Astrophysics II: Stellar Structure / Astrophysik II: Sternaufbau

838 Pages·1958·15.816 MB·English-German-French

by  Marshal H. Wrubel, H. C. Arp, G. R. Burbidge, E. Margaret Burbidge, Hans E. Suess, Harold C. Urey, Lawrence H. Aller, P. Ledoux, Th. Walraven, Armin J. Deutsch, E. Schatzman, Cecilia Payne-Gaposchkin, F. Zwicky (auth.)

ENCYCLOPEDIA OF PHYSICS
EDITED BY
S. FLUGGE
VOLUME LI
ASTROPHYSICS II: STELLAR STRUCTURE
WITH 197 FIGURES
SPRINGER-VERLAG
BERLIN· GOTTINGEN . HEIDELBERG
1958
HANDBUCH DER PHYSIK
HERAUSGEGEBEN VON
S. FLOCCE
BAND LI
ASTROPHYSIK II: STERNAUFBAU
MIT 197 FIGUREN
SPRINGER-VERLAG
BERLIN· GOTTINGEN . HEIDELBERG
1958
ISBN 978-3-642-45910-8 ISBN 978-3-642-45908-5 (eBook)
DOl 10.1007/978-3-642-45908-5
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© by Springer-Verlag OHG. Berlin· Gottingen· Heidelberg 1958
Softcover reprint of the hardcover 1st edition 1958
Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Vv'arenbezeichnungen llSW.
in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der
Annahme, dafi solche Namen im Sinn der Warenzeichen- und Markenschutz
Gesetzgebung als frei zu betrachten waren und daher von jedermann benutzt
werden diidten.
Inhaltsverzeichnis.
Seite
Stellar Interiors. By Dr. MARSHAL H. WRUBEL, Associate Professor, Indiana Uni
versity, Bloomington/Indiana (USA). (With 25 Figures).
A. Introduction . . . . . . .
I. Definitions. . . . . .
II. Outline of the problem 2
B. The physical problem . . . 5
I. The differential equations of a star in equilibrium. 5
II. The constitutive equations. 15
III. Perturbations 38
c. Particular solutions 42
I. Preliminary results 42
II. The properties of particular models 49
Acknowledgement . . 74
General references. 74
The Hertzsprung-Russell Diagram. By HALTON C. ARP, Assistant Astronomer, Mount
Wilson and Palomar Observatories, Pasadena/California (USA). (With 44 Figures) 75
Introduction. . . . 75
A. Historical resume 77
B. Spectroscopy and photometry. 80
C. The H-R diagram for galactic clusters 89
I. Galactic clusters and the standard main sequence. 90
II. Combining the galactic clusters in the H-R diagram. 101
D. The H-R diagram for globular clusters. . . . . . 107
I. Bright regions of the color-magnitude diagram 108
II. Faint regions of the color-magnitude diagram 114
E. Variable stars in the H-R diagram. . . . . . . . 119
I. Mean spectral types and color indices . . . . 119
II. Zero points of the RR Lyrae and classical cepheids 126
F. Population I and II 128
Bibliography . . . 131
Stellar Evolution. By Dr. E. MARGARET BURBIDGE, Research Fellow, and Dr. GEOFFREY
BURBIDGE, Assistant Professor, Yerkes Observatory, University of Chicago, Williams
Bay/Wisconsin (USA). (With 32 Figures) . . . . . . . . . . 134
General introduction . . . . . . . . . . . . . . . . . . . 134
A. Theory and observation of the evolution of individual stars. 135
I. Formation of stars . . . . . . . . . . . . . . . . 135
II. Gravitational contraction . . . . . . . . . . . . . 157
III. Historical sketch of ideas concerning evolution on and off the main sequence 160
IV. Stars on the main sequence. Observed masses and luminosities of solar neigh
borhood stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
VI Inhaltsverzeichnis.
s.it.
