, yet they should be an order of magnitude easier to find than the examples which show low D. We use low D / H as the best estimator of r\ and the baryon density. SBBN then gives predictions of the abundance of the other light nuclei. These predictions suggest that Yp is high, as suggested by Izotov, Thuan and collaborators. Low D also implies that 7 Li has been depleted by about a factor of two in the halo stars on the Spite plateau, which is more than some expect. The high Qb from SBBN plus low D / H is enough to account for about 1 /8th of the gravitating matter. Hence the remaining dark matter is not baryonic, a result which was established decades ago using SBBN and D / H in the ISM. The near coincidence in the mass densities of baryons and non-baryonic dark matter is perhaps explained if the dark matter is a supersymmetric neutralino [194]. At redshifts z ~ 3 the baryons are present and observed in IGM with an abundance similar to Qb. Hence there was little dark, or missing baryonic matter at that time. Today the same is true in clusters of galaxies. Outside clusters the baryons are mostly unseen, and they may be hard to observe if they have been heated to 105 — 107K by structure formation. The number of free parameters in BBN has been decreasing over the years: Fermi and Terkovich gave nuclear reaction rates, the half-life of the neutron was measured, and then the number of families of neutrinos was measured. In standard BBN we are now left with one parameter, the baryon density, which is today measured with D / H using SBBN. When, in the next few years, this parameter is also measured, SBBN will have no free parameters. When free parameters can be adjusted to obtain consistency with the data, it is hard to tell if a hypothesis is correct. The agreement between SBBN theory and measurement has grown stronger over the decades, as more parameters were constrained by independent measurements, and abundance measurements improved. This is the most convincing evidence that BBN happened and has been understood.
Acknowledgements This work was funded in part by grant G-NASA/NAG5-3237 and by NSF grants AST-9420443 and AST-9900842. We are grateful to Steve Vogt, the PI for the Keck HIRES instrument which enabled our work on D/H. Scott Buries and Kim Nollett kindly provided the figures for this paper. It is a pleasure to thank Scott Buries, Constantine Deliyannis, Carlos Frenk, George Fuller, Yuri Izotov, David Kirkman, Hannu Kurki-Suonio, Sergei Levshakov, Keith Olive, Jerry Ostriker, Evan Skillman, Gary Steigman and Trinh Xuan Thuan for suggestions and many helpful and enjoyable discussions. We thank the organizers of this meeting, Lars Bergstrom, Per Carlson and Claes Fransson for their gracious hospitality.
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Physica Scripta T85
Physica Scripta.Vol. T85, 32-36, 2000
Cosmology with Clusters of Galaxies Neta A. Bahcall* Princeton University Observatory, Princeton, NJ 08544 Received January 5, 1999; accepted August 2, 1999
PACS Ref: 9865Cw, 9880Es, 9535+d
Abstract Rich clusters of galaxies, the largest virialized systems known, place some of the most powerful constraints on cosmology. I discuss below the use of clusters of galaxies in addressing two fundamental questions: What is the mass-density of the universe? and how is the mass distributed? I show that several independent methods utilizing clusters of galaxies—cluster dynamics and mass-to-light ratio, baryon fractions in clusters, and cluster evolution— all indicate the same robust result: the mass-density of the universe is low, Qm — 0.2, and the mass approximately traces light on large scales.
1. Introduction Theoretical arguments based on standard models of inflation, as well as on the demand of no "fine tuning" of cosmological parameters, predict a flat universe with the critical density needed to just halt its expansion. The critical density, 1.9 x 10~29h2g cm" 3 (where h refers to Hubble's constant, see below), is equivalent to ~ 10 protons per cubic meter; this density provides the gravitational pull needed to slow down the universal expansion and will eventually bring it to a halt. So far, however, only a small fraction of the critical density has been detected, even when all the unseen dark matter in galaxy halos and clusters of galaxies is included. There is no reliable indication so far that most of the matter needed to close the universe does in fact exist. Here we show that several independent observations of clusters of galaxies all indicate that the mass density of the universe is sub-critical. These observations include the mass and mass-to-light ratio of clusters and superclusters of galaxies, the high baryon fraction observed in clusters, and the evolution of the number density of massive clusters with time; the latter method provides a powerful measure not only of the mass-density of the universe but also the amplitude of the mass fluctuations. The three independent methods- all simple and robust- yield consistent results of a low-density universe with mass approximately tracing light on large scales.
2. Cluster dynamics and the mass-to-light ratio Rich clusters of galaxies are the most massive virialized objects known. Cluster masses can be directly and reliably determined using three independent methods: (0 the motion (velocity dispersion) of galaxies within clusters reflect the dynamical cluster mass, within a given radius, assuming the clusters are in hydrostatic equilibrium [1-3]; (if) the temperature of the hot intracluster gas, like the galaxy motion, traces the cluster mass [4-6]; and
(Hi) gravitational lensing distortions of background galaxies can be used to directly measure the intervening cluster mass that causes the distortions [7-10]. All three independent methods yield consistent cluster masses (typically within radii of ~ 1 Mpc), indicating that we can reliably determine cluster masses within the observed scatter (~ ± 30%). The simplest argument for a low density universe is based on summing up all the observed mass (associated with light to the largest possible scales) by utilizing the well-determined masses of clusters. The masses of rich clusters of galaxies range from ~ 1014 to 1015 h - 1 M 0 within 1.5h_1 Mpc radius of the cluster center (where h = Ho/100 km s _1 M p c - 1 denotes Hubble's constant). When normalized by the cluster luminosity, a median mass-to-light ratio of M/LB — 300 ± 100 h in solar units ( M Q / L © ) is observed for rich clusters, independent of the cluster luminosity, velocity dispersion, or other parameters [3,11]. (LB is the total luminosity of the cluster in the blue band, corrected for internal and Galactic absorption.) When integrated over the entire observed luminosity density of the universe, this mass-to-light ratio yields a mass density of pm ~ 0.4 x 10~29 h 2 g c m - 3 , or a mass density ratio of Qm = pm/pctit ~ 0.2 ± 0.1 (where p crit is the critical density needed to close the universe). The inferred density assumes that all galaxies exhibit the same high M / L B ratio as clusters, and that mass follows light on large scales. Thus, even if all galaxies have as much mass per unit luminosity as do massive clusters, the total mass of the universe is only ~ 2 0 % of the critical density. If one insists on esthetic grounds that the universe has a critical density (Qm = 1), then most of the mass of the universe has to be unassociated with galaxies (i.e., with light). On large scales ( > 1 . 5 h" 1 Mpc) the mass has to reside in "voids" where there is no light. This would imply, for Qm = 1, a large bias in the distribution of mass versus light, with mass distributed considerably more diffusely than light. Is there a strong bias in the universe, with most of the dark matter residing on large scales, well beyond galaxies and clusters? An analysis of the mass-to-light ratio of galaxies, groups, and clusters by Bahcall et al. [11] suggests that there is not a large bias. The study shows that the M / L B ratio of galaxies increases with scale up to radii of R ~ 0 . 2 h _ 1 Mpc, due to very large dark halos around galaxies [see also 12,13]. The MIL ratio, however, appears to flatten and remain approximately constant for groups and rich clusters from scales of ~ 0 . 2 to at least 1.5h_1 Mpc and possibly even beyond (Fig. 1). The flattening occurs at M/L3 ~ 200-300h, corresponding to Qm ~ 0.2. (An M / L B — 1350 h is needed
* e-mail:
[email protected] Physica Scripta TIN
© Physica Scripta 1999
Cosmology with Clusters of Galaxies for a critical density universe, Qm = 1.) This observation contradicts the classical belief that the relative amount of dark matter increases continuously with scale, possibly reaching Qm = 1 on large scales. The available data suggest that most of the dark matter may be associated with very large dark halos of galaxies and that clusters do not contain a substantial amount of additional dark matter, other than that associated with (or torn-off from) the galaxy halos, plus the hot intracluster gas. This flattening ofM/L with scale, if confirmed by further larger-scale observations, suggests that the relative amount of dark matter does not increase significantly with scale above ~ 0.2h -1 Mpc. In that case, the mass density of the universe is low, O m ~ 0.2-0.3, with no significant bias (i.e., mass approximately following light on large scales). Recently the mass and mass-to-light ratio of a supercluster of galaxies, on a scale of ~ 6 h _ 1 Mpc, was directly measured using observations of weak gravitational lensing distortion of background galaxies (Kaiser et al. [14]). The results yield a supercluster mass-to-light ratio (on 6 h _ 1 Mpc scale) of M/L B = 280 ±40h, comparable to the mean value observed for the three individual clusters that are members of this supercluster. These results provide a powerful confirmation of the suggested flattening of M/LB (R) presented in Fig. 1 (Bahcall et al. [11,15]). The recent results confirm that no significant amount of additional dark matter exists on large scales. The results also provide a clear illustration that mass approximately traces light on large scales and that Qm is low, as suggested by Fig. 1.
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Mass-to—Light Ratio vs. Scale
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3. Baryons in clusters Clusters contain many baryons, observed as gas and stars. Within 1.5h_1 Mpc of a rich cluster, the X-ray emitting gas contributes ~ 6 h " L 5 % of the cluster virial mass [16-18]. Stars contribute another ~ 2 % . The baryon fraction observed in clusters is thus: Ob/Qm > 0 . 0 6 t r ' 5 + 0.02.
(1)
The observed value represents a lower-limit to the baryon fraction since we count only the known baryons observed in gas and stars; additional baryonic matter may of course exist in the clusters. Standard Big Bang nucleosynthesis limits the baryon density of the universe to [19,20]: flb~0.015h-2.
(2)
These facts suggest that the baryon fraction observed in rich clusters (Eq. (1)) exceeds that of an Qm = 1 universe (Ob/(fl m = 1) - 0.015h" 2 ; (Eq. (2)) by a factor of > 3 (for h>0.5). Since detailed hydrodynamic simulations [16,18] show that baryons do not segregate into rich clusters, the above results imply that either the mean density of the universe is lower than the critical density by a factor of > 3, or that the baryon density is much larger than predicted by nucleosynthesis. The observed high baryonic mass fraction in clusters (Eq. (1)), combined with the nucleosynthesis limit (Eq. (2)), suggest (for h~0.65±0.1): Qm * /
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R (Mpc) Fig. 1. The dependence of mass-to-light ratio, M/LB, on scale, R, for average spiral galaxies (spiral symbols), elliptical galaxies (elliptical symbols), and groups and clusters (filled circles). Adapted from Bahcall, Lubin and Dorman [11]; [15]. The large scale point at ~ 15 h _ 1 Mpc represents Virgo cluster infall motion results [11]. The location of Qm = 1 and Qm = 0.3 are indicated by the horizontal lines. A flattening of M/LB is suggested at Qm ~ 0.2 ± 0 . 1 . A recent result for a supercluster using weak gravitational lensing ( K ~ 6 h - 1 Mpc; [14]), M/LB = 280 ± 40 h, is consistent with the suggested flattening of M/L(R). © Physica Scripta 1999
4. Evolution of cluster abundance The observed present-day abundance of rich clusters of galaxies places a strong constraint on cosmology: osQm0'5— 0-5, where a% is the rms mass fluctuations on 8 h~ ! Mpc scale, and Qm is the present cosmological density parameter [21-26]. This constraint is degenerate in Qm and <jg; models with O m =l, erg ~ 0.5 are indistinguishable from models with O m ~ 0.25, c7 8 ~l. (A 0.5. Conversely, the evolution rate in low-Om high-o-g models is mild and the cluster abundance at z > 0.5 is much higher than in Qm = 1 models. In low-density models, density fluctuations evolve and freeze out at early times, thus producing only relatively little evolution at recent times (z 0.5 over ~ 103 deg2 of sky contradicts an Qm = 1 model where only ~ 10~2 such clusters would be expected (when normalized to the present-day cluster abundance). The evolution of the number density of Coma-like clusters was determined from observations using the CNOC cluster sample to z < 0.5 and compared with cosmological simulations [30-32]. The data show only a slow evolution of the cluster abundance to z ~ 0.5, with ~ 102 times more clusters observed at these redshifts than expected for Qm = 1. The results yield Q m ~0.3±0.1. The evolutionary effects increase with cluster mass and with redshift. The existence of the three most massive clusters observed so far at z ~ 0.5 — 0.9 places the strongest constraint yet on Qm and eg. These clusters (MS0016+16 at z = 0.55, MS0451-03 at z = 0.54, and MS1054-03 at z = 0.83, from the Extended Medium Sensitivity Survey, EMSS [35,36]), are nearly twice as massive as the Coma cluster, and have reliably measured masses (including gravitational lensing masses, temperatures, and velocity dispersions; [34,37-40]. These clusters posses the highest masses ( > 8 xlO 1 4 h" 1 M Q within 1.5 h _ 1 comoving Mpc radius), the highest velocity dispersions (>1200 km s _1 ), and the highest temperatures ( > 8 keV) in the z > 0.5 EMSS survey. The existence of these three massive distant clusters, even just the existence of the single observed cluster at z = 0.83, rules out Gaussian Qm = 1 models for which only ~ 10~5 z ~ 0.8 clusters are expected instead ofthe 1 cluster observed (or ~ 10~3 z > 0.5 clusters expected instead of the 3 observed). (See Bahcall and Fan [34]). In Fig. 2 we compare the observed versus expected evolution of the number density of such massive clusters. The expected evolution is based on the Press-Schechter [41] formalism; it is presented for different Qm values (each with the appropriate normalization as that satisfies the observed present-day cluster abundance, er8 ~ 0.5 Qm~°-5; [23,26]). The model curves range from Qm = 0.l (erg ~ 1.7) at the top of the figure (flattest, nearly no evolution) to Qm = 1 (CT8— 0.5) at the bottom (steepest, strongest evolution). The difference between high and low Qm models is dramatic for these high mass clusters: O m = 1 models predict ~ 105 times less clusters at z ~ 0.8 than do £2 m ~0.2 models. The large magnitude of the effect is due to the fact that these are very massive clusters, on the exponential tail of the cluster mass function; they are rare events and the evolution of their number density depends exponentially on their "rarity", i.e., depends exponentially on o%2 oc Qm [32,34]. The number of clusters observed at z ~ 0.8 is consistent with Qm ~ 0.2, and is highly inconsistent with the ~ 10~5 clusters expected if Qm = 1. The data exhibit only a slow, relatively flat evolution; this is expected only in low-£2m models. Qm = 1 models have a ~ 10~5 probability of producing the one observed cluster at z ~ 0.8, and, independently, a ~ 10~6 probability of producing the two observed clusters at z ~ 0.55. These results rule out £2m = 1 Gaussian models at a very high confidence level. The results are similar for models with or without a cosmological constant. The data provide powerful constraints on i3 m and er8: Om = 0 . 2 ^ J 5 Physica Scripta TIN
Fig. 2. Evolution of the number density of massive clusters as a function of redshift: observed versus expected (for clusters with mass y x 1014 h_1 MQ within a comoving radius of 1.5 h -1 Mpc). (Adapted from Bahcall and Fan 1998 [34]. The expected evolution is presented for different Qm values by the different curves. The observational data points (see text) show only a slow evolution in the cluster abundance, consistent with £2m ~ 0.2+jJ- J5. Models with Qm = 1 predict ~105 fewer clusters than observed at z ~ 0.8, and ~103 fewer clusters than observed at z ~ 0.6.
