o o
a m
'-1
HAN
ENCYCLOPEDIA OF PHYSICS EDITED BY S.
FLUGGE
VOLUME
ASTROPHYSICS
IV:
WITH
189
LIII
STELLAR SYSTEMS FIGURES
SPRINGER-VERLAG BERLIN GOTTINGEN HEIDELBERG •
•
1959
HANDBUCH DER PHYSIK HERAUSGEGEBEN VON S.
FLUGGE
BAND
LIII
ASTROPHYSIKIV: STERNSYSTEME MIT
189
FIGUREN
SPRINGER-VERLAG BERLIN GOTTINGEN HEIDELBERG .
1959
'
'
X CLASS
69802 No,
12 APR
?76j[^~"
U-
Uli4.UWftf
i*^-x:-ut*«Bf«
si
^
V- 2.
1
/'
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vervielfaltigen.
© by Springer-Verlag OHG. Berlin Printed in
*
Gottingen
Heidelberg 1959
Germany
Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, daS solche Namen im Sinn der Warenzeichen- und Markenschutz-
Gesetzgebung
als frei
zu betrachten waren und daher von jedermann benutzt
werden durften.
Druck der Universitatsdruckerei H.
Stiirtz
AG., Wurzburg
.
Inhaltsverzeichnis.
^
Kinematical Basis of Galactic Dynamics. By Dr. Frank K.Edmondson, Professor of OI Astronomy and Director of the Goethe Link nh Wrv»tnn, t„^;.„„ ti„.-,..L.-J ington/Indiana (USA). (With 12 Figures)
™
\
General features of observed stellar motions Kinematical considerations
I.
II.
.
.
11
Dynamics By Professor Dr. Berth. LIN db La D Astronomer of the Royal SwedClenCe
Galactic
,
Witlx
'
f
St ° Ckholm Observatory, Stockholm (Sweden).
21
....
Introduction
I.
™°
'
20KgU resf
Mass motions and velocity distribution in the gravitational
II.
21
the Ga-
field of
'
III. Velocity distribution
from
24 statistics of differential orbital
The
IV.
...
motions
57
dispersion of stellar velocities as function of the time 1516111 ° f SPifaI StrUCture and P roblems concerning the evolution of * th^s^t
V '
73 o*r
General references. 99
Radio-frequency Studies of Galactic Structure.
SSST^S^^.^T". 1.
2. 3-
4.
the
„ (jeneral
!
:
5-
7.
8.
Professor of Astro
100 100
,
surveys '.'.'.'.'.'.'. Units Origin of radiation .. Thermal emission Synchrotron radiation Line emission Distribution of neutral hydrogen. "spiral' structure Galactic rotation from observations .
.........
10 ° i0i
^
.
6.
*«^
Tan H. Oort oLrvatory
...
Introduction .
By Dr.
.
102 102
.
1(^4 .'
.
Distribution of ionized hydrogen 10. General radiation from the region close to the galactic' plane! 11. Corona of radio emission around the Galactic System. 9-
.
107 iVc
.'
:;;
.
.
General references.
.
'
'
'
iiq
' '
.
12 6
128
Sta C
terS
i
To r!^
ffij.
By
^ HE1 EN SAWYER HoGG -
a
Wt,£5£r:
'
^
Professor of Astronomy, University of °bSerVat Rich d Hm/OntL^
DaVld DUnlaP
°^
129
A. Introduction B. Galactic clusters I.
II.
.
\
Appearance and apparent distribution Methods of distance determination ...
32
.
III.
'
Stellar content
IV. Color and spectrum luminosity diagrams, evolution and ages V. Motions of stars VI. Some well-known clusters a) Pleiades
3
,*.
.
...
b)
Praesepe.
.
147 14 ° 14 9
.
153
Inhaltsverzeichnis.
yj
Seite
'''
1 ^ T
Coma
Berenices Persei d) The double cluster in Perseus, h and % e) Messier 11 f) Messier 67 Jewel Box g) x Crucis, the c)
154 ^5
^
;
57
1
VII. Moving clusters
16°
VIII. Disruption with time IX. Nebulous and very young clusters
"5
1
Stellar associations
X. C.
l63
Globular clusters l6°
Appearance and apparent distribution
I.
"72
1
Distance determinations
II.
174
Content of globular clusters
III.