V. Modern theories of evolution along and off the main sequence 172
VI. An empirical approach to evolution beyond the giant and supergiant stages 184
VII. Evolution of the Sun. . . . . . . . . . . . . . . . . . . . .. 191
B. Associations, clusters, and galaxies: Empirical approach to stellar evolution. 195
I. Associations . . . . . . . . . . . . . . . 197
II. H-R diagrams of galactic clusters. . . . . . . 201
III. Color-magnitude diagrams of globular clusters . 213
IV. Luminosity functions of field stars and clusters. 216
V. Stellar evolution on the galactic scale. . . . . 225
C. Interchange of matter between stars and the interstellar medium 238
I. Accretion of matter by stars 238
II. Mass loss from stars. . 241
D. Chemical evolution of stars. 249
I. Theory . . . . . . . 249
II. Observations. . . . . 263
E. Evolutionary aspects of stellar rotation, variability, and magnetism 276
I. Rotation of single stars: Discussion of observations 276
II. Stellar variability. . . . . . . . . 278
III. Magnetic fields and stellar evolution 284
References. . . . . . . . . . . . . . . 286
Die Haufigkeit der Elemente in den Planeten und Meteoriten. Von Dr. HANS E. SUESS,
Professor of Chemistry, und Dr. HAROLD CLAYTON UREY, Professor of Chemistry,
University of California, Berkeley/California (USA). (Mit 1 Figur) . 296
A. Einleitung . . . . . . . . . . . . . . . . . . . . . . . 296
B. Empirische Regeln fUr die relative Haufigkeit der Kernsorten . 297
C. Die empirischen Elementhaufigkeiten . . . . . . . . 298
I. Allgemeines . . . . . . . . . . . . . . . . . 298
II. Die Haufigkeit der leichteren Elemente bis Nickel 302
a) Die Elemente von Wasserstoff bis Fluor 302
b) Die Elemente von Natrium bis Nickel . . . . 303
III. Wichtige Haufigkeitsverhaltnisse homologer Elemente. 305
IV. Die Haufigkeiten der mittelschweren und schweren Kerne unter Beriick-
sichtigung der Haufigkeitsregeln . . . . 307
a) Die Elemente von Kupfer bis Yttrium . 307
b) Die Elemente von Zirkon bis Zinn . . . 309
c) Die Elemente von Antimon bis Barium. 310
d) Die Seltenen Erden, Hafnium, Tantal und Wolfram 311
e) Die Elemente von Rhenium bis Gold. . . . . . . 313
f) Quecksilber, Thallium, Blei, Wismut, Thorium und Uran 314
D. Zur Deutung der Haufigkeitsverteilung der Elemente 320
Literatur . . . . . . . . . . . . . . . . . . . . 323
The Abundances of the Elements in the Sun and Stars. By Dr. LAWRENCE HUGH ALLER,
Professor of Astronomy, University of Michigan, Ann Arbor/Michigan (USA). (With
5 Figures) . . . . . . . . . . . . . 324
I. Compositions of normal stars. . . . . 324
II. Isotope abundances. . . . . . . . . 345
III. Composition differences between stars. 346
Bibliography . . . . . . . . . . . . . . 351
Inhaltsverzeichnis. VII
Seite
Variable Stars. By Professor Dr. PAUL LEDOUX, The University of Liege, Institut d' Astro
physique, Cointe-Sclessin (Belgium). and Dr. THEODORE WALRAVEN, Director, Leiden
Southern Station, Transvaal (South-Africa). (With 51 Figures) . 353
A. Introduction . . . . . . . . . . . . . . . 353
I. General remarks . . . . . . . . . . . 353
II. Historical background and development. 354
a) Discovery and observations 354
b) Theory. . . . . . . . . . 357
B. Observational data . . . . . . . . 364
a) Cepheids and RR Lyrae stars 365
P
b) Cephei stars. . . . . . . 398
c) Long-period variable stars 402
d) The RV Tauri stars and yellow semiregular variables. 414
e) The red semiregular and irregular variables 417
f) The explosive variable stars. . 419