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0) The mass-to-light ratio of clusters (and superclusters) of
galaxies and the suggested flattening of the massto-light ratio on large scales suggest Qm ~ 0.2±0.1. The high baryon fraction observed in clusters of (2) galaxies suggests £?m 0.3 at the 2-a level. A new weak lensing study of a supercluster (Kaiser et al. 1998) on a scale of 6 h~' Mpc, yields a (surprisingly) low value of Qm (~0.05), under the assumption that there is no bias in the way that mass traces light. Small & Sargent (1998) have recently probed the matter density for the Corona Borealis supercluster (at a scale of ~ 20 h _ 1 Mpc), finding Qm ~ 0.4. Under the assumption of a flat universe, global limits can also be placed on Qm from studies of type la supernovae (see next section); currently the supernova results favor a value Qm ~ 0 . 3 . The measurement of the total matter density of the Universe remains an important and challenging problem. It should be emphasized that all of the methods for measuring Qm are based on a number of underlying assumptions. For different methods, the list includes diverse assumptions about how the mass distribution traces the observed light distribution, whether clusters are representative of the Universe, the properties and effects of dust grains, or the evolution of the objects under study. The accuracy of any matter density estimate must ultimately be evaluated in the context of the validity of the underlying assumptions upon which the method is based. Hence, it is non-trivial to assign a quantitative uncertainty in many cases but, in fact, systematic effects (choices and assumptions) may be the dominant source of uncertainty. An exciting result has emerged this year from atmospheric neutrino experiments undertaken at Superkamiokande (Totsuka, this volume), providing evidence for vacuum oscillations between muon and another neutrino species, and a lower limit to the mass in neutrinos. The contribution of neutrinos to the total density is likely to be small, although interestingly it may be comparable to that in stars. © Physica Scripta 2000
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Determining whether there is a significant, smooth underlying component to the matter density on the largest scales is a critical issue that must be definitively resolved. If, for example, some or all of the non-baryonic dark matter is composed of very weakly interacting particles, that component could prove very elusive and difficult to detect. It unfortunately remains the case that at present, it is not yet possible to distinguish unambiguously and definitively among Qm = 1, Qm + QA = I, and open universes with Qo < 1, models all implying very different underlying fundamental physics. The preponderance of evidence at the present time, however, does not favor the simplest case of Qm — 1 (the Einstein-de Sitter universe). 3. Determination of Q,i As illustrated in Fig. 2(a), the cosmological constant A has had a long and volatile history in cosmology. There have been many reasons to be skeptical about a non-zero value of the cosmological constant. To begin with, there is a discrepancy of > 120 orders of magnitude between current observational limits and estimates of the vacuum energy density based on current standard particle theory (e.g. Carroll, Press and Turner 1992). A further difficulty with a non-zero value for A is that it appears coincidental that we are now living at a special epoch when the cosmological constant has begun to affect the dynamics of the Universe (other than during a time of inflation). It is also difficult to ignore the fact that historically a non-zero A has been called upon to explain a number of other apparent crises, and moreover, adding additional free parameters to a problem always makes it easier to fit data. However, despite the strong arguments have been made for A = 0, there are growing reasons for a renewed interest in a non-zero value. Although the current value of A is small compared to the observed limits, there is no known physical principle that demands A = 0 (e.g., Carroll, Press & Turner 1992). Although Einstein originally introduced an arbitrary constant term, standard particle theory and inflation now provide a physical interpretation of A: it is the energy density of the vacuum (e.g., Weinberg 1989). Finally, a number of observational results can be explained with a low Qm and Qm + QA = 1: for instance, the observed large scale distribution of galaxies, clusters, and voids described previously, in addition to the recent results from type la supernovae described below. In addition, the discrepancy between the ages of the oldest stars and the expansion age (exacerbated if Qm = 1) can be resolved. Excitement has recently been generated by the results from two groups studying type la supernovae at high redshift (one team's results were reported at this meeting by Ariel Goobar). Both groups have found that the high redshift supernovae are fainter (and therefore further), on average, than implied by either an open (Qm = 0.2) or a flat, matter-dominated (Qm = 1) universe. The observed differences are ~0.25 and 0.15 mag, (Riess et al. 1998 and Perlmutter et al. 1999, respectively), or equivalently ~ 1 3 % and 8% in distance. A number of tests have been applied to search for possible systematic errors that might produce this observed effect, but none has been identified. Taken at face value, these results imply that the vacuum energy density of the Universe, (A), is non-zero. Physica Scripta T85
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Wendy L. Freedman
The early results from these two groups have evolved as more data have become available. Perlmutter et al. (1997) first reported results based on a sample of 7 high-redshift (z ~ 0.4) supernovae. Initially, they found evidence for a high matter density Qm ~ 0.9 ± 0 . 3 , with a value of QA consistent with zero. However, with the subsequent discovery of a z ~ 0.8 supernova, Perlmutter et al. (1998) found instead that a low-mass density (Qm ~ 0.2) universe was preferred. The second, independent group obtained preliminary results based on 4 supernovae which were also consistent with a lower matter density (Garnavich et al. 1998). The sample sizes have now grown larger, with 16 supernovae being reported by Riess et al. (1998) and 42 supernovae being reported by Perlmutter et al. (1999). These two new larger data sets are yielding consistent conclusions, and the supernovae are now indicating a non-zero and positive value for QA ~ 0.7, and a small matter density, Qm ~ 0.3, under the assumption that Qm + QA = 1. If a flat universe is not assumed, the best fit to the Perlmutter et al. data yields Qm = 0.73, QA = 1.32. The Hubble diagram for both the nearby (Hamuy et al. 1996) and the distant (Reiss ef al. 1998) samples of supernovae are shown in Fig. 3.
A possible weakness of all of the current supernova QA studies is that the luminosities of the high-redshift supernovae are all measured relative to the same set of local supernovae. Although in the future, estimates of QA at high redshift will be possible using the shape of the Hubble diagram alone (Goobar & Perlmutter 1995), at present, the evidence for QA comes from a differential comparison of the nearby sample of supernovae at z < 0.1, with those at z ~ 0.3 — 0.8. Hence, the absolute calibrations, completeness levels, and any other systematic effects pertaining to both datasets are critical. For several reasons, the search techniques and calibrations of the nearby and the distant samples are different. Moreover, the intense efforts to search for high-redshift objects have now led to the situation where the nearby sample is now smaller than the distant samples. While the different search strategies may not necessarily introduce systematic differences, increasing the nearby sample will provide an important check. Such searches are now underway by several groups. Although a 0.25 mag difference between the nearby and distant samples appears large, the history of measurements of Ho provides an interesting context for comparison. In The advantages of using type la supernovae for measure- the case of Ho determinations, a difference of 0.25 mag ments of QA are many. The dispersion in the nearby type in zero point only corresponds to a difference between 60 la supernova Hubble diagram is very small (0.12 mag or and 67 km/s/Mpc! Current differences in the published 6% in distance, as reported by Riess et al. 1996). They values for Ho result from a number of arcane factors: the are bright and therefore can be observed to large distances. adoption of different calibrator galaxies, the adoption of difIn principle, at z ~ 1, the shape of the Hubble diagram alone ferent techniques for measuring distances, treatment of can be used to separate Qm and QA, independent of the reddening and metallicity, and differences in adopted photonearby, local calibration sample (Goobar & Perlmutter metric zero point. In fact, despite the considerable progress 1995). Potential effects due to evolution, chemical compo- on the extragalactic distance scale and the Hubble constant, sition dependence, changing dust properties are all amenable recent Ho values tend to range from about 60 to 80 k m / s / M p c (see next section). (As recently as five years ago, to empirical tests and calibration. there was a factor of 2 discrepancy in these values, corresponding to a difference of 1.5 mag.) Type la s u p e r n o v a e In interpreting the observed difference between nearby 1 1111 1 1—I I I I I I I 1 1—I I I I 11 and distant supernovae, it is also important to keep in mind 0) 45 Reiss et al. (1998) T3 that, for the known properties of dust in the interstellar 3 medium, the ratio of total-to-selective absorption, (RB = *J ..-* AB/E(B — V)), (the value by which the colors are multiplied C 40 to correct the blue magnitudes), is ~ 4. Hence, very accurate £0 photometry and colors are required to ultimately understand Hamuy et al. ^ S this issue. A relative error of only 0.03 mag in color could .—v (1996) * 4 L - 0.0, Q 1.0 contribute 0.12 mag to the observed difference in magnitude. om = o.2, n! O.Oi ,.«* i 35 j&i Further tests and limits on A may come from gravitational 6 lens number density statistics (Fukugita et al. 1990; L = HOCLL is the "Hubble-constant-free" luminosity distance and MR = MB — 51og//o + 25 is the "Hubbleconstant-free" 5-band absolute magnitude at maximum of a SN la with width s = 1. (These quantities are, respectively, calculated from theory or fit from apparent magnitudes and redshifts, both without any need for Ho. mB°"=mB + Aco„{s), (11) The cosmological-parameter results are thus also completely where the correction term AC0Tr is a simple monotonic func- independent of Ho.) Both the low- and high-redshift tion of the "stretch factor," s, that stretches or contracts supernovae were fit simultaneously, so that MB and a, the time axis of a template SN la lightcurve to best fit the slope of the width-luminosity relation, could also be the observed lightcurve for each supernova (see [8,22]). A fit in addition to the cosmological parameters QM and similar relation corrects the V band lightcurve, with the QA- For most of the analyses in this paper, MR and a same stretch factor in both bands. For the supernovae dis- are statistical "nuisance" parameters; we calculate cussed in this paper, the template must be time-dilated by 2-dimensional confidence regions and single-parameter a factor 1 + z before fitting to the observed lightcurves to uncertainties for the cosmological parameters by integrating over these parameters, i.e., V(QM,QA) = ^V(QM-,QA, 2 MB, a)&MB da. for a discussion see also http: www-supernova.lbl.gov © Physica Scripta 2000
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(0. 0) (1.0) (2.0)
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redshift z redshift z Fig. 2. (a) Hubble diagram for 42 high-redshift Type la supernovae from the Supernova Cosmology Project, and 18 low-redshift Type la supernovae from the Calan/Tololo Supernova Survey, plotted on a linear redshift scale to display details at high redshift. The magnitude residuals from the best-fit flat cosmology for the Fit C supernova subset, (QM, QA) = (0.28,0.72). The dashed curves are for a range of flat cosmological models: (QM,QA) = (0,1) on top, (0.5,0.5) third from bottom, (0.75,0.25) second from bottom, and (1,0) is the solid curve on bottom. The middle solid curve is for (QM, QA) = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with (QM, &A) = (0.73,1.32). (c) The uncertainty-normalized residuals from the best-fit flat cosmology for the Fit C supernova subset, (QM,QA) = (0.28,0.72).
The residual dispersion in SN la peak magnitude after correcting for the width-luminosity relation is small, about 0.17 magnitudes, before applying any color-correction. This was reported in Hamuy et al. [21] for the low-redshift Calan-Tololo supernovae, and it is striking that the same residual is most consistent with the current 42 high-redshift supernovae (see Section 6). Figure 2(a) shows the Hubble diagram of effective rest-frame stretch-corrected B magnitude as a function of redshift for the 42 Supernova Cosmology Project highredshift supernovae, along with the 18 Calan/Tololo low-redshift supernovae. (Here, KBR is the cross-filter K correction from observed R band to restframe B band.) The inner error bars in Figs 2a,b represent the photometric uncertainty, while the outer error bars add in quadrature 0.17 magnitudes of intrinsic dispersion of SN la magnitudes that remain after applying the width-luminosity correction. For these plots, the slope of the width-brightness relation was taken to be a = 0.6, the best-fit value of Fit C discussed below. The theoretical curves for a universe with no cosmological constant are shown as solid lines, for a range of mass density, QM = 0,1,2. The dashed lines represent alternative flat cosmologies, for which the total mass-energy density QM + 0 ^ = 1. The range of models shown are for (QM,QA) = (0,1), (0.5,0.5), (1,0), which is covered by the matching solid line, and (1.5, —0.5). We have analyzed the total set of 60 low- plus highredshift supernovae in several ways. The most inclusive analyses are called A and B: Fit A is a fit to the entire dataset, while Fit B excludes two supernovae that are the most significant outliers from the average lightcurve width, s = \, and two of the remaining supernovae that are the largest residuals from Fit A. The remaining low- and high-redshift supernovae are well matched in their lightcurve width—the error-weighted means are (s) Hamuy = 0.99 ±0.01 and <J) S C P = 1.00± 0.01—making the results robust with respect to the width-luminosity-relation correction. Our primary analysis, Physica Scripta T85
Fit C, further excludes two supernovae that are likely to be reddened, and is discussed in the following section. Fits A and B give very similar results. Removing the two large-residual supernovae from Fit A yields indistinguishable results. The best-fit mass-density in a flat universe for Fit A is, within a fraction of the uncertainty, the same value as for Fit B, Q^ = 0.26+{J;^. The main difference between the fits is the goodness-of-fit: the larger X2 per degree of freedom for Fit A, x2 — 1 -76, indicates that the outlier supernovae included in this fit are probably not part of a Gaussian distribution and thus will not be appropriately weighted in a x2 fit- The x2 P e r degree of freedom for Fit B, x2 = 1 • 16, is over 300 times more probable than that of fit A, and indicates that the remaining 56 supernovae are a reasonable fit to the model, with no large statistical errors remaining unaccounted for. Of the two large-residual supernovae excluded from the fits after Fit A, one is fainter than the best-fit prediction and one is brighter. The photometric color excess for the fainter supernova, SN 19970, has an uncertainty that is too large to determine conclusively whether it is reddened. The brighter supernova, SN 1994H, is one of the first seven high-redshift supernovae, and is one of the few supernovae without a spectrum to confirm its classification as a SN la. After re-analysis with additional calibration data and improved .^-corrections, it remains the brightest outlier in the current sample, but it affects the final cosmological fits much less as one of 42 supernovae, rather than 1 of 5 supernovae 3 in the early analysis of the SCP data where the best fit was centered on a solution with a flat Universe with vanishing cosmological constant but with large uncertainties [22].