185
IV. Motions
V. Masses and
1
densities
%%
19 °
VI. Evolution, age and origin VII. Relation to elliptical galaxies VIII. Clusters associated with extragalactic systems
192 193
194
Appendix A. Catalogue of galactic clusters Appendix B. Catalogue of globular clusters General references
204
HanburyBrown
Reader
™
Robert Discrete Sources of Cosmic Radio Waves. By Macclesfield/Cheshire (Great BriRadio-Astronomy at the University of Manchester, tain).
(With 15 Figures)
Introduction A. Definitions and units
211
B. Techniques of observation C. The radio observations
231
D. Identification
General references Radio Frequency Radiation from External Galaxies
By Bernard
Y
Mills, Senior
and Industrial Research Or-
Principal Research Officer, Commonwealth Figures) ganisation, Sydney/N.S.W. (Australia). (With 22 Scientific
239
Introduction I.
II.
III.
24 °
The Magellanic Clouds a) The H line radiation b) The continuum radiation data c) Comparisons of optical and radio
j™ ** b
24s 25 °
Neighbouring bright galaxies The radio emission of normal galaxies
2 55
260
IV. Radio emission from clusters of galaxies
V. Radio galaxies
274
General references de Vaucouleurs,
By Dr. Gerard Classification and Morphology of External Galaxies. Cambridge/Massachusetts (USA). Research Associate Harvard College Observatory, (With 7 Figures) Introduction I.
II.
Classification
Morphology Qualitative morphology b) Quantitative morphology a)
'
°' -> Uj
VII
Inhaltsverzeichnis.
Seite
General Physical Properties of External Galaxies. By Dr. Gerard de Vaucouleurs, Research Associate, Harvard College Observatory, Cambridge/Massachusetts (USA). (With 36 Figures) 311 •
Introduction I.
b) c)
d) e)
II.
311
Optical properties a)
.
311
Photographic dimensions Integrated luminosities and colours Luminosity and colour distribution Absorption, diffraction and polarisation Spectra and energy distribution
3
1
-..315 319 333 338
Mechanical properties a) Rotation b) Masses of individual galaxies c) Mass luminosity ratio
343 343 348
360 366
Bibliography
Multiple Galaxies. By Dr. Fritz Zwicky, Professor of Astrophysics, California Institute of Technology, Pasadena/California (USA). (With 11 Figures) 373 I.
Historical
373
Morphology of multiple galaxies III. Permanent multiple galaxies IV. The kinematics and dynamics of multiple II.
374 galaxies.
375 Gravitational lenses 384
V. Colliding galaxies as radio sources
385
Bibliography
38Q
Clusters of Galaxies. By Dr. Fritz Zwicky, Professor of Astrophysics, California Institute of Technology, Pasadena/California (USA). (With 5 Figures) 390 I. Introduction 3o II. Well known clusters of galaxies 396 Structure of individual clusters 397 IV. Kinematics and dynamics of clusters of galaxies 406 V. Counts of clusters of galaxies in depth; numbers as a function of angular
III.
size
408
VI. Distribution of clusters of galaxies in breadth VII. Superclustering non-existent VIII.
The universal
redshift, extragalactic distances
409 410
and the methodology of the
study of clusters of galaxies
Bibliography
41
414
Large Scale Organization of the Distribution of Galaxies. By Dr. Jerzy Neyman, Professor of Statistics, Director of the Statistical Laboratory, and Research Professor in the Institute for Basic Research in Science, and Dr. Elizabeth L. Scott, Associate Professor, Statistical Laboratory, University of California, Berkeley/California (USA.) (With 7 Figures) I.
Introduction
416 4^5
Dynamical problem of infinite mass in infinite space Theory of simpje clustering of galaxies IV. Theory of multiple clustering of galaxies General references II.
417
III.
417 443
444
Distance and Time in Cosmology The Observational Data. By Dr. George C. McVittie, Professor and Head of Department of Astronomy, University of Illinois, Urbana, Illinois (USA). (With 9 Figures) 445 I. Observational methods of determining the distances of galaxies 447 II. Time and the age of the universe 485 Acknowledgments 488 :
General references
488
Inhaltsverzeichnis
VIII
Seite
Newtonsche und Einsteinsche Kosmologie. Von Professor Dr. Otto H.L.Heckmann, Direktor der Hamburger Sternwarte, und E.ScHttCKiNG, Hamburg-Bergedorf(Deutschland).
(Mit I.