g) The R Coronae Borealis stars . . . . 422
h) RW Aurigae and T Tauri stars. . . . 424
i) The spectrum and magnetic variables. 426
j) Stars with extremely rapid light variations 429
C. Theory. . . . . . . . . . . . . . . . . . . . 431
I. General equations . . . . . . . . . 432
a) Equation of continuity (Conservation of mass) . 434
b) Equation of motion (Conservation of momentum) 435
c) Conservation of energy. . . . . . . . . . . . 445
II. Linearized equations . . . . . . . . . . . . . . 452
III. Radial oscillations of a gaseous sphere under its own gravitation 455
IV. Non-radial oscillations of a gaseous sphere under its own gravitation 509
V. Non-linear radial oscillations. . . . . 538
VI. Progressive waves and shock waves. . 554
D. Interpretation and applications of the theory 570
a) The periods. . . . . . . . . . . 574
b) Origin and maintenance of finite oscillations. 585
c) The correlation between the amplitudes and the phases of the velocity and
light curves . . . 588
d) The asymmetry . . . . 592
E. Atmospheric phenomena ... " 593
a) The continuous spectrum 594
b) The line spectrum 598
Bibliography . . . . . . . . . 601
Stellar Stability. By Professor Dr. PAUL LEDOUX, The University of Liege, Institut
d' Astrophysique, Cointe-Sclessin (Belgium). (With 6 Figures) 605
A. Incompressible masses 611
B. Compressible masses. 636
Bibliography . . . 687
Magnetic Fields of Stars. By Dr. ARMIN J. DEUTSCH, Mount Wilson and Palomar Ob
servatories, California Institute of Technology, Pasadena/California (USA). (With
15 Figures) . . . . . . . . . . . . . 689
I. Introduction. . . . . . . . . . 689
II. Observations of magnetic stars. . 690
a) Zeeman effect in stellar spectra 690
b) The peculiar A stars . 694
c) Other magnetic stars. . . . . 711
VIII Inhaltsverzeichnis.
Sette
III. Theory of magnetic stars . . . . . . . . . . . . . 714
a) The generalized dynamo problem . . . . . 714
b) Magnetohydrostatic equilibrium of stars (a infinite) 716
c) Magnetohydrodynamical steady states (a infinite) 720
References ...................... . 722
Theorie des naines blanches. Par Dr. EVRY SCHATZMAN, Professeur a la Faculte des
Sciences de Paris, Institut d'Astrophysique, Paris (France). (Avec 4 Figures) 723
Introduction. . . . . . . . . 723
A. Physique de la matiere dense 724
I. Equation d'etat . . . 724
II. Proprietes thermodynamiques de la matiere dense 729
III. Conductibilite thermique et opacite . 729
IV. Production d'energie . . . . . . . . . 732
B. Constitution interne des naines blanches . . . 739
I. Configurations complHement degenerees. 739
II. Structure des couches superficielles . . . 742
III. Stabilite. . . . . . . . . . . . . . . 746
IV. Origine du debit d'energie des naines blanches 748
C. Conclusion . 750
Bibliographie 751
The Novae. By Dr. CECILIA PAYNE-GAPoSCHKIN, Harvard College Observatory, Cam-
bridge/Massachusetts (USA). (With 5 Figures) 752
I. Statistical information 752
II. Physical behavior. . . . . . . 755
III. Physical parameters . . . . . 762
IV. Relation of novae to other stars 762
V. Theories of the nova outburst 764
Bibliography . . . . . . . . . . . 765
Supernovae. By Dr. FRITZ ZWICKY, Professor of Astrophysics, California Institute of
Technology, Pasadena/California (USA). (With 9 Figures) 766
I. The history of supernovae. . 766
II. List of known supernovae . . 772
III. The properties of supernovae. 772
Sachverzeichnis (Deutsch/Englisch) 786
Subject Index (English/German) 808
Table des matieres (Fran~ais) 831
Stellar Interiors.