5. Systematic uncertainties and cross-checks With our large sample of 42 high-redshift SNe, it is not only possible to obtain good statistical uncertainties on the 3
Only 5 of the 7 reported supernovae were used for the primary analysis. i Physica Scripta 2000
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measured parameters, but also to quantify several possible sources of systematic uncertainties. The primary approach is to examine subsets of our data that will be affected to lesser extents by the systematic uncertainty being considered. The high-redshift sample is now large enough that these subsets each contain enough supemovae to yield results of high statistical significance. 5.1. Extragalactic
extinction
5.1.1. Color-excess distributions. Although we have accounted for extinction due to our Galaxy, it is still probable that some supemovae are dimmed by host galaxy dust or intergalactic dust. For a standard dust extinction law [17] the color, B—V, of a supernova will become redder as the Supernova (b) amount of extinction, As, increases. We thus can look Cosmology Project for any extinction differences between the low- and high-redshift supemovae by comparing their restframe colors. Since there is a small dependence of intrinsic color on the lightcurve width, supernova colors can only be compared for the same stretch factor; for a more convenient analysis, we subtract out the intrinsic colors, so that the remaining color excesses can be compared simultaneously for all stretch factors. To determine the restframe color excess E(B— V) for each supernova, we fit the rest-frame -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 B and V photometry to the B and V SN la lightcurve E(B-V) templates, with one of the fitting parameters representing the magnitude difference between the two bands at their Fig. 3. (a) The restframe B—V color excess distribution for 17 of 18 respective peaks. Note that these lightcurve peaks are ~ 2 Calan/Tololo supemovae (see text), corrected for Galactic extinction using values from Schlegel et al. 1998. (b) The restframe B— V color excess for days apart, so the resulting Bmax — Vmax color parameter, the 36 high-redshift supemovae for which restframe B—V colors were which is frequently used to describe supernova colors, is measured, also corrected for Galactic extinction. The darker shading not a color measurement on a particular day. The difference indicates those E(B— V) measurements with uncertainties less than 0.3 mag, of this color parameter from the Bmax - F m a x found for a unshaded boxes indicate uncertainties greater than 0.3 mag, and the light sample of low-redshift supemovae for the same lightcurve shading indicates the two supemovae that are likely to be reddened based on their joint probability in color excess and magnitude residual from Fit stretch-factor [23-25] does yield the restframe E(B—V) B. The dashed curve shows the expected high-redshift E(B— V) distribution color excess for the fitted supernova. if the low-redshift distribution had the measurement uncertainties of the
m
JI
For the high-redshift supemovae at 0.3 < z < 0.7, the matching R- and /-band measurements take the place of the restframe B and V measurements and the fit B and V lightcurve templates are AT-corrected from the appropriate matching filters, e.g. R(t) = B(t) + KBR(t) [11,12]. For the three supemovae at z > 0.75, the observed R—I corresponds more closely to a restframe U—B color than to a. B—V color, so E{B-V) is calculated from restframe E(U—B) using the extinction law of [17]. Similarly, for the two SNe la at z ~ 0 . 1 8 , E(B-V) is calculated from restframe E(V-R). Figure 3 shows the color excess distributions for both the low- and high-redshift supemovae, after removing the color excess due to our Galaxy. Six high-redshift supemovae are not shown on this E(B— V) plot, because six of the first seven high-redshift supemovae discovered were not observed in both R and / bands. The color of one low-redshift supernova, SN 1992bc, is poorly determined by the F-band template fit and has also been excluded. Two supemovae in the high-redshift sample are > 3<x red-and-faint outliers from the mean in the joint probability distribution of E(B— V) color excess and magnitude residual from Fit B. These two, SNe 1996cg and 1996cn (shown in light shading in Fig. 3), are very likely reddened supemovae. To obtain a more robust fit of the cosmological parameters, in Fit C we remove these supemovae from the sample. © Physica Scripta 2000
high-redshift supemovae indicated by the dark shading. Note that most of the color-excess dispersion for the high-redshift supemovae is due to the rest-frame K-band measurement uncertainties, since the rest-frame B-band uncertainties are usually smaller.
The likely-reddened supemovae do not significantly affect any of our results. The main distribution of 38 high-redshift supemovae thus is barely affected by a few reddened events. We find identical results if we exclude the six supemovae without color measurements. We take Fit C to be our primary analysis for this paper, and in Fig. 4, we show the two parameter confidence regions for this fit. 5.1.2. Cross-checks on extinction. The color-excess distributions of the Fit C dataset (with the most significant measurements highlighted by dark shading in Fig. 3) show no significant difference between the low- and high-redshift means. The dashed curve drawn over the high-redshift distribution of Fig. 3 shows the expected distribution if the low-redshift distribution had the measurement uncertainties of the high-redshift supemovae indicated by the dark shading. This shows that the reddening distribution for the high-redshift SNe is consistent with the reddening distribution for the low-redshift SNe, within the measurement Physica Scripta T85
52
A. Goobar et al. of the supernovae within these two redshift ranges. For a more thorough discussion on checks on extinction see [9].
Fig. 4. Left: Best-fit confidence regions in the QM-QA plane for our primary analysis, Fit C. The 68%, 90%, 95%, and 99% statistical confidence regions in the fljK-Q^ plane. Note that the spatial curvature of the universe—open, flat, or closed—is not determinative of the future of the universe's expansion, indicated by the near-horizontal solid line. In cosmologies above this near-horizontal line the universe will expand forever, while below this line the expansion of the universe will eventually come to a halt and recollapse. The upper-left shaded region, labeled "no big bang," represents "bouncing universe" cosmologies with no big bang in the past, see [26]. The lower right shaded region corresponds to a universe that is younger than the oldest heavy elements [27], for any value of H0 > 50 km s _1 Mpc - 1 . Right: Isochrones of constant H0t0, the age of the universe relative to the Hubble time, H^\ with the best-fit 68% and 90% confidence regions in the QM-QA plane for the primary analysis, Fit C. The isochrones are labeled for the case of H0 = 63 km s _1 Mpc"', representing a typical value found from studies of SNe la [21,23,28,29,]. If H0 were taken to be 10% larger, i.e., closer to the values in [30], the age labels would be 10% smaller. The diagonal line labeled accelerating/decelerating is drawn for qo = QM/2 - QA = 0, and divides the cosmological models with an accelerating or decelerating expansion at the present time.
uncertainties. The error-weighted means of the lowand high-redshift distributions are almost identical: (E(B- F)>Hamuy = 0-033 ± 0.014 mag and (E(B- V))SCP = 0.035 ±0.022 mag. We also find no significant correlation between the color excess and the statistical weight or redshift Physica Scripta T85
5.2. Malmquist bias and other luminosity biases In the fit of the cosmological parameters to the magnituderedshift relation, the low-redshift supernova magnitudes primarily determine MB and the width- luminosity slope a, and then the comparison with the high-redshift supernova magnitudes primarily determines QM and QA- Both lowand high-redshift supernova samples can be biased towards selecting the brighter tail of any distribution in supernova detection magnitude for supernovae found near the detection threshold of the search. This is known as "Malmquist bias" [31]. A width-luminosity relation fit to such a biased population would have a slope that is slightly too shallow and a zeropoint slightly too bright. A second bias is also acting on the supernova samples, selecting against supernovae on the narrow-lightcurve side of the widthluminosity relation since such supernovae. are detectable for a shorter period of time. Since this bias removes the narrowest/faintest supernova lightcurves preferentially, it culls out the part of the width-brightness distribution most subject to Malmquist bias, and moves the resulting best-fit slope and zeropoint closer to their correct values. If the Malmquist bias is the same in both datasets, then it is completely absorbed by MB and a. and does not affect the cosmological parameters. Thus, our principal concern is that there could be a difference in the amount of bias between the low-redshift and high-redshift samples. Note that effects peculiar to photographic SNe searches, such as saturation in galaxy cores, which might in principle select slightly different SNe la sub-populations should not be important in determining luminosity bias because lightcurve stretch compensates for any such differences. Moreover, the high-redshift SNe la we have discovered have a stretch distribution entirely consistent with those discovered in the Calan/Tololo search [9]. To estimate the Malmquist bias of the high-redshiftsupernova sample, we determined the completeness of our high-redshift searches as a function of magnitude, through an extensive series of tests inserting artificial SNe into our images [32] and find that the classical Malmquist bias should be 0.03 mag. (Note that this estimate is much smaller than the Malmquist bias affecting other cosmological distance indicators, due to the much smaller intrinsic luminosity dispersion of SNe la.) These highredshift supernovae, however, are typically detected before maximum, and their detection magnitudes and peak magnitudes have a correlation coefficient of only 0.35, so the effects of classical Malmquist bias should be diluted. Applying the formalism of [33] we estimate that the decorrelation between detection magnitude and peak magnitude reduces the classical Malmquist bias in the high-redshift sample to only 0.01 mag. We cannot make an exactly parallel estimate of Malmquist bias for the low-redshift-supernova sample, because we do not have information for the Calan/Tololo dataset concerning the number of supernovae found near the detection limit. However, the amount of classical Malmquist bias should be similar for the Calan/Tololo SNe since the amount of bias is dominated by the intrinsic luminosity dispersion of SNe la, which we find to be the © Physica Scripta 2000
The Acceleration of the Universe: Measurements
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same for the low-redshift and high-redshift samples (see Section 6). The major source of difference in the bias is expected to be due to the close correlation between the detection magnitude and the peak magnitude for the low-redshift supernova search, since this search tended not to find the supernovae as early before peak as the high-redshift search. We expect the Calan/Tololo SNe to have a bias closer to that obtained by direct application of the the classical Malmquist bias formula, 0.04 mag. 5.3. Gravitational lensing The clumping of mass in the universe could leave the line-of-sight to most of the supernovae under-dense, while occasional supernovae may be seen through over-dense regions. The latter supernovae could be significantly brightened by gravitational lensing, while the former supernovae would appear somewhat fainter. With enough supernovae, this effect will average out (for inclusive fits, such as Fit A, which include outliers), but the most over-dense lines of sight may be so rare that a set of 42 supernovae may only sample a slightly biased (fainter) set. The probability distribution of these amplifications and deamplifications has previously been studied both analytically and by Monte Carlo simulations. Given the acceptance window of our supernova search, we can integrate the probability distributions from these studies to estimate the bias due to amplified or deamplified supernovae that may be rejected as outliers. This average (de)amplification bias is less than 1% at the redshifts of our supernovae for simulations based on isothermal spheres the size of typical galaxies [34], JV-body simulations using realistic mass power spectra [35], and the analytic models of [36]. It is also possible that the small-scale clumping of matter is more extreme, e.g., if significant amounts of mass were in the form of compact objects such as MACHOs. This could lead to many supernova sightlines that are not just under-dense, but nearly empty. Once again, only the very rare line of sight would have a compact object in it, amplifying the supernova signal. To first approximation, with 42 supernovae we would see only the nearly empty beams, and thus only deamplifications. The appropriate luminositydistance formula in this case is not the FLRW-formula but rather the "partially filled beam" formula with a mass filling factor, r\ & 0 see [37] and references therein. We present the results of the fit of our data with this luminosity-distance formula as calculated using the code of [38] in Fig. 5. A more realistic limit on this point-like mass density can be estimated, because we would expect such point-like masses to collect into the gravitational potential wells already marked by galaxies and clusters. [39] estimate an upper limit of QM < 0.25 on the mass which is clustered like galaxies. In Fig. 5, we also show the confidence region, assuming that only the mass density contribution up to QM = 0.25 is point-like, with filling factor r\ = 0, and that n rises to 0.75 at QM — 1. We see that at low mass density, the Friedman-Robertson-Walker fit is already very close to the nearly empty-beam (n « 0) scenario, so the results are quite similar. At high mass density, the results diverge, although only minimally; the best fit in a flat universe is © Physica Scripta 2000
1
2
3
Fig. 5. Best-fit 68% and 90% confidence regions in the QM-®A plane for cosmological models with small scale clumping of matter (e.g., in the form of MACHOs) compared with the Friedman-Robertson-Walker model of Fit C, with smooth small-scale matter distribution. The shaded contours (Fit Q are the confidence regions fit to a Friedman-Robertson-Walker magnitude-redshift relation. The extended confidence strips (Fit K) are for a fit of the Fit C supernova set to an "empty beam" cosmology, using the "partially filled beam" magnitude-redshift relation with a filling factor r\ = 0, representing an extreme case in which all mass is in compact objects. The Fit L un-shaded contours represent a somewhat more realistic partially-filled-beam fit, with clumped matter (r\ - 0) only accounting for up to QM = 0.25 of the critical mass density, and any matter beyond that amount smoothly distributed (i.e., r\ rising to 0.75 at QM = !)•
5.4. Supernova evolution and progenitor environment evolution The spectrum of a SN la on any given point in its lightcurve reflects the complex physical state of the supernova on that day: the distribution, abundances, excitations, and velocities of the elements that the photons encounter as they leave the expanding photosphere all imprint on the spectra. So far, the high-redshift supernovae that have been studied have lightcurve shapes just like those of low-redshift supernovae [40], and their spectra show the same features on the same day of the lightcurve as their low-redshift counterparts having comparable lightcurve width. This is true all the way out to the z — 0.83 limit of the current sample [9,41]. We take this as a strong indication that the physical parameters of the supernova explosions are not evolving significantly over this time span. Theoretically, evolutionary effects might be caused by changes in progenitor populations or environments. For example, lower metallicity and more massive SN laprogenitor binary systems should be found in younger stellar populations. For the redshifts that we are considering, z < 0.85, the change in average progenitor masses may be small [42,43]. However, such progenitor mass differences or differences in typical progenitor metallicity are expected to lead to differences in the final C/O ratio in the exploding white dwarf, and hence affect the energetics of the explosion. The primary concern here would be if this changed the zero-point of the width-luminosity relation. We can look for such changes by comparing lightcurve rise times between low and high-redshift supernova samples, since this is a Physica Scripta T85
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A. Goobar et al.