II.
III.
1
Figur)
489 489
.
Einleitung
491
Newtonsche Kosmologie Einsteinsche Kosmologie
499
Andere kosmologische Theorien. Von Professor Dr. Otto H. L. Heckmann, Direktor der 520 Hamburger Sternwarte, und E. SchCcking, Hamburg-Bergedorf (Deutschland) .
.
1.
Ubersicht
520
2.
521
5.
Kosmologie und Mikrophysik Jordansche Kosmologie Die Theorie des stationaren Universums Milnesche Kosmologie
6.
Mathematischer Anhang
535
3.
4.
Literatur
522 525
530 537
Sachverzeichnis (Deutsch-Englisch)
538
Subject Index (English-German)
552
f
Kinematical Basis of Galactic Dynamics. By
Frank K. Edmondson. With 12
are frennentiy
,«« ™ t'hetZSa, SSS^S^ '^* * 1
brief survey of the
by a description cussion of basic
data of observation
kinemalS^SSS^
1,2 J
A
good
gene^s^
"
'
^^
«) Positions, fl
Prop er ty
^
° nvenient *> d^cuss ^l^toZi equatorial co-ordinates co ord^ T^are ™g« ascension l Tables^ tnJI^S^^^f^ ^/^ « - and ,atoic J& been ublish Graphs* IS).
The
C
W
galactic rn „rrU„ a(
or /J). son*.
and nomograms* a™ a"so Iva^hl. Fundamental positions must be Leisured
(i.e.,
„«„,«, I followed m ° ti0nS and a dis '
TOs
,.'
motions in galactic co-ordinates
declination
(6
^
"^f \
•»:
(and luminosity classes).
stellar
will first
of the general features „f ^k**
^0^)^^^ and
Figures.
with a constant
established,
it is
rate).
1
a^flcTent T,
positions measured at different epochs system the mo tl ons of the
strand
wll
01 ' 8
«
'
syl^T^ZTtLZs^Z^ the
329 stars
aDgUlar
^^cements on
The
^
lar S eSt
kno
™
'" Pe st^fs^^t^yTl peTy^aV^ 6 " Pr ° Per "«**" °'(r,X,P)
= r[a + b'lS m(X + X') + b' sin 2 {X + X")]
(5.
%
13)
This shows that, whatever the velocity distribution, there will in general be a non-zero if-effect, a first harmonic term that imitates the solar motion, and a second harmonic (or Oort term) in radial velocities as a function of longitude in any arbitrary plane. These first order terms are all proportional to the distance. If we introduce the specialization for galactic symmetry, U and V independent
W=
Z and 0, and transfer to cylindrical co-ordinates R, &, Z, with respect to the galactic center, the coefficients (5-12) become of
_
1
/ 1
8M
8L
.
L^
Rjo a,
= ~\ — J__8M_ R d&
dL
Z
dR
dL
8M
R d&
dR
1
_
cos 2
Rjo
^
R
o
/?
cos 2
(5.14)
fj,
cos 2 p,
M
where L is the velocity along the radius, and the velocity of rotation taken to be positive in the clockwise direction. Eq. (5-13) reduces to Q'{r,
X,P)
= r \aQ +
(a|
+ 6|)i sin (2 1 + arc tan
-
(5-15)
There are similar formulae for tangential velocity in longitude and latitude. We consider two special cases: (a) For the case of pure galactic expansion parallel to the galactic plane, M—0, L independent of §, Eq. (5.15) becomes Q'(r,X,P) (b) For the case becomes
=rcos 2 p\±-
is
,
L
dL_
Rio
BR
of pure galactic rotation,
g'(r, X, P)
This
dL
dR^
=rcos 2 p
Rio
cos 2 A
L = 0, M independent
dM
M
BR
Rio
sin 2 A
of
(5.16)
-&,
Eq.
(5.15)
(5-17)
identical with (4.4) for stars in the galactic plane.
The foregoing discussion shows that an observed second harmonic in radial velocities and proper motions is by itself not sufficient evidence for galactic rotation.
Additional independent information
is
required, such as the longitude
Frank K. Edmondson: Kinematical
14
of the galactic center
Basis of Galactic Dynamics.
from radio astronomy data, or the solar motion
Sects. 6,
7.
relative to
the globular clusters. 6. Second order effects. Extension of Milne's discussion to second order terms leads to the following form for the expressions for the radial velocity and
the components of tangential velocity in longitude and latitude: a
The
+ d^cosA + «
cos2A
2
+a
3
coefficients ait b { are functions of
tives of U, V,
and
+ ^sinA + &
cos$X
r, /?,
2
sin2A
+ d3 sin3A.