By
MARSHAL H. WRUBEL.
With 25 Figures.
A. Introduction.
I. Definitions.
The customary notation of physics is usually carried over to astrophysics.
There are, however, some quantities peculiar to astrophysics.
For example, the physical properties of stars are frequently expressed in
solar units where:
M8 = (1.991 ± 0.002) X 1033 grams;
R8 = (6.960 ± 0.001) X 1010 cm;
L8 = (3·86 ± 0.03) X 1033 ergs/sec.
The material of which stars are made is described in terms of
X = the fractional abundance of hydrogen, by mass;
Y = the fractional abundance of helium, by mass.
For some purposes, it is sufficient to group together all elements heavier than
helium as
Z = the fractional abundance of "heavy elements" or "metals ", by mass.
Z is used both to represent the gross abundance of elements beyond helium and
also the atomic number of a particular element. In general, however, there is
little danger of confusion.
It is also convenient to assign a value of
fl = mean molecular weight
to the material (Sect. 13). The perfect gas law then becomes
k
P=pH eT, (15.10)
where
H = mass of unit atomic weight.
From time to time the concept of stellar populations will be mentioned.
In this connection, the reader is referred to the article on the Hertzsprung-Russell
diagram by H. C. ARP in this volume.
Numerical values have generally been taken from ALLEN 1. All logarithms
are to the base 10 unless otherwise noted.
1 c. W. ALLEN: Astrophysical Quantities. London: Athlone Press 1955.
Handbuch der Physik, Bd. LI.
2 MARSHAL H. WRUBEL: Stellar Interiors. Sects. 1, 2.
II. Outline of the problem.
1. The scope of this article. It is the aim of the theory of the stellar interior
to explain the observed masses, luminosities and radii of stars.
Part of this problem is the study of the formation of stars; that is, the circum
stances under which a dark cloud of dust and gas can form a luminous star. Some
progress has been made along these lines in recent yearsl but it will not be treated
in this article. We will be concerned only with gaseous masses that are already
stars.
We will, however, discuss to some extent the changes a star undergoes during
its "lifetime". This is the study of stellar evolution, which is itself the subject
of another article in this volume 2. The theory of the stellar interior and stellar
evolution have recently become so intricately entwined that it is quite impossible
to discuss one and ignore the other. Nevertheless, our emphasis will be on the
techniques of model construction from which a theory of stellar evolution may
be devised, leaving the synthesis and speculation to the other chapter.
We will mainly be concerned with equilibrium models of stars. The processes
which cause a star to evolve are in most cases sufficiently slow that the stars
may be assumed to pass through a series of equilibrium configurations. These
models may be thought of as representing a star at an instant of time. Ultimately,
time must be introduced as an independent variable, but it is possible to build
evolutionary sequences in an approximate way by estimating the likely changes
in conditions and constructing equilibrium models accordingly. We thereby
replace the time-dependent partial differential equations by ordinary differential
equations and simplify the problem considerably.
Equilibrium models are also used as basic data in studying pulsating stars.
These interesting objects are discussed in another part of this volume 3 and will
not be treated here. It is worth mentioning, however, that those who work in
stellar evolution must soon come to grips with this problem and explain why
pulsation occurs at certain stages.
2. Historical resume and the status today. Although the masses, radii and
luminosities of stars have always been the basic data of the theory of the stellar
interior, the emphasis has been somewhat different in different generations.
At first it was of interest to see if it were possible to construct gaseous spheres in
hydrostatic equilibrium without much concern for the origin of the energy and
assuming a particular form of the equation of state. The milestone of this era
is R. EMDEN'S "Gaskugeln" [lJ, and the models studied were of a type called
polyt ropes (see Sect. 38). The next step forward was marked by A. S. EDDING
TON'S classic "The Internal Constitution of the Stars" [2J, in which the role
of the radiative transport of energy was extensively discussed. Here EDDINGTON
succeeded in establishing a theoretical basis for the observed relation between
mass and luminosity. (In spite of the progress made since this book was written
it remains an informative and delightful volume which no student of this subject
should neglect.)