sensitive indicator of explosion energetics. Preliminary indications suggest that no significant rise-time change is seen, with an upper limit of < 1 day for our sample, see forthcoming high-redshift studies of Goldhaber et al. 1998 and Nugent et al. 1998, and low-redshift bounds from [44-46]. This tight a constraint on rise-time change would theoretically limit the zero-point change to less than ~0.1 mag, see [47,48]. A change in typical C/O ratio can also affect the ignition density of the explosion and the propagation characteristics of the burning front. Such changes would be expected to appear as differences in lightcurve timescales before and after maximum [49]. Preliminary indications of consistency between such low- and high-redshift lightcurve timescales suggest that this is probably not a major effect for our supernova samples. Changes in typical progenitor metallicity should also directly cause some differences in SN la spectral features [48]. Spectral differences big enough to affect the B and F-band lightcurves see, for example, the extreme mixing models presented in Fig. 9 of [48] should be clearly visible for the best signal-to-noise spectra we have obtained for our distant supernovae, yet they are not seen [50,51]. The consistency of slopes in the lightcurve width-luminosity relation for the low- and high-redshift supernovae can also constrain the possibility of a strong metallicity effect of the type that [48] describes. An additional concern might be that even small changes in spectral features with metallicity could in turn affect the calculations of K corrections and reddening corrections. This effect, too, is very small, less than 0.01 magnitudes, for photometric observations of SNe la conducted in the restframe B or V bands see Figs. 8 and 10 of [48], as is the case for almost all of our supernovae. (Only two of our supernovae have primary observations that are sensitive to the restframe U band, where the magnitude can change by ~0.05 magnitudes, and these are the two supernovae with the lowest weights in our fits, as shown by the error bars of Fig. 2. In general the /-band observations, which are mostly sensitive to the restframe B band, provide the primary lightcurve at redshifts above 0.7.) The above analyses constrain only the effect of progenitor-environment evolution on SN la intrinsic luminosity; however, the extinction of the supernova light could also be affected, if the amount or character of the dust evolves, e.g. with host galaxy age. So far, we limited the size of this extinction evolution for dust that reddens, but evolution of "grey" dust grains larger than ~0.1/im, which would cause more color-neutral optical extinction, can evade these color measurements. The following two analysis approaches can constrain both evolution effects, intrinsic SN la luminosity evolution and extinction evolution. They take advantage of the fact that galaxy properties such as formation age, star-formation history, and metallicity are not monotonic functions of redshift, so even the low-redshift SNe la are found in galaxies with a wide range of ages and metallicities. It is a shift in the distribution of relevant host-galaxy properties occurring between z ~ 0 and z ~ 0.5 that could cause any evolutionary effects. 5.4.1. Width-Luminosity Relation Across Low-Redshift Environments. To the extent that low-redshift SNe la arise Physica Scripta T85
from progenitors with a range of metallicities and ages, the lightcurve width-luminosity relation discovered for these SNe can already account for these effects cf. [52]. When corrected for the width-luminosity relation, the peak magnitudes of low-redshift SNe la exhibit a very narrow magnitude dispersion about the Hubble line, with no evidence of a significant progenitor-environment difference in the residuals from this fit. It therefore does not matter if the population of progenitors evolves such that the measured lightcurve widths change, since the widthluminosity relation apparently is able to correct for these changes. It will be important to continue to study further nearby SNe la to test this conclusion with as wide a range of host-galaxy ages and metallicities as possible. 5.4.2. Matching Low- and High-Redshift Environments. Galaxies with different morphological classifications result from different evolutionary histories. To the extent that galaxies with similar classifications have similar histories, we can also check for evolutionary effects by using supernovae in our cosmology measurements with matching host galaxy classifications. If the same cosmological results are found for each measurement based on a subset of lowand high-redshift supernovae sharing a given host-galaxy classification, we can rule out many evolutionary scenarios. In the simplest such test, we compare the cosmological parameters measured from low- and high-redshift elliptical host galaxies with those measured from low- and high-redshift spiral host galaxies. Without high-resolution host-galaxy images for most of our high-redshift sample, we currently can only approximate this test for the smaller number of supernovae for which the host-galaxy spectrum gives a strong indication of galaxy classification. The resulting sets of 9 elliptical-host and 8 spiral-host high-redshift supernovae are matched to the 4 elliptical-host and 10 spiral-host low-redshift supernovae based on the morphological classifications listed in and excluding two with SB0 hosts [21]. We find no significant change in the best-fit cosmology for the elliptical host-galaxy subset (with both the low- and high-redshift subsets about one sigma brighter than the mean of the full sets), and a small ( 0. This is reflected in the high probability (99.8%) of £2A > 0. As discussed in [7], the slope of the contours in Fig. 4 is a function of the supernova redshift distribution; since most of the supernovae reported here are near z ~ 0.5, the confidence region is approximately fit by O.SQM — 0.6QA « —0.2 ± 0 . 1 . (The orthogonal linear combination, which is poorly constrained, is fit by 0.6 QM + 0.Si2A % 1.5 ±0.7.) The well-constrained linear combination is not parallel to any contour of constant current-deceleration-parameter:
the accelerating /decelerating universe line of Fig. 4 shows one such contour at qo = 0. Note that with almost all of the confidence region above this line, only currently accelerating universes fit the data well. As more of our highest redshift supernovae are analyzed, the long dimension of the confidence region will shorten. The time evolution of the deceleration parameter (q = —a(t)/ a{t)Hl) for a flat {QM =,0.3,£?,I =0.7) universe is shown in Fig. 7 (H0 set to 65 km s _ 1 Mpc - 1 ). The change in sign at about 7 Gyr after the Big Bang indicates a transition between a matter dominated and A dominated universe. 6.1. Error budget The supernova-specific statistical uncertainties include the measurement errors on SN peak magnitude, lightcurve stretch factor, and absolute photometric calibration. The two sources of statistical error that are common to all the supernovae are the intrinsic dispersion of SN la luminosities after correcting for the width-luminosity relation, taken as 0.17 mag, and the redshift uncertainty due to peculiar velocities, which are taken as 300 km s - 1 . Note that the statistical error in MB and a are derived quantities from our four-parameter fits. By integrating the four-dimensional probability distributions over these two variables, their uncertainties are included in the final statistical errors. All uncertainties that are not included in the statistical error budget are treated as systematic errors for the purposes of this paper. We have identified and bounded four potentially significant sources of systematic uncertainty: (1) the extinction uncertainty for dust that reddens, bounded at )=«a/I/Jv .
(6)
for different values of the factor/. If/ = bi/bj, then Eq. (4) shows that the (unknown) matter density fluctuations 5X will cancel out, and Ag will consist of mere shot noise whose covariance matrix i s N s {AgAg') = N (l) + / 2 N W .
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which can be interpreted as the number of "sigmas" at which the noise-only null hypothesis is ruled out. We choose Sa0 = £(l»"a - ^ l ) . where ra is the center of volume Va and E, is the correlation function measured by the LCRS [34]. We plot the results in Fig. 2 for each pair of clans i and j , and the corresponding valley-shaped curve tells us a number of things. The fact that v » 1 on the left-hand-side (as / ->• 0, with all the weight on clan i) means that there is a strong detection of cosmological fluctuations above the shot noise level (v ~ 1). Likewise, v » 1 on the right-hand-side (as / -*• oo), which demonstrates cosmological signal in c l a n / The fact that the curve dips for intermediate /-values tells us that the two density maps are correlated (r > 0) and have common signal. The minimum is attained at the v a l u e / which gives the best fit relative bias bi/bj for this common signal. However, the fact that v » 1 even at the minimum proves that even though some signal is shared in common, not all of it is: there are no values of bi for which Eq. (4) can hold for any pair of clans i and j .
^
" r • :' A„c be the eigenvalues of G, sorted from largest to smallest, with e, the corresponding unit where p denotes the one number that we can measure: the eigenvectors (Ge, = A,e,, e, • ej = 5y). It is instructive to correlation between clans 1 and 2. Since a correlation matrix decompose the fluctuation vector x into its uncorrelated cannot have negative eigenvalues, d e t R > 0 . After some principal components yt = e, • x: algebra, this gives the constraint
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Fig. 3. Predictions of standard solar models 1988. This figure, which is Fig. 1 of ref. [10], shows the predictions of 19 standard solar models in the plane defined by the 7Be and 8 B neutrino fluxes. The abbreviations that are used in the figure to identify different solar models are defined in the bibliographical item, ref. [45]. The figure includes all standard solar models with which I am familiar that were published in refereed journals in the decade 1988-1998. All of the fluxes are normalized to the predictions of the Bahcall-Pinsonneault 1998 solar model, BP98 [11]. The rectangular error box defines the 3
parameters, the relevant cross sections (^-factors) and the detector capture cross sections (/it-values for inverse beta-decay). Another critical condition is the reduction of production background. For this, both cosmic radiation and natural radioactivity must be reduced far below the normal environmental level, since secondary protons (Ep > lMeV) can mimic neutrino capture via (p , n) reactions in both cases. Cosmic rays can be shielded by going underground; all radiochemical solar neutrino experiments are located in deep mines or in mountain tunnels. An overburden of 1000 meters of rock corresponds to a shielding of 2500-3000 meter water equivalent (m.w.e.). The radiochemical purity must be, depending on the experiment, in the range of 10"10-10~16g U, Th per gram of target because the a-decay series interfere via (a, n) and (n, p) sequences. Another background source is (n, p)-reactions due to fast neutrons emitted from the rock walls of the underground lab. An important practical requirement is the feasibility of the chemical separation of the product nuclei from the target. Huge separation factors, up to 1030, are needed. Ideal are schemes where the neutrino capture product is volatile and can be flushed with a gas stream, as is the case in the Homestake- and in the Gallex experiments (see below). After the product nuclei are successfully separated from the target, they must be counted. The products from inverse beta decay are radioactive by electron capture; the detectable radiation in this process consists of keV - Auger electrons and X-rays. Such weakly ionizing low energy radiation is normally detected in low-level gas proportional counters which contain the radioactive species as an admixture to the counting gas. Typical decay rates are of order < 1/day. This calls for counter backgrounds < 1/week. Techniques towards achieving this goal are ultimate low-level procedures [13], radiochemical purity, counter miniaturization, as well as energy and pulse shape analysis with fast electronics (transient digitizer). Last not least, the material for a solar neutrino experiment must be obtainable and affordable in sufficient quantity and purity.
3. Homestake chlorine experiment Raymond Davis jr. was the first to demonstrate that it is indeed possible to detect a few atoms out of hundreds of tons of target material. In the late sixties, he constructed the first solar neutrino detector in the Homestake gold mine in Lead, South Dakota [14]. The aim was to detect 8 B-neutrinos via the reaction 37
C1 (ve, e") 37 Ar.
(9)
(8)
Large quantities of chlorine were conveniently available in where <j>i = neutrino flux, 244 keV) or Gd (ve , el 1 6 0 Tb* (Ev > 301 keV).
(13)
Characteristic beta-gamma coincidence signatures could help to achieve the required background reduction at very low energies. There are more planned experiments [60], but this is not the topic of this article. In any case, exciting new information is expected in this fast developing field of research.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12.
13. 14. 15. 16. 17.
* This item in the enumeration differs in nothing from the five others, starting with"-".
and
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Radiochemical Solar Neutrino Experiments and Implications 18. Cleveland, B. T. et al., Proceedings Fourth International Solar Neutrino Conference, (edited by W. Hampel), (published by: Max-Planck Institut fur Kernphysik, Heidelberg, Germany 1997), p.85. 19. Voloshin, M. B., Vysotsky, M. I. and L. B. Okun, Sov. Phys. JETP 64, 446 (1986). 20. Fukuda, Y. et al., Phys. Rev. Lett. 77, 1683 (1996). 21. Kuzmin, V. A., Sov. Phys. JETP 22, 1050 (1966). 22. Kirsten, T. A., in "Inside the Sun," (edited by G. Berthomieu and M. Cribier) (Kluwer Acad. Publ., Netherlands 1990), p.187. 23. Henrich, E. and Ebert, K. H., Angew. Chemie (Intern. Edit.) 31, 1283 (1992). 24. Kirsten, T. A., in Particles and Fields '91, Vancouver Meeting, (edited by D. Axen, D. Bryman, and M. Comyn), (World Scientific, Singapore 1992), 2, 942. 25. Gallex Collaboration: Anselmann, P. et al., Phys. Lett. B 285, 376 (1992). 26. Gallex Collaboration: Anselmann, P. et al., Phys. Lett. B 314, 445 (1993). 27. Gallex Collaboration: Anselmann, P. et al., Phys. Lett. B 327, 377 (1994). 28. Gallex Collaboration: Anselmann, P. et al., Phys. Lett. B 357, 237 (1995). 29. Gallex Collaboration: Hampel, W. et al, Phys. Lett. B 388, 384 (1996). 30. Gallex Collaboration: Hampel, W. et al, Phys. Lett. B 447, 127 (1999). 31. Kirsten, T. A., Progr. Particle Nucl. Phys. 40, 85 (1998). 32. Henrich, E., V. Ammon, R. and Ebert, K. H., in Proceedings Fourth International Solar Neutrino Conference, (edited by W. Hampel), (published by: Max-Planck Institut fur Kernphysik, Heidelberg, Germany 1997), p. 151. 33. Cribier, M. et al, Nucl. Instr. Meth. A 378, 233 (1996). 34. Gallex Collaboration: Anselmann, P. et al., Phys. Lett. B 342, 440 (1995). 35. Gallex Collaboration: Hampel, W. et al., Phys. Lett. B 420, 114 (1998). 36. Bahcall, J. N., Phys. Rev. C 56, 3391 (1997). 37. Gallex Collaboration: Hampel, W. etal, Phys. Lett. B436, 158 (1998). 38. Sage Collaboration: Abazov, A. I. et al.. Nuclear Phys. B (Proc. Suppl.) 19, 84 (1991). 39. Sage Collaboration: Abdurashitov, J. N. et al., in Proceedings Fourth International Solar Neutrino Conference, (edited by W. Hampel), (published by: Max-Planck Institut fur Kernphysik, Heidelberg, Germany 1997), p. 109. 40. Sage Collaboration: Abazov, A. I. et al, Phys. Rev. Lett. 67 , 3332 (1991).