(6.1)
and the first and second partial derivaand Z at the Sun. The general ex-
W with respect to X, Y,
by Edmondson 1
pressions have been published
.
motion as ordinarily defined is obtained by using (2.1) to (2.3) as equations of condition for a least squares solution. The first harmonic terms of (6.1) for distant stars will combine with the corresponding terms of (2.1) to (2.3) to give a "solar motion" which differs from the "local solar motion". The revised
The
solar
equations
(in galactic
co-ordinates) are
(a) Proper motions:
—
- f-^- - 3 r & cos
4.74 /Si
=
4.74^'
= ^i- cos X sinjS + l~--rQ
sin X
2 /?)
cos X,
cos 2
1
(6.2)
^ sin X sin - ^- cos /3
/?
(6.3)
.
(b) Radial velocities:
q It
=-
SJ cos X cos $
— (Sg — r
2
Q1 cos2 0)
should be noted that only the Y-component
is
sin X cos p
-
S% sin p.
(6.4)
affected.
may be
expressed in terms of the linear velocity or the angular velocity , which is
taken to be positive when the velocity vector detoward the center of the rotation. The galactic
viates Geometrical relationships Fig. 9. for galactic rotation, including a constant deviation from circular motion.
VG = V cos
[90°
-
rotation equations are (a) Radial velocities: {I
h)
~*-
the frequency function in the 1nreadily shown that we have the
d Pi
"5*7 ~rfT
when
A^idt
8H "dqi
\_ -
°
(4-2)
following the motion of an element
"^
dt
dpi)'
^-*>
write
Df :d7=°-
(4.4)
This means that the density of any element in phase space remains constant during its motion. In a non-rotating system x, y, z, we may write, if U, V, are the total velocity-components of a particle,
W
H = i{U* + V
2
+W )-(p(x, 2
y,z,t)
(4.5)
Bertil Lindblad Galactic Dynamics.
28
Sect.
:
5-
and have from Liouville's theorem ~BT
+
+
dx
V
dy
+
8z
This partial differential equation dt
dx _ ~ ~U~—
dy ~T~
+
^
8U
dx
dy
dV
^
dz
dW
u '
^ ">
equivalent with
is
dz_ _ dU _ ~ ~W~ dy_~
dx
dV
_ dW
,. '
dtp_~~ dy
By_ dz
_x
(
'
These are the equations of motion. If I^ = const, 7 2 = const, .../„ = const, are six independent integrals of the motion, we shall then have
=F(/1
f(x,y,z,U,V,W,t)
,
(4.8)
/„,...,/,),
where F is an arbitrary function. This consequence of Liouville's theorem was 1 It was established by Jeans as a basis for stellar first proved by Poincare dynamics in 4915 (Sect. 1). A specification of all the six integrals would mean a detailed description of the actual motions in the system. The importance of the theorem as to the general state of motion in a stellar system depends on the fact that, if the system settles down to a state in which cp is stationary (in a rotating or non-rotating system), certain simple integrals can be found. Moreover, the general complication of the individual motions along the surfaces defined by these integrals in phase space will mean a general process of mixing of matter, so that we can disregard a certain number of the six integrals in the frequency function / to be expected as a result of the mixing process. important case 5. Quasi-stationary system of rotational symmetry. The most stationary and is when above, mentioned
im)+i
nz) J s
(
)
(
+ jiS (w-0^= e (5-1)
admitting that Ix and J 2 may vary with time for an individual star, by local deviations from dynamical equilibrium, we shall assume that the matter in the system is "well mixed". In order to get a definite meaning to these words, we frequency shall assume that the velocity distribution at a given point resembles a function F^, I 2 at least so far that it is symmetrical with respect to the planes there in the velocity space. We need not assume, however, that and 77 Z have then shall We component 0. velocity the about symmetry is rotational Still
=
=
)
at an arbitrary point (R, &,
/7 1
= 0,
Z=
H. Poincar£: Lecons sur
etFils 1911.
z)
of the
0, les
system
77Z
= 0,
at the point considered, f
and
__
, ,)*-i*z*-mn(&-6