S. CHANDRASEKHAR summarized, in a complete and rigorous way, the pro
gress to 1939 when his book, "An Introduction to the Study of Stellar Struc
ture" [3J, was published. Here many extensions of previous work appeared,
as well as the detailed theory of white dwarfs.
1 L. G. HENYEY, ROBERT LE LEVIER and R. D. LEVEE: Pub!. Astronom. Soc. Pacific
67,154 (1955).
2 G. R. BURBIDGE and E. M. BURBIDGE, p. 134.
3 P. LEDOUX and TH. WALRAVEN, p. 353.
Sect. 3. Observational data. 3
Simultaneous with the publication of CHANDRASEKHAR'S book, however, the
entire subject took a new turn, for in a classic paper!, BETHE established the
nuclear origin of stellar energy. Thus for the first time not only the mode of
energy transport but also its source could be studied.
In addition to this fundamental physical advance, an important observational
result turned attention from the mass-luminosity relation to the Hertzsprung
Russell diagram. BAADE 2 persuasively showed that this diagram contains in
formation about the types of stellar population and, largely through the work
of SCHWARZSCHILD and HOYLE, the relation between the Hertzsprung-Russell
diagram and stellar evolution has been elucidated 3. SCHWARZSCHILD'S book
on stellar structure, to be published soon, promises to be the next milestone in
the subject.
The work immediately ahead is likely to be strongly influenced by the adoption
of new techniques of high speed computation 4. Our current knowledge of the
detailed processes of absorption and energy production cannot be fully utilized
if one is limited to laborious calculations by hand. The capacity of large electronic
computers makes it possible to include a variety of physical effects and to vary
parameters at will. As these devices become more powerful and as astrophysicists
learn more of the necessary techniques, the complexity of the problems we can
treat will increase. It is not impossible to hope that, aided by these devices, we
may ultimately follow in detail the history of a star from the onset of energy
production until it can no longer radiate.
This technical advance must be accompanied by improved physical theories.
Our knowledge of the mechanism of convective transport is still rudimentary
and the problem of the interactions between convection, rotation and magnetic
fields are only beginning to be studied. Furthermore, lest the impression be given
that the radiative opacity and nuclear processes are very accurately known,
it should be pointed out that the most recently published opacities are only
claimed to be accurate to within 10% 5 and the cross section of the N14 (P, y)
reaction in the carbon cycle is still uncertain 6.
Therefore it is wise to bear in mind that the model stars that will be discussed
in this article are to be viewed as explorations rather than as definitive answers;
and for this reason we will emphasize techniques rather than numerical results.
3. Observational data. Let us consider the basic observational data that our
models will be required to explain: masses, radii and luminosities. The accurate
determination of these quantities for all types of stars is a difficult observational
task but it is not our intention to go into detail. Masses are determined by
gravitational interaction and the most accurate masses are determined from
visual binaries7• This technique is limited to nearby stars, predominantly (if
not exclusively) of BAADE'S Population I, and containing only a limited variety
of spectral types.
1 H. BETHE: Phys. Rev. 55, 434 (1939).
2 W. BAADE: Astrophys. Journ. 100, 137 (1944).
3 For a discussion of the pertinent observations see the article by H. C. ARP in this
volume, p. 75.
4 See, for example, C. B. HASELGROVE and F. HOYLE: Monthly Notices Roy. Astronom.
Soc. London 116,515 (1956).
5 GEOFFREY KELLER and ROLAND E. MEYEROTT: Astrophys. Journ. 122, 32 (1955).
6 E. M. BURBIDGE, G. R. BURBIDGE, W. A. FOWLER and F. HOYLE: Rev. Mod. Phys.
29, 547 (1957).
7 Cf. VAN DE KAMP's contribution on visual binaries, Vol. L, this Encyclopedia.
1*