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41. Sage Collaboration: Gavrin, V. N. etal., Nuclear Phys. B(Proc. Suppl.) 35, 412 (1994). 42. Sage Collaboration: Abdurashitov, J. N. et al, Phys. Lett. B 328 , 234 (1994). 43. Sage Collaboration: Abdurashitov, J. N. et al., Nucl. Phys. B (Proceed. Suppl.) 77, 20 (1999). 44. Sage Collaboration: Abdurashitov, J. N. et al, Phys. Rev. Lett. 77 , 4708 (1996). 45. Sage Collaboration: Abdurashitov, J. N. et al, in Proceedings Fourth International Solar Neutrino Conference, (edited by W. Hampel) (published by: Max-Planck Institut fur Kernphysik, Heidelberg, Germany 1997), p.126. 46. Bahcall, J. N., Basu, S. and Pinsonneault, M. H., Phys Lett. B 433, 1 (1998). 47. Paterno, L., in Proceedings Fourth International Solar Neutrino Conference, (edited by W. Hampel) (published by: Max-Planck Institut fur Kernphysik, Heidelberg, Germany 1997), p.54. 48. Bahcall, J. N., and Bethe, H. A., Phys. Rev. Lett. 65, 2233 (1990). 49. Sage Collaboration: Gavrin, V. N., talk presented at Neutrino 90, XlVth International Conf. on Neutrino Physics and Astrophysics, Geneva, Switzerland, June 1990 (1990). 50. Gallex Collaboration: Anselmann, P. et al, Phys. Lett. B 285, 390 (1992). 51. Bahcall, J. N., Phys. Lett. B 338, 276 (1994). 52. Shi, X., Schramm, D. and Dearborn, D., 1994, Phys. Rev. D 50, 2414 (1994). 53. Kirsten, T. A., Ann. New York Acad. Sci. 759, 1 (1995). 54. Kirsten, T. A., Nuovo Cimento C 19, 821 (1996). 55. Bahcall, J. N., Krastev, P.I., and Smirnov, A. Y., Phys. Rev. D 58, 096016-1-22 (1998). 56. Mohapatra, R. N., in Neutrino 96, Proceedings 17th International Conf. on Neutrino Physics and Astrophysics, Helsinki, Finnland, June 1996, (edited by K. Enqvist, K. Huitu, and J. Maalampi), (published by: World Scientific, Singapore 1997), p.290. 57. Superkamiokande Collaboration, Phys. Lett. B 433, 9 (1998). 58. Valle, J. W. , Nuclear Phys. B (Proc. Suppl.) 48, 137 (1996). 59. Kajita, T., for the Superkamiokande Collaboration. Nucl. Phys. B (Proceed. Suppl.) 77, 123 (1999). 60. Kirsten, T. A., in "Neutrino Physics," (edited by K. Winter), (Cambridge University Press 1999), 2nd edition. 61. Bellotti, E., Proc. Fourth International Solar Neutrino Conference, (edited by W. Hampel), (published by: Max-Planck Institut fur Kernphysik, Heidelberg, Germany 1997), p. 173. 62. Kirsten, T. A., Nucl. Phys. B (Proceed. Suppl.) 77, 26 (1999).
Physica Scripta T85
Physica Scripta.Vol. T85, 82-90, 2000
Evidence for Neutrino Oscillation Observed in Super-Kamiokande Y. Totsuka Kamioka Observatory, Institute for Cosmic Ray Research, The University of Tokyo Higashi-Mozumi, Kamioka-cho, Yoshiki-gun, Gifu 506-1205, Japan Received February 25, 1999; accepted August 2, 1999 PACS Ref: 14.60.Pq
Abstract Super-Kamiokande recently provided new results on atmospheric neutrinos which clearly indicate that the observed ratio of muons to electrons is significantly smaller than what is expected. Moreover the zenith-angle distribution of atmospheric muon neutrinos shows a strong up-down asymmetry. These results are not consistent with standard calculations of atmospheric neutrinos, while the hypothesis of neutrino oscillations quantitatively reproduces all the observed results.
1. Introduction Super-Kamiokande is a 50 000 ton water Cerenkov detector at the Kamioka Observatory, Institute for Cosmic Ray Research, the University of Tokyo which is located 1000 m underground (2700m.w.e.) in the Kamioka zinc mine, Japan. Its construction was started in December 1991 and completed in March 1996. The operation immediately began on 1 April 1996. Since then, data have been steadily accumulated and their analyses are going on as scheduled. Super-Kamiokande is a second generation experiment after the successful Kamiokande experiment with a 4500 ton water Cerenkov detector. Kamiokande set a severe limit on proton lifetime, observed a neutrino burst from the supernova SN1987A in the Large Magellanic Cloud, observed solar neutrinos with visible energies larger than 7MeV and confirmed Homestake's solar-neutrino deficit. Kamiokande also observed atmospheric neutrinos and found that the observed vM /v e ratio was smaller than what one expected and moreover the zenith-angle distribution of the v^/Ve ratio did not follow the expectation and revealed a deficit in the upward-going direction. However, the Kamiokande detector was too small to further investigate the anomalies in the solar and atmospheric neutrinos and also to search for proton decay. Hence it was decided to build a 50 000 ton water Cerenkov detector, Super-Kamiokande. Specifically, it was designed to obtain optimum results for the following physics objectives; (1) search for proton decay with decay modes of e+7i°, vK + , e+vr, vK°, etc.; (2) study of basic properties of neutrinos, especially their masses and mixings from observations of solar and atmospheric neutrinos; (3) study of deep interior of some astrophysical objects such as the Sun and supernovae; (4) search for possible point sources in the sky that emit neutrinos by various processes. Atmospheric neutrinos have been observed with large underground detectors. Observed events are classified as four types; (i) fully contained events in which all the tracks are contained in the detector and the incident neutrino Physica Scripta T85
energy is well estimated, (ii) partially contained events in which some of the tracks escape the detector and the visible energy is less than the incident one, (Hi) upward through-going muons that are produced in the rock beneath the detector and pass through the detector, (z'v) upwardgoing stopping muons that are also produced in the rock beneath the detector, enter and stop in the detector. Fully contained events are produced by low-energy neutrinos of a few 100 MeV ~ a fewGeV, where the ratio (vH + v^)/ (ve + \Q is close to 2, as both ic* produced high in the atmosphere and their daughter particles u* also decay out, resulting in the above ratio, which is insensitive to details of 71* production mechanisms. Kamiokande [1] first announced an anomaly, namely, the ratio of the number of muons to that of electrons in the observed fully-contained sub-GeV data, N^/Ne, which, is a good approximation to the ratio (Vn + vv)/(ve + v^), was found to be significantly smaller than expected. Two experiments with iron-calorimetric detectors, NUSEX [2] and Frejus [3] on the contrary obtained a ratio consistent with expectation, though their statistical significance was not strong. The 1MB waterCerenkov experiment [4] later published a result on the N^/Ne ratio that was consistent with Kamiokande. Therefore the situation was a little controversial and more data were needed. Kamiokande [5] then analyzed the multi-GeV data and found that the zenith-angle distribution of the ratio Nn/Ne did not agree with the expected one. Note that produced u* (e*) closely follow the incident direction of v^ (ve) at these energies. If these results are indeed true, the most plausible explanation is that the neutrino oscillation takes place and v^ is converted to either ve or vT. Recently Super-Kamiokande [6,7] and Soudan 2 [8] reported new results which are in good agreement with Kamiokande's observations both in the sub-GeV and multi-GeV ranges. Upward through-going muons provide additional information, since the relevant neutrino energies are much higher than those in the sub-GeV and multi-GeV ranges. Upward-going stopping muons are produced by v^ whose energies are similar to those for multi-GeV events, and provide independent information. As for the multi-GeV case, the zenith angle is related to the path length, so that the shape of its distribution is sensitive to neutrino oscillation. Now MACRO [9], Kamiokande [10] and SuperKamiokande [11] have a large enough number of upwardgoing muons for serious analyses. Their results indeed support the oscillation hypothesis. Figure 1 shows energy regions of neutrinos that contribute to fully-contained events, multi-GeV events, upward through-going muons and upward-going stopping muons. The useful range of neutrino energy covers from 0.5 GeV to above 100 GeV. The path length of neutrinos also varies © Physica Scripta 2000
Evidence for Neutrino Oscillation Observed in Super-Kamiokande
Muon-Neutrino Response Contained interactions (x 1/10) A
Kamiokande ,-• multi-GeV
\Through-going \ muons
Ev (GeV) Fig. 1. Energy distributions of parent neutrinos that produce fully-contained events, multi-GeV events, upward through-going and stopping muons (adapted from [17]) They were calculated for the Super-Kamiokande detector but do not sensitively depend on the detector geometry. The original neutrino flux was adapted from Gaisser et al. [14] and the parton distribution function from (GRV94DIS) [18].
83
Water is continuously circulated and purified. Special care is taken to eliminate contamination of the Radon (Rn) radioactive gas dissolved in the water. The water tank as well as the water-purification system was completely sealed in order to prevent Rn-contaminated ambient air from being dissolved in the water. The present level of Rn contamination is about 5mBq/m 3 . Work is still going on to further reduce the Rn gas. Event trigger is obtained with a simple majority logic circuit, namely if the number of hit PMTs exceeds a preset number, the trigger signal is issued and all the information is stored and then read out by online computers. The trigger threshold energy was originally set at about 5.7 MeV and recently lowered to 4.5 MeV. However, the large background caused by the Rn contamination does not at present allow us to make useful analyses for visible energies below 5.5 MeV. Here the visible energy is meant by the total energy for electrons. Various calibrations are being carried out, some of which are:
(1) Absolute energy scale of low-energy electrons (EviS = 5 ~ 16 MeV), using electron beams from an electron LINAC and also using gamma rays (7~9 MeV) widely, namely from about 10 km for downward-going from a reaction Ni(n, y)Ni with a triggerable Cf neutrinos to more than 10000 km for upward-going neutron source. neutrinos which are produced on the other side of Earth (2) Angular and position resolutions of low-energy elecand traverse the whole Earth. These characteristics are ideal trons by means of the electron LINAC. for studying possible neutrino oscillation, since the probabil- (3) Absolute energy scale of high-energy (.Evis > 30 MeV) ity that one type of neutrino oscillates into another is given electrons and muons, using stopping cosmic-ray muons by an expression sin2(20) sin2(1.27A»i2 L/iT), where L is the and Michel electrons from mu-decay. neutrino path length in km, E the neutrino energy in GeV (4) Position resolutions of muons, using the same means as and Am2 the mass squared difference in eV2 of the two types for (3). ofneutrinos. Thus with atmospheric neutrinos one can inves- (5) Attenuation (absorption plus scattering) length of tigate the Am2 range between 10~4eV2 and 10 eV2. Cerenkov photons, using through-going muons and So far I briefly summarized the Super-Kamiokande experMichel electrons. Its wave-length dependence is also iment and the present status of atmospheric-neutrino measured with a system of a tunable laser, a spherical observations. Now I describe the Super-Kamiokande detecdiffuse ball which is placed in the water and tor in Chapter 2. Then I highlight the latest results on atmosisotropically emits light that is fed from the laser, pheric neutrinos observed by Super-Kamiokande in Chapter and a CCD camera which takes an image of the diffuse 3 and show the clear evidence for neutrino oscillations ball and measures light intensity as a function of the vM ->• vT (or vM -> vster;ie.) The results are based on analyses ball position in the water. of Super-Kamiokande's 736-day data. (6) Scattering length of Cerenkov photons, using a sharp pencil beam of laser light with various wave lengths. The beam is directed vertically downward. Scattered 2. Super-Kamiokande detector light is detected by the inner PMTs. Angular as well A cylindrical cavity of 39 m in diameter and 42 m in height as wave-length dependences are thus measured. was excavated to store 50 000 ton water, above which a semi-spherical dome of 16 m in height was additionally Having all the information from the calibrations, the detecexcavated in order to stabilize the whole cavity against about tor Monte Carlo simulator is tuned. Current levels of 270 atm rock pressure. The cavity was completely lined with accuracies and resolutions are listed in Table I. The data-taking efficiency (data-taking time divided by stainless-steel sheets of 3 ~4.5 mm in thickness. The cylindritotal elapsed time) was about 60% initially and went up cal tank is optically divided into two parts, inner and outer detectors, each having 32 000 ton and 18 000 ton water, quickly to the current level of about 90%. The loss is respectively. The wall of the inner detector, which is located due to frequent calibration runs. 2.6 ~ 2.75 m inside the tank wall, is uniformly equipped with 11,146 20-inch photomultiplier tubes (PMTs) viewing the 3. Atmospheric Neutrinos inner water. 1,885 8-inch PMTs are used in the outer detector to detect Cerenkov light produced by incoming We follow Kamiokande [1] to categorize the observed event cosmic-ray muons and gamma rays from the surrounding types; sub-GeV, multi-GeV, upward through-going muons rock. It also detects particles that go out of the inner and upward-going stopping muons, as described in Section 1. detector, thus discriminating fully-contained and partiallyExperiments for atmospheric neutrinos observe electrons contained events. and muons and compare their numbers to the expected ones. © Physica Scripta 2000
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Table I. Accuracies and resolutions of some important parameters of the Super-Kamiokande detector. Items energy scale (5 ~ 20 MeV) energy resolution (10.78 Me V) angular resolution (10.78 Me V) position resolution (10.78 Me V) energy scale (>30MeV) energy resolution (> lOOMeV) energy resolution (>200MeV/c) angular resolution (~ 500 MeV) position resolution (~ 500 MeV) light absorption length (420 nm) light scattering length b (420 nm)
Accuracies, Resolutions
Remarks
< 0.9%
electrons
14.8 %
electrons 3
25.3 deg
electrons"
74.4 cm
electrons 3
< 2.5 %
electrons and muons
2.5 %/ v /E(GeV) + 0.5 %
electrons (estimated)
v x a uncertainties. The uncertainties caused by the cross sections and nuclear effects are estimated to be < 3.6% and < 3 % for CC and NC reactions respectively, i.e., small numbers thanks to the cancellation. The experimental results are summarized in Table IV, in which the range of observed momenta and the exposure (Nt x ;0t,s in Eq. (2) in units of kt-yr) are shown. Note that the observed number of events is approximately proportional to the exposure. As one sees, Frejus and NUSEX, both employing fine-grain iron-calorimeters, obtained results consistent with expectation, while Kamiokande and 1MB with large waterTable II. Effects of uncertainties in the neutrino cross sections on e-like yields, \i-like yields and the ratio Nu/Ne in the sub-GeV region (for Super-Kamiokande). The sub-GeV energy range is defined as 100MeV/c— 1330MeV/c for e-like events and 200MeV/c— 1330MeV/c visible momentum for \i-like events respectively. The visible momentum of 1330MeV/c approximately corresponds to a muon momentum of 1400MeV/c.
±
where t stands for e or u*, pt the lepton momentum, Ev the neutrino energy, 0 the zenith angle, t0bs the observation time, N, the number of target particles, (j>v(Ev, 0) the neutrino flux, a(Ev, pt) the cross section. F(q^) takes into account nuclear effects like Fermi-momenta of target nucleons, Pauli blocking of recoil nucleons and so on. The summation (±) is done for vt and v7, since observations do not distinguish the lepton charge. The neutrino fluxes (j)Ve(Ev, 0) have been calculated most recently by the Bartol group [12] and Honda et al. [13]. Both calculations agree reasonably well (within 10% for 200 MeV < Ev lOOMeV/c, p^ > 200MeV/c and EviS < 1.33 GeV with obvious notations. The double ratio is then, R:
:
^ d a t a
=
0668+0.024±()052
(u/e)MC
(2)
For the multi-GeV region the numbers of observed events are 386 e-like and 301 u-like, while 352 and 419 are expected, respectively. Multi-GeV stands for fully-contained singlering events with £V;S > 1.33 GeV. Since muons have long ranges in this energy region, they tend to exit the inner detector and hit the outer one, resulting in the low detection efficiency. In order to collect more muons one needs to detect partially-contained (PC) events. Super-Kamiokande observed 374 PC events from 685-day observation, slightly shorter than the observation time of the fully-contained data, which should be compared with the expected number 509. A Monte Carlo simulation tells us that 98% of PC events are produced by charged-current vM interactions. Thus PC events can be added to the multi-GeV u-like sample. The double ratio is,
85
Super Kamiokande Preliminary 736 days
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momentum (GeV/c) 7 data ±0 079 -0.041 R = ((u/tpr /1 M C = °- 663 ±8™ + PC/e)
(3)
Hence Super-Kamiokande has confirmed the small R at both sub-GeV and multi-GeV regions. © Physica Scripta 2000
Fig. 2. R vs pt for fully-contained events observed in the Super-Kamiokande detector, (a) for sub-GeV enents and (b) for multi-GeV events. Dashed lines represent R os pi expected from the assumption of v,,v — x oscillation with Am2 = 3.5 x 10~3 eV2 and sin2 20 = 1. Physica Scripta T85
86
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many events as Kamiokande. Figure 3 shows the zenith angle distributions of e-like and u-like events obtained by Super-Kamiokande. Also shown is dR{©)/d cos © together with the Kamiokande result. The new result on di?(6>)/d cos © is consistent with Kamiokande's. It is clear that there are less u-like events in the upward direction (long L) than expected while the number of downward-going u-like events (short L) is consistent with the expectation. The distortion is not visible in the e-like events. Hence dR(0)/d cos © largely reflects the u-like distribution. Something interesting is indeed happening there. 3.3. Upward through-going Muons
-1
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Fig. 3. Zenith angle (cos 0 ) distributions observed in Super-Kamiokande. (a) electron-like sub-GeV events corresponding to 736 day observation (1607 events). Crossed bands are those expected from no oscillation hypothesis and their widths are the statistical accuracies of the Monte Carlo simulation. The dashed lines indicate those expected from the assumption of v,, — vT oscillation with Am2 = 3.5 x 10~3 eV2 and sin2 20 = 1. (b) same as (a) for muon-like sub-GeV events (736 days, 1617 events), (c) same as (a) for electron-like multi-GeV events (736 days, 386 events), (d) same as (a) for muon-like multi-GeV events (736 days, 301 events) plus partially-contained events (685 days, 374 events), (e) Multi-GeV R observed in Kamiokande. (f) same as (e) for Super-Kamiokande.
(3) The Soudan 2 detector has a capability of determining the track directionality, otherwise is similar with Frejus' fine-grain detector. Soudan 2 observed the small R which apparently did not confirm the NUSEX and Frejus results. Based on the new results, it is safe to say that the small R is now well established. Figure 2 shows R as a function of pi for fully-contained data obtained by Super-Kamiokande. 3.2. Zenith angle distribution The higher the neutrino energy, the better the produced charged lepton follows the neutrino direction. As discussed in Chapter 1, the zenith-angle is a direct measure of its flight length L, and hence neutrino oscillation may manifest itself as a possible distortion of the zenith-angle distribution. Since the shape itself does not depend on uncertainties in the absolute fluxes or cross sections, it is a sensitive way to search for neutrino oscillation. Kamiokande [5] published the zenith angle distribution of the double ratio R, which apparently did not follow the expected shape. Now Super-Kamiokande has 5.5 times as Physica Scripta T85
(thru-muons)
These muons are selected (i) by detecting entering and exiting points in the detector and (ii) by requiring their track lengths longer than a preset length 1^^ corresponding to a minimum energy Em\„. Normally track lengths of thrumuons in a detector are longer than jLmin due to the constraint of through-going. Therefore the detection efficiency in general increases from Emin and reaches a plateau at an energy Emax which is higher than ismin, and 2smax depends on the detector geometry. It was shown in Fig. 1 that parent neutrinos of thru-muons have much higher energies (< Ev > ~ 100 GeV) than those that produce sub-GeV, multi-GeV events or stop-muons. Therefore these muons will provide new and independent information which may shed new light on the origin of the small R and distorted zenith-angle distribution. Now let us discuss the new results. Table V presents the results from Kamiokande [10], MACRO [9] and SuperKamiokande [11]. MACRO is a large underground detector with a size of 12m(W) x 77m(L) x 9.5m(H) located in Gran Sasso. It consists of tracking detectors and scintillation counters. The direction of muons is determined by the time-of-flight information from the scintillation counters. MACRO has an excellent detection efficiency for near-vertical (up and down) muons but the efficiency decreases rapidly as the muon direction becomes horizontal. The detector, however, is thinner than Kamiokande or Super-Kamiokande, and ^ n is correspondingly smaller. The flux of thru-muons is calculated as d < ( £ v , ©) dD.0 dEv
dF(0, E, dQ© dE, X E
f
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Some comments are in order. (1) There are additional parameters ai, a 2 , • • • besides the oscillation parameters sin2 26, Am2. They are related to systematic uncertainties [16]. The most important -0.8 -0.6 -0.4 -0.2 0 one is the normalization factor of the theoretical flux a COS0 a.\. Since we are interested in the double ratios and 3 the shape of the zenith-angle distributions, we set «i Fig. 6. Zenith angle (cos 0) distributions of upward-going stopping muons observed by Super-Kamiokande. (The flux (left figure) and the ratio stopas a free parameter, namely aXl — oo, though a reason-muons/thru-muons (rightfigure),compared with the expected ones from able estimate of o„, is 0.25. no oscillation (solid line) and from vM — vT oscillation with Am2 = 3 2 2 We divide the data in the momentum bins (suffix j) in (2) 3.4 x 10" eV and sin 20 = 1 (dashed line.) such a way that there is a reasonable number of events in each bin. The total number of bins is 70 including stop-muon flux as well as of the ratio stop-u/thru-u the zenith-angle segmentation. (preliminary.) Now we minimize x2 a n d obtain the best fit values, assuming the following three cases: 3.5. Evidence for neutrino oscillation (1) v^ —> vT oscillation, The Super-Kamiokande experiment has revealed the small R * L , = 61.5/67 dof, in the sub-GeV and multi-GeV regions, the deformed sin2 26 = 1.05, Am2 = 2.9 x 10" 3 eV2. zenith-angle distribution in the multi-GeV region and also Constraining sin2 26 = 1, the deformed zenith-angle distribution in the upward (probability = : 0.65), I2- = 62.1/67 dof, 2 2 through-going muons. The experiment has also observed Am = 3.5 x 10"3 eV2. sin 20 = 1, a small ratio of stop-muons to thru-muons. Data are already (2) v, ve oscillation, 2 sufficiently large to quantitatively test the hypothesis of (probability = 8 x 10" 4 ), I - = 110/67 dof, 2 2 neutrino oscillation. sin 26 = 0.98, Am = 3.8 x 10" 3 eV2. Super-Kamiokande has made a quantitative analysis of (3) no oscillation the sub-GeV and multi-GeV data assuming the v^ — vT XL, = 175/69 dof, (probability = 5 x 10~9). oscillation [16]. Sub-GeV and multi-GeV data were comOne immediately notices the following: The no oscillation bined and a global x2 was calculated. The x2 is defined as case is ruled out; The v —>v oscillation is strongly disH e favored; The Vfi—>vT oscillation provides a very good fit 2 2 X = z (sub GeV FC) + z (multi - GeV FC) to all the sub-GeV and multi-GeV data. We have already (8) shown, in Figs. 2 and 3, the best fit estimates for momentum + x2(PC) + E f < and zenith-angle distributions. The agreement is excellent.
| 0-1
Io
Physica Scripta T85
© Physica Scripta 2000
Evidence for Neutrino Oscillation Observed in Super-Kamiokande Next, we calculate x2 for thru-muons and stop-muons combined. The definition of x2 is ,
a?
X
Xthn
itstop
+£*+
(14)
89
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where _ X M A W C O S Q Q - (1 + ai)A^exP'd(cos 0,)) 2 Athru
<X?
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10
(15)
2 _ y ^ ( A W a f c o S 0,-) - (1 + a Q ( l + >?)Afexp'd(CQS 0 , ) ) 2 Xstop — ^ 2 ' i=l °i
ffai = 0.22; for normalization-constrained fit ff, =0.14; for relative systematic error between thru and stop.
It is clear that the case for no oscillation is strongly disfavored and the oscillation provides a good fit. Note that analyses of upward-going muons just correspond to disappearence experiment and do not distinguish between vu—>vT and vu—>-ve oscillations. F i g u r e 7 s h o w s t h e a l l o w e d r e g i o n s o n t h e ( A w 2 , sin 2 26)
plane obtained by the x2 analyses outlined above. The two results are quite consistent and are quantitatively represented by the hypothesis that neutrino oscillation is taking place in atmospheric neutrinos. Finally we elaborate the analysis by combining all the data, namely sub-GeV, multi-GeV, thru-muon and stop-muon. x2 is denned as X2 = z2(sub-GeV FC) + * 2 (multi-GeV FC) + x2(PC) a2 + x 2 (thru-muon) + / 2 (stop-muon) + V^ -4r.
Each x is the same as before except that the expected numbers A^exp'd are expressed as,
© Physica Scripta 2000
10
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Fig. 7. Allowed regions on the (sin 20, Aw2) plane for the v^, -*• vT oscillation derived from the x2 analyses. Left figure; allowed region (68, 90 and 99% CL) obtained from the combined analysis of the sub-GeV and multi-GeV data. The Kamiokande result is also shown. Right figure
allowed region from the thru- and stop-muon data.
AreXp• vT (or Vp -*• ve) oscillation, (with normalization constraint): ^ = 7/13 dof, 2 sin 20 =1.05, Aw 2 : 3.7 x 10" 3 eV2. Constraining sin2 26 = 1, Xln = 8-0/13 dof, sin2 20 = 1, 2 3 2 Aw = 3.2 x 10" eV , (probability = 0.65), (2) no oscillation (probability = 0.02). Xmin = 28.9/15 dof,
AWd(sub - GeV) = (1 +
6 8 % C.L.
10
9 9 % C.L.
Since the neutrino energies responsible to thru- and stop-muons are different by an order of magnitute (see Fig. 1), one has to take into account possible systematic errors caused by the relative uncertainties in the neutrino fluxes and also in the cross sections, n represents these systematic errors. The minimium x2 occurs at the following points.
2
t-
^Vexp'd(thru - muon) = (1 + ai)(l + a 3 )(—~r—J x iVexp'd(sin2 26, Am2, a,), ffa2 = 0.07 ffa3 = 0.07 o-a| = oo, i.e. normalization free (18) Physica Scripta T85
90 ^
Y. Totsuka All these results indicate that the longer the path length of muon neutrinos in Earth, the fewer muon neutrinos are observed. This is exactly what one expects from neutrino oscillation. Detailed analyses have been carried out along this way, which showed that
1
(1) (2) (3) (4) (5)
the no oscillation hypothesis is completely ruled out; data are consistent with v^ ->• vT oscillations; vM -* VsterUe oscillations provide equally good fits; Vn -*• ve oscillations are strongly disfavored; based on a global fit to all the data, one can read from Fig. 8 that the oscillation parameters so determined are; Aw2 = 3.2 ± J j x 10" 3 eV2 and sin2 26 = 1.0 ±g 06 (68 %CL.)
There is no doubt that neutrino oscillation and hence finite neutrino mass has been discovered.
Acknowledgements
sin229 Fig. 8. Allowed region on the (sin2 28, Am2) plane for the v^ -* vT oscillation derived from the global •£• analyses. The dot, solid and dash lines are for 99%, 90% and 68%, respectively.
where 0C4 represents the uncertainty in the spectrum index of the primary cosmic ray flux. Thus (< Ev > /-fib)*4 is the amount of the flux uncertainties at respective mean energy < Ev >. EQ is the normalization factor. 0C2 and 0C3 take into account of the relative uncertainties in cross sections. The minimum x2 occurs at the following points: (or ve) (1) v, normalization constraint): „2. =_ ,6 9 . 4 / 8 2 dof, Zmin nn s i n 2 2 0 = 1.05, Am2
oscillation,
(without
Collaborating institutions are; Institute for Cosmic Ray Research, University of Tokyo; National Laboratory for High Energy Physics (KEK); Bubble Chamber Physics Laboratory, Tohoku University; Department of Physics, Tokai University; Department of Physics, Osaka University; Department of Physics, Niigata University; Department of Physics, Tokyo Institute of Technology; Department of Physics, Gifu University; Department of Physics, Kobe University; Department of Physics, Boston University; Brookhaven National Laboratory; Department of Physics, University of California, Irvine; California State University; George Mason University; Department of Physics, University of Hawaii; Los Alamos National Laboratory; Department of Physics, Louisiana State University; Department of Physics, University of Maryland; Department of Physics, State University of New York, Stony Brook; Department of Physics, University of Warsaw; Department of Physics, University of Wshington; Department of Physics, Seoul National University.
= 3.7 x 10" 3 eV 2 .
2
Constraining sin 20 = 1, X L = 70.2/82 dof, Am2 = 3.2 x 10" 3 eV2, (2) no oscillation X2min = 214.3/85 dof,
sin2 20 = 1, (probability
References 0.82), 11
(probability = 5 x 10" ).
Figure 8 shows the allowed region in the (sin2 26, Am2) space for the v^ -> vT oscillations. 4. Conclusion We have presented the latest results on atmospheric neutrinos from Super-Kamiokande. They can be summarized as follows: (1) Observed muons in the sub-GeV and multi-GeV energy range were fewer than expectation by about 40%. (2) The zenith-angle distribution of those muons showed strong up-down asymmetry, while electrons of similar energies had a symmetric zenith-angle distribution. Muons in the upward direction were about half compared with the downward muons. (3) The observed zenith-angle distribution indicates that upward through-going muons were relatively fewer that those in the horizontal direction. (4) Observed upward-going stopping muons were only about 60 % of expectation.
Physica Scripta T85
Hirata, K. S. etal, Phys. Lett. B 205,416 (1988); Phys. Lett. B 280,146 (1992). Aglietta, M. et al, Europhys. Lett. 8, 611 (1989). Berger, Ch. et al, Phys. Lett. B 227, 489 (1989); Phys. Lett. B 245, 305 (1990); Daum, K. et al, Z. Phys. C 66, 417 (1995). Casper, D etal, Phys. Rev. Lett. 66, 2561 (1991); Becker-Szendy, R. et al, Phys. Rev. D 46, 3720 (1992). Fukuda, Y. et al, Phys. Lett. B 335, 237 (1994). Fukuda, Y. et al, Phys. Lett. B 433, 9 (1998). Fukuda, Y. et al, Phys. Lett. B 436, 33 (1998). Allison, W. W. M. et al, Phys. Lett. B 391,491 (1997); Peterson, E. A., talk presented at the 18th International Conference on Neutrino Physics and Astrophysics, NEUTRIN098, (Takayama, 1998). Ahlen, S. et al, Nucl. Instr. Meth. A 234, 337 (1993); Ambrosio, M. et al., Phys. Lett. B 357, 481 (1995); Phys. Lett. B 434, 451 (1998). Hatakeyama, S. et al, Phys. Rev. Lett. 81, 2016 (1998). Super-Kamiokande collaboration, to be published (1998). Barr, G., Gaisser, T. K. and Stanev, T. Phys. Rev. D 39, 3532 (1989), Agrawal, V. etal, Phys. Rev. D 53,1314 (1996); calculations have been updated several times. Honda, M. et al, Phys. Lett. B 248, 193 (1990); Phys. Rev. D 52, 4985 (1995); calculations have been updated several times. Gaisser, T. K. et al, Phys. Rev. D 54, 5578 (1996). Kasuga, S. et al, Phys. Lett. B 374, 238 (1996). Fukuda, Y. et al, Phys. Rev. Lett. 81, 1562 (1998). 17. Gaisser, T. K. talk presented at The 17th International Conference on Neutrino Physics and Astrophysics, NEUTRIN096, (Helsinki, 1996). 18. Gluck, M. Reya, E. and Vogt, A., Z. Phys. C 67, 433 (1995).
© Physica Scripta 2000
Physica Scripta.Vol. T85, 91-99, 2000
Neutrino Oscillations Eligio Lisi Istituto Nazionale di Fisica Nucleare, Sezione di Bari,Via Amendola 173, 70126 Bari, Italy Received January 29, 1999; accepted August 2, 1999
PACS Ref: 14.60.Pq, 26.65.+t, 95.85.Ry
Abstract Experimental and theoretical works on neutrino oscillations have been recently boosted by new and sometimes unanticipated results from flavor transition searches with solar, atmospheric, and accelerator neutrino beams. In particular, the Super-Kamiokande experiment has found robust evidence for muon flavor disappearance in atmospheric neutrinos, with a preference for Vj, -*• vT transitions. The long-standing evidence for electron flavor disappearance in solar neutrinos (ve -+• v;r) has been confirmed, although the specific oscillation mechanisms remain elusive. Weaker evidence for v ii -*• ve transitions has also been found in accelerator searches. These results globally suggest that all three active neutrinos ve,^iT (and possibly additional sterile neutrinos vs) have mass and are mixed, although an unambiguous theoretical pattern for the neutrino mass matrix has not yet emerged. An attempt is made to highlight the relevant issues in this growing and rapidly evolving field of research.
1. Introduction Understanding the origin and the pattern of the fermion masses represents one of the outstanding problems in contemporary physics, which is made more difficult by the paucity of information in the neutrino sector (as compared with quarks and charged leptons). On the other hand, it is just from this sector that we are moving the first steps beyond the standard model of particle physics [1]. It goes without saying that the issue of neutrino masses is extremely relevant also for our understanding of the Universe, as emphasized in many contributions to this Symposium. Neutrino oscillations [2] represent the most promising tool to access the neutrino mass matrix, given the negative results and the difficulty of direct mass measurements. Reviews of the theory of neutrino oscillations in vacuum and in a matter background can be found in [3] (see also [4] for a recent phenomenological exposition and for a rich bibliography). We discuss mainly the most recent developments after the v'98 Conference [1], and just recall the basic notation to be used in the following. Assuming three-flavor mixing among active neutrinos (sterile neutrinos will be considered later), the flavor and mass eigenstates are related by a unitary matrix £/„•, /ve\
vJ
\vt/
(Uei
=
[/„
Ue2
Up
V£/Xi uz2
£/d\/vi\
E/,3
v2
,
tWVW
with mass(vi, v 2 , V3) = (m\, m2, W3) , conventionally ordered as m\ © Physica Scripta 2000
<m2<m^.
It is useful to parametrize the mixing matrix Uxi in terms of three mixing angles, a>, <j>, and xj/:
where c = cos, s = sin, and we have neglected a possible CP violating phase (that would be practically unobservable in many cases of phenomenological interest). The mixing angles (co,(j),\j/) are also indicated as (#12, #13, #23) in the literature. A complete exploration of the three-flavor neutrino parameter space would be exceedingly complicated. Therefore, data-driven approximations are often used to simplify the analysis (see, e.g., [5] and references therein). One of the most frequently used is: \m\ - m\\ = dm1 -— 1) SG electrons. On the other hand, all the muon samples show a significant slope in the zenith distributions, especially for multi-GeV data. 1 The deficit of upward-going MG muons, as compared with the down-going muons in the same sample, represents the most solid piece of evidence for muon neutrino oscillations. In fact, a strong up-down muon asymmetry cannot be explained by experimental systematics (the detector is intrinsically symmetric) nor by theoretical uncertainties (simple geometry predicts a cos 6 -»• — cos 6 flux symmetry up to small geomagnetic effects). Neutrino oscillations in the vM -*• vx channel can easily reproduce the shape of the muon angular distributions. The subcase of pure v^ - • vT oscillations is obtained by setting to zero the parameters dm2, co, and , so that (Am2, sin2 20) = (m2, sm22i/j). Since the atmospheric muon anomaly is a large effect, the amplitude sin 2 2i^ of the oscillation probability in Eq. (2) is also expected to be large. Fig. 2 [21] shows the effect of vM -» vT oscillations for maximal mixing (sin2 2\j/ = 1) and for representative values of m2. It can be seen that values of m2 in the range 10~ 2 -10~ 2 eV2 can reproduce the slope of the MGu and UPu distributions, and that the SGn distribution prefer values closer to 10~3 eV2. Therefore, we expect the favored oscillation parameters to be close to {m1, sin 2\p) (few x 10~ 3 ,1).
Two-flavor analysis
sin 2(p
s'\n22(p
Fig. 3. Two-flavor oscillation fits to the SK zenith distributions (SG, MG, and UPu combined), (a) Fit for v^, **• vT (0 = 0) in the plane (m2, sin2 2^). The cases \j/ < rc/4 and \ji > n/4 are equivalent, (b) Fit for v,, •**• ve (i/r = 7t/2) in the plane (m2, sin2 2$), for 4> < jt/4. (c) Fit for v,! •«+ ve (i/< = 7t/2) in the plane (m2,sin22 > TI/4. The cases (b) and (c) are different, due to earth matter effects. The limits coming from the CHOOZ experiment are also shown in panel (d), as derived by our reanalysis. The solid and dotted curves correspond to 90% and 99% C.L., i.e., to variations of X2 — Zmin = 4 . 6 1 , 9.21 for two degrees of freedom (the oscillation parameters).
2.3. Interpretation 2.3.1. Two-flavor oscillations. The simplest interpretation of the Superkamiokande atmospheric neutrino data is in terms of pure Vn -*• vT oscillations. The region of oscillation parameters favored by the data is shown in the first panel of Are vM ->• ve oscillations excluded? The answer is yes, for Fig. 3, as derived by a %2 analysis [21]. The value of Xm\„ two independent reasons. Pure v^ ->• ve oscillations are is ~ 1 per degree of freedom, indicating a good fit. obtained by setting to zero 8m2, co, and \jj. The relevant parameters are (m2, sin22(/>), but matter effects distinguish 1 It must be said that, in general, one cannot expect very strong zenith devia- the two cases < TT/4 and <j> > n/4 [21]. The regions allowed tions in the SG data distribution, since the neutrino-lepton scattering angles in the parameter space are shown in the second and third are typically large at low energies (60°, on average) and therefore the flux of leppanel of Fig. 3. The value of / ^ is ~ 2 per degree of freedom tons is more diffuse in the solid angle. © Physica Scripta 2000
Physica Scripta T85
94
Eligio Lisi
in both cases, indicating that this solution is strongly disfavored. The second reason to discard pure v^ -> ve oscillations is that the corresponding allowed regions are independently excluded by the CHOOZ reactor experiment, as shown in the last panel of Fig. 3. Finally, v^ -> vs oscillations (not shown) also represent a viable explanation of the Super-Kamiokande data (see, e.g., [24] and references therein). The allowed region is similar to the vH -> vz case, with some differences due to the presence of matter effects in the oscillations of upgoing neutrinos. Discriminating among v^ ->• vT and vM -*• vs is difficult, in the absence of vT appearance signals. However, the two channels lead to different predictions for the rates of neutral current events in In production processes. Preliminary pion data seem to favor the v^ ->• vT option. 2.3.2. Three-flavor oscillations. The Super-Kamiokande data indicate that the amplitude of vM -»• vT oscillations must be large and that the amplitude of v^ -> ve oscillations must be small (consistently with CHOOZ). Such indications are confirmed by a thorough analysis in terms of three-flavor oscillations [21], which shows that the mixing matrix elements U22 and £/23 must be both close to 1/2, and that the element Uj3 cannot be larger than ~ 0.2, the precise bounds depending on the specific value of m2. The limits on m2 obtained through a three-flavor fit are shown in Fig. 4. It can be seen that values of m2 close to fewxlO - 3 eV2 are favored, with or without inclusion of the CHOOZ data. Probing such relatively low values of m2 will be a real challenge for future long-baseline (LB) experiments, aiming to test the atmospheric v anomaly with accelerator neutrino
Bounds on m 2 for unconstrained 3u mixing 60 r.
..|
,.,,,,,,
:
SK
(30 dota fitted)
:
-
SK +CHOOZ
(31 data fitted)
-
50 -
-
3 0 '; ;
I--"I"
2 0 L10
^ " y "'"'' *
•
• .
4
.-.•!_ 10
•
90 99 % C.L. f ----! limits
•
_
3
m
10 2
2
2
—
— - J _ _ 10
beams oscillating over distances of hundreds of km's [25,26]. The LB option is crucial to test vT appearance. Three-flavor oscillations naturally predict also subdominant ve appearance, so an important test of this interpretation will come from higher-statistics electron samples in SuperKamiokande. 2.3.3. Alternative explanations Although the evidence for oscillations in Super-Kamiokande is rather robust, it is useful to bear in mind other possible phenomena that could explain (part of) the data. Two alternatives have been considered in some detail: neutrino decay [27], and flavor-changing neutral currents [28]. In both cases one can obtain a deficit of u-like events in the lower hemisphere, but the a more detailed analysis [29] seem to show that it is difficult to reproduce closely the data pattern. Therefore, neutrino oscillations still represent the best-fit solution, although one cannot exclude the joint occurrence of other effects at present.
3. Solar neutrinos The long-standing deficit of the observed solar neutrino flux, as compared to the expectations of standard solar models, has represented for many years one of the few pieces of evidence in favor of neutrino oscillations [30]. In fact, it is very difficult to explain the deficit by "stretching" the predictions of the standard solar model or by "massaging" the experimental data [31]. A careful analysis shows that the deficit is inconsistent with standard physics at the level of more than 3• ve channel. Fig. 8 [46] shows the region of mass and mixing favored by such experiment (in gray). It can be seen that the preferred values of Am2 are in the eV2 range, much higher than in the solar or atmospheric case, and more interesting from a cosmologist's point of view. The evidence comes mainly from total rates (i.e., it is flux-dependent), since the statistics is too poor to show possible deviations of event spectral shapes (flux-independent information). However the KARMEN experiment [46], probing the same oscillation channel with comparable sensitivity, has not confirmed the LSND signal (see Fig. 8). It appears that the issue nust be solved by a new experiment, significantly more sensitive to oscillations than LSND and KARMEN, such as Boone at FNAL.
5. Neutrino mass-mixing patterns The three values of Aw2 indicated by solar, atmospheric, and LSND experiments are separated by orders of magnitude, indicating the possible occurrence of very different oscillation frequencies. Since three neutrinos can accommodate only two independent frequencies, not all the data can be explained at the same time with active neutrinos. Either some data have to be sacrificed, or a fourth (sterile) neutrino must invoked to provide a third frequency. Here no attempt is made to review the growing literature on the subject; © Physica Scripta 2000
10 "^
10"'
-,
1
sin" 2 9 Fig. 8. Region of the vH —>• vc oscillation parameter space favored by LSND (gray), together with the zone excluded by KARMEN (to the right of the leftmost curve) [46]. The two experiment are basically in contradiction. Also shown are the limits placed by earlier oscillation searches at accelerator (CCFR, BNLE776) and reactors (Bugey).
the reader is referred to [4,47] as starting points for the bibliography. 5.1. Four neutrinos With four neutrinos (3 active + 1 sterile) it is possible to accommodate solar, atmospheric, and LSND data. It turns out that the four mass eigenstates must be arranged in two almost decoupled doublets (responsible for solar and atmospheric neutrino oscillations), separated by a large mass gap (responsible for LSND oscillations). Solar oscillations can be either ve -> vT or ve -*• vs; atmospheric neutrino oscillations have to be, correspondingly, either Vn -*• vs or vR ->• vT. The present data are unable to distinguish among these two cases, but future experiments could. This scenario is very interesting phenomenologically, however it should be emphasized that it depends on the assumption that the LSND experiment is right and KARMEN is wrong. Only future experiments can resolve this issue. 5.2. Three active neutrinos The most popular three-neutrino scenarios discard the LSND data and assume only solar and atmospheric neutrino oscillations (although other choices are possible). In this case, it can be proven that solar neutrino basically measure the parameters (dm2, a>, ) = {dm2, t/ 2 ; ), while atmospheric neutrinos probe (m2, \j/,<j)) = (m2, U23). Physica Scripta T85
98
Eligio Lisi
All experiments are consistent with small values of (j> References (<j) ~ 0). Atmospheric neutrinos indicate that if/ must be large 1. Neutrino '98, Proceedings of the XVIII International Conference on (i/f ~ TI/4) in order to obtain large v^ ->• vT oscillations. Solar Neutrino Physics and Astrophysics, Takayama, Japan, June 1998, neutrinos still allow several options for co; for instance, co to appear. See also the scanned transparencies, available at the should be very small (co ~ 0) for the small mixing MSW URL http://www-sk.icrr.u-tokyo.ac.jp/nu98/scan/. solution, while it should be large (co ~ TI/4) for vacuum oscil- 2. Pontecorvo, B., Zh. Eksp. Teor. Fiz. 53, 1717 (1967) [Sov. Phys. JETP 26, 984 (1968)]; Maki, Z., Nakagawa, M. and Sakata, S., Prog. Theor. lations; the corresponding mixing matrices have then the Phys. 28, 870 (1962). approximate textures: t£(MSW)~
w
/l 0 0 1/2 VO 1/2
0 \ 1/2 , 1/2/
1/2 1/4 1/4
0N 1/2 1/2,
1/2 1/4 1/4
(up to small additional corrections). So we can already narrow the possible patterns of neutrino masses and mixings! Needless to say, the literature on possible theoretical models producing the patterns above, and their allowed variations, is exploding after the recent Super-Kamiokande results, and we expect to learn a lot in this field as further data will help to discriminate the many available options. 6. Conclusions and prospects This is an exciting time for neutrino physics. The evidence for oscillations found by the Super-Kamiokande atmospheric v experiment is solid and represents now a "fixed point" in the field. The values of the mass/mixing parameters that fit such data are already well constrained, but we still need to identify the oscillating partner (vT or vs), to assess the amplitude of vM -» ve subdominant oscillations, and to refine the theoretical flux calculations. The solar neutrino deficit is also a persistent evidence, but a clear interpretation has not emerged yet. The most likely solutions involve oscillations in vacuum or in matter, with rather different consequences for the structure of the signal in the time/energy domain. Therefore, these options can be experimentally tested and discriminated, although it might require some time to collect sufficiently accurate data and to assess the oscillation pattern unambiguously. Great help will be provided by experiments such as SNO and Borexino, as well as by higher statistics data from Super-Kamiokande. Solar modelists and nuclear physicists should also try to estimate the hep flux contribution with smaller uncertainties. The LSND claim persists, but is at variance with the KARMEN experiment. A new, more sensitive experiment is needed to (dis)prove this claim. The mass-mixing parameters begin to be rather constrained, within relatively few options. Models that generate the possible textures for the neutrino mass matrix are flourishing. From both the experimental and the theoretical point of view, the field of neutrino oscillations appears to be in rapid evolution and open to unanticipated, challenging new results. Acknowledgements I am indebted to G. L. Fogli, D. Montanino, A. Marrone, G. Scioscia, and A. Palazzo, for useful discussions and for collaboration on the subject of this talk. Physica Scripta T85
3. Bilenky, S. M. and Petcov, S. T., Rev. Mod. Phys. 59, 671; Kuo, T. K. and Pantaleone, J., Rev. Mod. Phys. 61, 937; Mikheyev, S. P. and Smirnov, A. Yu., Prog. Part. Nucl. Phys. 23, 41 (1989). 4. Bilenky, S. M., Giunti, C. and Grimus, W. hep-ph/9812360. 5. Fogli, G. L., Lisi, E., Montanino, D. and Scioscia, G., Phys. Rev. D 56, 4365 (1997). 6. Wolfenstein, L., Phys. Rev. D 17, 2369 (1978); Mikheyev, S. P. and Smirnov, A. Yu., Yad. Fiz. 42, 1441 (1985) [Sov. J. Nucl. Phys. 42, 913 (1986)]. 7. Kamiokande Collaboration, Hirata, K. S. et al, Phys. Lett. B 205,416 (1988); 280, 146 (1992). 8. Kamiokande Collaboration, Fukuda, Y. et al, Phys. Lett. B 335, 237 (1994). 9. 1MB Collaboration, Casper, D. etal, Phys. Rev. Lett. 66, 2561 (1991); Becker-Szendy, R. et al., Phys. Rev. D 46, 3270 (1992). 10. Soudan2Collaboration, Allison, W. W. M. etal, Phys. Lett. B391,491 (1997). Kafka, T., in TAUP'97, Proceedings of the 5th International Conference on Topics in Astroparticle and Underground Physics (Gran Sasso, Italy, 1997), ed. by A. Bottino, A. Di Credico and P. Monacelli, Nucl. Phys. B (Proc. Suppl.) 70 (1999), p. 340. 11. Totsuka, Y. these Proceedings. 12. Kajita, T., Report hep-ex/98010001, to appear in Neutrino '98, [1]. 13. Super-Kamiokande Collaboration, Fukuda, Y.etal., Phys. Lett. B 433, 9 (1998). 14. Super-Kamiokande Collaboration, Fukuda, Y. et al., ICRR Report No. 418-98, hep-ex/9805006, submitted to Phys. Lett. B. 15. Super-Kamiokande Collaboration, Fukuda, Y. et al., Phys. Rev. Lett. 81, 1562 (1998). 16. Honda, M., Kajita, T., Kasahara, K. and Midorikawa, S., Phys. Rev. D 52, 4985 (1995). 17. Agrawal, V., Gaisser, T. K., Lipari, P. and Stanev, T., Phys. Rev. D 53, 1314 (1996). 18. Kamiokande Collaboration, Hatakeyama, S. et al., Phys. Rev. Lett. 81, 2016 (1998). 19. Peterson, E., for the Soudan2 Collaboration, in Neutrino '98 [1], to appear. 20. MACRO Collaboration, Ambrosio, M. et al, Phys. Lett. B 434, 451 (1998); F. Ronga, Report hep-ex/9807005, in Neutrino '98 [1]. 21. Fogli, G. L., Lisi, E., Marrone, A. and Scioscia, G., hep-ph/9808205, to appear in Phys. Rev. D (Feb. 1999). 22. CHOOZ Collaboration, Apollonio, M. et al, Phys. Lett. B 420, 397 (1998). 23. Bemporad, C. for the CHOOZ Collaboration, in Neutrino '98 [1], to appear. 24. Gonzalez-Garcia, M. C , Nunokawa, H., Peres, O. L. G., Stanev, T. and Valle, J. W. F., Phys. Rev. D 58,033004 (1998); Foot, R., Volkas, R. R. and Yasuda, O., Phys. Lett. B 421, 245 (1998). 25. Pietropaolo, F., in Neutrino '98 [1], to appear. 26. Fogli, G. L. and Lisi, E., Phys. Rev. D 54, 3667 (1996). 27. Barger, V., Learned, J. G. Pakvasa, S. and Weiler, T. J., astroph/9810121 28. Gonzalez-Garcia, M. C. et al, hep-ph/9809531. 29. Lipari, P. and Lusignoli, M., hep-ph/9901350. 30. Bahcall, J. N., "Neutrino Astrophysics" (Cambridge University Press, Cambridge, 1989). 31. Hata, N. and Langacker, P., Phys. Rev. D 56, 6107 (1997). 32. Bahcall, J. N., Krastev, P. I. and Smirnov, A. Yu., Phys. Rev. D 58, 096016 (1998). 33. Super-Kamiokande Collaboration, Fukuda, Y. etal, hep-ex/9812011. 34. Bahcall, J. N. and Krastev, P., hep-ph/ 9807525, to appear in Phys. Lett. B. 35. Fogli, G. L., Lisi, E., Montanino, D. and Palazzo, A. updated solar neutrino analysis after the Conference Neutrino '98 (unpublished). 36. Bahcall, J. N., Basu, S. and Pinsonneault, M. H., Phys. Lett. B 433, 1 (1998). © Physica Scripta 2000
Neutrino Oscillations 37. 38. 39. 40.
McDonald, A., for the SNO Collaboration, in [1]. Oberauer, L., for the Borexino Collaboration, in [1]. Fogli, G. L., Lisi, E. and Montanino, D., Phys. Lett. B 434, 333 (1998). Fad, B., Fogli, G. L., Lisi, E. and Montanino, D., University of Bari Report BARI-TH-299-98, hep-ph/9805293, to appear in Astropart. Phys. 41. Fogli, G. L., Lisi, E. and Montanino, D., Phys. Rev. D 54, 2048 (1996).
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42. Barbieri, R., Hall, L. J., Smith, D. Strumia, A. and Weiner, N., University of Pisa Report IFUP-TH-25-98, hep-ph/9807235. 43. Barger, V. and Whisnant, K., hep-ph/9812273. 44. Fogli, G. L., Lisi, E. and Scioscia, G., Phys. Rev. D 52, 5334 (1995). 45. LSND Collaboration, Athanassopoulos, C. et al., Phys. Rev. C 54 2685 (1996); White, D. H., in [1], 46. Karmen Collaboration, Zeitniz, B. et al, in [1]. 47. Smirnov, A. Yu., hep-ph/9901208.
Physica Scripta T85
Physica Scripta.Vol. T85, 100-105, 2000
Primary Cosmic Rays, Antiprotons and Atmospheric Neutrinos* T. K. Gaisser Bartol Research Institute, University of Delaware, Newark, De 19716 USA Received January 19, 1999; accepted August 2, 1999 PACS Ref: 95.85.Ry
Abstract A series of recent measurements of protons and a-particles is providing an improved determination of the normalization and shape of the cosmic-ray spectrum. This is a necessary component for a more precise calculation of production of antiprotons in the interstellar medium and of neutrinos in the atmosphere. From this perspective, I review calculations of the atmospsheric neutrino beam for neutrino oscillations and of the equilibrium antiproton spectrum in interstellar space.
1. Introduction Several experiments designed to measure antiprotons above the atmosphere in the energy range from below 1 GeV to several GeV also measure the primary spectrum of protons and helium up to ~ 100 GeV. In addition, in several cases measurements of muons have been made on the ground and during ascent with the same detectors. The flux of muons, especially at high altitudes, is related very directly to the atmospheric neutrinos. Neutrinos in the GeV energy range are produced by primary cosmic rays with a wide range of energy, but 5 to 100 GeV/nucleon is most important for the neutrinos that show evidence for oscillations in Super-Kamiokande [1]. Table I summarizes the various detectors and dates on which they were flown. Interpretation of evidence for neutrino oscillations depends in part on the normalizaton of the neutrino flux, which in turn depends on the primary spectrum. What is observed in the detectors is the rate of neutrino interactions as manifested by charged particles produced above the detector threshold. The most numerous events are quasi-elastic, charged-current interactions in which a recoil nucleon and a single lepton with a flavor corresponding to that of the incident neutrino are produced. For the water detectors, which have the greatest statistics, recoil protons are rarely above Cherenkov threshold. More complex events with pion production are also observed. Early experiments focussed on the ratio of electron-like to muon-like events in the GeV range; that is, on the ratio (ve + v e )/ 0v + v^), which was found to be significantly higher than expected [2-4]. If it could be shown that the calculated flux of neutrinos gives the observed rate of electron-like events but predicts more muon-like events than observed, then this would indicate vM -• vT oscillations. If, however, the calculation leads to a prediction that is below the observed rate of ve interactions but still above the observed v^ interactions, then this would suggested V/i «* ve oscillations. In fact, there is an excess of electron-like events [5] as compared to predictions [6,7], *Talk given at the Nobel Symposium "Particle Physics and the Universe", August 20-25,1998. Physica Scripta T85
but the preferred interpration of the anomaly is not ve •«-» v^. For one thing, the CHOOZ reactor experiment [8] rules out a large mixing of ve in the range of parameter space favored for explaining the atmospheric neutrino anomaly. More importantly, Superkamiokande has measured the angular distribution of both electron-like and muon-like events as a function of energy. The evidence favors oscillations that involve predominantly v^ rather than ve. Because of the large assumed systematic uncertainty in the normalization of the neutrino fluxes, this single constraint has little weight in the fit which involves approximately 70 degrees of freedom when all angular, energy and flavor bins are accounted for. After reviewing the current improved state of the measurments of the primary spectrum in Section 2, I discuss atmospheric neutriinos in Section 3. The normalization and shape of the primary cosmic-ray spectrum in approximately the same (~ 10 to ~ 100 GeV/nucleon) energy range also determines the production of ~ GeV antiprotons in the interstellar gas in the disk of the galaxy. These secondary antiprotons are interesting as a probe of cosmic-ray propagation, as a beam for studying charge sign-dependent solar modulation and as the background for any primary antiprotons that may exist. (Examples of primary p could be products of neutralino annihilation in the halo of the galaxy, evaporation from primordial black holes or cosmic rays from distant anti-matter galaxies.) I discuss antiprotons in Section 4.
2. Primary spectra Before 1991 the standard reference for the primary spectrum up to 100 GeV/nucleon was the work of Webber et al. [9]. This was based on two balloon flights, one in 1976 and one in 1979, in which the spectra of hydrogen and helium were measured and compared. The LEAP experiment [10] flew in 1987 during solar minimum. It covered a similar
Table I. Measurements of primary cosmic-rays, pheric muons and cosmic-ray antiprotons.
Webber LEAP MASS IMAX CAPRICE BESS HEAT
atmos-
year flown
Primary
Muons
Antiprotons
'76,79 '87 '89,'91 '92 '94 '95,'97 '94,'95
p,He [9] p,He [10] P.He [29] p,He[ll] p,He [12] p[13]
_ -
_
-
[27,29] [30] [31] [32] [33]
[39] [42] [40] [41] [43]
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© Physica Scripta 2000
Primary Cosmic Rays, Antiprotons and Atmospheric Neutrinos energy range with the same spectrometer in a different configuration. The LEAP experiment gave results with a normalization for protons about 50% lower than the Webber results. The difference is larger than the uncertainty of either measurement and therefore implies the existence of systematic uncertainties that have not been fully understood. Since the atmospheric neutrino flux is proportional to the normalization of the primary spectrum, there is a corresponding ambiguity in the calculated flux of atmospheric neutrinos. This was the situation until about two years ago when a series of magnetic spectrometer experiments started to appear. The results of these more recent experiments support the lower normalization of the LEAP measurement. In Fig. 1 and Table I I summarize the measurements of primary spectra of protons and helium, indicating in each case the date(s) on which the balloons were flown. The IMAX [11] and CAPRICE [12] groups used modified versions of the same magnetic spectrometer as in Refs. [9] and [10], but they were designed to provide two independent mearurements of each particle trajectory through the spectrometer so that efficiencies could be determined with greater certainty. The most recent result is from the BESS group [13], which uses a completely different spectrometer and magnet with cylindrical geometry [14]. The BESS results also are in good agreement with the LEAP measurements. The higher energy data in Fig. 1 from Refs. [15-18] is obtained with calorimeters rather than spectrometers, and may therefore have larger systematic uncertainties.
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Et0t , GeV/nucleon Fig. 1. Spectra of hydrogen (top panel) and helium (lower panel). Open circles show data of Webber [9]; inverted triangles, LEAP [10]; crosses, IMAX [11],filledsquares, MASS91 [29]; stars, CAPRICE [12]; triangles [15]; piusses [16] open squares [17]; diamonds [18]. Solid lines show the spectra used in the calculation of Ref. [6]; dashed lines show the input spectra for the calculation of Ref. [7].
geomagnetic cutoffs, 7Z, and the yield of neutrinos per incident nucleon, Y(E, Ev). Eq. (2) shows the structure of the calculation for v, = ve, ve, v^ or v^:
