Astronomy and Astrophysics) (Volume 2)

Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology New Series / Editor in Chief: W...

Author: L.H. Aller | I. Appenzeller | B. Baschek | K. Butler | C. de Loore | H.W. Duerbeck | M.F. El Eid | H.H. Fink | T. Herczeg | T. Richter | H. Schneider | M. Scholz | W. Seggewiss | W.C. Seitter | J. Trümper

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Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology New Series / Editor in Chief: W. Martienssen

Group VI: Astronomy and Astrophysics Volume 3

Astronomy and Astrophysics Extension and Supplement to Volume 2 Subvolume B Stars and Star Clusters

Editor: H.H. Voigt Contributors: L.H. Aller, I. Appenzeller, B. Baschek, K. Butler, C. de Loore, H.W. Duerbeck, M.F. El Eid, H.H. Fink, T. Herczeg, T. Richtler, H. Schneider, M. Scholz, W. Seggewiss, W.C. Seitter, J. Trümper, P. Ulmschneider, R. Wehrse, V. Weidemann

13

ISSN og4z-8011 (Astronomy and Astrophysics)

ISBN 3-540-56080-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-56080-7 Springer-Verlag New York Berlin Heidelberg Library of Congress Cataloging in Publication Data Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie Editor in Chief: W. Martienssen Vol. VIC3B: Editor: H.H.Voigt At head of title: Landolt-Biirnstein. Added tp.: : Numerical data and functional relationships in science and technology. Tables chiefly in English. Intended to supersede the Physikalisch-chemische Tabellen by H. Landolt and R. Biirnstein of which the 6th ed. began publication in 1950 under title: Zahlenwerte und Funktionen aus Physik, Chemie,Astronomie, Geophysik und Tech& Vols. published after v. 1 of group I have imprint: Berlin, New York, Springer-Verlag Includes bibliographies. 1. Physics--Tables. z..Chemistry--Tables. 3. Engineering--Tables. I. Barnstein, R. (Richard), 185z-lg13. II. Landolt, H. (Hans), 1831-lglo. III. Physikalisch-chemische Tabellen. IV. Title: Numerical data and functional relationships in science and technology. QC61.23

502~x2

62-53136

This work is subject to copyright. All rights are reserved, whether the whole or part oftbe material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfdm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of theGermanCopyrightLawofSeptemberg,1g65,initscurrentversion,andpermissionforusemustalwaysbe obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law. 0 Springer-Verlag Berlin Heidelberg1996 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. product Liability: The data and other information in this handbook have been carefully extracted and evaluated by experts from the original literature. Furthermore, they have been checked for correctness by authors and the editorial staff before printing. Nevertheless, the publisher can give no guarantee for the correctness of the data and information provided. In any individual case of application, the respective user must check the correctness by consulting other relevant sources of information. Production: PRODUSERV Springer Produktions-Gesellschaft Cover layout: Erich Kirchner, Heidelberg Typesetting: Thomson Press India Ltd.; Camera ready copy from Redaktion Landolt-BBmstein, Printing: Mercedes-Druck, Berlin Binding: Liideritz & Bauer, Berlin SPIN: 10057805

63/3020 - 5 4 3 a 1 o - Printed of acid-free paper

Darmstadt

Editor H. H. Voigt Universitätssternwarte, Geismarlandstraße 11, D-37083 Göttingen, Germany

Contributors to subvolume VI/3 b L.H. Aller Department of Astronomy, University of California, 405 Hilgard Avenue, Los Angeles, CA 90024-1562, USA Planetary nebulae

M.F. El Eid Universitätssternwarte, Geismarlandstraße 11, D-37083 Göttingen, Germany Stellar structure and evolution

I. Appenzeller Landessternwarte, Königstuhl, D-69117 Heidelberg, Germany Protostars, pre-main sequence objects

H.H. Fink Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany Compact objects, X-ray and γ-ray sources

B. Baschek Institut für Theoretische Astrophysik, Tiergartenstraße 15, D-69121 Heidelberg, Germany Physics of stellar atmospheres

T. Herczeg Department of Physics and Astronomy, University of Oklahoma, 440 West Brooks, Norman, OK 73019-0225, USA Double stars

K. Butler Universitäts-Sternwarte, Scheinerstraße 1, D-81679 München, Germany Physics of stellar atmospheres

T. Richtler Universitätssternwarte, Auf dem Hügel 71, D-53121 Bonn, Germany Star clusters and associations

C. de Loore Astrophysical Institute, Pleinlaan 2, B-1050 Brussels, Belgium Stellar structure and evolution

H. Schneider Universitätssternwarte, Geismarlandstraße 11, D-37083 Göttingen, Germany Magnitudes and colors

H.W. Duerbeck Astronomisches Institut der Westfälischen Wilhelms-Universität, Wilhelm-KlemmStraße 10, D-48149 Münster, Germany Variable stars

M. Scholz Institut für Theoretische Astrophysik, Tiergartenstraße 15, D-69121 Heidelberg, Germany Physics of stellar atmospheres

VI

Contributors

W. Seggewiss Observatorium Hoher List der Universitätssternwarte Bonn, D-54550 Daun Star clusters and associations W.C. Seitter Astronomisches Institut der Westfälischen Wilhelms-Universität, Wilhelm-KlemmStraße 10, D-48149 Münster, Germany Variable stars J. Trümper Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany Compact objects, X-ray and g-ray sources

P. Ulmschneider Institut für Theoretische Astrophysik, Tiergartenstraße 15, D-69121 Heidelberg, Germany Physics of stellar atmospheres R. Wehrse Institut für Theoretische Astrophysik, Tiergartenstraße 15, D-69121 Heidelberg, Germany Physics of stellar atmospheres V. Weidemann V.W. Institut für Astronomie und Astrophysik, Universtät Kiel, D-24118 Kiel, Germany White dwarfs

Preface

This subvolume is the second part, 3b, of volume VI/3 "Astronomy and Astrophysics", the first part of which, 3a, has been published two years ago in 1993. Concerning the general concept I therefore refer to the preface of subvolume 3a. The following pages give again a synoptic list of contents for subvolumes VI/2b and VI/3b. Unfortunately some chapters belonging to the present subvolume 3b had to be postponed to the forthcoming subvolume 3c, as it already happened in subvolume 2b. The manuscripts of these chapters did not reach the editor in time. It was impossible to decelerate the publication, even more since the manuscripts of those authors who submitted their contributions in time arrived already three years ago and we could not let them wait even longer. My thank first of all is due to the authors of the various sections. They have had to do the scientific work proper in collecting the data and bear the final responsibilty. They followed the suggestions of editor and publisher without grambling. I also want to thank the editorial staff of Landolt-Börnstein, especially Frau G. Burfeindt and Dr. W. Finger who are responsible for the present LB volumes on astronomy and astrophysics. Thanks are also due to Springer, always being willing to follow our wishes as far as possible.

Göttingen, September 1995

The Editor

Logarithmic scales

Scale

Interval

Correspondence*) interval

ratio

exp

exponential interval

n exp

en

dex

interval in powers of 10

n dex

10n

dB

decibel: interval in 0.1 powers of 10

n dB

100.1n

mag

interval of magnitudes

n mag

10–0.4n

*) Correspondence of logarithmic interval and ratio of intensity variable. 1.000 dex = 10.000 dB = 2.303 exp = – 2.5 mag

Conversion of distance scales

12

0.1

·10+n 10

+5n 0

9 10 9 0.15

8 7

0.2

5

0.25

5

5

3

2.5

0.5

–2

2.5

15

1.5

1.5

7

–3

5

10 9 8

4 –4 3 2.5

6 5

8

·10

18+n

1.2 ·10

18+n

1 ·10–n

1

–5

·10+n

+5n

30

15

2 ·105+n

6 10

5

3

·10+n

15

9 8

2.5

7 10

6

9

5

8 7

2

1.5

4

6 5

3 2.5

4

3

25

20

0.9 3

·1013+n

9

7

0.8

20

4

8

6

2

0.6

2

0.7 4

20

light year

0.3

0.4

3

4

·1013+n

7

10

7 6

25

AU

4

9 8

30

9

p ["]

10

6

inch [ in ]

cm

15

20

–1

6

·1017+n 10

15

7

m–M

20

·10+n

8

parsec [ pc ]

25

·105+n

km

30

·10–n

statute mile

·1018+n

foot [ ft ]

·1018+n

1 ·1017+n

2 ·10

4

3 13+n

·1013+n

Nomogram • Conversion of distance scales With this nomogram, distance data given in different units can be converted into each other. For this purpose we make use of the index line which is always put into horizontal position. Horizontal position is easily realized with the help of the outer scales at left (cm) and at right (km): since the two scales are identical (there is only a difference in the powers of 10 associated with them), the index line is in horizontal position if it crosses these two scales at points which do exactly correspond to each other. When using the nomogram, always a suitable value — positive or negative integer — is to be taken for the number n which appears at top and at bottom of the scales.

Nomogram and text are taken from LB, NS Vol. VI/1 (H. Strassl)

Example: given the distance 3650 pc. The numerical values for "parsecs" are on the right-hand side of 3 the second (from left) double scale. We write 3650 = 3.650⋅10 ; the value n = 3, therefore, is to be used in all scales. We put the index line through the point 3.650 of the parsec-scale; with the help of the outermost scales (cm and km) it is made horizontal. Then we can read off: 3 22 21 8 3.650⋅10 pc = 1.124⋅10 cm = 4.426⋅10 in = 7.529⋅10 AU 4 20 = 1.190⋅10 light years = 3.688⋅10 ft 16 17 = 6.985⋅10 statute miles = 1.124⋅10 km. –4 Moreover, we find the parallax π = 2". 74 ⋅10 and the distance modulus (m – M) = 12.811.

4.2 Magnitudes and colors

Ref. p. 61

1

4 The stars

4.1

see LB VIl2b

4.2

Magnitudes and colors

4.2.0

General remarks

This chapter gives a supplement to some photoelectric systems and an extension to space-borne photometry. General remarks, definitions, photographic photometry and references to these subjects (subsects.4.2.2 to 4.2.4) can be found in LB VI/2b [a]. The present supplements are organized following the notations of the sections given in [a]. All referencesnot given immediately are placed at the end of each subsection.

4.2.1

Data dissemination centers

Many photometric catalogs as well as tables published in major journals can be ordered from the Centre des DonnCes Stellaires (CDS) in Strasbourg. The development of the CDS Archive is described in [9201] and up-dates of the stored data are published frequently in the Bulletin dInformation du CDS. An anonymous account is available from any Internet node via FTP (File Transfer Protocol) to copy catalogs directly (directory pub/cats; for more information see[9202]): ftp cdsarc. u-strasbg.fr or ftp 130.79.128.5 Username: anonymous Password: full name and institute

4.2.2-4.2.4

Landolt-BGmstein New Series V1/3b

see LB VU2b

2

4.2.5 Photoelectric photometry: Introduction

4.2.5

Photoelectric photometry

4.2.5.0

Introduction

[Ref. p. 6

Apart from very special photometric systemsused to match special astrophysical problems and used only by one observer or institute, most photometric systems lost their importance over the last decade.A synopsis of usual systemscan be found in Table 1. A detailed description of the following systemscan be found in LB VI/2b: Photometric system

see[a] subsect.

Photometric system

see[a] subsect.

UBV system(Vilnius) DDO system Borgman 7-color system uvgr system

4.2.5.2 4.2.5.3 4.2.5.5 4.2.5.6

Wood 12-color system Vilnius WBVR system Vilnius UPXYZVS system Johnson et al. 13-color system color systems(Southern hemispehere)

4.2.5.8 4.2.5.9 4.4.5.10 4.2.5.11 4.2.5.13

Filter systems for cometary research (e.g. the IHW filter set) are discussed in LB Vi/3a, subsect. 3.3.3.2. Due to the rapid development of new infrared equipment, IR photometry has become very important during the last decade. Therefore, instead of supplementing the Johnson UBVRIJ...Q system (subsect. 4.2.5.12 in [a]), the author has introduced a new subsect. (4.2.5.18) dealing only with near- and mid-infrared photometry. Here the following systemsare supplemented: Photometric system

in subsect.

Photometric system

UBV system Striimgren uvby (incl. HP) Geneva 7-color system

4.2.5.1 4.2.5.4 4.2.5.7

Walraven VBLUW system UBVRI system (Besselet al.) Cousin V(RI), system

in subsect. 4.2.5.14 4.2.5.15 4.2.5.15

On the other hand, the rapid development of CCDs and their use for photometric purposes have brought about new photometric systems,but as of yet no single system has been established world wide. The principles of photometric reduction of CCD images is given in [h]. In subsect. 4.2.5.19 some technical realizations and a summary of photometric reduction algorithms and software packages are given. In recent years, space-borne astronomy has become more and more important. In subsect.4.2.20 the photometric capabilities of some satellites are summarized. [9iY, 92Y] and referencestherein discuss the accuracy and improvements made in photoelectric photometry. More general articles on this subject can be found in [b, i, k]. The textbooks [c] and fi] provide a modern introduction in photometry. Catalogs of photometric data: general

The general catalog of photometric data (GCPD), published by Hauck and coworkers [90Hl], contains information about 165998 stars observed in one or more of 78 different photometric systems and was completed in July 1989. Table 1 gives a synopsis of the photometric systems taken from Hauck et al., in alphabetical order. The catalog is based on compiled and homogenized data. Most of the homogenized catalogs mentioned in Table 1 are available from the Centre des DonnCes Stellaires (CDS) in Strasbourg including the GCPD. A description of the homogenization of photometric data can be found in [77N, 78N1, 80H]. Land&-BBmstein New Series VI/3b

Ref. p. 61


3

Table 1. Synopsis of photoelectric photometric systems.

The original literature (source in column four) also provides an extended bibliography; unpublished means that thus far (1989), no homogenized data have been compiled. The last column gives the number of stars in the GCPD for the different photometric systems,corresponding roughly to the number of stars published in the literature. Name BCD BVRI Celescope CMT,T,V Cl...C8 DA0 DDO gnkmf g’n’m’b-v 4 I-4 H&i HB IJHKLMN jhk K-line

Origin

Barbier et al. Moffet and Barnes III Deutschman and Davis Washington Barbier-Morguleff Walker and Morris McClure Gyldenkerne Miner Cester Dachs, Schmidt-Kaler Baliunas Striimgren Johnson Bahng Henry and Hesser Neff mvzx3 M45 Ge Ce Haggkvist and Oja narrow bands Alexander nh Landolt Eggen PVE Argue r r8 r9 i Weistrop %4v Becker RGU Wade et al. iI Eggen RI Kron RI Jacobson RQPNMLK Borgmann Andrews Ra Beer R, TDl Carnochan Willstrop ub,bA ubvr Westerlund ubVr Sandage ubygri Bahng UBGR Thuan and Gunn UBV Johnson UBV, Eggen UBV iyz Jennensand Helfer UBVB,B,V,G Geneva UBVGRI Kron UBVri Rydgren UBVRI Johnson UBVRI Neckel and Chini Land&BBmstein .Ncw S&s V1/3b

Reference

Homogenized catalog

Chalonge and Divan, 1952 Moffet and Barnes III, 1979 Deutschman and Davis, 1976 Canterna, 1976 Morguleff and Gerbaldi, 1975 Walker et al., 1971 McClure and Racine, 1969 Gyldenkerne, 1955 Miner, 1966 Cester et al., 1977 Dachs, Schmidt-Kaler, 1975 Baliunas et al., 1975 Crawford and Mander, 1966 Mendoza, 1953 Bahng, 1969 Henry and Hesser, 1971 Neff and Travis, 1967 Haggkvist and Oja, 1987 Jones et al., 1981 Landolt, 1970 Eggen, 1955 Argue, 1967 Weistrop, 1976 Trefzger et al., 1983 Wade et al., 1979 Eggen, 1965 Kron and Smith, 1951 Jacobson, 1970 Borgmann, 1960 Peat, 1964,Andrews, 1968 Beer, 1964 Thompson et al., 1978 Willstrop, 1960 Westerlund, 1966 Sandageand Visvanathan, 1978 Bahng, 1958 Thuan and Gunn, 1976 Johnson and Morgan, 1953 Eggen and Sandage, 1960 Jennens and Helfer, 1975 Golay, 1963 Stebbins and Kron, 1956 Kunkel and Rydgren, 1979 Mendoza, 1963 Neckel and Chini, 1980

[75Ml

WLI [76Dl C9W

unpublished [77Ml

[89M2] [77Ml [77Ml WMI

[80M] WA

Stars in GCPD 732 1150 5724 1000 773 49 6446 1160 106 293 124 56

seeuvby Strijmgren [84M] 2360 81 [77W 485 unpublished 188 P4Ml unpublished 64 unpublished 1216 unpublished 163 831 [77Ml 348 [77Ml 319 P4Ml 23 unpublished 104 F34Ml 8762 [90N3] ibid. 330 unpublished 439 177Ml 1713 WMI 461 ww 53760 [78Tl 221 [77W unpublished 35 11 unpublished 82 [77Ml 49 v34Ml 87116 [89Ml] 10594 F3w 1297 P34Ml 30401 w3Rl 1297 [78N2] 466 wm 6843 ww 252 P36Ll


4

[Ref. p. 6

Table 1. (cont.)

Name

Origin

Reference

Homogenized catalog

Stars in GCPD

UBVR,, U,BV UPXYVTSZ uvby uvby uvby u’ubvv’ UVBGR VBLUW VRL WBVR UP 4 UP up:, @bw

Sandage Cape Vilnius Eggen Kruszewski Strijmgren Smith Tifft Walraven Cousins Vilnius Ducati Tebbe Peton Feinstein Abt and Golsen Mendoza Sinnerstad Bawu Maitzen Newell Wing Cook and Aaronson Lockwood

Sandageand Smith, 1963 Arp, 1956 Kakaras et al., 1968 Eggen, 1978 Kruszewski, 1966 Stromgren and Perry, 1965 Smith, 1968 Tifft, 1958 Walraven and Walraven, 1960 Cousins, 1980 Meistas et al., 1975 Strauss and Ducati, 1981 Tebbe, 1969 Peton et al., 1972 Feinstein, 1974 Abt and Golsen, 1966 Mendoza, 1976 Sinnerstad et al., 1967 Bappu et al., 1962 Maitzen, 1976 Newell, 1973 White and Wing, 1978 Cook and Aaronson, 1989 Lockwood and McMillan, 1971 Eggen, 1967 Tedescoet al., 1982 Faber, 1972 Yorka, 1983 Wood, 1969 Johnson and Mitchell, 1976 ibid.

unpublished [75Nl

unpublished unpublished unpublished unpublished F34Ml

366 7329 2594 4469 104 44891 290 95 11982 3703 101 279 80 94 307 56 402 67 176 1791 174 127 88 99

[77Ml unpublished [77Ml unpublished [77Ml [77Ml [77Ml

783 50 148 26 92 1196 1007

i!jHeI I-’ Aa 4 filters, Hi 8 flux 77-81 78 87 88 103 105 102 65 62 88colors lO-colors l&colors 12-colors 13-colors (88colors)

Eggen Tedescoet al. Faber Yorka Wood Johnson ibid.

W’W

[90N2] [77Ml [9OH2] unpublished [77W [90Nl] unpublished unpublished unpublished

PW WMI F30Ml k30Ml P4Ml

WMI ww

References for Table 1

Abt, H. A., Golson, J. C.: 1966,Astrophys. J. 143,306. Andrews, P. J.: 1968,Mem. R. Astron. Sot. 72, 35. Argue, A. N.: 1967,Mon. Not. R. Astron. Sot. 135,23. Arp, H. C.: 1958,Astron. J. 63, 118. Bahng, J. D. R.: 1958,Astrophys. J. 128, 572. Bahng, J. D. R.: 1969,Mon, Not. R. Astron. Sot. 143, 73. Baliunas, S. L., Ciccone, M. A., Guinan, E. F.: 1975,Publ. Astron. Sot. Pac. 87,969. Bappu, M. K. V., Chandra, S., Sanwal, N. B. Sinvhal, S. D.: 1962, Mon. Not. R. Astron. Sot. 123, 521. Beer, A.: 1964, Mon. Not. R. Astron. Sot. 128, 261. Landolt-Btmstein New Series VU3b


5

Borgman, J.: 1960,Bull. Astron. Inst. Netherlands 15,255. Canterna, R.: 1976,Astron. J. 81,228. Cester, B., Guiricin, G., Mardirossian, F., Puccillo, M., Castelli, F., Flora, U.: 1977, Astron. Astrophys. Suppl. 30, 1. Chalonge, D., Divian, L.: 1952,Ann. Astron. 15,201. Cook, K. H., Aaronson, M.: 1989,Astron. J. 97,923. Cousins, A. W. J.: 1980, South African Obs. Circ. 1, 234. Crawford, D. L., Mander, J.: 1966,Astron. J. 71, 114. Dachs, J., Schmidt-Kaler, T.: 1975,Astron. Astrophys. Suppl. 21, 18. Deutschman, W. A., Davis, R. J.: 1976,Astron. Astrophys. Suppl. 30,97. Eggen, 0. J.: 1955,Astron. J. 60, 55. Eggen, 0. J.: 1965,Astron. J. 70, 19. Eggen, 0. J.: 1967,Astrophys. J. Suppl. 14, 307. Eggen, 0. J.: 1978,Astrophys. J. Suppl. 37,251. Eggen, 0. J.; Sandage,A. R.: 1960, Mon. Not. R. Astron. Sot. 120,79. Faber, S. M.: 1972,Astron. Astrophys. Suppl. 10,201. Feinstein, A.: 1974, Mon. Not. R. Astron. Sot. 169, 171. Golay, M.: 1963,Publ. Obs. Genevestrie A 64, 171. Gyldenkerne, K.: 1955,Astrophys. J. 121, 38. Haggkvist, L., Oja, T.: 1987,Astron. Astrophys. Suppl. 68, 259. Henry, R. C., Hesser,J. E.: 1971,Astrophys. J. Suppl. 23,421. Jacobsen,R. U.: 1970,Astron. Astrophys. 4, 302. Jaschek, M., Egret, D.: 1982, “Catalogue of stellar groups, part I: the earlier group”, Special Publication of the CDS No. 4. Jennens,P. A., Helfer, H. L.: 1975, Mon. Not. R. Astron. Sot. 172, 667. Johnson, H. L., Mitchell, R. I.: 1976,Rev. Mex. Astron. Astrofis. 1, 299. Johnson, H. L., Morgan, W. W.: 1953,Astrophys. J. 117, 313. Jones, D. H. P., Sinclair, J. E., Alexander, J. B.: 1981, Mon. Not. R. Astron. Sot. 194, 403. Kakaras, G., Straizys, V., Sudzius, J., Zdanavicius, K.: 1968,Bull. Vilnius Obs. 22, 3. Kron, G. E., Smith, J. L.: 1951,Astrophys. J. 113, 324. Kruszewski, A.: 1966,Acta Astron. 16,285. Kunkel, W. E., Rydgren, A. E.: 1979Astron. J. 84, 633. Landolt, A. U.: 1970,Astron. J. 75, 337. Lockwood, G. W., McMillan, R.C.: 1971,Publ. Kitt Peak Nat. Obs. 554, 171. Maitzen, H. M.: 1976,Astron. Astrophys. 51, 223. McClure, R. D., Racine, R.: 1969,Astron. J. 74, 1000. Meistas, E., Zdanavicius, K., Straizys, V., Gurklyte, A.: 1975,Vilnius Astron. Obs. Bull. 42, 3. Mendoza, E. E. V.: 1963,Bol. Tonantzinla y Tacubaya 3, 137. Mendoza, E. E. V.: 1976,Rev. Mex. Astron. Astrofis. 1, 363. Miner, E. D.: 1966,Astrophys. J. 144, 1101. Moffet, T. J., Barnes III, T. G.: 1979,Publ. Astron. Sot. Pac. 91, 180. Morguleff, N., Gerbaldi, M.: 1975,Astron. Astrophys. Suppl. 19, 189. Neckel, T., Chini, R.: 1980,Astron. Astrophys. Suppl. 39,411. Neff. J. S., Travis, L. D.: 1967,Astron. J. 72,48. Newell, E. B.: 1973,Astrophys. J. Suppl. 26, 37. Peat, D. W.: 1964,Mon. Not. R. Astron. Sot. 128,435. Peton, A., Bigay, J. H., Garnier, R. Paturel, G.: 1972,Astron. Astrophys. 17,47. Sandage,A., Smith, L. L.: 1963,Astrophys. J. 137, 1057. Sandage,A., Visvanathan, N.: 1978,Astrophys. J. 223, 707. Sinnerstad, U., Arkling, J., Alm, S. H., Brattlund, U.: 1967,Arkiv for Astron. 5, 105. Smith, L. L.: 1968, Mon. Not. R. Astron. Sot. 140,409. Stebbnis, J., Kron, G. E.: 1956,Astrophys. J. 123,440. Landolt-Bb;mstein New Series VU3b

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Strauss,F. M., Ducati, J.: 1981,Astron. Astrophys. Suppl. 44, 337. Striimgren, B., Perry, C. L.: 1965,Astron. J. 71,709. Tebbe, P. L.: 1969,Astron. J. 74, 920. Tedesco,E. F., Tholen, D. J., Zellner, B.: 1982,Astron. J. 87, 1585. Thompson, G. L., Nandy, K., Jamar, C., Monfils, A., Houziaux, L., Carnochan, D. L., Wilson, R.: 1978,“Catalogue of stellar ultraviolet fluxes”, ScienceResearchCouncil publication. Thuan, T. X., Gunn, J. E.: 1976,Publ. Astron. Sot. Pac. 88, 543. Tifft, W. G.: 1958,Astron. J. 63, 127. Trefzger, C. F., Cameron, L. M., Spaenhauer, A., Steinlin, U. W.: 1983, Astron. Astrophys. 117, 347. Wade, R. A., Hoessel,J. G., Elias, J. H., Huchra, J. P.: 1979,Publ. Astron. Sot. Pac. 92, 35. Walker, G. A. H., Andrews, D. H., Hill, G., Morris, S. C., Smyth, W. G., White, J. R.: Publ. Dom. Astrophys. Obs. 13, 415. Walraven, T., Walraven, J. H.: 1960,Bull. Astron. Inst. Netherlands 15, 67. Weistrop, D.: 1976,Astron. J. 81,427. Westerlund, B. E.: 1966,Astrophys. J. 145, 724. White, N. M., Wing, R. F.: 1978,Astrophys. J. 222,209. Willstrop, R. V.: 1960,Mon. Not. R. Astron. Sot. 121, 17. Wood, D. B.: 1969,Astron. J. 74, 177. Yorka, S. B.: 1983,Astron. J. 88, 1816. Sensitivity functions of photometric systems

Fairly often the sensitivity functions of filters used in photometric systemsare given in the form of graphs. Hauck and Mermilliod [76H] have converted these responsesinto tables and published the data of 28 photometric systemswith a constant step for each filter. These tables are available from the CDS (seesubsect.4.2.1) in the directory /pub/cats/vi file 5. Standard stars: general

Catalogs of standard stars: see individual sections. A microfiche of standard stars containing, among other data, photometry in different systemsis published in [85P]. List of spectrophotometric standards: [83G, 92H]. The latter one also includes secondary and tertiary standards. A review of stellar absolute fluxes and energy distributions (incl. Vega) can be found in [85H]. Actual problems of standard stars in different photometric systems, new fluxes and absolute calibrations are published frequently in the Standard Star Newsletter.

References for 42.0 to 4.2.5.0 General references

a Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New SeriesVol. VI/2b (eds. K. Schaifers, H. H. Voigt), Sect. 4.2, Berlin: Springer (1982). b Borucki, W. J., Young, A. (eds.): Proceedings of the workshop on Improvements to Photometry, NASA Conf. Publ. 2350 (1984). c Kitchin, C. R.: Astrophysical Techniques, Bristol: Adam Hilger Ltd. (1984). d Philip, A. G. D., Hayes, D. S. (eds.): Multicolor photometry and the theoretical HR diagram, Dudley Obs. Rep. No. 9 (1975). e Philip, A. G. D. (ed.): Problems of calibration of multicolor photometric systems, Dudley Obs. Rep. No. 14 (1979). Land&-Bdmstein New Series VII3b


7

f Hayes, D. S. et al. (eds.): IAU Symp. 111, Calibration of fundamental stellar quantities, Dordrecht: D. Reidel Publishing Company (1985) pp.223-302,485-569. g Philip, A. G. D. (ed.): Spectroscopy and photometry of population II stars, Van Vleck Obs. Contr. No. 5 (1980). h Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New SeriesVol. Vi/3a (ed. H.H. Voigt), Sect. 1.3, Berlin: Springer (1993). i Butler, C. J., Elliot, I. (eds.): IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments, Cambridge: Cambridge Univ. Press(1993). j Sterken, C., Manfroid, J.: Astronomical photometry. A guide, (1992), ASSL 175, Dordrecht: Kluwer Academic Publishers (1992). k Borucki, W. J. (ed.): Proceedings of the second workshop on Improvements to Photometry, NASA Conf. Publ. 10015(1988). Special references

75M 75N 76D 76H 77M 77N

Magnenat, P.: Bull. Inform. CDS 8 (1975) 17. Nicolet, B.: Astron. Astrophys. Suppl. 22 (1975) 239. Deutschman, W. A., Davis, R. J.: Astron. Astrophys. Suppl. 30 (1976) 97. Hauck, B., Mermilliod, M.: Bull. Inform. CDS 10 (1976) 28. Magnenat, P.: Bull. Inform. CDS 13 (1977) 95. Nicolet, B., Hauck, B., in: Compilation, critical evaluation and distribution of stellar data (eds. C. Jaschek, G. A. Wilkins), Dordrecht: D. Reidel Publishing Company (1977) p.121. 78Nl Nicolet, B.: Astron. Astrophys. Suppl. 31 (1978) 1. 78N2 Nicollier, C., Hauck, B.: Astron. Astrophys. Suppl. 31 (1978) 437. 78T Thompson, G. L., Nandy, K., Jamar, C., Monfils, A., Houziaux, L., Carnochan, D. L., Wilson, R.: Catalogue of stellar ultraviolet fluxes, ScienceResearchCouncil publication (1978). 80H Hauck, B., Mermilliod M.: Astron. Astrophys. Suppl. 40 (1980) 1. 80M Mermilliod, J.-C., Mermilliod, M.: Bull. Inform. CDS 19 (1980) 65. 80N North, P.: Astron. Astrophys. Suppl. 41 (1980) 395. 83G Glushneva, I. N.: Bull. Inform. CDS 24 (1983) 7. 84M Mermilliod, J.-C., Mermilliod, M.: unpublished (1984). 85H Hayes, D. S.: in [fl p. 225. 85P Philip, A. G. D., Egret, D.: in [fJ p. 353 and p. 611. 86L Lanz, T.: Astron. Astrophys. Suppl. 65 (1986) 195. 86M Mermilliod, J.-C., Mermilliod, M.: in prep. (1986). 88R Rufener, F.: 4’hGeneva Photometric Catalogue, Geneva Observatory (1988). 89Ml Mermilliod, J.-C.: cited in [90Hl]. 89M2 Mermilliod, J.-C., Nitschelm, C.: Astron. Astrophys. Suppl. 81 (1989) 401. 90Hl Hauk, B., Nitschelm, C., Mermilliod, M., Mermilliod, J.-C.: Astron. Astrophys. Suppl. 85 (1990) 989. 90H2 Hauck, B., Mermilliod, M.: Astron. Astrophys. Suppl. 86 (1990) 107. 90M Mermilliod, J.-C., Nitschelm, C.: Astron. Astrophys. Suppl. 84 (1990) 133. 90Nl Nitschelm, C., Mermilliod, J.-C.: Astron. Astrophys. Suppl. 82 (1990) 331. 90N2 Nitschelm, C., Mermilliod, J.-C.: Astron. Astrophys. Suppl. 85 (1990) 839. 90N3 Nitschelm, C., Mermilliod, J.-C.: cited in [90Hl]. 91Y Young, A. T., Genet, R. M., Boyd, L. J., Borucki, W. J., Lockwood, C. W., Henry, G. W., Hall, D. S., Pyper Smith, D., Baliunas, S. L., Donahue, R.: Publ. Astron. Sot. Pac. 103 (1991)221. 92H Hamuy, M., Walker, A. R., Suntzeff, N. B., Gigoux, P., Heathcote, S. R., Phillips, M. M.: Publ. Astron. Sot. Pac. 104 (1992) 533. 9201 Ochsenbein, F.: Bull. Inform. CDS 41 (1992) 65. 9202 Ochsenbein, F., Florsch, J., Halbwachs, J.-L.: Bull. Inform. CDS 41 (1992) 83. 92Y Young, A. T.: Astron. Astrophys. 257 (1992) 366. Land&-Bhstein New Series V1/3b

4.2.5 Photoelectric photometry: Johnson UBV and Stromgren uvby system

8

4.2.5.1

[Ref. p. 14

Johnson UBV system

Installation at different sites: ESO, La Silla, Chile: [92L]. Calibration

M, (normal A5 to F5 dwarf and giant stars): [85G]. Selection of larger sets of photometric data

Crawford, D. L., Barnes, J. V., Golson, J. C.: Four-color, HP, and UBV photometry for bright Btype stars in the northern hemisphere, Astron. J. 76 (1971) 1048. Cousins, A. W. J.: UBV photometry of Equatorial Stars, South African Astron. Circ. 8 (1984) 69.

References for 4.2.5.1 85G Grenier, S., Gomez, A. E., Jaschek, C., Jaschek, M., Heck, A.: Astron. Astrophys. 145 (1985) 331. 92L Lindgren, H.: ES0 operation manual No.16 (1992). 4.2.5.2 and 4.2.5.3 see LB VU2b 4.2.5.4

Striimgren uvby system (incl. HB)

Discussion of instrumental effects:[87M]. Discussion of color transformation effects:[92M]. Installation at different sites: ESO, La Silla, Chile [92L]. Extinction at different sites: ESO, La Silla, Chile [92S]. The intensities measured in four photometric bands define three indices, namely the color index b - y (temperature indicator) and the color index differences cl = (u - v) - (u - b) nzI = (u - b) - (b - u)

Balmer discontinuity index, metal-line index.

The Stromgren photometry is often supplemented with 2HP filters: HPwideand the HP,,,, w bands are centered on wavelength of the H/I line at 4860 A with a bandwidth of 150A and 30 A, respectively. The HP index (often called only H/3) is defined as It is free from interstellar and - in the case of simultaneous measurements- from atmospheric extinction effects(under the assumption that the filters are symmetrical on exactly the same central wavelength, a condition seldom met). Transformation from the instrumental to the standard system [66G]: I’=A+B(b-y)(stand)+y(instr), (b-y)(stand)= C+D(b-y)(instr), m,(stand) = E+Fm,(instr)+J(b -~)(stand), c,(stand) = G+Hc,(instr)+I(b -y)(stand).

Landolt-Bbmstein New Series V1/3b

Ref. p. 141

4.2.5 Photoelectric photometry: Strijmgren uvby system

Reddening-free parameters:

9

[m,]=m,+0.32(b-y), [c,] = c1- 0.20(b -y), [u--]=(u--)+1.56(b-y).

Calibration

Intrinsic colors for B-, A- and F-type stars. All stars

B-type stars [78C] (Hfic2.86)

A-type stars [79Cl]

F-type stars [75Cl]

m,=m,+0.32E(b-y) c,=c,-0.20E(b-y)

(b-y),=

2.88>H/?>2.72 6c, s 0.28

2.72>@>2.59 6c, co.280 if HP>2.630 &,1.190, 6c,>O.28

Calibration of G-and K-type dwarfs: [840, 9401. Calibration of A- and early F-type supergiants: [92G]; erratum in [93G]. Calibration of F- and early G-type supergiants: [91G]. More about calibration: [710,740,75B, 75C2,75P, 79C2,79P, 8OC,8801. T,, (A-, B- and F-type stars): [85M]. log g (A-, B- and F-type stars): [85M]. log g (CPl stars): [86D]. Mv (normal B5 to F5 dwarfs and giant stars): [85G]. Analysis of compiled data: [76P, 8OP]. Table 2 gives the standard relations for B-, A- and F-type stars used in the calibration algorithms while Table 3 gives intrinsic indices with reference to spectral types.

Land&-BBmstein New Series VI/3b

10

4.2.5 Photoelectric photometry: Strijmgren uvby system

[Ref. p. 14

Table 2. Standard relations B7Pl.

HB

b-y

ml

Cl

M”

hl

k*l

-6.51 - 5.84 - 5.22 - 4.65 -4.12 - 3.62 -3.17 - 2.75 - 2.36 -2.01 - 1.69 - 1.39 - 1.12 - 0.87 - 0.65 - 0.45 - 0.27 -0.10 0.04 0.18 0.30 0.41 0.51 0.60 0.68 0.76 0.83 0.90 0.97 1.03 1.10 1.17 1.24 1.31 1.39 1.46

0.005 0.017 0.029 0.040 0.046 0.047 0.049 0.055 0.060 0.066 0.072 0.076 0.078 0.079 0.085 0.091 0.094 0.095 0.098 0.103 0.106 0.108 0.108 0.108 0.110 0.112 0.116 0.118 0.120 0.123 0.127 0.131 0.134

- 0.223 -0.103 -0.051 - 0.001 0.045 0.087 0.129 0.170 0.211 0.253 0.295 0.337 0.377 0.418 0.461 0.503 0.546 0.588 0.628 0.665 0.701 0.732 0.763 0.793 0.819 0.840 0.863 0.885 0.906 0.931 0.955 0.980 1.004

2.30 2.40 2.50 2.57 2.64 2.67 2.70 2.73 2.76 2.79

0.220 0.225 0.231 0.235 0.240 0.242 0.244 0.245 0.247 0.247

0.917 0.895 0.873 0.851 0.829 0.812 0.795 0.773 0.751 0.729

B-type stars 2.560 2.570 2.580 2.590 2.600 2.610 2.620 2.630 2.640 2.650 2.660 2.670 2.680 2.690 2.700 2.710 2.720 2.730 2.740 2.750 2.760 2.770 2.780 2.790 2.800 2.810 2.820 2.830 2.840 2.850 2.860 2.870 2.880 2.890 2.900 2.910

-0.134 -0.126 -0.120 -0.118 -0.114 -0.109 -0.105 -0.100 - 0.096 - 0.091 - 0.086 - 0.080 - 0.075 - 0.070 - 0.065 - 0.061 - 0.055 - 0.050 - 0.046 - 0.044 - 0.042 -0.041 - 0.040 - 0.039 - 0.038 - 0.037 - 0.035 - 0.034 - 0.032 - 0.029 - 0.026 - 0.023 - 0.020

0.045 0.055 0.065 0.075 0.080 0.080 0.081 0.085 0.089 0.093 0.098 0.100 0.100 0.100 0.105 0.109 0.110 0.110 0.112 0.116 0.119 0.120 0.120 0.120 0.121 0.123 0.126 0.128 0.130 0.132 0.135 0.138 0.140

2.880 2.870 2.860 2.850 2.840 2.830 2.820 2.810 2.800 2.790

0.066 0.076 0.086 0.096 0.106 0.116 0.126 0.136 0.146 0.156

0.200 0.202 0.205 0.206 0.208 0.207 0.206 0.204 0.203 0.200

- 0.250 -0.128 - 0.075 - 0.025 0.022 0.065 0.108 0.150 0.192 0.235 0.278 0.321 0.362 0.404 0.448 0.491 0.535 0.578 0.619 0.656 0.693 0.724 0.755 0.785 0.811 0.833 0.856 0.878 0.900 0.925 0.950 0.975 1.ooo A-type stars 0.930 0.910 0.890 0.870 0.850 0.835 0.820 0.800 0.780 0.760

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11

4.2.5 Photoelectric photometry: Striimgren uvby system

Ref. p. 141

Table 2. (cont.)

HP 2.780 2.770 2.760 2.750 2.740 2.730 2.720

b-y

ml

0.166 0.176 0.186 0.196 0.206 0.216 0.226

Cl

0.740 0.720 0.700 0.680 0.660 0.630 0.600

0.196 0.192 0.188 0.185 0.182 0.180 0.177

[m,l

4

hl

2.82 2.85 2.88 2.92 2.96 3.03 3.10

0.246 0.245 0.244 0.244 0.244 0.245 0.245

0.707 0.685 0.663 0.641 0.619 0.587 0.555

3.14 3.21 3.29 3.38 3.48 3.60 3.74 3.88 4.04 4.20 4.36 4.52 4.70 4.90

0.244 0.244 0.246 0.248 0.251 0.256 0.263 0.272 0.281 0.292 0.304 0.317 0.332 0.350

0.536 0.513 0.481 0.443 0.411 0.383 0.355 0.327 0.304 0.281 0.258 0.235 0.211 0.188

F-type stars 2.720 2.710 2.700 2.690 2.680 2.670 2.660 2.650 2.640 2.630 2.620 2.610 2.600 2.590

0.222 0.233 0.245 0.258 0.271 0.284 0.298 0.313 0.328 0.344 0.360 0.377 0.394 0.412

0.580 0.560 0.530 0.495 0.465 0.440 0.411 0.390 0.370 0.350 0.330 0.310 0.290 0.270

0.177 0.174 0.172 0.171 0.170 0.171 0.174 0.178 0.183 0.189 0.196 0.204 0.214 0.226

Table 3. Average photometric indices for MK types. MK type

Luminosity HB

BO B0.5 Bl B1.5 B2 B2.5 B3 B4 B5 B6 B7 B8 B9 B9.5

Luminosity

class V (b-y),

m,

cn

m,

co

2.577 2.583 2.596 2.604 2.605

0.058 0.069 0.074 0.084 0.080

-0.10 - 0.07 0.00 0.04 0.10

2.644

0.084

0.32

2.686 2.705 2.707 2.718 2.740 2.796

0.102 0.102 0.105 0.110 0.110 0.120

0.45 0.57 0.55 0.61 0.80 0.96

0.133

1.03

0.174

1.14

HP B-type stars [78C]

0.055 0.074 0.082 0.092 0.096 0.097 0.104 0.100 0.106 0.110 0.107 0.118 0.126 0.134

2.606 2.604 2.609 2.633 2.646 2.650 2.681 2.672 2.701 2.716 2.723 2.748 2.795 2.827

- 0.06 - 0.04 0.02 0.12 0.22 0.25 0.32 0.38 0.42 0.50 0.55 0.66 0.83 0.97

class III (b-y),

A-type stars [79Cl] A0 A2 A3 A4 Landolt-BBmstein New Series V1/3b

2.861 2.885 2.871 2.864

0.029 0.055 0.071

0.154 0.169 0.172 0.184

1.01 1.08 1.08 1.05

2.822 2.869

0.048

12


[Ref. p. 14

Table 3. (cont.)

MK type

Luminosity classV

A5 A7 A8 FO

HP 2.841 2.824 2.789 2.768

@-~1, 0.090 0.107 0.132 0.158

Luminosity class III m. 0.195 0.201 0.194 0.191

co 0.96 0.90 0.87 0.79

HP 2.855 2.823

(b-~), 0.079 0.097

m. 0.191 0.204

co 1.05 1.oo

Catalogs of standard stars

G-, K- and M-type stars in [940]. Cousins, A. W. J.: Secondary standard for the Stromgren uvby system, South African Astron. Circ. 11 (1987) 93. Cousins, A. W. J.: Secondary standard for HP photometry in the E regions, South African Astron. Obs. Circ. 13 (1989) 15. Cousins, A. W. J.: Secondary standard for HP photometry in the Southern hemisphere, South African Astron. Obs. Circ. 14 (1990). Crawford, D. L., Barnes, J. V.: Standard stars for uvby photometry, Astron. J. 75 (1970) 978. Crawford, D. L., Mander, L.: Standard stars for photoelectric HP photometry, Astron. J. 71 (1966) 114. Gronbech, B., Olsen, E. H., Striimgren, B.: Standard stars for uvby photoelectric photometry South of declination t-10, Astron. Astrophys. Suppl. 27 (1966) 155. Kilhenny, D., Laing, J. D.: Secondary uvby standards in Harvard E-regions, Mon Not. R. Astron. Sot. 255 (1992) 308. Kilhenny, D., Menzies, J. W.: Four-color observations of primary and secondary standard stars, Mon. Not. R. Astron. Sot. 222 (1986) 373. Perry, C. L., Olsen, E. H., Crawford, D. L.: A catalog of bright uvbyb standard stars, Publ. Astron. Sot. Pac. 99 (1987) 1184. Philip, A. G. D., Philip, K. D.: Four-color observations of early-type stars. I. Standards and secondary standards, Astrophys. J. 179 (1973) 855. Twarog, B. A.: uvby secondary standards near the South galactic pole, Astron. J. 89 (1984) 523. Selection of larger sets of photometric data

Cousins, A. W. J.: Striimgren uvby photometry of E region stars, Mon. Not. Astron. Sot. Southern Africa 44 (1985) 54. Crawford, D. L.: Four-color and HP photometry of O-type stars, Publ. Astron. Sot. Pac. 87 (1975) 481. Crawford, D. L., Barnes, J. V., Golson, J. C.: Four-color, HP, and UBV photometry for bright Btype stars in the Northern hemisphere, Astron. J. 76 (1971) 1048. Crawford, D. L., Barnes, J. V., Golson, J. C., Hube, D. P.: Four-color and HP photometry for the bright B8-and B9-type stars in the Northern hemisphere, Astron. J. 78 (1973) 73. Gray, R. O., Olsen, E. H.: The calibration of the Stromgren photometric system for A, F and early G supergiants. The observational data, Astron. Astrophys. Suppl. 87 (1991) 541. Gronbech, B., Olsen, E.H.: Four-color uvby photometry for bright 0 to GO type stars South of declination +lO”, Astron. Astrophys. Suppl. 25 (1976) 213. Knude, J. K.: Photoelectric uvby and H/I photometry of 750 A and F stars in 63 Selected Areas with lb] < 30”, Astron. Astrophys. Suppl. 30 (1977) 297. Olsen, E. H.: Four-color photometry of late-type stars, Astron. J. 79 (1974) 1424. Olsen, E. H.: Four-color uvby and HP photometry of A5 to GO stars brighter than 8.3”, Astron. Astrophys. Suppl. 54 (1983) 55. Landolt-BBrnstein New Series VI/3b


Ref. p. 141

13

Olsen, E. H.: Striimgren four-color uvby photometry of GS-type HD stars brighter than mv= 8.6, Astron. Astrophys. Suppl. 102 (1993) 89. Olsen, E. H.: A large, complete, volume-limited sample of G-type dwarfs. I. Completion of Strijmgren uvby photometry, Astron. Astrophys. Suppl. 104 (1994) 429. Perry, C. L.: A catalogue of four-color photometry of late F-type stars, Astron. J. 74 (1969) 705. Perry, C. L.: Interstellar reddening in the Southern hemisphere. I. The uvbyfl observations, Publ. Astron. Sot. Pac. 103 (1991) 494. Schuster, W. J., Nissen, P. E.: Four-color uvby and HP photometry of high-velocity and metal-poor stars. I. The catalogue of observations, Astron. Astrophys. Suppl. 73 (1988) 225. Stomgren, B., Perry, C.: Photoelectric uvby photometry for 1217stars brighter than V= 6.5”, mostly of spectral classesA, F and G, 2”dedition, preprint, Inst. for Adv. Studies, Princeton, NJ (1965). Extension of the Striimgren system

Anthony-Twarog and coworkers [91A] developed a fifth filter centered on Ca H and K for use with the standard uvby system. The filter, called Ca, has a FWHM of = 90 A centered at = ;Z3960. To date two filters are in use. Table 4 gives the transmission of the filters and Fig. 1, the corresponding curves.

Oeal< 0.5 -

Newercalciumfilter

0.4 -

I .g 0.3‘E E s 0.2 -

0.1-

01

3800 3850

3900

I

I

3950

4000

4050 S,4100 Fig. 1. Transmission curves for the Ca filters used to

I-

date.

Table 4. Transmission curves for the Ca filters. A

Ca

PI

Old

3850 3860 3870 3880 3890 3900 3910 3920

1

Land&-BBmstein New Series VU3b

/I

Ca

New

[Al

Old

0.000 0.000

0.000 0.010

0.004 0.015 0.039 0.090 0.211 0.341

0.010 0.030 0.070 0.150 0.260 0.330

3930 3940 3950 3960 3970 3980 3990 4000

0.430 0.472 0.500 0.515 0.495 0.418 0.293 0.170

A

Ca

New

[Al

Old

New

0.360 0.380 0.390 0.400 0.390 0.350 0.250 0.140

4010 4020 4030 4040 4050 4060 4070

0.119 0.090 0.063 0.033 0.010 0.002 0.000

0.070 0.030 0.020 0.010 0.000 0.000 0.000

14


The filter is designed primarily for applications to metal-poor dwarfs and red giants, regions where the metallicity index m, loses some sensitivity. An index hk is defined by replacing v in m, by Ca: hk=(Ca-b)-(b-y). The effect of interstellar extinction are found to be modest and relatively sensitive to spectral types. Observations of 163 in NKprimary standards are given in [91A].

References for 4.254 66G 710 740 75B 75Cl 75C2 75P 76P 78C 79Cl 79C2 79P 80C 80P 83H 840 85G 85M 86D 87M 87P 880 91A 91G 92G 92L 92M 92s 93G 940

Gronbech, B., Olsen, E. H., Stromgren, B.: Astron. Astrophys. Suppl. 27 (1966) 155. Olsen, E. H.: Astron. Astrophys. 15 (1971) 161. Olsen, E. H.: Publ. Astron. Sot. Pac. 86 (974) 80. Breger, M.: Dudley Obs. Rep. No. 9 (1975) 31. Crawford, D. L.: Astron. J. 80 (1975) 955. Crawford, D. L.: Dudley Obs. Rep. No. 9 (1975) 7. Philip, A. G. D., Matlock, L. T.: Dudley Obs. Rep. No. 9 (1975) 45. Philip, A. G. D., Miller, T. M.: Dudley Obs. Rep. No. 12 (1976). Crawford, D. L.: Astron. J. 83 (1978) 48. Crawford, D. L.: Astron. J. 84 (1979) 1858,erratum [8OC]. Crawford, D. L.: Dudley Obs. Rep. No. 14 (1979) 23. Philip, A. G. D.: Dudley Obs. Rep. No. 14 (1979) 35. Crawford, D. L.: Astron. J. 85 (1980) 621. Philip, A. G. D., Egret, D.: Astron. Astrophys. Suppl. 40 (1980) 199. Hilditch, R. W., Hill, G., Barnes, J. V.: Mon. Not. R. Astron. Sot. 204 (1983) 241. Olsen, E. H.: Astron. Astrophys. Suppl. 57 (1984) 443. Grenier, S., Gomez, A. E., Jaschek, C., Jaschek, M., Heck, A.: Astron. Astrophys. 145 (1985) 331. Moon, T. T., Dworetsky, M. M.: Mon. Not. R. Astron. Sot. 217 (1985) 305. Dworetsky, M. M., Moon, T. T.: Mon. Not. R. Astron. Sot. 220 (1986) 787. Manfroid, J., Sterken, C.: Astron. Astrophys. Suppl. 71 (1987) 539. Perry, C. L., Olsen, E. H., Crawford, D. L.: Publ. Astron. Sot. Pac. 99 (1987) 1184. Olsen, E. H.: Astron. Astrophys. 189 (1988) 173. Anthony-Twarog, B. J., Laird, J. B., Payne, D., Twarog, B. A.: Astron. J. 101 (1991) 1902. Gray, R. 0.: Astron. Astrophys. 252 (1991) 237. Gray, R. 0.: Astron. Astrophys. 265 (1992) 704. Lindgren, H.: ES0 operation manual No. 16 (1992). Manfroid, J., Sterken, C.: Astron. Astrophys. 258 (1992) 600. Sterken, C., Manfroid, J.: Astron. Astrophys. 266 (1992) 619. Gray, R. 0.: Astron. Astrophys. 273 (1993) 349. Olsen, E. H.: Astron. Astrophys. Suppl. 104 (1994) 429.

4.2.5.5 and 4.2.5.6 seeLB VIl2b

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4.2.5 Photoelectric photometry: Geneva 7 color system

15

4.2.5.7 Geneva 7 color system General

An updated review of the Geneva multicolor photometric systemcan be found in [80G]. New responsesof the Geneva photometry passbands (to an equiphotonic flux) and their absolute calibration are given in [88R]. Extinction at ESO, La Silla, Chile: [86R]. Catalog

Rufener, F.: Catalogue of stars measured in the Geneva observatory photometric system, 4’h edition, Geneva Observatory (1988). Calibration

Reddening-free parameters X, Y, Z [79C]: X. . . T,,

Y.. .hydrogen lines, Z.. .spectral peculiarities in V band, e.g. II 5200 depletion [8OCl]. -t-1.3764 - 1.2162 -0.8498 -0.1554 -to.8450 +0.3235 -2.3228 +2.3363 +0.7495 - 1.0865 +0.0255 -0.1740 +0.4696 - 1.1205 +0.7994 Absolute magnitude Mv (B-type stars): [79C]. Age (early type stars): [81N]. Intrinsic colors of 0,B and early A-type stars: [93C]. For values as a function of the MK type see Table 5. Interstellar reddening: [82C]. log g (B-type stars): [90N]. log g (A4- to GS-type stars): [90K]. Luminosity (B-type stars): [79C]. Mass (B-type stars): [90N]. Mass (A4- to GS-type stars): [9OK]. Metallicity [Fe/H] (A4- to GS-type stars): [90K]. Photometric boxes; [8OG]. Surface magnetic field intensities (CP stars): [SOCl, 80N]. A list of photometrically estimated mean surface fields H, for 258 stars is given in [8OC2]. T,, (B-type stars): [9ON]. T,, (A4- to GS-type stars): [9OK]. T,, (CP stars): [93H].

Landolt-BBmstein New Series V1/3b

4.2.5 Photoelectric photometry: Geneva 7 color system

16

Table 5. Intrinsic colors versus MK type for the 0,B and A-type stars.

MK type

X

Y

[U-B],

[V-B],

LB,-Blo [4-aJ

w-1-ql

[G-40

1.645 1.640 1.633 1.620 1.604 1.591 1.583 1.580 1.573 1.566 1.554 1.534 1.507 1.497 (1.485)

2.002 1.994 1.976 1.946 1.909 1.880 1.860 1.851 1.832 1.814 1.787 1.743 1.677 1.654 (1.622)

2.568 2.560 2.539 2.504 2.461 2.426 2.402 2.390 2.366 2.342 2.309 2.257 2.180 2.153 (2.116)

1.642 1.639 1.628 1.621 1.606 1.589 1.577 1.573 1.571 1.568 1.551 1.529 1.512 1.489 (1.477)

1.995 1.986 1.961 1.944 1.907 1.866 1.837 1.826 1.821 1.814 1.774 1.723 1.683 1.629 (1.6597)

2.559 2.549 2.520 2.500 2.456 2.406 2.368 2.354 2.348 2.338 2.289 2.231 2.185 2.122 (2.086)

Luminosity class V

07 9 BO 1 2 3 4 5 6 7 8 9 A0 (:,

0.010 0.026 0.050 0.020 0.130 0.017 0.270 0.009 0.440 0.002 0.590 0.002 0.700 0.008 0.760 0.014 0.028 0.880 1.ooo 0.040 1.160 0.048 1.360 0.040 1.550 0.006 1.580 - 0.014 (1.620) (-0.040)

0.084 0.155 0.278 0.428 0.559 0.653 0.704 0.805 0.906 1.042 1.218 1.404 1.442 (1.494)

0.040 0.028 0.080 0.028 0.200 0.024 0.280 0.022 0.470 0.024 0.700 0.034 0.880 0.049 0.950 0.058 0.980 0.060 1.030 0.066 1.290 0.085 1.540 0.079 1.650 0.054 1.700 - 0.002 (1.730) (-0.030)

0.076 0.112 0.217 0.287 0.452 0.650 0.803 0.862 0.887 0.929 1.147 1.363 1.471 1.547 (1.592)

0.049

1.347 1.332 1.308 1.268 1.227 1.195 1.175 1.164 1.146 1.128 1.101 1.058 0.990 0.966 (0.934)

0.738 0.742 0.750 0.764 0.780 0.792 0.800 0.803 0.810 0.816 0.827 0.845 0.873 0.883 (0.895)

Luminosity class III

09 BO 1 2 3 4 5 6 7 8 9 A0 1 2 (3)

1.338 1.325 1.290 1.268 1.224 1.181 1.152 1.142 1.137 1.131 1.092 1.039 0.996 0.937 (0.901)

0.740 0.744 0.755 0.762 0.778 0.794 0.805 0.809 0.811 0.813 0.828 0.849 0.866 0.890 (0.903)

Comparison

-

with with with with with

models (0,B and early A-type stars): [82C]. MK types (0,B and early A-type stars): [82C, 93C]. H/I photometry (B-type stars): [84Cl]. H/3, uvby photometry (B-type stars): [79C]. Johnson UBV instrinsic colors (B-type stars): [84C2].

References for 4.2.5.7 79C Cramer, N., Maeder, A.: Astron. Astrophys. 78 (1979) 305. 8OCl Cramer, N., Maeder, A.: Astron. Astrophys. 88 (1980) 135. 8OC2 Cramer, N., Maeder, A.: Astron. Astrophys. Suppl. 41 (1980) 111. 80G Golay, M.: Vistas in Astronomy 24 (1980) 141. 80N North, P.: Astron. Astrophys. 82 (1980) 230. Land&-BBmstein New Series VI/3b

Ref. p. 181 81N 82C 84Cl 84C2 86R 88R 90K 90N 93C 93H 94N

4.25 Photoelectric photometry: Walraven VBLUW system

17

North, P., Cramer, N.: Astron. Astrophys. Suppl. 43 (1981) 395. Cramer, N.: Astron. Astrophys. 112 (1982) 330. Cramer, N.: Astron. Astrophys. 141 (1984) 222. Cramer, N.: Astron. Astrophys. 132 (1984) 283. Rufener, F.: Astron. Astrophys. 165 (1986) 275. Rufener, F.: Nicolet, B.: Astron. Astrophys. 206 (1988) 357. Kobi, D., North, P.: Astron. Astrophys. Suppl. 85 (1990) 999. North, P., Nicolet, B.: AstronAstrophys. 228 (1990) 781, erratum [94N]. Cramer, N.: Astron. Astrophys. 269 (1993) 457. Hauck, B., North, P.: Astron. Astrophys. 269 (1993) 403. North, P., Nicolet, B.: Astron. Astrophys. 286 (1994) 348.

4.2.5.8-4.2.5.13 seeLB VU2b 4.2.5.14 Walraven VBLUW system The only existing Walraven photometer at La Silla, ESO/Chile was closed in 1991. Nevertheless, becauseof the large amount of published data on this photometric system, a few corrections and somenew relations are given. Lub and Pel [77L] have presented a detailed analysis of the Walraven photometric system. The basic principle laid out by them is still valid, but the system specifications have changed somewhat since then. The new values for the effective wavelengths of the filters and bandwidths are given in Table 6. Table 6. Effective wavelength (&J and bandwidth (BW) [88B].

4, PI BWIAl

V

B

L

u

W

5441 708

4298 423

3837 221

3623 232

3235 157

From the five photometric bands, four independent color indices can be constructed. For early type stars they have the following use: determines the reddening; measuresthe Balmer jump. For 0- and B-type stars it is mainly a temperature indicator; (B-U) (B-L) mainly depends on gravity (through the Balmer lines in the L-band); (U- w> measuresthe slope of the Balmer continuum and is both gravity and temperature dependent.

(V-B)

Reddening-free color indices [88B]: [B-L]=(B-L)-0.39(V-B), [B- V]=(Bv>-0.61(V-B), [U- w]=(UW)-0.45(V-B).

Intrinsic colors as a function of T,, and log g for solar abundance can be found in [88B] p. 120. LandokB6mstein New Series VI13b

Ref. p. 181 81N 82C 84Cl 84C2 86R 88R 90K 90N 93C 93H 94N

4.25 Photoelectric photometry: Walraven VBLUW system

17

North, P., Cramer, N.: Astron. Astrophys. Suppl. 43 (1981) 395. Cramer, N.: Astron. Astrophys. 112 (1982) 330. Cramer, N.: Astron. Astrophys. 141 (1984) 222. Cramer, N.: Astron. Astrophys. 132 (1984) 283. Rufener, F.: Astron. Astrophys. 165 (1986) 275. Rufener, F.: Nicolet, B.: Astron. Astrophys. 206 (1988) 357. Kobi, D., North, P.: Astron. Astrophys. Suppl. 85 (1990) 999. North, P., Nicolet, B.: AstronAstrophys. 228 (1990) 781, erratum [94N]. Cramer, N.: Astron. Astrophys. 269 (1993) 457. Hauck, B., North, P.: Astron. Astrophys. 269 (1993) 403. North, P., Nicolet, B.: Astron. Astrophys. 286 (1994) 348.

4.2.5.8-4.2.5.13 seeLB VU2b 4.2.5.14 Walraven VBLUW system The only existing Walraven photometer at La Silla, ESO/Chile was closed in 1991. Nevertheless, becauseof the large amount of published data on this photometric system, a few corrections and somenew relations are given. Lub and Pel [77L] have presented a detailed analysis of the Walraven photometric system. The basic principle laid out by them is still valid, but the system specifications have changed somewhat since then. The new values for the effective wavelengths of the filters and bandwidths are given in Table 6. Table 6. Effective wavelength (&J and bandwidth (BW) [88B].

4, PI BWIAl

V

B

L

u

W

5441 708

4298 423

3837 221

3623 232

3235 157

From the five photometric bands, four independent color indices can be constructed. For early type stars they have the following use: determines the reddening; measuresthe Balmer jump. For 0- and B-type stars it is mainly a temperature indicator; (B-U) (B-L) mainly depends on gravity (through the Balmer lines in the L-band); (U- w> measuresthe slope of the Balmer continuum and is both gravity and temperature dependent.

(V-B)

Reddening-free color indices [88B]: [B-L]=(B-L)-0.39(V-B), [B- V]=(Bv>-0.61(V-B), [U- w]=(UW)-0.45(V-B).

Intrinsic colors as a function of T,, and log g for solar abundance can be found in [88B] p. 120. LandokB6mstein New Series VI13b

18

4.2.5 Photoelectric photometry: UBVRI system

[Ref. p. 21

Transformation into the Johnson system (noted with index “J”), valid in the spectral range from 05 to K5 and all luminosity classes[@PI: V, = 6.886 - 2.5 V- 0.082( V- B), (B- V),=2.571(V-B)1.020(1/-B)2+0.500(1/-B)3-0.010. The relation between E(b - v) and E( V- B) can be expressedby [77L]: E(b-y)=

1.653E(l/-B).

The relation between (B - v>, and E( V- B) can be expressedby [91v]: E(B- v>,=2.39E(V-B)-0.17E2(V-B) with E( V- B) on a iOlogscale. For color excessE seeLB VI/2b subsect.4.1.1.6 and LB VI/2c subsect.7.1.2.4. Visual absorption A,(for R= A,/E,- y= 3.2) [91v]: A = A,,+O.O82E( V-B) 2.39~.qE(v-B)-[L!gi]E2(v-B) V 2.5 = =3.092E(V-B)-0.218E2(V-B). Intrinsic magnitudes are then computed as V, = Y+A,.

References for 4.2.5.14 77L 88B 88P 91V

Lub, J., Pel, J. W.: Astron. Astrophys. 54 (1977) 137. Brand, J., Wouterloot, J. G. A.: Astron. Astrophys. Suppl. 75 (1988) 117. Pel, J. W., Trefzger, C. F., Blaauw, A.: Astron. Astrophys. Suppl. 75 (1988) 29. Verschueren, W.: Ph.D. thesis, Vrije Univ. Brussel(1991).

4.2.5.15

UBVRI system (incl. Cousins V(RI),, subsect. 4.2.5.16 in LB W2b)

The UBV part of this system is the one of Johnson while RI defines a color system of its own right. In the beginning VRI was measured with a Quantacon and the UBV part with a Sl 1 tube. During later years, all bands were measured with the samephototube (seeTable IO). A detailed discussion of the passbands for the UBVRI system is given by Bessel[90B] together with small adjustments to previously published passbands. In Table 7 the standard passband responsesfor the UBVRI system are listed. U, and B, should be used for computing (U- B) colors. B, V, R and I should be used for the other colors and magnitudes. The extinction should be removed from the Ux responsebefore matching with instrumental U passbands. In Table 8 zero-point magnitudes and effective wavelengths are listed derived for each passband using the Vega model of Dreiling and Bell [80D]. Table 9 gives computed colors in the UBVRI system for Vilnius spectra [72S] of different spectral and luminosity types using the passbandsof Table 7. In Table 10 glass filter combinations with a GaAs, S20R or Sl l/S4 phototube recommended for the UBVRI photometry are listed. Bessel mentioned that the best passband matches are possible with the GaAs tube. Land&-BOrnstein New Series VI/3b

18


[Ref. p. 21

Transformation into the Johnson system (noted with index “J”), valid in the spectral range from 05 to K5 and all luminosity classes[@PI: V, = 6.886 - 2.5 V- 0.082( V- B), (B- V),=2.571(V-B)1.020(1/-B)2+0.500(1/-B)3-0.010. The relation between E(b - v) and E( V- B) can be expressedby [77L]: E(b-y)=

1.653E(l/-B).

The relation between (B - v>, and E( V- B) can be expressedby [91v]: E(B- v>,=2.39E(V-B)-0.17E2(V-B) with E( V- B) on a iOlogscale. For color excessE seeLB VI/2b subsect.4.1.1.6 and LB VI/2c subsect.7.1.2.4. Visual absorption A,(for R= A,/E,- y= 3.2) [91v]: A = A,,+O.O82E( V-B) 2.39~.qE(v-B)-[L!gi]E2(v-B) V 2.5 = =3.092E(V-B)-0.218E2(V-B). Intrinsic magnitudes are then computed as V, = Y+A,.

References for 4.2.5.14 77L 88B 88P 91V

Lub, J., Pel, J. W.: Astron. Astrophys. 54 (1977) 137. Brand, J., Wouterloot, J. G. A.: Astron. Astrophys. Suppl. 75 (1988) 117. Pel, J. W., Trefzger, C. F., Blaauw, A.: Astron. Astrophys. Suppl. 75 (1988) 29. Verschueren, W.: Ph.D. thesis, Vrije Univ. Brussel(1991).

4.2.5.15

UBVRI system (incl. Cousins V(RI),, subsect. 4.2.5.16 in LB W2b)

The UBV part of this system is the one of Johnson while RI defines a color system of its own right. In the beginning VRI was measured with a Quantacon and the UBV part with a Sl 1 tube. During later years, all bands were measured with the samephototube (seeTable IO). A detailed discussion of the passbands for the UBVRI system is given by Bessel[90B] together with small adjustments to previously published passbands. In Table 7 the standard passband responsesfor the UBVRI system are listed. U, and B, should be used for computing (U- B) colors. B, V, R and I should be used for the other colors and magnitudes. The extinction should be removed from the Ux responsebefore matching with instrumental U passbands. In Table 8 zero-point magnitudes and effective wavelengths are listed derived for each passband using the Vega model of Dreiling and Bell [80D]. Table 9 gives computed colors in the UBVRI system for Vilnius spectra [72S] of different spectral and luminosity types using the passbandsof Table 7. In Table 10 glass filter combinations with a GaAs, S20R or Sl l/S4 phototube recommended for the UBVRI photometry are listed. Bessel mentioned that the best passband matches are possible with the GaAs tube. Land&-BOrnstein New Series VI/3b

Ref. p. 211


19

Table 7. Normalized standard passbands [90B].

3000 3050 3100 3150 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 3700 3750 3800 3850 3900 3950 4000 4050 4100 4150 4200

0.000 0.016 0.068 0.167 0.287 0.423 0.560 0.673 0.772 0.841 0.905 0.943 0.981 0.993 1.ooo 0.989 0.916 0.804 0.665 0.423 0.238 0.114 0.051 0.019 0.000

3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500 5600

0.000 0.026 0.120 0.523 0.875 0.956 1.ooo 0.998 0.972 0.901 0.793 0.694 0.587 0.470 0.362 0.263 0.169 0.107 0.049 0.010 0.000

0.000 0.030 0.163 0.458 0.780 0.967 1.ooo 0.973 0.898 0.792 0.684 0.574 0.461 0.359 0.270 0.197 0.135 0.081 0.045 0.025 0.017 0.013 0.009 0.000

4700 4800 4900 5000 5100 5200 5300 5400 5500

0.000 0.030 0.134 0.567 0.920 0.978 1.ooo 0.978 0.935 0.835 0.740 0.640 0.536 0.424 0.325 0.235 0.150 0.095 0.043 0.009 0.000

5700 5800 5900 6000 6100 6200 6300 6400 6500 6600 6700 6800 6900 7000

Table 8. Zero-point (ZP) magnitudes and effective wavelengths in [A] for a A- and a K-type star [90B].

ZP AOV KOIII

Land&-Bdmstein New Series VI/3b

4 0.790 3659 3656

Bx -0.104 4382 4537

B

V

R

I

-0.102 4363 4520

0.008 5448 5524

0.19 6407 6535

0.043 7982 8028

5500 5600 5700 5800 5900 6000 6100 6200 6300 6400 6500 6600 6700 6800

7300 7400 7500 8000 8500 9000

0.00 0.23 0.74 0.91 0.98 1.oo 0.98 0.96 0.93 0.90 0.86 0.81 0.78 0.72 0.67 0.61 0.56 0.51 0.46 0.40 0.35 0.14 0.03 0.00

7000 7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 8100 8200 8300 8400 8500 8600 8700 8800 8900 9000 9100 9200

0.000 0.024 0.232 0.555 0.785 0.910 0.965 0.985 0.990 0.995 1.ooo 1.ooo 0.990 0.980 0.950 0.910 0.860 0.750 0.560 0.330 0.150 0.030 0.000

20


[Ref. p. 21

Table 9. Computed colors for Vilnius spectra [90B]. MK

U-B

B-V

V-R

R-I

V-I

U-B

Luminosity class V 0 B3 B5 B8 A5 FO F5 GO G5 G8 KO K2 K3 K5 K7 MO M2 M3 M4 M5 M6

-

1.16 0.756 0.576 0.28 0.111 0.036 -0.031 0.078 0.19

- 0.326 -0.193 -0.139 - 0.068 0.128 0.311 0.411 0.575 0.654

-0.158 - 0.073 - 0.032 - 0.024 0.063 0.197 0.27 0.352 0.388

-0.172 - 0.09 - 0.066 - 0.044 0.077 0.22 0.266 0.363 0.358

- 0.33 -0.163 - 0.098 - 0.068 0.14 0.417 0.536 0.715 0.746

0.422

0.823

0.461

0.392

0.853

0.771 1.048 1.256 1.26 1.169

0.974 1.182 1.382 1.444 1.479

0.582 0.733 0.839 0.866 0.99

0.497 0.626 0.761 0.849 1.08

1.079 1.359 1.60 1.735 2.07

1.191 1.263

1.513 1.703

1.092 1.191

1.36 1.571

2.452 2.762

BO Ia B8 Ia A2 Ia FOI M2 Iab

0.285 0.418 0.639

0.717 0.855 0.931

0.406 0.483 0.505

0.37 0.458 0.481

V-R

R-I

V-I

Luminosity class III

Luminosity class IV B5 F5 F8 GO G2 G5 G8 KO K2 K3

B-V

0.10 0.132

0.14 0.274

0.095 0.163

0.08 0.17

0.175 0.333

0.411 0.643 0.866 1.177 1.507 1.865

0.852 0.926 0.977 1.155 1.31 1.555

0.471 0.498 0.495 0.603 0.664 0.83

0.436 0.468 0.459 0.537 0.566 0.784

0.907 0.966 0.954 1.14 1.23 1.614

1.959 1.962 1.871 1.785 1.556 1.242

1.554 1.583 1.621 1.55 1.57 1.575

0.878 0.919 1.029 1.166 1.302 1.664

0.898 1.008 1.22 1.524 1.742 1.967

1.776 1.927 2.249 2.69 3.04 3.631

Luminosity class Ib -0.724 - 0.085 -0.012 -0.056 - 0.068 0.254 0.214 0.214 0.428 0.393 0.268 0.519 0.363 0.55 0.251 0.653 0.447 0.716 0.358 0.295 0.352 0.751 0.62 0.85 0.399 0.776 0.764 0.816 0.969 0.413 0.351 0.941 1.03 1.338 1.263 0.558 0.472 0.986 1.573 1.423 0.649 0.57 1.219 1.552 0.745 1.601 0.575 1.32

- 1.083 -0.232 -0.081 -0.107 -0.188 0.029 0.045 0.074 - 0.652 - 0.053 0.115 0.034 0.034 0.062 - 0.252 0.203 0.134 0.149 0.283 0.233 1.111 1.278 2.389 2.155 1.844

Table 10. Glass filter combinations for phototubes. Band

Cathode

Filters

U B V

Sl l/S4

UGI (1 mm) (+ WG320(2 mm) with UV tubes) GG395(2 mm) +BG12(1 mm) GG5 15(3 mm)

U B V R I

GaAslS20R

UGl(1 mm)+BG39(1 mm) GG385(2 mm)+BG12(1 mm)+BG18(1 mm) GG495(2 mm)+BG18(1 mm) (+BG38(1 mm) with GaAs tube) OG570(2 mm) + KG3(2 mm) RG9(3 mm)


21

It should be mentioned that the T, and T2 bands of the Washington photometric system [76C, 90G] are very close to R and I of the Cousins systems. Transformation between (R-I), (V-I) and ( TI - TJ are [90B]: (R-Z)= -0.002+0.9814(T,-T,)-O.O089(T,T,)2-0.070(T,T2)3, (~-1)=+0.004+1.777(T,-T,)-0.869(T,-T,)2-0.811(T~-T2)3, (T,-T2)=+0.002+1.015(R-Z)-0.0047(R-Z)2-0.070(R-Z)3. For realization of the UBI/RZphotometric system in use with CCDs seesubsect.4.2.5.19. Installation at different sites: ESO: [92L]; CT10 (Cerro To1010Interamerican Observatory): [82G].


Graham, J. A.: UBVRI standard stars in the E-regions, Publ. Astron. Sot. Pac. 94 (1982) 244. Landolt, A. U.: UBVRI photometric standard stars around the celestial equator, Astron. J. 88 (1983) 439. Landolt, A. U.: UBVRI photometric standard stars in the magnitude range 11.5 < V < 16.0 around the celestial equator, Astron. J. 104 (1992) 340. Menzies, J. W., Cousins, A. W. J., Banfield, R. M., Laing, J. D.: UBV(RI), standard stars in the Eand F-regions and in the Magellanic clouds - a revised catalogue, South African Astron. Obs. Circ. 13 (1989) 1. Vogt, N., Geisse, H. S., Rojas, S.: Up-to-date UBVRI values for the E-region standard stars, Astron. Astrophys. Suppl. 46 (1981) 7.

Selection of larger sets of photometric data

Cousins, A. W. J.: VRI photometry of E and F region stars, Mon. Not. Astron. Sot. Southern Africa 37 (1978) 8. Cousins, A. W. J.: VRI photometry of nearby stars, South African Astron. Obs. Circ. 5 (1980) 166. Cousins, A. W. J.: VRI photometry of Southern stars, South African Astron. Obs. Circ. 5 (1980) 234. Laing, J. D.: UBV(RI), photometry of faint nearby stars, South African Astron. Obs. Circ. 13 (1989) 29.

References for 4.2.5.15 72s 76C 80D 90B 90G 92L

Straizys, V., Sviderskiene, Z.: Bull. Vilnius Astron. Obs. No. 35 (1972). Caterna, R.: Astron. J. 81 (1976) 228. Dreiling, L. A., Bell, R. A.: Astrophys. J. 241 (1980) 736. Bessel,M. S.: Publ. Astron. Sot. Pac. 102 (1990) 1181. Geisler, D.: Publ. Astron. Sot. Pac. 103 (1990) 344. Lindgren, H.: ES0 operation manual No. 16 (1992).

4.2.5.17 see LB VI/2b Landolt-Bb;mstein New Series V1/3b

22 4.2.5.18

4.2.5 Photoelectric photometry: Infrared photometry

[Ref. p. 27

Infrared photometry (C30 pm)

It is usually believed that there are as many IR photometric systemsas there are observatories. The reasons for this are the different equipment used at different sites and the different influences on the passbands of atmospheric transparency. Recently Young, Milone and Staggs [94yl critically compared the passbands used at a number of observatories and atmospheric effects on the passbands. They found that the existing passbandsare very diverse and that no semblanceof a standard set is in use! Consequently, they recommend an improved set of passbands (Table 13) which are optimized for reproducibility and transformability of photometric results. The main photometric systemsin the near IR (~5 pm) used at major observatories are listed in Table 12. Photometric systems in the far infrared (>30 pm) can be used only from space. In subsects. 4.2.5.20.1 (IRAS) and 4.2.5.20.3 (ISO) some details are discussed. In LB Vi/3a, subsect. 1.8 [a] general remarks about infrared techniques, including detectors and telescopes,are given. Installation at different sites: ESO: [89B]; OAN: [91C]; UKIRT: [92D].

Extinction

Detailed discussions of problems concerning infrared extinction and standardization can be found in [b], while Table 11 gives explicit extinction values at different sites.

Table 11. Extinction values [mag airmass-‘] at different sites.

Band

UKIRT

AA0

[92~1

P1‘41

0.12...0.18 0.113 1.2 0.06...0.10 1.6 0.068 0.10...0.15 2.2 0.094 0.210 3.4 0.120 0.11...0.16 3.8 0.241 4.8 0.413 7.8 0.134 8.7 9.6 0.181 0.174 10.0 0.109 10.3 0.095 11.6 12.5 0.163 0.468 20.0 Q Z 32.0 1.62 AAO: Anglo Australian Observatory ESO:EuropeanSouthernObservatory OAN: MexicanNational AstronomicalObservatoryat SanPedroMartir UKIRT: United Kingdom 3.8mInfrared Telescope,Mauna Kea/Hawaii J H I( L L’ M 7.8 8.7 9.6 N 10.3 11.6 12.5

ES0 [91J31 0.125 0.110

OAN [91Cl 0.092 0.032 0.045

0.170

Land&-Biknstein New Series VU3b

23


Ref. p. 271

Effective temperature and angular diameter

The effective temperature Teffand angular diameter B of stars up to 8000K can be determined by the infrared flux method (IRFM) [80B]. A list of T,, and Bfor 114 F- to M-type stars is given in [90B]. 4.2.5.18.1

Near-infrared photometry (JHKLM)

Responsefunctions S(1) and technical realization as a part of the Johnson UBVRIJK...Z color system can be found in [c, p.7lQ. Table 12 gives a synopsis of systemsused at major observatories. Table 12. Near IR standard star systems.

System“)

Bands

No. of stars

ARIZ SAA0

JKLM JHKL JHKL JHKLM JHKL JHKL JHK JHK JHKL JHKL’M JHK JHKL’LM

256 145 230 10 87 63 28 44 40 24 90 43

Range

Accuracy b,

Ref.

Krnin’Krna.x

ES0 AA0 MSSSO CIT UNAM UKIRT

- 4.015.8 - 1.3/5.1 -0.518.1 -0.114.6 - 3.016.6 1.516.0 2.315.5 -2.116.5 4.517.8 - 0.914.7 - 3.4185 - 3.417.5

2% (5% L) =2% 3% 1% 1% (3% J) 1...2% = 2%

645 74G2 84C, 9OC 81W 81E 83A 825 78F 82E, 83E 86T 92D 92D

“) ARIZ: Lunar and Planetary Laboratory (Arizona system) SAAO: South African Astronomical Observatory ESO: European Southern Observatory AAO: Anglo Australian Observatory MSSSO: Mount Stromolo and Siding Spring Observatory CIT: Californian Institute of Technology UNAM: Universita Autonoma de Mexica UKIRT: United Kingdom 3.8m Infrared Telescope. “) Internal consistency.

In [88B, 93L], tables of linear transformation equation coefficients for most of the near-IR systems can be found. Explicit comparisons between different sites include: Site

versus

Ref.

AA0 CT10 ES0 IRTF OAN SAA0 UKIRT

CIT CIT AAO, AAO, AAO, AAO, CIT

83E 82E 91B2 84H 91c 9oc 92D

CTIO, MSSSO, SAA0 CIT CIT, ES0 ESO, CTIO, MSSO

CTIO: Cerro To1010Inter-American Observatory IRTF: Infrared TelescopeFacility (NASA) For all other sites seeexplanation Tables 11 and 12. Land&-Bhstein New Series VU3b

24


[Ref. p. 27

Table 13 gives the wavelengths at the 5%, 50%, 80% and 100%points on the adopted band profiles of the filter recommended in [94yl. These bandpassesare similar to the existing systems but are slightly narrower. They are chosen to give maximum throughput and to reduce the effects of molecular absorption and atmospheric thermal emission. Table 13. Recommended band profiles [94Y]. All wavelengths have nominal tolerances of 1%. The filters are prefixed with the letter “i” to avoid confusion with existing passbands. “z” and “n” are newly proposed filters.

Band iz iJ iH iK iL iL’ iM in iN

0.970 1.170 1.514 2.047 3.374 3.654 4.564 8.731 9.756 16.656

iQ

50%

80%

100%

80%

50%

b-4

D-W

[wl

[wl

[wl

0.996 1.201 1.555 2.100 3.483 3.763 4.618 8.873 10.100 17.106

1.016 1.225 1.585 2.141 3.554 3.834 4.652 8.968 10.369 17.439

1.032 1.240 1.628 2.196 3.620 3.900 4.675 9.030 11.100 17.900

1.047 1.254 1.672 2.240 3.686 3.966 4.698 9.101 11.832 18.329

1.069 1.280 1.707 2.288 3.757 4.037 4.732 9.196 12.100 18.712

1.099 1.315 1.754 2.353 3.882 4.162 4.784 9.339 12.444 19.231


List of standard stars for the different systems could be found in the references to Table 12. Furthermore in [91B2] for ESO.

Absolute calibration

Table 14 gives the absolute infrared flux of Vega between 1.24 and 5.0 pm [85M]. A comparison with model calculation shows a significant excess,rising to 11% at 5 pm. An empirical blackbody formula for a temperature of IO4K can be used to calculate F, within 3%:

“=

A5[exp(1.4388/l) - l]

Wm-‘p.rn-‘.

Care should be taken, however, for 1~2.2 l.trn because of the presence of several hydrogen absorption lines. Table 14. Absolute infrared flux of Vega [85M].

3,[r,lml Flux [lO-lo Wm-*&I

1.24 30.6

1.50 15.6

2.00 5.76

2.50 2.54

3.00 1.28

3.50 0.719

4.00 0.435

4.50 0.280

5.00 0.188

Absolute calibrations using different methods for 0-mag fluxes in the JHKL filters can be found in Table 15. Near-infrared magnitudes of calibration stars derived from continuous, observed spectra [93C] are given in Table 16. Land&Bdmstein New Series VIl3b


Ref. p. 271

25

Table 15. Absolute calibrations [9 1B I].

Method “)

0-mag fluxes [10-13Wcrne2&] J

H

K

1 1.25 2.2 2 1.25 1.65 2.2 2 1.25 1.65 2.2 1 2.22 4 2.3 1 1.25 1.65 2.2 2 1.20 1.64 2.19 4 1.25 1.65 2.2 3 1.24 2.20 1 1.26 1.60 2.22 2 1.22 1.63 2.19 “) 1 : solaranalogmethod; 2 : starmodel; 3 : blackbodycomparison; 4 : extrapolationfrom blackbody.

L

J

3.4 3.5 3.6 3.6 3.6 3.6 3.8 3.6 3.76 3.54 3.45

3.4 2.92 3.03 3.18 3.41 3.14 3.06 3.03 3.12

H 1.08 1.17 1.18 1.15 1.20 1.26 1.14

K

L

0.39 0.384 0.402 0.414 0.339 0.417 0.406 0.412 0.419 0.406 0.394

0.081 0.0686 0.0618 0.0638 0.0641 0.0623 0.0519 0.0641 0.0544 0.0690 0.0699

Accuracy

Ref.

10%

655 72W 73T 73T 74Gl 81W 82W 83K 83B 85C 86B

lO%K, 15%L 5% 4% 4% 3% 3%

Table 16. Near-infrared magnitudes of calibration stars. clLyr and &Ma

have calibrated

Kurucz models, the other represent calibrated, observed spectra [91Bl]. Star

Jn’)

Kn”)

Ln”)

0.00 0.00 0.00 aLyr &Ma - 1.39 - 1.37 - 1.36 - 1.94 - 2.06 /?And -0.89 - 3.06 clTau - 1.97 - 2.93 - 2.49 PM - 1.18 -2.33 aBoo - 2.27 - 3.08 -3.17 “) Narrowbandfilters accordingto [S&S].

J

H

K

0.00 - 1.39 - 0.79 - 1.84 - 1.09 -2.14

0.00 - 1.40 - 1.74 - 2.74 - 2.09 -2.96

-

0.00 1.37 1.90 2.90 2.29 3.05

L

L’

0.00 - 1.36 - 2.03 - 3.04 - 2.45 -3.16

0.00 - 1.36 -2.04 - 3.05 - 2.47 -3.16

M 0.00 - 1.36 - 1.78 - 2.77 - 2.20 -2.91

Selection of larger sets of photometric data

The data base of infrared observations in the range 1. . . 1000pm [93G] contains 206000 individual observations of more than 20000 different IR sources.The data were collected from over 4100 journal articles and 10 major survey catalogs covering the years 1965-90.

4.2.5.18.2

Mid-infrared

photometry (5 to 30 km)

Table 17 gives a synopsis of the filter used at ESO. Corresponding filter curves can be found in Fig. 2. N,, N,, N, are narrow band filters to trace the dust features around 10 pm. Landolt-Bdmstein New Series V1/3b

[Ref. p. 27


26

Table 17. Mid-infrared filters used at ESO.

Filter

4

b-4

WI

N NI N2 N3

10.36 8.36 9.67 12.89

5.2 0.85 1.65 3.7

AC?

Filter ::

Q*

4

Ail

[ml

W4

18.56 >19.7 >23

5.6

Nl

or 7

I_ 8

9

IO

11

;1-

12

13 pm

a

16

18

9

20

22

26

IO I"-

11 pm

26 pm 28

A-

Fig. 2. Transmission curves of the N, N,, N,, N,, Q0 filters used at ESO. The response of the detector is not considered in thesecurves.

Calibration

N,, N,, N,, N, Q, : Epchtein, N: These d’Etat, Observatoire de Paris (1980). Land&Bbmstein New Series VI/3b

27

4.2.5 Photoelectric photometry: Infrared photometry Table 18. Mid-infrared magnitudes of calibration stars. Seealso caption to Table 16.

Star

8.7 pm

aLyr &Ma PAnd clTau Peg clBoo

-

0.00 1.35 1.96 2.95 2.37 3.09

N

11.7u.m

Q

IRAS12

IRAS25

0.00 - 1.35 - 2.04 - 3.02 - 2.44 -3.14

0.00 - 1.35 -2.11 - 3.07 - 2.49 -3.17

0.00 - 1.34 -2.11 - 3.08 -2.51 -3.17

0.00 - 1.35 - 2.09 - 3.08 - 2.48 -3.17

- 1.34 -2.11 -3.10 -2.51 -3.16

References for 4.2.5.18 General references

a Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New SeriesVol. Vi/3a (ed. H. H. Voigt), Sect. 1.8, Berlin: Springer (1993). b Milone, E. F. (ed.): Infrared Extinction and Standardization, Lecture Notes in Physics 341, Berlin: Springer (1989). c Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New SeriesVol. VI/2b (eds. K. Schaifers, H. H. Voigt), Sect.4.2, Berlin: Springer (1982).

Special references

645 Johnson, H. L.: Bol. Tonantzinla y Tacubaya 3 (1964) 305. 655 Johnson, H. L.: Comm. Lunar and Planetary Lab. 3 (1965) 73. 72W Wilson, W. J., Schwartz, P. R., Neugebauer, G., Harvey, P. M., Becklin, E. E.: Astron. J. 177 (1972) 523. 73T Thomas, J. A., Hyland, A. R., Robinson, G.: Mon. Not. R. Astron. Sot. 165 (1973) 201. 74Gl Gherz cited in [9 1B 11. 7462 Glass, I. S.: Mon. Not. Astron. Sot. S. Africa 33, 53 and 51 (erratum) (1974). 78F Frogel, J. A., Persson, S. E., Aaronson, M., Matthews, K.: Astrophys. J. 220 (1978) 75. 80B Blackwell, D. E., Petford, A. D., Shallis, M. J.: Astron. Astrophys. 82 (1980) 249. 8 1A Allen, D. A.: IRPS User Guide, Anglo-Australian Observatory (1981). 81E Engels, D., Sherwood, W. A., Wamsteker, W., Schultz, G. V.: Astron. Astrophys. Suppl. 45 (1981) 5. 81W Wamsteker, W.: Astron. Astrophys. 97 (1981) 329. 82E Elias, J. H., Frogel, J. A., Matthews, K., Neugebauer, G.: Astron. J. 87 (1982) 7. 825 Jones, T. J., Hyland, A. R.: Mon. Not. R. Astron. Sot. 200 (1982) 509. 82W Ward, M., Allen, D. A., Wilson, A. S., Smith, M. G., Wright, A. E.: Mon. Not. R. Astron. Sot. 199 (1982) 953.

83A Allen, D. A., Cragg, T. A.: Mon. Not. R. Astron. Sot. 203 (1983) 777. 83B Blackwell, D. E., Leggett, S. K., Petford, A. D., Mountain, C. M., Selby, M. J.: Mon. Not. R. Astron. Sot. 205 (1983) 897. 83E Elias, J. H., Frogel, J. A., Hyland, A. R., Jones, T. J.: Astron. J. 88 (1983) 1027. 83K Koornneef, L.: Astron. Astrophys. 128 (1983) 84. 84C Carter, B.S.: M. SC.Thesis, University of Cape Town (1984). 84H Humphreys, R. M., Jones, T. J., Sitko, M. L.: Astron. J. 89 (1984) 1155. 85C Campins, H., Rieke, G. H., Lebowsky, M. J.: Astron. J. 90 (1985) 896. 85M Mountain, C. M., Legget, S. K., Selby, M. J., Blackweell, D. E., Petford, A. D.: Astron. Astrophys. 151 (1985) 399. Land&-BBmstein New Series VI/3b

28

4.2.5 Photoelectric photometry: CCD photometry

[Ref. p. 29

86T Tapia, M., Neri, L., Roth, M.: Rev. Mex. Astron. Astrof. 13 (1986) 115. 88B Bessel,M. S., Brett, J. M.: Pub]. Astron. Sot. Pac. 100 (1988) 1134. 88s Selby, M. J., Hepburn, I., Blackwell, D. E., Booth, A. J., Haddock, D. J., Arribas, S., Leggett, S. K., Mountain, C. M.: Astron. Astrophys. Suppl. 74 (1988) 127. 89B Bouchet, P.: ES0 operation manual No. 11, ES0 (1989). 90B Blackwell, D. E., Petford, A. D., Arribas, S., Haddock, D. J., Selby, M. J.: Astron. Astrophys. 232 (1990) 396. 90C Carter, B. S.: Mon. Not. R. Astron. Sot. 242 (1990) 1. 91Bl Bersanelli, M., Bouchet, P., Falomo, R.: Astron. Astrophys. 252 (1991) 854. 91B2 Bouchet, P., Manfroid, J., Schmider, F.-X.: Astron. Astrophys. Suppl. 91 (1991) 409. 91C Carrasco, L., Recillas-Cruz, E., Garcia-Barreto, A., Cruz-Gonzalez, I., Serrano, A.: Publ. Astron. Sot. Pac. 103 (1991) 987. 92D Davies, J. K.: UKIRT Observer’s Manual (1992). 93C Cohen, M., Walker, R. G., Barlow, M. J., Deacon, J. R., Witteborn, F. C., Carbon, D. F., Augason, G. C.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p.59. 93G Gezari, D. Y., Schmitz, M., Pitts, P. S., Mead, J. M.: Catalog of infrared observations, 31d edition, NASA Ref. Publ. 1294(1993). 93L Legett, S. K., Smith, J. A., Oswalt, T. D.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press (1993) p.66. 93Y Young, A. T., Milone. E. F., Stagg, C. R.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press (1993) p.235. 94Y Young, A. T., Milone, E. F., Stagg, C. R.: Astron. Astrophys. Suppl. 105 (1994) 259. 4.2.5.19

CCD photometry

As was mentioned in the introduction, no new photometric systems using CCDs has been established so far. Mainly, the Johnson UVB (UVBRI) and Striimgren uvby are used. In [a, b, c, d] general information about photometry with CCDs can be found; basic referencesfor stellar photometry with CCDs are provided in [89R]. A general discussion of photometric work with CCDs is given in [93w]. The principles of photometric reduction of CCD images are given in [e]. 4.2.5.19.1

Photometric reduction algorithms, methods and software packages

Aperture photometry

DoPHOT INVENTORY

Howell, S. B.: in [b] p. 312. Knude, J., Jsnch-Sorensen, H.: in [a] p.173. Mateo, M., Schechter, P. L.: in [a] p. 69. West, R. M., Kruszewski, A.: Irish Astron. J. 15 (1981) 25. Kruszewski, A.: in [a] p. 29.

Stellar photometry in dense regions

CAPELLA

Auriere, M., Cordoni, J.-P.: Astron. Astrophys. Suppl. 46 (1981) 347. Blecha, A.: Astron. Astrophys. 135 (1984) 401. Debray, B., Llebaria, A., Dubout-Crillon, R., Petit, M.: Astron. Astrophys. 281(1994) 613. Land&-Bb;mstein New Series VV3b

28


[Ref. p. 29

86T Tapia, M., Neri, L., Roth, M.: Rev. Mex. Astron. Astrof. 13 (1986) 115. 88B Bessel,M. S., Brett, J. M.: Pub]. Astron. Sot. Pac. 100 (1988) 1134. 88s Selby, M. J., Hepburn, I., Blackwell, D. E., Booth, A. J., Haddock, D. J., Arribas, S., Leggett, S. K., Mountain, C. M.: Astron. Astrophys. Suppl. 74 (1988) 127. 89B Bouchet, P.: ES0 operation manual No. 11, ES0 (1989). 90B Blackwell, D. E., Petford, A. D., Arribas, S., Haddock, D. J., Selby, M. J.: Astron. Astrophys. 232 (1990) 396. 90C Carter, B. S.: Mon. Not. R. Astron. Sot. 242 (1990) 1. 91Bl Bersanelli, M., Bouchet, P., Falomo, R.: Astron. Astrophys. 252 (1991) 854. 91B2 Bouchet, P., Manfroid, J., Schmider, F.-X.: Astron. Astrophys. Suppl. 91 (1991) 409. 91C Carrasco, L., Recillas-Cruz, E., Garcia-Barreto, A., Cruz-Gonzalez, I., Serrano, A.: Publ. Astron. Sot. Pac. 103 (1991) 987. 92D Davies, J. K.: UKIRT Observer’s Manual (1992). 93C Cohen, M., Walker, R. G., Barlow, M. J., Deacon, J. R., Witteborn, F. C., Carbon, D. F., Augason, G. C.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p.59. 93G Gezari, D. Y., Schmitz, M., Pitts, P. S., Mead, J. M.: Catalog of infrared observations, 31d edition, NASA Ref. Publ. 1294(1993). 93L Legett, S. K., Smith, J. A., Oswalt, T. D.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press (1993) p.66. 93Y Young, A. T., Milone. E. F., Stagg, C. R.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press (1993) p.235. 94Y Young, A. T., Milone, E. F., Stagg, C. R.: Astron. Astrophys. Suppl. 105 (1994) 259. 4.2.5.19

CCD photometry

As was mentioned in the introduction, no new photometric systems using CCDs has been established so far. Mainly, the Johnson UVB (UVBRI) and Striimgren uvby are used. In [a, b, c, d] general information about photometry with CCDs can be found; basic referencesfor stellar photometry with CCDs are provided in [89R]. A general discussion of photometric work with CCDs is given in [93w]. The principles of photometric reduction of CCD images are given in [e]. 4.2.5.19.1

Photometric reduction algorithms, methods and software packages

Aperture photometry

DoPHOT INVENTORY

Howell, S. B.: in [b] p. 312. Knude, J., Jsnch-Sorensen, H.: in [a] p.173. Mateo, M., Schechter, P. L.: in [a] p. 69. West, R. M., Kruszewski, A.: Irish Astron. J. 15 (1981) 25. Kruszewski, A.: in [a] p. 29.

Stellar photometry in dense regions

CAPELLA

Auriere, M., Cordoni, J.-P.: Astron. Astrophys. Suppl. 46 (1981) 347. Blecha, A.: Astron. Astrophys. 135 (1984) 401. Debray, B., Llebaria, A., Dubout-Crillon, R., Petit, M.: Astron. Astrophys. 281(1994) 613. Land&-Bb;mstein New Series VV3b


29

DOAPHOT

Stetson, P. B.: Publ. Astron. Sot. Pac. 99 (1989) 191. Stetson, P. B., Davis, L. E., Crabtree, D. R.: in [b] p. 289. Stetson, P. B.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments, (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p. 291. Buonanno, R., Buscema, G., Corsi, C. E., Iannicola, G.: Mem. Sot. Astron. ELIA-ROMAFOT Ital. 51 (1980) 483. Buonanno, R., Buscema, G., Corsi, C. E., Ferraro, F. R., Iannicola, G.: Astron. Astrophys. 126 (1983) 278. HOAPHOT Gilliland, R. L., Brown, T. M.: Publ. Astron. Sot. Pac. 100 (1988) 754. Lund package Linde, P.: in [b] p. 651. PAWSPHOT Mighell, K. J.: Mon. Not. R. Astron. Sot. 238 (1989) 807. RICHFLD Tody, D.: Image Processingin Astronomy, SPIE 35 (1980) 171. STARMAN Penny, A. J., Dickens, R. J.: Mon. Not. R. Astron. Sot. 220 (1986) 845. WOLF Lupton, R. H., Gunn, J. E.: Astron. J. 91 (1986) 317. Some of the algorithms/packages mentioned above are implemented in data reduction systemslike MIDAS [88E] or IRAF [86T]. 4.2.5.19.2

Technical realization of photometric systems

Bessel[90B] suggestedthe filter combinations given in Table 19 to match the standard passbands of the UBVRI systemwith coated CCDs. Becauseof differences between batches of filter glassesand in coatings, no two responseswill precisely match, but the combinations in Table 19 should be close. Table 19. UBVRI: glass filter combinations for coated CCDs.

Band

Filters

U B V R I

UGl (lmm)+BG39(lmm) (+WG305(3mm) fill) GG385(2mm)+BG12(lmm)+BG39(2mm) GG495(2mm)+BG39(3mm) OG570(2mm)+KG3(3mm) RG9(3mm) (+ WG305 (2mm) fill)

4.2.5.19.3

Standard fields

Johnson UBV:

calibration sequencesin V, B- V and in some cases U-B, including finding charts: [93Dl, 93D2]. Cousin UBVRI: calibration sequences(stars and galaxies) in BVR: [93Cl], calibration sequences(stars and galaxies) in V and R: [93C2], calibration sequences(open clusters) in BVR: [920], calibration sequences(open clusters) in UBVRI: [93Jl]. Striimgren uvbyHb: field stars: [9OJ,93521.

References for 4.2.5.19 General references

a Grosbsl, P. J., Murtagh, F., Warmels, R. H. (eds.): 1st ESO/ST-ECF Data Analysis Workshop, European Southern Observatory, Garching (1989). b Rufener, F. (ed.): Stellar Photometry with Modern Array Detectors in Highlights in Astronomy, Vol. 8 (ed. D. McNally), Dordrecht: Kluwer Academic Press(1989) 615ff. Land&-BBmstein New Series VI/3b

4.2.5 Photoelectric photometry: Photometry from space

30

[Ref. p. 40

c Jacoby, G. H. (ed.): CCDs in Astronomy, Publ. Astron. Sot. Pac. Conf. Ser. Vol. 8, San Fransisco (1990). d Philip, A. G. D., Hayes, D. S., Adelman, S. J. (eds.): CCDs in Astronomy II, L. Davis Press, Schenectady,NY (1990) (Van Vleck Obs. Contr. No. 10). e Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New SeriesVol. Vi/3a (ed. H. H. Voigt), Sect. 1.3, Berlin: Springer (1993). Special references

86T 88E 89R 90B 90J 920 93Cl 93C2 93D1 93D2 9351 9352 93W

Tody, D.: SPIE 627 (1986) 733. ES0 Image Processing Group: MIDAS User’s Guide A & B, European Southern Observatory, Garching (1988). Rufener, F.: in [b], p. 617. BesselM. S.: Publ. Astron. Sot. Pac. 102 (1990) 1181. Jonch-Sorensen,H., Knude, J.: Astron. Astrophys. 238 (1990) 75. Odewahn, S. C., Bryja, C., Humphreys, R. M.: Publ. Astron. Sot. Pac. 104 (1992) 553. Cunow, B.: Astron. Astrophys. Suppl. 97 (1993) 541. Cunow, B., Wargau, W. F.: Astron. Astrophys. Suppl. 102 (1993) 331. Demers, S., Lamontagne, R., Wesemael, F., Fontaine, G., Barneoud, R., Irwin, M. J.: Astron. Astrophys. Suppl. 99 (1993) 461. Demers, S., Lamontagne, R., Wesemael, F., Fontaine, G., Barneoud, R., Irwin, M. J.: Astron. Astrophys. Suppl. 99 (1993) 437. Jones, D. H. P.: IAU Coll. 136, Stellar Photometry-Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p.73. Jonch-Sorensen,H.: Astron. Astrophys. 267 (1993) 54. Walker, A. R.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p. 278.

4.2.5.20

Photometry from space

The number of space observatories containing photometers and plans for launching such satellites in the near future is increasing. Here the photometric capabilities and characteristics of the photometric systemsof some satellites will be introduced. 4.2.5.20.1

Infrared Astronomical Satellite (IRAS)

An overview of the optical characteristics of the system is given in Table 20. Table 21 lists the spectral responses while Figs. 3 and 4 show the responses and passbands, respectively. A detailed description of the data reduction and analysis can be found in [88B].

Landolt-BBmstein New Series VI/3b


30

[Ref. p. 40

c Jacoby, G. H. (ed.): CCDs in Astronomy, Publ. Astron. Sot. Pac. Conf. Ser. Vol. 8, San Fransisco (1990). d Philip, A. G. D., Hayes, D. S., Adelman, S. J. (eds.): CCDs in Astronomy II, L. Davis Press, Schenectady,NY (1990) (Van Vleck Obs. Contr. No. 10). e Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New SeriesVol. Vi/3a (ed. H. H. Voigt), Sect. 1.3, Berlin: Springer (1993). Special references

86T 88E 89R 90B 90J 920 93Cl 93C2 93D1 93D2 9351 9352 93W

Tody, D.: SPIE 627 (1986) 733. ES0 Image Processing Group: MIDAS User’s Guide A & B, European Southern Observatory, Garching (1988). Rufener, F.: in [b], p. 617. BesselM. S.: Publ. Astron. Sot. Pac. 102 (1990) 1181. Jonch-Sorensen,H., Knude, J.: Astron. Astrophys. 238 (1990) 75. Odewahn, S. C., Bryja, C., Humphreys, R. M.: Publ. Astron. Sot. Pac. 104 (1992) 553. Cunow, B.: Astron. Astrophys. Suppl. 97 (1993) 541. Cunow, B., Wargau, W. F.: Astron. Astrophys. Suppl. 102 (1993) 331. Demers, S., Lamontagne, R., Wesemael, F., Fontaine, G., Barneoud, R., Irwin, M. J.: Astron. Astrophys. Suppl. 99 (1993) 461. Demers, S., Lamontagne, R., Wesemael, F., Fontaine, G., Barneoud, R., Irwin, M. J.: Astron. Astrophys. Suppl. 99 (1993) 437. Jones, D. H. P.: IAU Coll. 136, Stellar Photometry-Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p.73. Jonch-Sorensen,H.: Astron. Astrophys. 267 (1993) 54. Walker, A. R.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p. 278.

4.2.5.20

Photometry from space

The number of space observatories containing photometers and plans for launching such satellites in the near future is increasing. Here the photometric capabilities and characteristics of the photometric systemsof some satellites will be introduced. 4.2.5.20.1

Infrared Astronomical Satellite (IRAS)

An overview of the optical characteristics of the system is given in Table 20. Table 21 lists the spectral responses while Figs. 3 and 4 show the responses and passbands, respectively. A detailed description of the data reduction and analysis can be found in [88B].


Ref. p. 401


Table 20. IRAS survey array optical characteristics [88B].

Band 12pm

25pm

60pm

1OOpm

short-wavelength blocking

MLIF

MLIF

MLIF+ sapphire+ ZnO powder

short-wavelength cuton

MLIF

MLIF

long-wavelength cutoff long-wavelength blocking

MLIF BaF,+ MLIF Si:As

Si:Sb Si:Sb

Sapphire + MLIF KRS-5 KRS:5

MLIF+ sapphire + CaF,+KCL+ diamond powder KCL

Ge MLIF

Si MLIF

/l/4

114

parylene-C

parylene-C

Filter functions

Ge:Ga Ge:Ga

Field lens

materials anti-reflecting coating focal length [mm] exit pupil diameter [mm]

Ge

Ge

6.53 1.0

6.59

6.98

8.34

1.0

1.0

1.0

Si:As 1.0 x 1.78

Si:Sb 1.0 x 1.78 0.71

Ge:Ga 1.5 x 1.25 1.0

Ge:Ga 1.0 x 1.25 1.25

11.15 0.50

32.5 0.29

0.34

6> - 90’).

0.2-

7

8

9 10

12

15

20

25

30

I-

40

50

60

70 80 90 100110 pm140

Fig. 3. Responsevs. wavelength of optical components. Solid lines show the transmission of filter and lenses. Dashed lines show relative detector responseto constant energy input [88B].

30 2-

Fig. 4. Relative systemspectral response[88B]. Land&-BBmstein New Series VU3b

40

50

60

70

80 90 100110 urn140

34


4.2.5.20.2

[Ref. p. 40

TYCHO

The TYCHO photometric experiment ([92H] and references therein) on-board the HIPPARCOS satellite, i.e. photometry using the star mapper data, will give a full sky coverage photometric survey of quasi B and V magnitudes for the 900000 brightest stars and one broad-band magnitude T for further 100000stars. Approximately 150 million single observations of these stars will be collected during a 4.5-year mission of the satellite. The expected accuracy of the photometric data is 0.03 mag on the average at B= 10.5mag for nonvariable stars. The two channels BTychoand vTTycho, with effective wavelengths of M280A and 15340A, respectively, closely match the Johnson BJ and V, filters used in ground-based photometry: while the TYCHO bands have roughly the same limits as those of the Johnson system, they differ in shape. Figure 5 shows the transmission of the two channels in comparison to the Johnson bands.

10 Fig. 5. Nominal TYCHO filters B,, V, and Johnson B,, V, WA.

The relation between V, and VJ [92S] is given by

VT-v,=

0.1 (B-

V),.

A similar but somewhat more complicated relationship exists for the B channel, where terms up to (B- v>,”are required to give a representation to within 0.01 mag [89G]. An approximate formula [93S]with a maximum error of 0.05 mag is

h-4

= 0.3 (B-

V),.

The broad-band T magnitude covering both BT and VT bands is defined such that T= V, for BT- VT=0 [93G].

A more explicit overview on the calibration procedures and some results can be found in [92S, 93G].

The compiled photometric catalog will be the first to contain measurements from both the Northern and Southern hemispheresmade with the same equipment in a well-defined color system. The catalog is scheduled to be releasedon optical disks in 1997. Land&-Bhwtein New Series VI/3b

4.2.5.20.3

35


Ref. p. 401

Infrared Space Observatory (ISO)

The Infrared SpaceObservatory (ISO) has various capabilities for making photometric, polarimetric and spectroscopic observations between 2.5 and 240 pm. A detailed description of its mission aspectscan be found in [941].The launch of the satellite is scheduled for September 1995. Among other things, ISO’s instrumentation contains an imaging photo-polarimeter (PHT). ISOPHOT-P, a multiband, multiaperture photometer with three single detectors covering the range 3 to 120 l.trn in single-element photometry, is one of its three sub-systems.It is designed for sensitive, high-precision photometry and polarimetry. At best, a relative photometric accuracy with respect to sky standards of about 5% could be achieved. Details of the detector characteristics and sensitivity as measured in the preflight calibration campaign are given in Tables 22 and 23. The responsitivity and noise-equivalent power (NEP) were measured at the flux levels produced by a blackbody source at 900K. The last column of Table 23 contains the NEP recalculated for a standard flux of lo-l6 W/pixel. For Pl and P2, the latter are read-noise dominated. All sensitivities are computed at the peak spectral responsewavelength of the subject detector material. Table 22. ISOPHOT-P detector characteristics 194L,94w].

Detector

PHP-P 1 PHP-P2 PHP-P3

Detector material Si:Ga Si:Ba Ge:Ga

Peak response

Cut on/off ( 10%limit)

bml

[wl

17 25 108

3...19 9...29 37...129

Field of view [arcsec] 5.. .180 circular 18.. .180 circular 52.. .180 circular

Table 23. ISOPHOT-P detector sensitivity 194Ll.

Detector

PHP-P 1 PHP-P2 PHP-P3

Bias

9ov 1ov 250mV

TKI

Flux 900K w/pixel]

Responsivity [AW-‘1

NEP [WHzzl’*]

NEP [WHz- “*I at 10-16W/px

2.9 3.6 2.8

1.4.10-15 5.0.10-15 5.9.10-16

0.42 0.8 9.6

2.3.10-16 1.8.10-16 6.0.10-‘8

1.6.10-16 8.5.10-17 4.0.10-18

An overview of the ISOPHOT instrument can be found in [911, 94K, 94L]. The calibration facility for ISOPHOT and preflight results are given in [94w]. The filters available for PHT-P are given in Table 24. Let R(A) be the actual bandpass, which is the filter transmission function convolved with the spectral detector response (i.e. detector response normalized to its maximum value), the central wavelength A,, filter width 111and the average relative systemresponseR,,,, are defined as:

Landolt-Bhstein New Series VU3b


36

[Ref. p. 40

I- R(J.)dL 0

Rmean =

A1

AI is the width of a rectangular filter having the sameintegrated relative system response as the actual bandpass (the factor of 2V? is a normalizing factor forcing the filter width to be equal to that of a rectangular filter with height R,,,,).

Table 24. ISOPHOT-P filters characteristics [94K]. 1, is the central wavelength, AL is the filter width and R,,,, the average relative system responsederived from the bandpasses.dAiryis the diameter of the Airy disc taken at 1,. The minimum aperture is the smallest one recommended; it is the minimum aperture that completely covers the Airy disc.

Filter label

1,

AR

b-d

WI

R

d*iry

mea” [“I

Min. aperture

Scientific objective

[7

Pl detector

P-3.29 P-3.6

3.30 3.59

0.22 1.oo

0.12 0.14

2.8 3.0

5 5

P-4.85 P-7.3 P-7.7 P-10 P-1 1.3 P-11.5

4.86 7.43 7.64 9.99 11.36 11.89

1.55 3.38 0.84 1.86 0.77 6.51

0.17 0.29 0.26 0.35 0.31 0.51

4.1 6.2 6.4 8.4 9.5 10.0

5 7.6 7.6 10 10 10

P-12.8 P-16

12.83 15.14

2.33 2.86

0.55 0.38

10.8 12.7

10 13.8

PAH cosmological gap, common with ISOCAM continuum to # 1,4 and 5 6.2, 7.7, 8.6 pm PAH complex PAH silicate feature PAH IRAS 12 ym band common with ISOCAM continuum to # 7 general purpose

21.08 23.81

9.43 9.18

0.33 0.39

17.7 20.0

18 23

close to standard Q band IRAS 25 pm band

25.48 0.12 P-60 60.06 P-100 101.63 40.15 0.32 PAH: polycyclicaromatichydrocarbons ISOCAM: IS0 instrument:camera

50.3 83.9

52 79

IRAS 60 ym band IRAS 100 pm band

P2 detector

P-20 P-25 P3 detector

Plots of the PHT filter bandpassescan be found in [94K]. Figs. 6 and 7 give a general view of the relative systemresponseof the filter bandpasses.

Land&B6mstein New Series VI/3b


Ref. p. 401

37

P-12.8

0.6 I 0.5 E 0.4 ti M L 0.3 E 2 0.2

0

5

10

15

20

25

30

pm

Fig. 6. Relative system response(i.e. detector responsenormalized to its maximum value) of PHT-P near- and mid-infrared filters.

0.7, 1

P-11.5

Fig. 7. Relative system response (i.e. detector responsenormalized to its maximum value) of IRAS filters (see

subsect.4.2.5.20.1, Fig. 4, for comparison with original IRAS filters).

Landolt-BBmstein New Series V113b

38


4.2.5.20.4

[Ref. p. 40

Hubble Space Telescope (HST)

Currently three possibilities doing photometry with the HST exist: the Fine Guidance Sensors (FGSs), the Wide Field and Planetary Camera (WFPC), and the Faint Object Camera (FOC). Photometry with Fine Guidance Sensors (FGSs)

After the removal of the the High SpeedPhotometer (HSP) on board the Hubble SpaceTelescope during the refurbishment mission in 1993 the FGSs, with their 25-ms time resolution, become the only high-speed photometric devices on the spacecraft. A full description of the instrument can be found in [95H2]. Bucciarelli et al. [94B] discussedthe photometric properties and showed that a photometry (in the V band) with a precision of f 0.05 mag is possible with an accuracy of & 0.05 mag over two years. Photometry with the Wide Field and Planetary Camera (WFPC2)

The original Wide Field and Planetary Camera (WFIPC-1) was a two-dimensional spectrophotometer with rudimentary polarimetric and transmission-grating capabilities. It imaged the center of the field of the Hubble SpaceTelescope(HST). The instrument was designed to operate from 11508, to 11000A with a resolution of 0.1 arcsecondsper pixel (Wide Field camera, f/12.9) or 0.043 arcseconds per pixel (Planetary Camera, f/30), each camera mode using an array of four 800 x 800 CCD dectors. The WF/PC-1 was replaced by a second Wide Field and Planetary Camera (WFPC2) during the refurbishment mission in 1993. A modification of the internal WF/PC optics could correct for the spherical aberration and restore most of the originally expected performance. A full description of the instrument can be found in [95B]. A set of 48 filters are included in WFPC2 with the following features: (1) (2) (3) (4) (5) (6)

It approximately replicates the WF/PC-1 UBVRIphotometry series. The broad-band filter seriesis extended into the far UV. There is a new Strijmgren series. A Wood’s filter is included for far-UV imaging without a red leak. There is a 1% bandpass linear ramp filter seriescovering 3700.. .9800 A. The narrow-band seriesis more uniformly specified and better calibrated.

The categories of simple filters (F) are long-pass (LP), wide (W), medium (M), and narrow (N). Most of these filters are either flat single substrates or sandwiches. Table 25 lists the ‘F’ filters. The mean wavelength 1 is similar to that defined in Schneider, Gunn and Hoessel (Astrophys. J. 264, p. 337). The width is the FWHM of a Gaussian filter with the same second moment and is reasonable close to the FWHM. The values tabulated in Table 25 do not include the CCD DQE or the transmission of the system optics. In [95B] more detailed data can be found, including a summary of normalized filter curves (Figure 3.1 in [95B]). The extraction of photometric data from the WFPC2 images can be carried out with software packageslike DOAPHOT (seesubsect.4.2.5.19). A photometric accuracy of 5.. ,lO% is easily possible, an accuracy of 2.. .5% if a few corrections are made [95Wl]. A practical guide for doing photometry with the WFPC2 is given in [95Wl], while a demonstration IRAFKTSDAS script to perform aperture photometry on WFPC2 images can be found in [95W2]. Holtzman et al. [95Hl] published a comprehensive article about the performance and calibration of WFPC2, presenting the best technique for the reduction of WFPC2 data. In the STECF Newsletter and STScI Newsletter various articles about the reduction of stellar photometry using HST images are frequently published. Available data in the HST archive can be obtained via anonymous FTP or WWW. The actual addressesof the data archives can be found in the Newsletters. Landolt-B6rnstein New Series VU3b

Ref. p. 401


39

Table 25. WFPC2 simple (‘F’) filter set [95B]. Name F122M F130LP F 160AW F160BW F165LP F170W F185W F218W F255W F300W F336W F343N F375N F380W F390N F410M F437N F439W F450W F467M F469N F487N F502N F547M F555W F569W F588N F606W F622W F631N F656N F658N F673N F675W F702W F785LP F791W F814W F850LP F953N F1042M

Land&-Bihstein New Series VI13b

Remarks H Ly alpha-Red Leak CaF2 Blocker (zero focus) Woods A-readleak from pinholes Woods B Suprasil Blocker (zero focus) Interstellar Feature Wide U WFPC2 U NeV [011] 3727 RS CN Stromgren v [OIII] WFPC2 B Wide B Striimgren b He II H beta [OIII] Striimgren y (but wider) WFPC2 V F555W generally preferred He I & Na I (NaD) Wide V

ro11

H alpha

WI WI1

WFPC2 R Wide R F8 14W generally preferred F8 14W generally preferred WFPC2 I [SIII] -

In WFIPC-l?

x

AX

Peak T

Peak J.

[Al

[WI

WI

L-4

Y N N

1292 3847 1471

263.5 5568.1 457.2

18.9 94.7 10.1

1240 4344 1403

N N

1471 4327

457.2 5505.7

10.1 92.1

1403 3109

N N N N N Y N Y N N N Y Y N N Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y N Y

1689 1907 2136 2557 2924 3327 3430 3736 3934 3889 4088 4369 4292 4445 4682 4695 4865 5012 5454 5252 5554 5892 5843 6157 6306 6562 6590 6733 6735 6997 9366 8006 8269 9703 9546 10443

434.9 302.9 355.9 408.2 727.6 370.7 24.3 26.2 694.7 45.3 146.9 25.2 464.4 925.0 171.5 24.9 25.8 26.8 486.6 1222.5 965.8 49.1 1578.7 935.4 30.8 22.0 28.5 47.2 889.4 1480.7 2094.7 1304.2 1758.0 1669.5 52.5 610.9

30.3 23.7 21.3 15.5 51.8 80.3 19.7 17.2 65.6 37.8 70.1 52.0 67.3 92.4 75.3 52.4 58.6 63.8 91.3 94.8 94.2 91.5 98.3 95.6 85.1 77.9 79.7 87.0 97.9 98.5 96.0 99.7 98.4 95.5 95.6 95.2

1667 1849 2091 2483 2760 3447 3433 3736 3981 3886 4098 4368 416 5061 4728 4699 4863 5009 5361 5151 5309 5895 6183 6034 6302 6561 6592 6733 6796 6539 9960 8081 8386 10026 9528 10139

40


References for 4.2.5.20 88B 89G 911 92H

92s 93G 94B 941 94K 94L 94w 95B 95Hl

95H2 95Wl 95W2

Beichman, C. A., Neugebauer, G., Habing, H. J., Clegg, P. E., Chester, T. J.: Infrared Astronomical Satellite (IRAS) catalogs and atlases, Vol. 1. Explanatory supplement, NASA Ref. Publ. 1190(1988). Grenon, M.: The Hipparcos Mission (eds. M. A. C. Perryman, C. Turon) ESA SP-1111Vol. II (1989) p. 141. ISO-SSD-8805, Scientific Capabilities of the IS0 Payload, Issue 1.O,ESA (1991). Hog, E., Bastian, U., Egret, D., Grewing, M., Halbwachs, J. L., Wicenec, A., Bhsgen, G., Bernacca, P. L., Donati, F., Kovalevsky, J., van Leeuwen, F., Lindegren, L., Pedersen, H., Perryman, M. A. C., Petersen, C., Scales, D., Snijders, M. A. J., Wesselius, P. R.: Astron. Astrophys. 258 (1992) 177. Scales,D. R., Snijders, M. A. J., Andreasen, G. K., Grenon, M., Grewing, M., Hog, E., van Leeuwen, F., Lindegren, L., Mauder, H.: Astron. Astrophys. 258 (1992) 211. GroDmann, V.: IAU Coll. 136, Stellar Photometry - Current Techniques and Future Developments (eds. C. J. Butler and I. Elliot) Cambridge: Univ. Press(1993) p. 246. Buccairelli, B., Holfeltz, S.T., Lattanzi, G.M., Taff, L.G., Vener-Saavedra, P.C.: Publ. Astron. Sot. Pacific 106 (1994) 417. IS0 ScienceOperations Team: Infrared SpaceObservatory Observer’s Manual, version 2.0, ESA/ESTEC, Noordwijk (1994). Klass, U., Kruger, H., Heinrichsen, I., Heske, A., Laureijs, R. (eds.): ISOPHOT Observer’s Manual, version 3.1, ESA/ESTEC, Noordwijk (1994). Lemke, D., Garzon, F., Gemiind, H.-P., GrBzinger, U., Heinrichsen, I., Klaas, U., Kratschmer, W., Kreysa, E., Liitzow-Wentzky, P., Schubert, J., Wells, M., Wolf, J.: Optical Engineering. 33 (1994) 20. Wolf, J., Gabriel, C., Grozinger, U., Heinrichsen, I., Hirth, G., Kirches, S., Lemke, D., Schubert, J., Schulz, B., Tilger, C., Boison, M., Frey, A., Rasmussen,I., Wagner, R., Proetel, K.: Optical Engineering 33 (1994) 26. Burrows, C.J. (ed.): Wide Field and Planetary Camera 2 Instrument Handbook, Version 3.0, Baltimore: STScI publication (1994). Holtzman, J., Hester, J.J., Casertano, S., Trauger, J.T., Waltson, A.M., Ballester, G.E., Burrows, C.J., Clarke, J.T., Crisp, D., Evans, R.W., Gallagher III, J.S., Griffiths, R.E., Hoessel,J.G., Scowen,P.A., Stapelfeldt, K.R., Westphal, J.A.: Publ. Astron. Sot. Pacific 107 (1995) 156. Holfeltz, S.T., Nelan, E.P., Taff, L.G., Lattanzi, G.M.: Fine Guidance Sensors Instrument Handbook, Version 5.0, Baltimore: STScI publication (1995). Whitmore, B.: preprint, Baltimore: STScI publication (1995) Whitmore, B., Heyer, I.: Instrument ScienceReport WFPC2 95-04 (draft), Baltimore: STScI publication (1995).

Land&-Biknstein New Series VI/3b

4.3 Physics of stellar atmospheres

41

4.3 Physics of stellar atmospheres Since the publication of the last contribution on "Physics of Stellar Atmospheres" in the LandoltBörnstein New Series Vol. VI/2b [a] by Baschek and Scholz in 1982, progress has been made mostly in the following fields: — mathematical methods to solve the radiation transport equation, — model construction including numerous lines, also if the LTE approximation does not hold, — connecting the atmospheres with general hydrodynamics, in particular modelling convection and stellar winds, — calculation of nonstandard atmospheres, — calculation of extensive new opacity data. In this supplement contribution we concentrate on giving information on these fields. A more detailed and comprehensive description will be given in the "Handbook of Stellar Atmospheres" [b] to be published by the same authors. Progress has also been achieved in the modelling of atmospheres of accretion disks, where the physics and the methods are strongly related to those of stellar atmospheres. We therefore include also information and references to this field. The subsections in this contribution supplement the following parts of [a]: 4.3.1 Radiative transfer 4.3.2 Line blanketing 4.3.3 Convective energy transport 4.3.4 Chromospheres and coronae 4.3.5 Stellar winds 4.3.6 Atomic and molecular data 4.3.7 Atmospheres of accretion disks

[a] 4.3.3, 4.3.6, 4.3.7 [a] 4.3.6.3 [a] 4.3.6.2 [a] 4.3.7.2 [a] 4.3.7.1 [a] 4.3.4, 4.3.5.1-3 new.

In the appendix, p. 61, errata to [a] are given. As for nomenclature and symbols, we refer to subsect. 4.3.2 of [a].

General references General references which appeared before 1980 are listed in subsect. 4.3.1 of [a]. a

b c d e f

Baschek, B., Scholz, M., in: Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, NS, Vol. VI/2b (K. Schaifers, H.H. Voigt, eds.), Berlin: Springer (1982) p. 91. Baschek, B., Butler, K., Scholz, M., Ulmschneider, P., Wehrse, R.: Handbook of Stellar Atmospheres, Berlin: Springer (1994), in preparation. Böhm-Vitense, E.: Introduction to Stellar Astrophysics, Vol. 2. Stellar Atmospheres, Cambridge: Cambridge University Press (1989). Crivellari, L., Hubeny, I., Hummer, D.G. (eds.): Stellar Atmospheres: Beyond Classical Models, Dordrecht: Kluwer (1991). Gray, D.F.: The observation and analysis of stellar photospheres, 2nd ed., Cambridge: Cambridge University Press (1992). Mihalas. D., Mihalas, B.W.: Foundation of Radiation Hydrodynamics, Oxford: Oxford University Press (1984).

Lando lt -Bö rnst ein New Series VI/3b

42

4.3.2 Stellar atmospheres: Line blanketing

[Ref. p. 44

4.3.1 Radiative transfer Progress has been made mainly in the areas listed in subsections 4.3.1.1-3.

4.3.1.1 Fast numerical methods for 1D media In these methods the 1D radiative transfer equations of the form  ρ ( − kI + σ J + κ B ) ,  DI =  ρ ( − kI +σ J + κ B ) ,  − ρ k ( I − S ) ,

coherent scattering , complete redistribution ,

(1)

general case ,

with  µ  D=  µ 

∂ ∂r ∂ ∂r

,

+

plane - parallel case , 1− µ r

2

∂ ∂µ

(2) ,

spherical case ,

(I = specific intensity, r = radial coordinate, µ = cos of angle between normal and ray direction, σ = scattering coefficient, κ = absorption coefficient, B = Planck function, J = mean intensity, J = mean intensity averaged over a line profile, S = isotropic source function) are considered, i.e., it is assumed that the scattering process is isotropic and that non-LTE as well as velocity effects do not lead to additional terms that depend on the direction. A radiative transfer problem can then be written by means of the Λ operator (see e.g. [73C, 84S, 87K] ), S = Λ S + Sbc ,

(3)

(Sbc represents the boundary conditions) with the solution S = ( 1 − Λ ) −1 Sbc .

(4)

The discretization of eq. (3) with respect to depth, angle and frequency variables usually leads to a very large system of linear equations whose inversion by Gaussian elimination would be extremely costly. Therefore, iterative algorithms like the Jacobi iteration (called "accelerated lambda iteration" in the astronomical literature, c.f. [73C, 84S, 87K]), the conjugate gradient algorithm [87A], or the multigrid method [91S1] are used for eq. (4). These methods usually converge well and consist mainly of vector-vector and matrix-vector operations that are extremely fast on computers of modern architecture. For comprehensive descriptions see [91K]. These algorithms therefore allow fast and reliable solutions of the transfer problem in the cases indicated.

4.3.1.2 Methods for moving envelopes The radiative transfer equation in the Lagrangian ("comoving") frame for fast moving spherical shells that includes all special-relativistic terms,

Landolt-Börnstein New Series VI/3b

Ref. p. 44]

γ ( µ0 + β )

4.3.1 Stellar atmospheres: Radiative transfer 2  1 + βµ γ ∂β 2 0 + γ (1 − µ 0 )  − (1 + βµ 0 ) −γ  r ∂r c ∂t

∂I 0

 β (1− µ 2 ) γ 2 ∂β 0 −γ  + +γ (1 + β µ 0 )  ∂t r c

2

µ0 ( µ0 + β )

2

( µ0 + β )

43 ∂β  ∂I 0  ∂ r  ∂µ 0

∂I ∂β   ν0 0 ∂ r  ∂ν 0

(5)

 β (1 − µ 2 ) γ 2 µ ∂β ∂β  2 0 0  I 0 = ρ k 0 ( S 0 − I 0 ), + 3γ  + +γ µ 0 ( µ 0 + β ) (1 + β µ 0 )  ∂t ∂ r  r c is given in [f, sect. 95]. The subscript 0 indicates quantities in the comoving frame, β = v / c is the ratio of the matter velocity to the speed of light, and γ = 1 / 1 − β 2 . Note that due to the frequency derivative and the additional extinction-type term (last term on the left hand side) frequency averages of the extinction become velocity-dependent and therefore, e.g., the use of static Rosseland mean values in gray calculations can introduce large errors. In the Eulerian frame this effect is a result of the direction dependence of the extinction. If the velocity field is monotonic the determination of the radiation field represents a boundary value problem in the spatial and angle coordinates and an initial value problem in the frequencies, otherwise it is a full three-dimensional boundary value problem that, however, is not yet satisfactorily solved. In the former case, two methods of solution have emerged: (i) The frequency derivative is discretized in the upwind direction leading to a form that is equivalent to the static equation. However, it contains the intensities at the previous frequency and a modified opacity. With the assumption of a Dirichlet boundary condition at either very high or very low frequencies (depending on the sign of the motion) it can then be solved by the standard methods for spherical radiative transfer [87P, 91H]. (ii) The characteristic equation is solved piecewise from spatial grid point to spatial grid point. The transfer equation is then solved by integration along the characteristics [f, 92H]. The Sobolev method [60S] has recently also been generalized to treat continuum absorption [85H] and relativistic velocities [93J]. However, advection and aberration terms are neglected.

4.3.1.3 Methods for multidimensional configurations The calculation of a 3D radiation field is straightforward if LTE can be assumed since the rays do not couple in this case and therefore only integrations along light rays are required (cf. the transfer equation (6) given in subsect. 4.3.3). If, however, scattering is nonnegligible the different directions and possibly also the frequencies couple and therefore the full five- or six-dimensional integrodifferential equation (depending whether or not velocities are involved) has to be solved. Recently, grid methods that can cope with the associated huge amount of data have been developed for static and slowly moving media (in which aberration and advection can be neglected). In these cases an Euclidian coordinate system can be employed in which the angles couple only in the scattering integral. In a simple finite difference method [91S2] the spatial coordinates of the transfer equation are discretized in the upwind direction. If the source function is assumed to be known the discretized equations can efficiently be solved by recursion. The source function is then found in an outer loop by a lambda iteration, a successive overrelaxation iteration or an extrapolation method (cf. [91K]). The disadvantages of this method (fixed grid, slow convergence in high scattering cases) can be overcome by nonconforming finite element methods on unstructured grids [93T]. For the solution of the resulting linear system the bi-stab variant of the conjugate gradient method with preconditioning has been found to be extremely advantageous. Existence and uniqueness of such solutions has been demonstrated in [93F].


44


[Ref. p. 45

References for 4.3.1 For general references [a]⋅⋅⋅[f] see p. 41 60S 73C 84S

Sobolev, V.: Moving Envelopes of Stars, Cambridge, MA.: Harvard University Press (1960). Cannon, C.: J. Quant. Spectrosc. Radiat. Transfer. 13 (1973) 627. Scharmer, G.B., in: Methods in radiative transfer (W.Kalkofen, ed.), Cambridge: Cambridge University Press (1984) p. 173. 85H Hummer, D.G., Rybicki, G.: Astrophys. J. 293 (1985) 258. 87A Auer, L.H., in: Numerical radiative transfer (W. Kalkofen, ed.), Cambridge: Cambridge University Press (1987) p. 101. 87K Kalkofen, W., in: Numerical radiative transfer (W. Kalkofen, ed.), Cambridge: Cambridge University Press (1987) p. 191. 87P Peraiah, A., in: Numerical radiative transfer (W. Kalkofen, ed.), Cambridge: Cambridge University Press (1987) p. 305. 91H Hauschildt, P.H., Wehrse, R.: J. Quant. Spectrosc. Radiat. Transfer. 46 (1991) 81. 91K Kincaid, D., Cheney, W.: Numerical Analysis, Pacific Grove: Brooks/Cole Publ. Comp. (1991). 91S1 Steiner, O., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 19. 91S2 Stenholm, L.G., Störzer, H., Wehrse, R.: J. Quant. Spectrosc. Radiat. Transfer. 45 (1991) 47. 92H Hauschildt, P.H.: J. Quant. Spectrosc. Radiat. Transfer. 47 (1992) 433. 93F Führer, Ch.: Diploma Thesis, Universität Heidelberg (1993). 93J Jefferey, D.J.: Harvard-Smithsonian Center for Astrophysics, Preprint (1993). 93T Turek, S.: Impact of Computing on Science and Engineering 5 (1993) 201.

4.3.2 Line blanketing 4.3.2.1 Statistical treatment Radiation transport in static stellar atmospheres whose spectra are dominated by numerous lines is routinely treated either by the technique of opacity {probability} distribution function (O{P}DF; see [78M sect. 7.2, and 79K]) or by the technique of opacity sampling (OS; see [76S]). See [92J] for an extensive review. In the ODF approach, the total spectrum is split up into frequency intervals so chosen that both the Planck functions belonging to the temperatures of all atmospheric layers and the continuous absorption and scattering coefficients are approximately constant over the interval width. Within each interval, the run of the sum of line absorption coefficients is rearranged in such a way that it becomes a monotonous function of frequency which thereafter is approximated by a step function, i.e., by a sequence of constant ODF values within appropriate sub-intervals. The radiation transport equation is solved for each sub-interval, and the radiative flux of each interval is obtained by frequency integration over its sub-intervals. The ODF technique assumes that the extinction coefficient may be written as the sum of the coefficients of line absorption, continuous absorption and continuous scattering, and that these coefficients may be pre-computed in the LTE approximation ([a] subsect. 4.3.4.6) as functions of temperature and gas pressure. It also assumes that, if, for any pair of frequencies within the interval, the line absorption coefficient at one of these frequencies is larger in one layer, it is also larger in any other layer so that the typical behaviour of monochromatic optical depths as functions of the geometrical depth is not altered by the rearrangement of coefficients. Therefore, stellar atmospheres in which different species of important lines (e.g. molecular lines) occur in different layers within the same frequency range must not be treated by the ODF formalism. Pre-computed ODF tables refer to a given chemical composition and a given microturbulent velocity. For spectra dominated by molecular lines, the Voigt-analogue-Elsasser band model (VAEBM, [69G]) is widely used as a simple and often


44


[Ref. p. 45

References for 4.3.1 For general references [a]⋅⋅⋅[f] see p. 41 60S 73C 84S

Sobolev, V.: Moving Envelopes of Stars, Cambridge, MA.: Harvard University Press (1960). Cannon, C.: J. Quant. Spectrosc. Radiat. Transfer. 13 (1973) 627. Scharmer, G.B., in: Methods in radiative transfer (W.Kalkofen, ed.), Cambridge: Cambridge University Press (1984) p. 173. 85H Hummer, D.G., Rybicki, G.: Astrophys. J. 293 (1985) 258. 87A Auer, L.H., in: Numerical radiative transfer (W. Kalkofen, ed.), Cambridge: Cambridge University Press (1987) p. 101. 87K Kalkofen, W., in: Numerical radiative transfer (W. Kalkofen, ed.), Cambridge: Cambridge University Press (1987) p. 191. 87P Peraiah, A., in: Numerical radiative transfer (W. Kalkofen, ed.), Cambridge: Cambridge University Press (1987) p. 305. 91H Hauschildt, P.H., Wehrse, R.: J. Quant. Spectrosc. Radiat. Transfer. 46 (1991) 81. 91K Kincaid, D., Cheney, W.: Numerical Analysis, Pacific Grove: Brooks/Cole Publ. Comp. (1991). 91S1 Steiner, O., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 19. 91S2 Stenholm, L.G., Störzer, H., Wehrse, R.: J. Quant. Spectrosc. Radiat. Transfer. 45 (1991) 47. 92H Hauschildt, P.H.: J. Quant. Spectrosc. Radiat. Transfer. 47 (1992) 433. 93F Führer, Ch.: Diploma Thesis, Universität Heidelberg (1993). 93J Jefferey, D.J.: Harvard-Smithsonian Center for Astrophysics, Preprint (1993). 93T Turek, S.: Impact of Computing on Science and Engineering 5 (1993) 201.

4.3.2 Line blanketing 4.3.2.1 Statistical treatment Radiation transport in static stellar atmospheres whose spectra are dominated by numerous lines is routinely treated either by the technique of opacity {probability} distribution function (O{P}DF; see [78M sect. 7.2, and 79K]) or by the technique of opacity sampling (OS; see [76S]). See [92J] for an extensive review. In the ODF approach, the total spectrum is split up into frequency intervals so chosen that both the Planck functions belonging to the temperatures of all atmospheric layers and the continuous absorption and scattering coefficients are approximately constant over the interval width. Within each interval, the run of the sum of line absorption coefficients is rearranged in such a way that it becomes a monotonous function of frequency which thereafter is approximated by a step function, i.e., by a sequence of constant ODF values within appropriate sub-intervals. The radiation transport equation is solved for each sub-interval, and the radiative flux of each interval is obtained by frequency integration over its sub-intervals. The ODF technique assumes that the extinction coefficient may be written as the sum of the coefficients of line absorption, continuous absorption and continuous scattering, and that these coefficients may be pre-computed in the LTE approximation ([a] subsect. 4.3.4.6) as functions of temperature and gas pressure. It also assumes that, if, for any pair of frequencies within the interval, the line absorption coefficient at one of these frequencies is larger in one layer, it is also larger in any other layer so that the typical behaviour of monochromatic optical depths as functions of the geometrical depth is not altered by the rearrangement of coefficients. Therefore, stellar atmospheres in which different species of important lines (e.g. molecular lines) occur in different layers within the same frequency range must not be treated by the ODF formalism. Pre-computed ODF tables refer to a given chemical composition and a given microturbulent velocity. For spectra dominated by molecular lines, the Voigt-analogue-Elsasser band model (VAEBM, [69G]) is widely used as a simple and often



45

adequate variant of the ODF method. Surface fluxes emitted in specific filter bands may be calculated directly from sufficiently narrow ODF intervals. In the OS approach, the radiation transport equation is solved at randomly sampled frequencies, and the radiative flux is obtained by frequency integration based on these sampled frequencies. The number of sampled frequencies is successively increased until further augmentation does not change the atmospheric stratification and the radiative flux within the requested accuracy limits. The extinction coefficient at any sampled frequency is the sum of all core and wing absorption contributions of neighbouring lines and of the continuous absorption and scattering coefficients. The LTE approximation ([a] subsect. 4.3.4.6) is assumed to hold. Though the OS method (typically 103 to a few times 103 frequencies) is usually more costly than the ODF technique (typically 102 to a few times 102 frequency intervals with < 5 to 10 subintervals), it has gained wide acceptance because it is not restricted to a specific frequency-layer-dependence of absorption coefficients and because it is more flexible with respect to varying chemical compositions, turbulent velocities and large-scale velocity fields (not treatable by ODFs). Computation of surface fluxes emitted in specific filter bands, however, requires an individual sampling procedure for each filter, eventually resulting in a huge number of monochromatic radiation transport equations to be solved for calculating realistic spectra. A statistical scheme for treating line blanketing in kinetic equilibrium instead of assuming LTE is proposed by Anderson [87A, 91A] and has tentatively been employed to selected stellar model atmospheres. 4.3.2.2 Individual lines outside LTE Except for the above mentioned statistical approach [87A, 91A], lines are treated individually in models without the LTE approximation. Progress has been made here mainly due to the implementation of fast solvers for the radiative transfer equation (cf. subsect. 4.3.1.1), the use of modern variants of the Newton-Raphson scheme for the effective solution of large systems of nonlinear algebraic equations (such as the quasi-Newton approach in [65B], see also [92P]) in the evaluation of the rates, the availability of large sets of accurate cross-sections (see subsect. 4.3.6) and last but not least due to the improvements in computer technology (fast processors, vector processors, fast access memory). By utilizing these advantages it is now not only possible to take the proper depth variation of the profile function into account but also to include up to approximately 200 levels with 800 transitions from about a dozen ions consistently in a single model atmosphere [91R]. With some compromises regarding the accuracy of the radiative transfer it is even possible to replace for hot stars the assumption of hydrostatic equilibrium by a hydrodynamic description that also takes stellar winds ([91P], cf. subsect. 4.3.5) into account.

References for 4.3.2 For general references [a]⋅⋅⋅[f] see p. 41 65B 69G 76S 78M 79K 87A 91A 91P

Broyden, C.G.: Math. Comput. 19 (1965) 577. Golden, S.A.: J. Quant. Spectrosc. Radiat. Transfer 9 (1969) 1067. Sneden, C., Johnson, H.R., Krupp, B.M.: Astrophys. J. 204 (1976) 281. Mihalas, D.: Stellar Atmospheres, 2nd ed., San Francisco: Freeman (1978). Kurucz, R.L.: Astrophys. J. Suppl. 40 (1979) 1. Anderson, L.S., in: Numerical Radiative Transfer (W. Kalkofen, ed.), Cambridge: Cambridge University Press (1987) p. 163. Anderson, L., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 29. Puls, J., Pauldrach, A.W.A., in: Stellar Atmospheres Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 175.


46

4.3.3 Stellar atmospheres: Convective energy transport

91R 92J 92P

[Ref. p. 47

Rauch, T., Werner, K., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 165. Jørgensen, U.G.: Rev. Mex. Astron. Astrofis. 23 (1992) 195. Press, W., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes, Cambridge: Cambridge University Press (1992).

4.3.3 Convective energy transport Diverse modifications and extensions of the mixing length approach have been developed in the past two decades (see [90S] for a comprehensive review), including non-local generalizations describing, e.g., overshooting of convective motions into stable layers. Since these formalisms are of only limited usefulness for the treatment of atmospheric layers, recent work has been concentrated on the solution of the general set of radiation transport and hydrodynamic equations with various simplifying assumptions. The equation of radiation transport is 1 ∂ Iν + n ⋅ ∇ Iν = − ρ ( kν Iν − jν ) = − ρ kν ( Iν − Sν ) , c ∂t

(6)

in Cartesian coordinates (otherwise see [f, chs. 6/7]), and its solution yields both the radiative flux vector, ∞

π F rad = ∫ 0 ∫ Iν n d Ω dν ,

(7)

and the radiative acceleration, g rad = −

1 1 1 ∇ ⋅ Prad = − ∇⋅ ( c ρ ρ

∞

∫0 ∫ Iν nn d Ω dν ) ,

(8)

expressed through the radiation pressure tensor Prad . Here, ρ is the local density of matter, and the ray of intensity Iν propagates in the direction of the unit vector n. Current computations adopt isotropic extinction (kν ) and emission ( jν ) coefficients (neglecting the strong anisotropy of line coefficients in the presence of turbulent convective motions) and a LTE type source function, jν = kν Sν = kν Bν , resulting in a very simple representation of the radiative flux gradient (cf. subsect. 4.3.1.3), ∞

π ∇ ⋅ F rad ≅ − 4 π ρ ∫ kν ( Jν − Bν ) dν , 0

(9)

from eq. (6) where ∂ I ν ∂ t is always negligible in practice. The equation of momentum conservation (Navier-Stokes equation) is  ∂v  ρ + v ⋅ ∇ v  = −∇Pg + ρ ( g + g rad + g visc + ) ,  ∂t 

(10)

where v is the local velocity of matter, Pg the local gas pressure, g the gravitational acceleration, grad the radiative acceleration after eq. (8), and gvisc the viscous acceleration, g visc = −

1 ∇ ⋅ Pvisc , ρ

(11a)

expressed through the viscous stress tensor Pvisc with  ∂v ∂v j  1  − (η ′− 2η ) δ ij ∇ ⋅ v . Pij = −η  i +  ∂ x j ∂ xi  3

(11b)


46


91R 92J 92P

[Ref. p. 47

Rauch, T., Werner, K., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 165. Jørgensen, U.G.: Rev. Mex. Astron. Astrofis. 23 (1992) 195. Press, W., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes, Cambridge: Cambridge University Press (1992).

4.3.3 Convective energy transport Diverse modifications and extensions of the mixing length approach have been developed in the past two decades (see [90S] for a comprehensive review), including non-local generalizations describing, e.g., overshooting of convective motions into stable layers. Since these formalisms are of only limited usefulness for the treatment of atmospheric layers, recent work has been concentrated on the solution of the general set of radiation transport and hydrodynamic equations with various simplifying assumptions. The equation of radiation transport is 1 ∂ Iν + n ⋅ ∇ Iν = − ρ ( kν Iν − jν ) = − ρ kν ( Iν − Sν ) , c ∂t

(6)

in Cartesian coordinates (otherwise see [f, chs. 6/7]), and its solution yields both the radiative flux vector, ∞

π F rad = ∫ 0 ∫ Iν n d Ω dν ,

(7)

and the radiative acceleration, g rad = −

1 1 1 ∇ ⋅ Prad = − ∇⋅ ( c ρ ρ

∞

∫0 ∫ Iν nn d Ω dν ) ,

(8)

expressed through the radiation pressure tensor Prad . Here, ρ is the local density of matter, and the ray of intensity Iν propagates in the direction of the unit vector n. Current computations adopt isotropic extinction (kν ) and emission ( jν ) coefficients (neglecting the strong anisotropy of line coefficients in the presence of turbulent convective motions) and a LTE type source function, jν = kν Sν = kν Bν , resulting in a very simple representation of the radiative flux gradient (cf. subsect. 4.3.1.3), ∞

π ∇ ⋅ F rad ≅ − 4 π ρ ∫ kν ( Jν − Bν ) dν , 0

(9)

from eq. (6) where ∂ I ν ∂ t is always negligible in practice. The equation of momentum conservation (Navier-Stokes equation) is  ∂v  ρ + v ⋅ ∇ v  = −∇Pg + ρ ( g + g rad + g visc + ) ,  ∂t 

(10)

where v is the local velocity of matter, Pg the local gas pressure, g the gravitational acceleration, grad the radiative acceleration after eq. (8), and gvisc the viscous acceleration, g visc = −

1 ∇ ⋅ Pvisc , ρ

(11a)

expressed through the viscous stress tensor Pvisc with  ∂v ∂v j  1  − (η ′− 2η ) δ ij ∇ ⋅ v . Pij = −η  i +  ∂ x j ∂ xi  3

(11b)



47

Current studies use rough representations of the viscosity η (turbulent viscosity expressed in terms of v and its derivatives, e.g. [91S]) and neglect the bulk viscosity η ′ . The equations of energy and mass conservation are ∂u = − π ∇ ⋅ ( Frad + Fmat + ) , ∂t

(12)

∂ρ = −∇ ⋅ ( ρ v ) , ∂t

(13)

and

respectively. The energy density per unit volume, u, comprises the energy of the radiation field as well as of the matter (gravitational, kinetic, internal). The radiative flux vector π Frad is given by eq. (7), and its divergence is approximated by eq. (9). The quantity π Fmat contains the energy flux contributions carried by matter (gravitational, kinetic, heat content), and its divergence must describe the transport and the transformation of turbulent kinetic energy and heat in an adequate approximation (e.g. [91S]). Apart from the already mentioned approximations and from the omission of magnetic forces in the momentum equation and of magnetic flux contributions in the energy equation, numerous further simplifications are adopted in present radiation-hydrodynamic modelling of convection which, therefore, is usually called numerical simulation of convection. Typical simplifying assumptions found in the literature include: grey approximation using the Rosseland mean k R in eq. (9) or quasi-gray treatment based on a small set of mean extinction coefficients mimicking the opacity distribution in the relevant frequency range; neglect of grad and/or gvisc in eq. (10); cylindrical symmertry; anelastic approximation with ∇ ⋅ ( ρ v ) = 0 ; etc. Numerical restrictions include: minimal spatial and time resolution; size and boundary conditions of the model domain; duration and initial conditions of the model evolution; etc. More details and literature may be found, e.g., in [90S, 91S, 92S].

References for 4.3.3 For general references [a]⋅⋅⋅[f] see p. 41 90S 91S 92S

Spruit, H.C., Nordlund, Å., Title, A.M.: Annu. Rev. Astron. Astrophys. 28 (1990) 263. Steffen, M., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 247. Schüssler, M., in: The Sun – a Laboratory for Astrophysics (J.T. Schmelz, J.C. Brown, eds.), Dordrecht: Kluwer (1992) p. 81.


48

4.3.4 Stellar atmospheres: Chromospheres and coronae

[Ref. p. 52

4.3.4 Chromospheres and coronae Essentially stellar chromospheres and coronae. (Sun only so far as relevant for application for stellar atmospheres.) 4.3.4.1 Mechanical heating and modification of the energy equation Chromospheres and coronae owe their existence to mechanical heating. Mechanical heating, associated with a flux π Fmech , is a process which converts hydrodynamic or magnetic energy into microscopic random (thermal) motion. Here a distinction is made against the physics of stellar photospheric and interior layers, where the energy input is exclusively due to radiation, thermal conduction and convection (associated with the fluxes π Frad , π Fcond , π Fconv , respectively). From the mechanical flux π Fmech (energy per unit area and unit time) a heating rate per unit volume and unit time, ρ ε mech , is obtained from the expression

ρε mech

 ∂( π Fmech ) , −  ∂z =  1 ∂( r 2 π Fmech ) , − 2  r ∂r

plane atmosphere , (14) spherical atmosphere ,

where z is the geometrical height and r the radial direction (both z and r are in outward direction, measured from optical depth τ = 1). Note that the physical fluxes are denoted throughout this chapter by π F in order to be consistent with the definition of the radiative flux π Frad in [b] (here F = "astrophysical flux"). 4.3.4.1.1 Classification of heating mechanisms The mechanical heating mechanisms can broadly be devided into hydrodynamic mechanisms and magnetic mechanisms; the latter are further subdivided into AC (alternating current) or wavemechanisms and DC (direct current) or nonwave mechanisms [90N, 91U]. The following heating mechanisms have been proposed: Hydrodynamic mechanisms acoustic waves pulsational waves accretion flows turbulent flows shear flows

AC magnetic mechanisms slow MHD waves fast MHD waves transverse Alfvén waves torsional Alfvén waves Alfvén surface waves

DC magnetic mechanisms current heating flare heating magnetic flux emergence

4.3.4.1.2 Simple heating laws Often, heating rates proportional to the density or the volume are used [82M1, 89A2]:

ρε mech ∝ ρ , or ε mech = const. ,

(15)

or heating rates with a prescribed constant damping length lmech [74L, 80H, 82H1],

ρε mech =

π Fmech . l mech

(16)

Together with eq. (14), they represent simple heating laws.


Ref. p. 52]


49

4.3.4.1.3 Hydrodynamic shock heating laws Weak shock heating law For linear small-amplitude sawtooth waves (often called weak shock waves) the shock strength is defined as

η ≡ (ρ 2 − ρ1) / ρ1 ,

(17)

where ρ1 , ρ2 are the densities in front and behind the shock, respectively. With η, the mechanical flux of the waves can be written [70U] π Fmech =

1 γ Pg c s η 2 , 12

(18)

where γ is the ratio of specific heats, cs the sound speed and Pg the unperturbed gas pressure. Note that according to various reasonings other numerical factors on the right hand side of eq. (18) are given: 1/8 in [49S, p.210] and [61O, eqs. 64, 66], 1/12 in [60W, p. 454], 1/3 in [65K, p. 30, 31] and [74B, eqs. 7.23, 7.30). The shock heating rate for a wave of frequency ν is given by

ρε mech =

1 γ ( γ + 1) ν Pg η 3 . 12

(19)

From eqs. (18) and (19) a weak shock heating law can be derived [61O, 70U] in terms of the shock strength, ∂η ∂z

=

2 η  γ g 3 ∂ c s (γ + 1)ην   2 − 2  , − 2  cs 2 cs ∂ z cs 

(20)

where g is the gravitational acceleration. For an isothermal, neutral or fully ionized atmosphere eq. (20) shows that the shocks eventually reach a limiting strength

η lim =

γg , ( γ + 1) ν cs

(21)

with a limiting wave flux lim = π Fmech

γ 3g2 1 Pg . 12 ( γ + 1) 2 ν 2cs

(22)

A different form of the weak shock heating law is ∂( π Fmech ) πF 1 ∂cs2 =− 2 πFmech − mech , ∂z cs ∂z lmech

(23)

with the weak shock acoustic damping length l mech

 γ P c3 g s =   12 (γ + 1) 2 

   

1/ 2

1

ν ( π Fmech )

12

=

cs (γ + 1) ν η

.

(24)

The validity of eq. (21) for realistic cases is discussed in [88C]. For applications of the weak shock heating law see e.g. [70U, 80C, 81H, 82H1, 89K1]. Strong acoustic shock heating laws Using the shape similarity invariance found experimentally, strong shock heating laws are derived by [64B1, 64B2, 67U] based on the work of Brinkley and Kirkwood [47B]. See also [71U, 79P, 83F].


50


[Ref. p. 52

Time-dependent acoustic shock heating Shock heating in time-dependent cases is treated according to the employed numerical scheme. In characteristics methods the shocks are treated as discontinuities, where the physical variables on both sides of the discontinuity are known. One has  P2 = ln  γ (γ − 1)  P1 2

ρε mech

ν ρ 1 cs

ρ   2   ρ1

−γ

 ,  

(25)

where P1 , P2 are the pressures in front and behind the shock, respectively. In finite difference methods the shock heating, using an artificial viscosity q, is smeared out over several regular grid points [67R (eq. 12.41), 79T]. Here the shock heating rate is

ρε mech

 ∂( q v ) ,  =  ∂r  ∇ ⋅ (q v ) ,

plane case , (26) spherical case .

See [76K, 77U, 83M1, 83M2] for a review of time-dependent calculations of radiative (magneto-) hydrodynamic wave propagation in stellar atmospheres see [86U]. 4.3.4.1.4 Magnetic heating laws For fast- and slow-mode magnetohydrodynamic waves time-independent weak shock heating formulae are given in [61O], see also [74B]. These and other time-independent heating formulas for body and surface Alfvén waves are reviewed in [90N]. A review of the heating of Alfvén waves is given by [91P], see also [92M4]. Alfvén wave trapping and heating is discussed by [91M] and [91R]. For timedependent longitudinal magnetohydrodynamic waves the shock heating rate is calculated from the known physical state in front and behind the shock [85H]. Heating formulas by anomalous Joule dissipation in a thin sheet around coronal loops are given by [78R]. Heating formulas valid for reconnection of entangled magnetic fields are given by [85V, 86V]. For a review of magnetic non-wave heating mechanisms see [90N].

4.3.4.2 Modelling of chromospheres and coronae 4.3.4.2.1 Empirical chromosphere models There are two types of empirical chromosphere models: continuum and line models. Continuum models For a given atmospheric temperature distribution, assuming multilevel non-LTE radiative transfer as well as hydrostatic and statistical equilibrium, the UV-continua of H I, He I, C I, Si I, Fe I together with other spectral features are simulated and compared with observations. An optimal fit of the observed and simulated continuum spectra determines the temperature distribution [76V, 81V, 85A]. Inclusion of the energy balance in the transition-layer and of ambipolar diffusion removes artifacts, such as a chromospheric temperature plateau [90F, 91F]. The chromospheric energy balance is considered in [89A1, 89A2]. Line models These models are constructed similarly to the continuum models, except that instead of continua, the strong chromospheric lines of Ca II K and Mg II h+k are fitted, assuming partial redistribution. Fitting the wings of the line leads to a photospheric temperature enhancement compared to a radiative equilibrium temperature distribution. The fit of the emission core determines the chromospheric temperature rise. The procedure is described by [78K, 79L]. For the Sun see models by [76A, 78L, 79B2, 79L]; for the stars see the reviews [80L, 87J2, 90R].


Ref. p. 52]


51

4.3.4.2.2 Empirical transition-layer models Starting from chromospheric line models the structure of the upper chromosphere and the transition layer can be improved by fitting lines of C II, Si II and Si III in addition to the Ca II and Mg II lines [79B1, 80S2], see also [80A]. Transition-layer models based upon emission-measure modelling are independent from chromosphere models and can be used to check the consistency of the two types of empirical models. High chromosphere and transition-layer emission line fluxes are used to derive loci of local emission 2 measure, E m = ∫ n e dr , versus temperature for individual lines as well as an emission-measure distribution versus temperature for the entire transition layer. It is assumed that the lines are collisionally excited and effectively thin. From the emission-measure distribution, the pressure distribution is computed assuming hydrostatic equilibrium on the basis of an estimated value of the pressure Ptop at the top of the transition layer. A consistent fit of the emission-measure loci of densitysensitive forbidden lines with the global emission-measure distribution is used to determine Ptop . For details see [81B, 81J, 87J1, 92H, 92M1].

4.3.4.2.3 Empirical corona models Using upper transition layer emission lines and X-ray observations, high transition layer and corona models can be constructed on basis of various plausible magnetic field configurations [76G, 77G, 87J1, 88W, 92H]. 4.3.4.2.4 Theoretical chromosphere models Theoretical chromosphere models are constructed by assuming a heating mechanism (or heating law) and an incident heating flux at the inner boundary of the model. In time-independent models the heating law is solved together with a radiative cooling law satisfying the energy balance and hydrostatic equilibrium. In the transition layer, thermal conduction is taken into account. For models of this type see [70U1, 71U, 82M2]. These models may be improved by including wave pressure [90G]. Time-dependent models have so far been attempted only for acoustic or magnetohydrodynamic wave heating mechanisms. In these models for a given incident wave energy flux, the time-dependent hydrodynamic equations are solved together with the non-LTE radiative transfer equations and statistical equilibrium equations for a few dominant chromospheric emitters. For the procedure of model construction see [77U, 85S, 87U], for the Sun see [87U, 85S, 87U, 92R], for stars [79U, 80S1, 81S, 89U]. For a full time-dependent treatment, also solving the time-dependent rate equation, see [92C1].

4.3.4.2.5 Theoretical corona models Simple isothermal models Good insight into the general behaviour of coronae is provided by a simple model which represents the corona by an isothermal atmospheric slab, to which at the bottom a thin transition layer is attached, and which extends up to the critical point. The model is constructed [75H, 79E], by requiring hydrostatic equilibrium as well as energy balance between mechanical heating and radiative cooling, thermal conductive cooling and wind cooling. The radiative cooling is provided by a simple radiation law using the thin plasma approximation [75M, 77M]. The model requires a heating mechanism which specifies both the incident mechanical heating flux πFmech at the bottom and the way by which this heating flux is to be dissipated. As the coronal heating mechanism is unknown, a simple heating formula is used with a specified constant damping length lmech . The models thus depend on two free parameters πFmech Lando lt -Bö rnst ein New Series VI/3b

52


and lmech . At the fitting point between the corona and the transition layer, thermal conduction, which dominates the transition-layer losses, is discontinuous. Therefore, for consistency, at this point the largest mechanical dissipation must occur. To satisfy this condition, the height of the fitting point has to be chosen roughly equal to lmech . This choice removes models with the same πFmech but other fitting heights. Time-independent models Time-independent models for the transition layer and corona are constructed by solving the mass , momentum, and energy conservation laws. The energy balance is similar as in the isothermal corona model. The heating mechanism is represented by a simple heating law with the incident mechanical heating flux πFmech and a damping length lmech as free parameters. Similarly as in the case of the isothermal corona model, these two quantities uniquely determine the corona model. The stellar wind equation, derived from the mass and momentum equations, is solved by requiring that the solution goes through the critical point (supersonic wind solution) and at infinity shows vanishing gas pressure. For different solution methods, solar type models and scaling laws for stellar models see [81H, 82H1, 82H2, 84H]. Time-dependent models Time-dependent solar and stellar models using a weak shock acoustic heating law are constructed by solving the time-dependent versions of the mass, momentum and energy conservation equations over the entire range from the chromosphere up to roughly 1000 stellar radii. As the weak shock heating law automatically provides a damping length, the models depend only on one free parameter, πFmech . It was found that if πFmech becomes larger than a critical value, the corona model has a time-dependent behaviour, in which the corona is periodically collapsing and rebuilding itself [88K, 89K1, 89K2, 89K3]. 4.3.4.2.6 Tube models and other special geometries Time-independent siphon flows in magnetic flux tubes have been computed by [88T], time-dependent flows in coronal loops or spicules by [80N, 83M1, 83M2, 88H, 92C2, 92C3, 92C4]. 4.3.4.3 Coronae of accretion disks Corona models of accretion disks are discussed by [79G, 82W, 84S, 86S, 88A], and more recently by [92M2, 92M3];see also [91H].

References for 4.3.4 For general references [a]⋅⋅⋅[f] see p. 41 47B 49S 60W 61O 64B1 64B2 65K 67R 67U 70U 71J

Brinkley, S.R., Kirkwood, J.G.: Phys. Rev. 71 (1947) 606. Schatzman, E.: Ann. Astrophys. 12 (1949) 203. Weymann, R.: Astrophys. J. 132 (1960) 452. Osterbrock, D.E.: Astrophys. J. 134 (1961) 347. Bird, G.A.: Astrophys. J. 139 (1964) 675. Bird, G.A.: Astrophys. J. 139 (1964) 684. Kuperus, M.: Rech. Astron. Observ. Utrecht 17 (1965) 1. Richtmyer, R.D., Morton, K.W.: Difference Methods for Initial Value Problems, 2nd ed.,New York: Interscience (1967). Ulmschneider, P.: Z. Astrophys. 67 (1967) 193. Ulmschneider, P.: Sol. Phys. 12 (1970) 403. Jordan, C., Wilson, R., in: Physics of the Solar Corona (C.J. Macris, ed.), Dordrecht: Reidel (1971) p. 219.


4.3.4 Stellar atmospheres: Chromospheres and coronae 71U 74B 74L 75H 75M 76A 76G 76K 76V 77G

77M 77U 78K 78L 78R 78U 79B1 79B2 79E 79G 79L 79P 79T 79U 80A 80C 80H 80L 80N 80S1 80S2 81B 81H 81J 81S 81V 82H1 82H2 82M1 82M2 82W 83F 83M1

53

Ulmschneider, P.: Astron. Astrophys. 12 (1971) 297. Bray, R.J., Loughhead, R.E.: The Solar Chromosphere, London: Chapman and Hall (1974). Lamers, H.J.G.L.M., Kuperus, M., in: Ph.D. Thesis H.J.G.L.M. Lamers, Univ. Leiden, Netherlands (1974) p. 169. Hearn, A.G.: Astron. Astrophys. 40 (1975) 355. McWhirter, R.W.P., Thonemann, P.C., Wilson, R.: Astron. Astrophys. 40 (1975) 63. Ayres, T.R., Linsky, J.L.: Astrophys. J. 205 (1976) 874. Gabriel, A.H.: Philos. Trans. R. Astron. Soc. London A 281 (1976) 339. Klein, R.I., Stein, R.F., Kalkofen, W.: Astrophys. J. 205 (1976) 499. Vernazza, J.E., Avrett, E.H., Loeser, R.: Astophys. J. Suppl. 30 (1976) 1. Gabriel, A.H., in: The Energy Balance and Hydrodynamics of the Solar Chromosphere and Corona, IAU Coll. 36 (R.M. Bonnet, Ph. Delache, eds.), Clermont-Ferrand: G. de Bussac (1977) p. 375. McWhirter, R.W.P., Thonemann, P.C., Wilson, R.: Astron. Astrophys. 61 (1977) 859. Ulmschneider, P., Kalkofen, W., Nowak, T., Bohn, H.U.: Astron. Astrophys. 54 (1977) 61. Kelch, W.L., Linsky, J.L., Basri, G.S., Chiu, H.-Y., Chang, S.-H., Maran, S.P., Furenlid, I.: Astrophys. J. 220 (1978) 962. Linsky, J.L., Ayres, T.R.: Astrophys. J. 220 (1978) 619. Rosner, R., Golub, L. Coppi, B., Vaiana, G.S.: Astrophys. J. 222 (1978) 317. Ulmschneider, P., Schmitz, F., Kalkofen, W., Bohn, H.U.: Astron. Astrophys. 70 (1978) 487. Baliunas, S.L., Avrett, E.H., Hartmann, L., Dupree, A.K.: Astrophys. J. 233 (1979) L129. Basri, G.S., Linsky J.L., Bartoe, J.-D.F., Brueckner, G., Van Hoosier, M.E.: Astrophys. J. 230 (1979) 924. Endler, F., Hammer, R., Ulmschneider, P.: Astron. Astrophys. 73 (1979) 190. Galeev, A.A., Rosner, R., Vaiana, G.S.: Astrophys. J. 229 (1979) 318. Linsky, J.L., Worden, S.P., McClintock, W., Robertson, R.M.: Astrophys. J. Suppl. 41 (1979) 47. Pineau des Forêts, G.: Astron. Astrophys. 78 (1979) 159. Tscharnuter, W.M., Winkler, K.-H.: Comput. Phys. Commun. 18 (1979) 171. Ulmschneider, P., Schmitz, F., Hammer, R.: Astron. Astrophys. 74 (1979) 229. Ayres, T.R., Linsky, J.L.: Astrophys. J. 235 (1980) 76. Couturier, P., Mangeney, A., Souffrin, P., in: Solar and Interplanetary Dynamics, IAU Symp. 91 (M. Dryer, E. Tandberg-Hanssen, eds.), Dordrecht: Reidel (1980) p. 127. Hartmann, L., MacGregor, K.B.: Astrophys. J. 242 (1980) 260. Linsky, J.L.: Annu. Rev. Astron. Astrophys. 18 (1980) 439. Nagai, F.: Sol. Phys. 68 (1980) 351. Schmitz, F., Ulmschneider, P.: Astron. Astrophys. 84 (1980) 191. Simon, T., Kelch, W.L., Linsky, J.L.: Astrophys. J. 237 (1980) 72. Brown, A., Jordan, C.: Mon. Not. R. Astron. Soc. 196 (1981) 757. Hearn, A.G., Vardavas, I.M.: Astron. Astrophys. 98 (1981) 230. Jordan, C., Brown, A., in: Solar Phenomena in Stars and Stellar Systems (R.M. Bonnet, A.K. Dupree, eds.), Dordrecht: Reidel (1981) p. 199. Schmitz, F., Ulmschneider, P.: Astron. Astrophys. 93 (1981) 178. Vernazza, J.E., Avrett, E.H., Loeser, R.: Astrophys. J. Suppl. 45 (1981) 635. Hammer, R.: Astrophys. J. 259 (1982) 767. Hammer, R.: Astrophys. J. 259 (1982) 779. Mariska, J.T., Boris, J.P., Oran, E.S., Young jr., T.R.., Doschek, G.A.: Astrophys. J. 255 (1982) 783. Musielak, Z.E.: Astron. Astrophys. 105 (1982) 23. White, N.E., Holt, S.S.: Astrophys. J. 257 (1982) 318. Flower, D.R., Pineau des Forêts, G.: Astron. Astrophys. 119 (1983) 321. Mariska, J.T., Boris, J.P.: Astrophys. J. 267 (1983) 409.


54 83M2 84H 84S 85A 85H 85S 85V 86S 86U

86V 87J1 87J2 87U 88A 88C 88H 88K 88T 88W 89A1 89A2 89K1 89K2 89K3 89U 90F 90G 90N 90R 91F 91H

91M 91P 91R 91U 92C1 92C2 92C3 92C4 92H 92M1 92M2 92M3

4.3.4 Stellar atmospheres: Chromospheres and coronae McClymont, A.N., Canfield, R.C.: Astrophys. J. 265 (1983) 483. Hammer, R.: Astrophys. J. 280 (1984) 780. Stella, L., Rosner, R.: Astrophys. J. 277 (1984) 312. Avrett, E.H., in: Chromospheric Diagnostics and Modelling (B.W. Lites, ed.), Sunspot NM: Nat. Solar Observatory (1985) p. 67. Herbold, G., Ulmschneider, P., Spruit, H.C., Rosner, R.: Astron. Astrophys. 145 (1985) 157. Schmitz, F., Ulmschneider, P., Kalkofen, W.: Astron. Astrophys. 148 (1985) 217. Van Ballegooijen, A.A.: Astrophys. J. 298 (1985) 421. Shaviv, G., Wehrse, R.: Astron. Astrophys. 159 (1986) L5. Ulmschneider, P., Muchmore, D., in: Small Scale Magnetic Flux Concentrations in the Solar Photosphere (W. Deinzer, M. Knölker, H.H. Voigt, eds.), Göttingen: Vandenhoeck and Ruprecht (1986) p. 191. Van Ballegooijen, A.A.: Astrophys. J. 311 (1986) 1001. Jordan, C., Ayres, T.R., Brown, A., Linsky, J.L., Simon, T.: Mon. Not. R. Astron. Soc. 225 (1987) 903. Jordan, C., Linsky, J.L., in: Exploring the Universe with the IUE Satellite (Y. Kondo, ed.), Dordrecht: Reidel (1987) p. 259. Ulmschneider, P., Muchmore, D., Kalkofen, W.: Astron. Astrophys. 177 (1987) 292. Adam, J., Störzer, H., Shaviv, G., Wehrse, R.: Astron. Astrophys. 193 (1988) L1. Cuntz, M., Ulmschneider, P.: Astron. Astrophys. 193 (1988) 119. Hasan, S.S.: Astrophys. J. 332 (1988) 499. Korevaar, P., Van Leer, B.: Astron. Astrophys. 200 (1988) 153. Thomas, J.H.: Astrophys, J. 333 (1988) 407. Withbroe, G.L.: Astrophys. J. 325 (1988) 442. Anderson, L.S., Athay, R.G.: Astrophys. J. 336 (1989) 1089. Anderson, L.S., Athay, R.G.: Astrophys. J. 346 (1989) 1010. Korevaar, P.: Astron. Astrophys. 226 (1989) 209. Korevaar, P., Hearn, A.G.: Astron. Astrophys. 220 (1989) 177. Korevaar, P., Hearn, A.G.: Astron. Astrophys. 224 (1989) 141. Ulmschneider, P.: Astron. Astrophys. 222 (1989) 171. Fontenla, J.M., Avrett, E.H., Loeser, R.: Astrophys. J. 355 (1990) 700. Gail, H.-P., Cuntz, M., Ulmschneider, P.: Astron. Astrophys. 234 (1990) 359. Narain, U., Ulmschneider, P.: Space Sci. Rev. 54 (1990) 377. Robinson, R.D., Cram, L.E., Giampapa, M.S.: Astrophys. J. Suppl. 74 (1990) 891. Fontenla, J.M., Avrett, E.H., Loeser, R.: Astrophys. J. 377 (1991) 712. Heyvaerts, J., in: Structure and Emission Properties of Accretion Disks (C. Bertout, S. CollinSouffrin, J .P. Lasota, J. Tran Thanh Van, eds.), Gif-sur-Yvette: Editions Frontières (1991) p. 109. Moore, R.L., Musielak, Z.E., Suess, S.T., An, C.-H.: Astrophys. J. 378 (1991) 347. Parker, E.N.: Astrophys. J. 372 (1991) 719. Rosner, R., An, C.-H., Musielak, Z.E., Moore, R.L., Suess, S.T.: Astrophys. J. 372 (1991) L91. Ulmschneider, P., Priest, E., Rosner, R. (eds.): Mechanisms of Chromospheric and Coronal Heating, Berlin: Springer (1991). Carlsson, M., Stein, R.F.: Astrophys. J. 397 (1992) L59. Cheng, Q.-Q.: Astron. Astrophys. 262 (1992) 581. Cheng, Q.-Q.: Astron. Astrophys. 266 (1992) 537. Cheng, Q.-Q.: Astron. Astrophys. 266 (1992) 549. Harper, G.M.: Mon. Not. R. Astron. Soc. 256 (1992) 37. Mariska, J.T.: The Solar Transition Region, Cambridge: Cambridge University Press (1992). Melia, F., Zylstra, G.J., Fryxell, B.: Astrophys. J. 396 (1992) L27. Murray, S.D., Lin, D.N.C.: Astrophys. J. 384 (1992) 177.


Ref. p. 56]

4.3.5 Stellar atmospheres: Stellar winds

55

92M4 Musielak, Z.E.: Mem. Soc. Astron. Ital. 63 (1992) 635. 92R Rammacher, W., Ulmschneider, P.: Astron. Astrophys. 253 (1992) 586.

4.3.5 Stellar winds For general reviews see [79C, 91J2, 91L].

4.3.5.1 Empirical mass loss The empirical determinations of mass-loss rates from red giants has been reviewed in [88D]. According to [92J1] the best general estimate of the mass loss of red giants is still given by the Reimers [75R] formula, multiplied by an efficiency factor α of about 0.4, −2

−1 1.5  L   M   Teff  −13 M = 4 ⋅ 10 α   ,      L~   M~   Teff, ~ 

(27)

where M is measured in solar masses per year.

4.3.5.2 Thermal winds The basic equations for thermal stellar winds are derived in [63P], see also [72H]. As late-type stars close to the main sequence with thermal winds also have significant magnetic fields, Alfvén waves occur which modify the winds of these stars, see [77H, 80H2, 83H, 88W, 91P]. For thermal wind models of stars other than the Sun see [82H1, 82H2, 84H1].

4.3.5.3 Winds driven by radiation pressure Radiation pressure on atoms and ions The basic theory is given by [60S, 75C, 79C], and is greatly expanded in the time-dependent treatment by [84O, 85O, 88O], see also the reviews [88A, 92O]. For stationary winds see also [90P]. Radiation pressure on molecules For oxygen-rich or carbon-rich cool red giants see [89E, 92G] as well as [92J2]. Radiation pressure on dust Earlier models are given by [71G], hydrodynamic aspects are first discussed in [74S1, 74S2]. For models with explicit calculations of the dust formation rate in M-stars see [80D, 84K], and in C-stars see [87G, 88G, 89D, 90D, 91J1, 92F], see also literature cited in the section on pulsation-driven winds. For reviews of dust-driven winds see [90G, 91J2, 91L].

4.3.5.4 Pulsation-driven winds Semianalytical treatments of shock-driven winds are given in [79W1] as well as in [85B]. Timedependent models are computed by [79W2, 88B, 89B, 92F], see also literature cited in the section on dust-driven winds. For reviews of pulsation-driven winds see [90G, 91L, 92B].


Ref. p. 56]


55

92M4 Musielak, Z.E.: Mem. Soc. Astron. Ital. 63 (1992) 635. 92R Rammacher, W., Ulmschneider, P.: Astron. Astrophys. 253 (1992) 586.

4.3.5 Stellar winds For general reviews see [79C, 91J2, 91L].

4.3.5.1 Empirical mass loss The empirical determinations of mass-loss rates from red giants has been reviewed in [88D]. According to [92J1] the best general estimate of the mass loss of red giants is still given by the Reimers [75R] formula, multiplied by an efficiency factor α of about 0.4, −2

−1 1.5  L   M   Teff  −13 M = 4 ⋅ 10 α   ,      L~   M~   Teff, ~ 

(27)

where M is measured in solar masses per year.

4.3.5.2 Thermal winds The basic equations for thermal stellar winds are derived in [63P], see also [72H]. As late-type stars close to the main sequence with thermal winds also have significant magnetic fields, Alfvén waves occur which modify the winds of these stars, see [77H, 80H2, 83H, 88W, 91P]. For thermal wind models of stars other than the Sun see [82H1, 82H2, 84H1].

4.3.5.3 Winds driven by radiation pressure Radiation pressure on atoms and ions The basic theory is given by [60S, 75C, 79C], and is greatly expanded in the time-dependent treatment by [84O, 85O, 88O], see also the reviews [88A, 92O]. For stationary winds see also [90P]. Radiation pressure on molecules For oxygen-rich or carbon-rich cool red giants see [89E, 92G] as well as [92J2]. Radiation pressure on dust Earlier models are given by [71G], hydrodynamic aspects are first discussed in [74S1, 74S2]. For models with explicit calculations of the dust formation rate in M-stars see [80D, 84K], and in C-stars see [87G, 88G, 89D, 90D, 91J1, 92F], see also literature cited in the section on pulsation-driven winds. For reviews of dust-driven winds see [90G, 91J2, 91L].

4.3.5.4 Pulsation-driven winds Semianalytical treatments of shock-driven winds are given in [79W1] as well as in [85B]. Timedependent models are computed by [79W2, 88B, 89B, 92F], see also literature cited in the section on dust-driven winds. For reviews of pulsation-driven winds see [90G, 91L, 92B].


56


4.3.5.5 Wave-driven winds Alfvén-wave-driven winds Late-type giants with sufficient magnetic field coverage allow the formation of Alfvén-wave-driven winds. Alfvén waves are also known to help to drive the solar wind [88W, 91M, 91P]. The basic model has been developed by [80H1]. Additional work is provided by [82H3, 83H, 84H2, 88K, 89K, 90Y]. Wind acceleration by Alfvén-wave reflection has been discussed in [90A, 91R]. For a review see [91L]. Acoustic-wave-driven winds Strong shocks generated by overtaking of smaller amplitude shocks which develop from a spectrum of short-period acoustic waves can produce episodic mass loss as shown in [87C, 90C] as well as in [89C]. Steady mass loss needs acoustic waves of long period. Such waves may be generated by the driving of chromospheric oscillations by short-period acoustic waves [92R, 92U]. Because damping and shock formation of acoustic waves is well understood, it is not possible to treat the acoustic damping length as a free parameter, therefore the results by [89P2] as well as [89P1] must be used with utmost caution. For a review see [91L].

References for 4.3.5 60S 63P 71G 72H 74S1 74S2 75C 75R 77H 79C 79W1 79W2 80D 80H1 80H2 82H1 82H2 82H3 83H 84H1 84H2 84K 84O 85B 85O 87C 87G 88A 88B

Sobolev, V.V.: Moving Envelopes of Stars, Cambridge, MA: Harvard University Press (1960). Parker, E.N.: Interplanetary Dynamical Processes, New York: Interscience (1963). Gehrz, R.D., Woolf, N.J.: Astrophys. J. 165 (1971) 285. Hundhausen, A.J.: Coronal Expansion and the Solar Wind, Berlin: Springer (1972). Salpeter, E.E.: Astrophys. J. 193 (1974) 579. Salpeter, E.E.: Astrophys. J. 193 (1974) 585. Castor, J.I., Abbott, D.C., Klein, R.I.: Astrophys. J. 195 (1975) 157. Reimers, D., in: Problems in Stellar Atmospheres and Envelopes (B. Baschek, W.H. Kegel, G. Traving, eds.), Berlin: Springer (1975) p. 229. Hundhausen, A.J., in: Coronal Holes and High Speed Solar Wind Streams, Boulder, CO: Colorado Assoc. Univ. Press (1977) p. 225. Cassinelli, J.P.: Annu. Rev. Astron. Astrophys. 17 (1979) 275. Willson, L.A., Hill, S.J.: Astrophys. J. 228 (1979) 854. Wood, P.R.: Astrophys. J. 227 (1979) 220. Deguchi, S.: Astrophys. J. 236 (1980) 567. Hartmann, L., MacGregor, K.B.: Astrophys. J. 242 (1980) 260. Holzer, T.E., Leer, E.: J. Geophys. Res. 85 (1980) 4665. Hammer, R.: Astrophys. J. 259 (1982) 767. Hammer, R.: Astrophys. J. 259 (1982) 779. Hartmann, L., MacGregor, K.B.: Astrophys. J. 257 (1982) 264. Holzer, T.E., Fla, T., Leer, E.: Astrophys. J. 275 (1983) 808. Hammer, R.: Astrophys. J. 280 (1984) 780. Hartmann, L., Avrett, E.H.: Astrophys. J. 284 (1984) 238. Kozasa, T., Hasegawa, H., Seki, J.: Astrophys. Space Sci. 98 (1984) 61 Owocki, S.P., Rybicki, G.B.: Astrophys. J. 284 (1984) 337. Bertschinger, E., Chevalier, R.A.: Astrophys. J. 299 (1985) 167. Owocki, S.P., Rybicki, G.B.: Astrophys. J. 299 (1985) 265. Cuntz, M.: Astron. Astrophys. 188 (1987) L5. Gail, H.-P., Sedlmayr, E.: Astron. Astrophys. 171 (1987) 197. Abbott, D.C., in: Proceedings of the Sixth International Solar Wind Conference 1 (V.J. Pizzo, T.E. Holzer, D.G. Sime, eds.), NCAR, Boulder CO (1988) p. 149. Bowen, G.H.: Astrophys. J. 329 (1988) 299.


Ref. p. 59] 88D 88G 88K 88O 88W 89B 89C 89D 89E 89K 89P1 89P2 90A 90C 90D 90G 90P 90Y 91J1 91J2 91L 91M 91P 91R 92B 92F 92G 92J1 92J2 92O 92R 92U

4.3.6 Stellar atmospheres: Atomic and molecular data

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de Jager, C., Nieuwenhuijzen, H., van der Hucht, K.A.: Astron. Astrophys. Suppl. 72 (1988) 259. Gail, H.-P., Sedlmayr, E.: Astron. Astrophys. 206 (1988) 153. Krogulec, M.: Acta Astron. 38 (1988) 107. Owocki, S.P., Castor, J.I., Rybicki, G.B.: Astrophys. J. 335 (1988) 914. Withbroe, G.L.: Astrophys. J. 325 (1988) 442. Bowen, G.H., in: Evolution of Peculiar Red Giants (H.B. Johnson, B. Zuckerman, eds.), Cambridge: Cambridge University Press (1989) p. 269. Cuntz, M., Muchmore, D.: Astron. Astrophys. 209 (1989) 305. Dominik, C., Gail, H.-P., Sedlmayr, E.: Astron. Astrophys. 223 (1989) 227. Elitzur, M., Brown, J.A., Johnson, H.R.: Astrophys. J. 341 (1989) L95. Krogulec, M.: Acta Astron. 39 (1989) 51. Pijpers, F.P., Habing, H.J.: Astron. Astrophys. 215 (1989) 334. Pijpers, F.P., Hearn, A.G.: Astron. Astrophys. 209 (1989) 198. An, C.H., Suess, S.T., Moore, R.L., Musielak, Z.E.: Astrophys. J. 350 (1990) 309. Cuntz, M.: Astrophys. J. 353 (1990) 255. Dominik, C., Gail, H.-P., Sedlmayr, E., Winters, J.M.: Astron. Astrophys. 240 (1990) 365. Gail, H.-P.: Rev. Mod. Astron. 3 (1990) 156. Pauldrach, A.W.A., Puls, J.: Rev. Mod. Astron. 3 (1990) 124. Yong, Z., Li, X.-Q.: Astrophys. Space Sci. 167 (1990) 1. Johnson, H.R.: Astron. Astrophys. 249 (1991) 455. Johnson, H.R., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 281. Lafon, J.-P.J., Berruyer, N.: Astron. Astrophys. Rev. 2 (1991) 249. Moore, R.L., Musielak, Z.E., Suess, S. T., An, C. H.: Astrophys. J. 378 (1991) 347. Parker, E.N.: Rev. Mod. Astron. 4 (1991) 1. Rosner, R., An, C.H., Musielak, Z.E., Moore, R.L., Suess, S.T.: Astrophys. J. 372 (1991) L91. Bowen, G.H., in: Instabilities in Evolved Super- and Hypergiants (C. de Jager, ed.), Royal Netherlands Arts and Sci., Amsterdam: North-Holland (1992) p. 104. Fleischer, A.J., Gauger, A., Sedlmayr, E.: Astron. Astrophys. 266 (1992) 321. Gustafsson, B., Plez, B., in: Instabilities in Evolved Super- and Hypergiants (C. de Jager, ed.), Royal Netherlands Arts and Sci., Amsterdam: North-Holland (1992) p. 86. Jørgensen, U.G.: Newsletter Chemically Peculiar Red Giant Stars (S.B. Yorka, ed.), 13 (1992) 3. Jørgensen, U.G., Johnson, H.R.: Astron. Astrophys. 265 (1992) 166. Owocki, S.P.: Rev. Mod. Astron. 3 (1992) 98. Rammacher, W., Ulmschneider, P.: Astron. Astrophys. 253 (1992) 586. Ulmschneider, P., Rammacher, W., Gail, H.-P., in: Cool Stars Stellar Systems and the Sun (M.S. Giampapa, J.A. Bookbinder, eds.), ASP Conference Series 26 (1992) 471.

4.3.6 Atomic and molecular data The major advances in the field of accurate atomic and molecular data have been realised by the Opacity Project (OP) [94S] and by Kurucz [92K], both of which have made an enormous amount of radiative data of good to moderate accuracy available. A follow-up to the OP, the IRON project [93H] is intended to provide collisional and intermediate-coupling radiative data, in particular for iron group elements. A bibliography on ''Atomic and molecular data for fusion'' is issued biannually by the Atomic Energy Authority in Vienna and is available on request. The data cited are also useful for astrophysical purposes. A reasonably complete but uncritical bibliography is given in [93B], and a fuller description of the methods and data in [b].


Ref. p. 59] 88D 88G 88K 88O 88W 89B 89C 89D 89E 89K 89P1 89P2 90A 90C 90D 90G 90P 90Y 91J1 91J2 91L 91M 91P 91R 92B 92F 92G 92J1 92J2 92O 92R 92U


57

de Jager, C., Nieuwenhuijzen, H., van der Hucht, K.A.: Astron. Astrophys. Suppl. 72 (1988) 259. Gail, H.-P., Sedlmayr, E.: Astron. Astrophys. 206 (1988) 153. Krogulec, M.: Acta Astron. 38 (1988) 107. Owocki, S.P., Castor, J.I., Rybicki, G.B.: Astrophys. J. 335 (1988) 914. Withbroe, G.L.: Astrophys. J. 325 (1988) 442. Bowen, G.H., in: Evolution of Peculiar Red Giants (H.B. Johnson, B. Zuckerman, eds.), Cambridge: Cambridge University Press (1989) p. 269. Cuntz, M., Muchmore, D.: Astron. Astrophys. 209 (1989) 305. Dominik, C., Gail, H.-P., Sedlmayr, E.: Astron. Astrophys. 223 (1989) 227. Elitzur, M., Brown, J.A., Johnson, H.R.: Astrophys. J. 341 (1989) L95. Krogulec, M.: Acta Astron. 39 (1989) 51. Pijpers, F.P., Habing, H.J.: Astron. Astrophys. 215 (1989) 334. Pijpers, F.P., Hearn, A.G.: Astron. Astrophys. 209 (1989) 198. An, C.H., Suess, S.T., Moore, R.L., Musielak, Z.E.: Astrophys. J. 350 (1990) 309. Cuntz, M.: Astrophys. J. 353 (1990) 255. Dominik, C., Gail, H.-P., Sedlmayr, E., Winters, J.M.: Astron. Astrophys. 240 (1990) 365. Gail, H.-P.: Rev. Mod. Astron. 3 (1990) 156. Pauldrach, A.W.A., Puls, J.: Rev. Mod. Astron. 3 (1990) 124. Yong, Z., Li, X.-Q.: Astrophys. Space Sci. 167 (1990) 1. Johnson, H.R.: Astron. Astrophys. 249 (1991) 455. Johnson, H.R., in: Stellar Atmospheres: Beyond Classical Models (L. Crivellari, I. Hubeny, D.G. Hummer, eds.), Dordrecht: Kluwer (1991) p. 281. Lafon, J.-P.J., Berruyer, N.: Astron. Astrophys. Rev. 2 (1991) 249. Moore, R.L., Musielak, Z.E., Suess, S. T., An, C. H.: Astrophys. J. 378 (1991) 347. Parker, E.N.: Rev. Mod. Astron. 4 (1991) 1. Rosner, R., An, C.H., Musielak, Z.E., Moore, R.L., Suess, S.T.: Astrophys. J. 372 (1991) L91. Bowen, G.H., in: Instabilities in Evolved Super- and Hypergiants (C. de Jager, ed.), Royal Netherlands Arts and Sci., Amsterdam: North-Holland (1992) p. 104. Fleischer, A.J., Gauger, A., Sedlmayr, E.: Astron. Astrophys. 266 (1992) 321. Gustafsson, B., Plez, B., in: Instabilities in Evolved Super- and Hypergiants (C. de Jager, ed.), Royal Netherlands Arts and Sci., Amsterdam: North-Holland (1992) p. 86. Jørgensen, U.G.: Newsletter Chemically Peculiar Red Giant Stars (S.B. Yorka, ed.), 13 (1992) 3. Jørgensen, U.G., Johnson, H.R.: Astron. Astrophys. 265 (1992) 166. Owocki, S.P.: Rev. Mod. Astron. 3 (1992) 98. Rammacher, W., Ulmschneider, P.: Astron. Astrophys. 253 (1992) 586. Ulmschneider, P., Rammacher, W., Gail, H.-P., in: Cool Stars Stellar Systems and the Sun (M.S. Giampapa, J.A. Bookbinder, eds.), ASP Conference Series 26 (1992) 471.

4.3.6 Atomic and molecular data The major advances in the field of accurate atomic and molecular data have been realised by the Opacity Project (OP) [94S] and by Kurucz [92K], both of which have made an enormous amount of radiative data of good to moderate accuracy available. A follow-up to the OP, the IRON project [93H] is intended to provide collisional and intermediate-coupling radiative data, in particular for iron group elements. A bibliography on ''Atomic and molecular data for fusion'' is issued biannually by the Atomic Energy Authority in Vienna and is available on request. The data cited are also useful for astrophysical purposes. A reasonably complete but uncritical bibliography is given in [93B], and a fuller description of the methods and data in [b].


58


[Ref. p. 59

4.3.6.1 Atomic energies and wavelengths The situation has been reviewed by [93M]. Evaluated energy level data for K through Ni have been collected in [85S].

4.3.6.2 Collisional data Collisional ionization A critical evaluation of data up to the year 1992 has been produced by [92I]. Similar evaluations for ground state ionization have been performed by the Belfast group [83B1, 88L, 89H]; in [88L, 89H] are also provided analytical fits to their recommendations. Simple fits valid for a few times ionized species but for all states are given by [91C2]. Collisional excitation Recommended data for electron excitation by ions are given by [92I, 93P]. The latter is an extension of the work of [85G] where the data are also presentd in tabular form. Fits for hydrogenic ions are available from [88S] while high-lying states of non-hydrogenic atoms and ions may be treated using the prescriptions in [77P]. This method is semi-classical in origin and also provides an estimate of proton collisional rates. The most accurate data for H to date are those of [90S1] where fits for the 1s-2s and 1s-2p transitions are given, while data for other transitions have been given by [91A1]. The fits in [87G, 89G] are not to be recommended [91C1]; instead those in [72J] are to be preferred although they have been largely superceded by the aforementioned work. Fits to the data of [91A2] for the lowest states of He II are provided by [92A]. Heavy-particle collisions and charge exchange The excellent book of Bransden and McDowell [92B] covers this topic in full giving many references to data sources. Rough estimates of charge exchange rates may be obtained using the prescription of [80B] or the computer program based on it [83B2]. 4.3.6.3 Line broadening Critical reviews for neutral and singly ionized species have been made by [84K1, 84K2]. The situation up to 1991 is summarized in [91D]. A fast method of obtaining profiles for hydrogenic systems including line dissolution effects is given by [90S2]. Data of moderate accuracy are given by the formulae in [87D]. The 4th supplement of the bibliography on atomic line shapes and shifts [93F] covers the literature from 1978 to 1992. 4.3.6.4 Radiative data As stated at the outset, the Opacity Project (OP) and [92K] have completely revolutionized this area. Data for 58,000,000 line transitions (in intermediate coupling) in iron group elements including radiative and collisional damping constants are provided in [92K] making them a good source of data for spectral synthesis. They are available on CD-Roms. The OP is summarised in [90S2] where also a full list of references is given. TOPBASE [92C] is a UNIX–based program making the data available to the user. It has been recently installed at the Centre de Données Astronomiques de Strasbourg (France), providing anonymous FTP access (see [93C] for details) to the OP data. A bibliography of photoionization data predating the OP has been published in [91L]. New Rosseland mean opacity tables calculated with the OPAL code are given in [92R].



59

4.3.6.5 Molecular data The source for the most complete set of molecular data is [92K]. A summary of available data is given by [92J].

References for 4.3.6 For general references [a]⋅⋅⋅[f] see p. 41 72J 77P 80B 83B1 83B2 84K1 84K2 85G 85S 87D 87G 88L 88S 89G 89H 90S1 90S2 91A1 91A2 91C1 91C2 91D 91L 92A 92B 92C 92I 92J 92K 92R 93B 93C

Johnson, L.C.: Astrophys. J. 174 (1972) 227. Percival, I.P., Richards, D.: J. Phys. B: At. Mol. Phys. 10 (1977) 1497. Butler, S.E., Dalgarno, A.: Astrophys. J. 241 (1980) 838. Bell, K.L., Gilbody, H.B., Hughes, J.G., Kingston, A.E., Smith, F.J.: J. Phys. Chem. Ref. Data 12 (1983) 891. Bienstock, S.: Comput. Phys. Commun. 29 (1983) 333. Konjevic, N., Dimitrijevic, M.S., Wiese, W.L.: J. Phys. Chem. Ref. Data 13 (1984) 619. Konjevic, N., Dimitrijevic, M.S., Wiese, W.L.: J. Phys. Chem. Ref. Data 13 (1984) 649. Gallagher, J.W., Pradhan, A.K.: JILA Report No. 30 (1985). Sugar, J., Corliss, C.: J. Phys. Chem. Ref. Data 14 (1985) Suppl. 2. Dimitrijevic, M.S., Konjevic, N.: Astron. Astrophys. 172 (1987) 345. Giovanardi, C., Natta, A., Palla, F.: Astron. Astrophys. Suppl. 70 (1987) 269. Lennon, M.A., Bell, K.L., Gilbody, H.B., Hughes, J.G., Kingston, A.E., Murray, M.J., Smith, F.J.: J. Phys. Chem. Ref. Data 17 (1988) 1285. Sampson, D.H., Zhang, H.L.: Astrophys. J. 335 (1988) 51. Giovanardi, C., Palla, F.: Astron. Astrophys. Suppl. 77 (1989) 157. Higgins, M.J., Lennon, M.A., Hughes, J.G., Bell, K.L., Gilbody, H.B., Kingston, A.E., Smith, F.J.: UKAEA Report CLM-R294 (1989) Scholz, T.T., Walters, H.R.S., Burke, P.G., Scott, M.P.: Mon. Not. R. Astron. Soc. 242 (1990) 692. Seaton, M.J.: J. Phys. B: At. Mol. Phys. 23 (1990) 3255. Aggarwal, K.M., Berrington, K.A., Burke, P.G., Kingston, A.E., Pathak, A.: J. Phys. B: At. Mol. Phys. 24 (1991) 1411. Aggarwal, K.M., Berrington, K.A., Kingston, A.E., Pathak, A.: J. Phys. B: At. Mol. Phys. 24 (1991) 1757. Chang, E.S., Avrett, E.H., Loeser, R.: Astron. Astrophys. 247 (1991) 580. Clark, R.E.H., Abdallah jr., J., Mann, J.B.: Astrophys. J. 381 (1991) 597. Dimitrijevic, M.S., Sahal-Bréchot, S.: J. Phys. (Paris) 1 (1991) Colloq. 1, Suppl. JP II, 3, (C.J. Zeippen, M. Le Dourneuf, eds.), p.111. Le Dourneuf, M.: J. Phys. (Paris) 1(1991) Colloq. 1, Suppl. JP II, 3 (C.J. Zeippen, M. Le Dourneuf, eds.), p.227. Aggarwal, K.M., Callaway, J., Kingston, A.E., Unnikrishnan, K.: Astrophys. J. Suppl. 80 (1992) 473. Bransden, B.H., McDowell, M.R.C.: Charge Exchange and the Theory of Ion-Atom Collisions, Oxford: Clarendon Press (1992). Cunto, W., Mendoza, C.: Rev. Mex. Astron. Astrofis. 23 (1992) 107. Itikawa, Y.: At. Data Nucl. Data Tables 49 (1992) 209. Jørgensen, U.G.: Rev. Mex. Astron. Astrofis. 23 (1992) 49. Kurucz, R.L.: Rev. Mex. Astron. Astrofis. 23 (1992) 45. Rogers, F.H., Iglesias, C.A.: Astrophys. J. Suppl. 79 (1992) 507. Butler, K., in: Planetary Nebulae, IAU Symp. 155 (R. Weinberger, A. Acker, eds.), Dordrecht: Kluwer (1993) p. 73. Cunto, W., Mendoza, C., Ochsenbein, F. , Zeippen, C.J.: Astron. Astrophys. 275 (1993) L5.


60

4.3.7 Stellar atmospheres: Atmospheres of accretion disks

93F 93H

Fuhr, J.R., Lesage, A.: NIST Spec. Publ. 366 (1993) Suppl. 4. Hummer, D.G., Berrington, K.A., Eissner, W., Pradhan, A.K., Saraph, H.E., Tully, J.A.: Astron. Astrophys. 279 (1993) 298. 93M Martin, W.C., in: Atomic and Molecular Data for Space Astronomy: Needs, Analysis, and Availability (P.L.Smith, W.L. Wiese, eds.), Berlin: Springer, Lecture Notes in Physics 407 (1993) 121. 93P Pradhan, A.K., Gallagher, J.W.: At. Data Nucl. Data Tables 52 (1993) 227. 94S Seaton, M.J., Yu Yan, Mihalas, D., Pradhan, A.K.: Mon. Not. R. Astron. Soc. 266 (1993) 805.

4.3.7 Atmospheres of accretion disks The atmospheres of accretion disks differ from those of normal stars in four important aspects: (i) They are intrinsically two (or three)-dimensional. (ii) There may be a heating term in the energy equation at all depths. (iii) The total optical depth in the vertical direction may be so low that the atmosphere is not semiinfinite and a reflective inner boundary condition at the symmetry plane has to be assumed. (iv) The gravity increases with height. This implies that for accretion disks model atmospheres cannot be calculated separately from the disk's interior (if it exists). Up to now only atmospheres for geometrically thin accretion disks (i.e., accretion disks in which the vertical extension is much smaller than the radial one) have been calculated since here the assumption is well justified that the disk is composed of essentially independent rings. The structure equations for each ring are then very similar to those of extended atmospheres and the methods of solution are also similar [91S, 93H, 93S] if only continuum radiation (for which Doppler shifts are unimportant) is considered. However, the numerics is often in details much more demanding (e.g., there does not exist an Eddington approximation that can serve, e.g., as a starting approximation for non-grey calculations) and time-consuming (one accretion disk atmosphere is numerically equivalent to some 1000 stellar atmospheres). In addition, multiple solutions for the vertical run of the temperature are frequent. Furthermore, thermal instabilities frequently occur that lead to the formation of coronae (see subsect. 4.3.4.3 for references). If line blanketing is to be included a 2D or 3D radiative transfer problem with differential rotation has to be solved in most cases [93B].

References for 4.3.7 91S 93B 93H

93S

Shaviv, G., Wehrse, R.: Astron. Astrophys. 251 (1991) 117. Baschek, B., Papkalla, R., Wehrse, R., in: Cataclysmic Variables and Related Physics (O. Regev, G. Shaviv, eds.), Ann. Isr. Phys. Soc. 10 (1993) 176. Hubeny, I., in: Structure and Emission Properties of Accretion Disks (C. Bertout, S. CollinSouffrin, J.-P. Lasota, J. Tran Thanh Van, eds.), Gif-sur-Yvette: Editions Frontières (1993) p. 227. Shaviv, G., Wehrse, R., in: Accretion Disks around Compact Objects (J.C. Wheeler, ed.), World Scientific (1993), p. 148.


60

4.3.7 Stellar atmospheres: Atmospheres of accretion disks

93F 93H

Fuhr, J.R., Lesage, A.: NIST Spec. Publ. 366 (1993) Suppl. 4. Hummer, D.G., Berrington, K.A., Eissner, W., Pradhan, A.K., Saraph, H.E., Tully, J.A.: Astron. Astrophys. 279 (1993) 298. 93M Martin, W.C., in: Atomic and Molecular Data for Space Astronomy: Needs, Analysis, and Availability (P.L.Smith, W.L. Wiese, eds.), Berlin: Springer, Lecture Notes in Physics 407 (1993) 121. 93P Pradhan, A.K., Gallagher, J.W.: At. Data Nucl. Data Tables 52 (1993) 227. 94S Seaton, M.J., Yu Yan, Mihalas, D., Pradhan, A.K.: Mon. Not. R. Astron. Soc. 266 (1993) 805.

4.3.7 Atmospheres of accretion disks The atmospheres of accretion disks differ from those of normal stars in four important aspects: (i) They are intrinsically two (or three)-dimensional. (ii) There may be a heating term in the energy equation at all depths. (iii) The total optical depth in the vertical direction may be so low that the atmosphere is not semiinfinite and a reflective inner boundary condition at the symmetry plane has to be assumed. (iv) The gravity increases with height. This implies that for accretion disks model atmospheres cannot be calculated separately from the disk's interior (if it exists). Up to now only atmospheres for geometrically thin accretion disks (i.e., accretion disks in which the vertical extension is much smaller than the radial one) have been calculated since here the assumption is well justified that the disk is composed of essentially independent rings. The structure equations for each ring are then very similar to those of extended atmospheres and the methods of solution are also similar [91S, 93H, 93S] if only continuum radiation (for which Doppler shifts are unimportant) is considered. However, the numerics is often in details much more demanding (e.g., there does not exist an Eddington approximation that can serve, e.g., as a starting approximation for non-grey calculations) and time-consuming (one accretion disk atmosphere is numerically equivalent to some 1000 stellar atmospheres). In addition, multiple solutions for the vertical run of the temperature are frequent. Furthermore, thermal instabilities frequently occur that lead to the formation of coronae (see subsect. 4.3.4.3 for references). If line blanketing is to be included a 2D or 3D radiative transfer problem with differential rotation has to be solved in most cases [93B].

References for 4.3.7 91S 93B 93H

93S

Shaviv, G., Wehrse, R.: Astron. Astrophys. 251 (1991) 117. Baschek, B., Papkalla, R., Wehrse, R., in: Cataclysmic Variables and Related Physics (O. Regev, G. Shaviv, eds.), Ann. Isr. Phys. Soc. 10 (1993) 176. Hubeny, I., in: Structure and Emission Properties of Accretion Disks (C. Bertout, S. CollinSouffrin, J.-P. Lasota, J. Tran Thanh Van, eds.), Gif-sur-Yvette: Editions Frontières (1993) p. 227. Shaviv, G., Wehrse, R., in: Accretion Disks around Compact Objects (J.C. Wheeler, ed.), World Scientific (1993), p. 148.


4.4.1 Equations of stellar structure

62

4.4

[Ref. p. 120

Stellar structure and evolution

4.4.1

Equations of stellar structure

Basic equations

For each time interval, the structure of a stellar model for a given mass and initial chemical composition is determined by integrating the equations of conservation of momentum, mass, and energy and by assuming a mode of energy transport. In the case of spherical symmetry, i.e. without rotation and magnetic field, these equations, when expressedin Lagrangian coordinates and using the massm interior to a given radius Yas an independent variable, are [78w]: du = _ 4&?!ft

am

at

_ Gm

3

ar -- 1 am - 4crzp ’ (3) dT -=-am

ar ---=u

at

T aPV Pam ’

(4)

’

where G is the gravitational constant. It is easy to seethat the term in eq. (3) containing (Y*u),can be replaced by P d V/at, where V= l/p is the specific volume. These equations are only valid for nonrelativistic stars, but they can be generalized to include relativistic effects(see[77P]). Five dependent variables have been introduced in eqs. (1 - 5) as a function of m and time t: u (velocity), Y(radius), p (density), T (temperature), L, (luminosity). The pressure P, and the internal energy per unit mass, E,are described in subsect.4.4.2.1. The nuclear energy generation rate E, and the neutrino energy loss rate E, are described in subsects.4.4.2.4 and 4.4.2.5, respectively. The calculation of E, requires the solution of a network of thermonuclear reactions at each time interval to determine the chemical abundances in the course of evolution (subsect. 4.4.2.4.7). In addition, the variation of the abundances due to mixing processes(seebelow) has to be taken into account. In eq. (4), where the acceleration term has been omitted, the temperature gradient V= dln7”dlnP depends on the mode of energy transport. As described below, certain criteria can be used to distinguish between the radiative (or conductive) and convective energy transport. In the caseof radiative energy transport, V is given by the radiative temperature gradient:

Vrad = ---L I6nacG

ULP *’

where a is the radiation constant, c is the velocity of light, and K is the Rosseland mean opacity. In the caseof convection, V has to be replaced by V,, which should be determined by a model of convection. In the deep interior of stars, V, = V, is a good approximation. In the outer layers, where convection is superadiabatic, V, is more difficult to obtain. In stellar evolution, one “standard” method to calculate V, is simply to use the mixing length theory (MLT) for convection. The details Land&BBmstein New Series VI/3b

4.4.1 Equations of stellar structure

Ref. p. 1201

63

of the MLT will not be described here (see [68Cl, 90K2]). For alternative, more elaborated models of convection, the reader is referred to the works [83E, 85X, 86K1, 89R, 91Z]. These models also include nonlocal convection, but their numerical implementation has not yet been sufficiently explored. Boundary conditions

The boundary conditions for eqs. (1 - 5) are at the center (m = 0): r: = 0,

L,: = 0,

u: = 0.

0

For the behavior of these equations near the center for a given time, see[90K2]. At the surface (m=M), strict boundary conditions are rather complicated. In stellar evolution, one commonly assumes the outermost regions of the atmosphere to be in radiative equilibrium, and uses the Eddington approximation of radiative transfer. In addition, the atmosphere may be assumed to be geometrically thin, i.e. plane parallel. With these assumptions, one can use the following simple conditions for the effective temperature T,, and effective density peff(see[77P]): L = 471~ R2T4efv

GM 2 2-F 3’ is the so-called Eddington luminosity, CJis the Stefan-Boltzmann constant, R is where L,=4ncGMk the stellar radius, p is the mean molecular weight at the surface, and % is the gas constant. In eq. (9) the optical depth r=2/3 has been chosen, which means that the photosphere is considered as the “surface” of the star from which the bulk of radiation is emitted. A modification of eq. (9) suitable for relativistic stars is given in [77P]. For a possible modification of eqs. (8) and (9) for a spherically extended atmosphere, see[91E3]. A discussion of the influence of the surface conditions on the properties of envelope solutions is given in [90K2]. Criteria of convection

Whether convection occurs in certain regions of a star is a question of stability. Criteria for stability (or instability) can be given in a simple way under certain assumptions: (i) that a moving element may be assumedto remain in pressure balance with the surroundings, since it will expand immediately until this balance is achieved. The expansion goes with the velocity of sound [90K2], i.e. much faster than any other motion of the element; (ii) that a moving mass element may be assumednot to exchange an appreciable amount of heat with the surroundings, i.e. to move adiabatically. This type of instability is called dynamical. These assumptions lead (see [90K2], for details) to the following instability criterion for convection:

where V, = (dln T/din P), describes the temperature variation in the element during its motion, and V,=(dln @din P)s describes the variation of the mean molecular weight in the surroundings. The quantities rp, 6 are defined by

(19 Land&-BBmstein New Series VU3b

4.4.2 Properties of stellar matter

64

[Ref. p. 120

In the event of ideal gas and radiation (see subsect. 4.4.2.l), 50= 1, 6 = (4 - 38)//I, where /? is the ratio of the gas pressure to the total pressure (subsect.4.4.2.1). Thus, in this case,eq. (10) becomes

In eq. (6), Vraddescribes the temperature gradient for radiative or conductive energy transport, so that V = Vradin such layers. The assumption of an adiabatic motion (see above) means V,= V,,, Then, eq. (10) becomes

Vrad > V.&,-tf v, = IV,. This is the so-called Ledoux criterion for convective instability. The Schwarzschild criterion for convective instability is obtained when V,= 0 (homogeneous composition), i.e.

Vmd’ Vad.

(14)

A layer is called marginally stable if both sides of the inequalities (13) and (14) are equal. Obviously, the difference between the two criteria occurs only in layers of radially variable chemical composition. This is the casein evolving stars, where heavier elements are produced below lighter ones, i.e. where the p gradient increasesinward with the pressure, so that V, > 0 always in this case (cp,6 are always positive). Therefore, the second term in eq. (13) clearly has a stabilizing effect and tends to inhibit convection. The convective instability may be induced by either a large Vraddue to a large flux or high opacities, or by a decreaseof V,, due to ionization in the outer layers of the star. A rather complicated situation occurs when in regions of variable p gradient the condition

Vad< Vrad< VL

(15)

is fulfilled. This means that such layers are dynamically stable but vibrationally unstable and will be mixed on a slower time scale than convection. Such layers are called semiconvective. The treatment of mixing in such layers is not clear yet. In several works [83L, 85L, 88W4, 89L2, 91E1, 92S1, 95E] the mixing is treated by diffusion with different treatments of the diffusion coefficient. A discussion of semiconvective mixing is also given in the review paper of [86Cl], where earlier descriptions of semiconvection are outlined. Another uncertain phenomenon in stellar evolution is the possibility of convective overshooting. In many computations ([86C4], for a review) it is argued that the mass of the convective core may be larger than that obtained by using the Schwarzschild criterion. However, the exact mass of the convective core with overshooting is still not well determined. A recent critical analysis of this phenomenon is given in [87B2, 87R, 91Z]. More comments on overshooting are given in subsect. 4.4.3.5.

4.4.2

Properties of stellar matter

4.4.2.1

The equation of state

Ideal gas and radiation

For a gas consisting of n free particles per unit volume that are noninteracting and nondegenerate, the pressure is P,=nkT,

(19 Landolt-B6mstein New Serm VI/3b


64

[Ref. p. 120

In the event of ideal gas and radiation (see subsect. 4.4.2.l), 50= 1, 6 = (4 - 38)//I, where /? is the ratio of the gas pressure to the total pressure (subsect.4.4.2.1). Thus, in this case,eq. (10) becomes

In eq. (6), Vraddescribes the temperature gradient for radiative or conductive energy transport, so that V = Vradin such layers. The assumption of an adiabatic motion (see above) means V,= V,,, Then, eq. (10) becomes

Vrad > V.&,-tf v, = IV,. This is the so-called Ledoux criterion for convective instability. The Schwarzschild criterion for convective instability is obtained when V,= 0 (homogeneous composition), i.e.

Vmd’ Vad.

(14)

A layer is called marginally stable if both sides of the inequalities (13) and (14) are equal. Obviously, the difference between the two criteria occurs only in layers of radially variable chemical composition. This is the casein evolving stars, where heavier elements are produced below lighter ones, i.e. where the p gradient increasesinward with the pressure, so that V, > 0 always in this case (cp,6 are always positive). Therefore, the second term in eq. (13) clearly has a stabilizing effect and tends to inhibit convection. The convective instability may be induced by either a large Vraddue to a large flux or high opacities, or by a decreaseof V,, due to ionization in the outer layers of the star. A rather complicated situation occurs when in regions of variable p gradient the condition

Vad< Vrad< VL

(15)

is fulfilled. This means that such layers are dynamically stable but vibrationally unstable and will be mixed on a slower time scale than convection. Such layers are called semiconvective. The treatment of mixing in such layers is not clear yet. In several works [83L, 85L, 88W4, 89L2, 91E1, 92S1, 95E] the mixing is treated by diffusion with different treatments of the diffusion coefficient. A discussion of semiconvective mixing is also given in the review paper of [86Cl], where earlier descriptions of semiconvection are outlined. Another uncertain phenomenon in stellar evolution is the possibility of convective overshooting. In many computations ([86C4], for a review) it is argued that the mass of the convective core may be larger than that obtained by using the Schwarzschild criterion. However, the exact mass of the convective core with overshooting is still not well determined. A recent critical analysis of this phenomenon is given in [87B2, 87R, 91Z]. More comments on overshooting are given in subsect. 4.4.3.5.

4.4.2

Properties of stellar matter

4.4.2.1

The equation of state

Ideal gas and radiation

For a gas consisting of n free particles per unit volume that are noninteracting and nondegenerate, the pressure is P,=nkT,

(19 Landolt-B6mstein New Serm VI/3b


Ref. p. 1201

65

where the subscript g means “gas”, and k= 1.38.10-16erg/K is the Boltzmann constant. The density of the gas,p, is related to the mean molecular weight where m, = lg/N, = 1.6605.10-*4g is the atomic massunit, NA is the Avogadro number. Since% = N,k, eq. (16) can be written as

(17)

P,= ;PT,

where p is in [g cmm3]. To calculate P, for given (p and T), p must be related to the composition of the gas. In the stellar interior, the gas is fully ionized. Thus, a mixture of nuclei and free electrons can be assumed.Let Xi be the relative mass abundance of the particle of type i (number of grams of particles of type i per gram of mixture), and Ai = milmu as the mass number (Ai = pi). Then the relation between X1and the number density n, is simply X,

= 1

‘Pimu

-

P

Aini

(18)

0.4

By using q = p N,XJA, and eq. (16), the total pressure of the mixture (nuclei and electrons) is P= n, + xni kT, (19) ( i) where n, denotes the number density of the free electrons. The completely ionized atom of type i and atomic number Zi contributes (I+ Zi) free particles. Thus, the total number of free particles is n=n,+~n,=~(l+Z,)n,. i I With eqs. (18) and (19), it follows P= kTpN,x

(20)

(21) i

Introducing the mean molecular weight ,Das c1= lIc(l+z,)$’ i

I

recovers the form of eq. (17). The meaning of introducing p is that a mixture of ideal gasescan be treated as a uniform gas. The mean molecular weight for a neutral (non-ionized) gas ,u~simply follows from eq. (22):

The mean molecular weight per electron, nL,,is defined for fully ionized gas by

If the mixture contains nuclei heavier than helium with Zi = A,/2, then 2 &= 1+x,’

(25)

where Xheavy = 1 -X,-X,, has been used. In the stellar interior, the photon gas also makes an important contribution to the total pressure. Since the radiation is practically that of a blackbody, the radiation pressure, &, is given by Prad= $aT’= Landolt-Bbmstein New Series VI13b

f Urad,

66


[Ref. p. 120

where Uradis the energy density of a blackbody gas, and a=7.56464.10-is erg cm-3 K-4 is the radiation constant. The total pressure (gas plus radiation) is then (27)

The corresponding internal energy per unit mass u is given by 3

(28)

where fi is defined in eq. (29). In eq. (27), the pressure is uniquely determined as a function of T, p and composition, if the gas is nondegenerate and either fully ionized (p as in eq. 22), or neutral (pO as in eq. 23). Two casesstill to be considered are partial ionization, and degeneracy of the electrons. These are described below. Before doing that, some useful thermodynamic quantities are summarized.

Useful thermodynamic quantities A measureof the significance of the radiation pressure is the quantity b defined as p: = p,lP,

1 - p = p,,,IP.

(29)

Clearly, /I = 1 when the radiation pressure is zero. The differentiation of eq. (29) leads to

The specific heat per gram at constant volume is

C=du V (

aT 1 Q’

(31)

The relation between the specific heat per gram at constant pressure C, and C, at constant volume for any given equation of state is (32)

The adiabatic exponents, r,, IY,,r3 are obtained by (for derivation, see[68Cl]) (33)

(34)

(35)

(39 The subscript (ad) means “adiabatic”, and V,, is the adiabatic temperature gradient. Land&-BCrnstein New Series VV3b

Ref. p. 1201


67

Applying the above equations to the case of an ideal gas plus radiation (eq. 27) and using eq. (29) for p and eq. (28) for U, one obtains the following expressions:

(38)

l+(l-P)(4+B) P” Vad= 5 4(1-@(4-t/3) 2+ P’

’

pp+2X

3 /?+S(l -p) ’

r,,1+2*. 3 B+8(1 -P> For j3 -+ 1: C,= %/~3/2, C,= ‘%2/p512,V,, = 215,r, = r, = 513= C,IC, all known values for an ideal gas. For /I -+ 0: Vad= l/4, C, becomes infinite, since P does not depend on the volume in case of blackbody radiation.

Partial ionization

Partial ionization occurs in the stellar envelope, where the effects of degeneracy are not important. Thus, one deals with a mixture of atoms (in a certain state of ionization), electrons and photons contained in a unit volume of gas in thermodynamic equilibrium (LTE). Many thermodynamic quantities, such as p, C,, Vad,depend on the degree of ionization of hydrogen, helium and heavier elements. In stellar evolution, a common method to calculate the degree of ionization is to use the “Saha equation”. The derivation and handling of that equation is discussedin detail in [62B, 68C1, 90K2], and will not be repeated here. It may be important to note that the Saha equation has a limited range of application. This is the casewhen the LTE cannot be assumed,like in stellar corona or in the deep interior of a star, where the density is relatively high and the so-called pressure ionization is to be taken into account (see[90K2] for this point). In stellar evolution calculations, a transition to complete ionization may be done whenever the Saha equation gives a decreaseof the degree of ionization toward deeper layers. A criterion for the transition from temperature ionization to pressure ionization can be found in [73E].

The degenerate electron gas

The thermodynamic properties of an electron gas that becomes degenerate are described on the basis of the Fermi-Dirac statistics. In stellar evolution, the “Fermi-Dirac” integrals with suitable approximations are widely used. A comprehensive representation of this issue is given in [68Cl]. In the following, only the general integrals for a perfect Fermi-gas will be given. The integrals below Landoll-Bdmstein New Series VI/3b

68


[Ref. p. 120

can be used to determine number density n,, the pressure P, and the energy density U, of the electron gas, respectively:

p,= +A,,(

x3j2( l+$?x)ii2

f(x, ?j) dx,

u,=AkT[

x3/2( l+;jx)112

x = Elk T,

fi = kTlm,c2 = T/5.93 . 109K,

E(P)= m,c2 [(1+Q2-

(l+flx)

f(x, q) dx,

11,

(46)

(47)

1

f(x, 1?> = 1+exp(x - q) (Fermi function),

(48)

v] = ,ulkT,

(49)

A = 4n(2m,kT)3’21h3.

In these equations, m, is the mass of the electron, q is the degeneracy parameter (11is the chemical potential of the electron gas), and E is the kinetic energy as a function of the momentum p of the electrons. For evaluating the integrals in eqs. (43-49, several approximations (see [75E]) may be used as indicated in Fig. 1, which shows lines of constant r] in the log T- log n, plane. For y < - 1.O(nondegenerate regime) power seriesof modified Besselfunctions can be utilized (see[68Cl], for details). In the partially degenerate regime (- 1.O< rl G 29, numerical integration is required, since accurate analytical approximations are not possible. For q > 25, analytical expressions are obtained on the basis of the “Sommerfeld lemma” (see[68Cl] for details). In the following, we consider three limiting cases to increase the feasibility of eqs. (43-45): (i) nonrelativistic gas, (ii) extremely relativistic gas, (iii) completely degenerategas. (i) Nonrelativistic electron gas

In this case,j -+ 0, I

ne= A

=p212me,and q is assumedto be arbitrary. Then (50)

F,,,(v),

4 = $AkTF,,,(r),

(51)

(52)

where Fv(rl>= \- x”f(x,i,j)dx,

v>--1,

(53)

0 Landolt-B6mstein New Series VI/3b


Ref. p. 1201

69

are the “Fermi-Dirac” integrals. Numerical values of these integrals can be found in [68Cl, 68C2, 82Ml]. Numerical evaluation of these integrals with an accuracy of one part in lOlo is given in [89C]. This work also contains tables for v = - l/2, l/2, 3/2, 5/2, and a Fortran code to produce tables and to perform accurate interpolation. Note that P,=2/3 U, follows from eqs. (51) and (52), while eqs. (50) and (51) lead to

p = 2 F3,2(4y1kT e 3 Fm(v) e

(54)

’

which shows how the pressure is modified due to degeneracy.

(ii) Extremely relativistic electron gas

In this case,p -+ 00,s(P)=pc, and v is assumedto be arbitrary. Then 12,= +r)l

pe

=

&

F,(y)>

W-j4

(55)

(59

F,(q),

u, = 3g WI4 F,(v).

(57)

From eqs. (56) and (57): P,= 1/3u,. Accurate analytical approximations of F,, F,, etc., are given in [78Tl].

(iii) Completely degenerate electron gas

Complete degeneracyof the electron gas is achieved for very large values of q, where the Fermi function f(x, $ becomesnearly a step-like function. In momentum space, this means that according to the Pauli-principle, all quantum states are occupied up to a momentum pf, and all states are unoccupied above pf. Without derivation (see[68Cl]), the relations for n,, P,, U, are: 8nm3c3 y1e=&x3 3h3 ’

(58)

(59)

(60)

The functions f(x) and g(x), where x E pfImec (relativity parameter), are given by f(x)=x(l+~~)~‘~(2~*-3)+3ln g(x) = 8x3 [(x2+ l)r’* - l] - f(x). Land&Biirnstein New Series V1/3b

[x+(1+x’)“‘],

(61) (62)


70

[Ref. p. 120

Eqs. (59) and (60) lead to p,lu, = f(x)lg(x).

(63)

The relation between the density p and n, is given by the condition of charge neutrality:

where pL,is given by eq. (24). The relation between x and p is (65)

In the limit of completely nonrelativistic electron gas (x + 0), the functions f(x) and g(x) have the following asymptotic behavior: g(x) + F x5.

f(x) + f x5, Hence, P, becomes:

(67)

P,= 2/3 U,follows from eq. (63). For the extremely relativistic, completely degenerategas (x + m): f(x) + 2x4,

g(x) + 6x4.

(68)

Therefore,

80 M,). Therefore, this burning phase proceeds explosively and may lead to partial or complete disruption of the star depending on the oxygen core mass (the so-called “pair creation supernovae”), (see [830, 86E, 86W1, 89H3, 91E2], for details of such calculations). 4.4.2.2

Functions of V,, and C,, see LB W2b, p. 159

4.4.2.3

Stellar opacities

For more than a decade, the Rosseland mean opacities from the Los Alamos Opacity Library (LAOL) created by Huebner et al. [77H] have been used, These opacities are usually available for a temperature range down to T= 1.O eV, or T= 1.16.lo4 K. A detailed description of these tables is given in LB VI/2b (p. 159), and will not be repeated here. A recent comprehensive compilation of the Rosseland mean opacities from the LAOL for 22 mixtures of chemical composition has been presented by Weiss et al. [9Ow], where some supplementary tables are also included for T < 1.OeV. Meanwhile, improved computations of radiative Rosseland-mean opacities for stellar envelopes have been performed by two independent groups: the so-called (OPAL) opacities according to [921, 92R] calculated at Lawrence Liver-more National Laboratory, and the opacities according to [91S2, 93Sl] obtained by using atomic data calculated in an international collaboration referred to as the Opacity Project (OP). Fortunately, there is a genera1agreement between the OPAL and OP caIculations, and both find significantly higher opacities than those known from the LAOL. The most remarkable effect of the new opacities is their significant enhancement in the temperature range log T[K] N 5.0.. .6.OK as shown in Figs. 3a- 3c. There are several bumps characterizing the OPAL opacities: the first near log T= 4.0 is due to H, the second near log T= 4.7 is due to H, He and He+, the third bump near log T= 5.3 stemsfrom the photoabsorption by the M-shell of Fe, and the last bump near log T= 6.3 is due in part to photoabsorption by the L-shell of iron and photoionization from the K-shell of C, 0 and Ne. Note that the third opacity bump was absent in the LAOL opacities. The new opacities are expected to modify the stellar models. For example, the new calculations concerning the pulsation of fl-cepheid stars [92K] show that the OPAL opacities lead to excitation of radial and nonradial pulsations of these stars, i.e. their pulsational instability is well explained by the rc-mechanism. The treatment of the opacity due to electron conduction is described in LB VI/2b (p. 178). Analytical approximations for these opacities are given by Iben [751], which are used to follow the evolution of thermally pulsating AGB stars.

Fig. 3a. Rosseland mean opacities vs. temperature for log R= -4.0, where R=plTz (p is the density in [g cm-‘], T, the temperature in units of lo6 K). The solid and dashed lines represent the new Liver-more opacities (OPAL opacities, subsect. 4.4.2.3) for the chemical composition (X, 2) = (0.70,0.03) and (0.70, 0.02), respectively. The mixture of heavy elements is according to [89Al] (seehowever, ref. [921]).The dashed-dotted and dotted lines represent the respective Los Alamos opacities (LAOL) for the samemixtures. The new opacities are particularly enhanced in the range log T= 5.0...6.0 (sect. 4.4.2.3, for some details). Fig.3b. OPAL opacities as in Fig. 3a, but for (X, 2)=(0.70, 0.02) andlog R= -4.0, -4.5, -5.0, -5.5, -6.0 from top to bottom. Fig. 3c. OPAL and LAOL opacities vs. temperature for the mixture (X, Z) = (0.735,0.005) and log R = - 4.0. Land&-B6rnstein New Series VV3b

Ref. p. 1201

4.4.2.4


75

Nuclear burning phases in stars

In this section, only the hydrostatic burning phases will be summarized. A discussion of the explosive burning phases which occur during the dynamical evolutionary stages of stars (e.g., novae,

7 glj 9 6

(X,Zl =(0.70,0.03) OPAL

5 4 I a3 i ,_

1

I-

I ,yJ 9 E,4,-

I: x

I1!-

IIlricm; T 4t-

I1: N ;!-

lI

Land&-B6rnstein New Series VI/3b

W,Z) =I0.70,0.02) OPAL

76


[Ref. p. 120

supernovae, accretion on white dwarfs or neutron stars) is beyond the scope of the present work. The principles of the explosive nucleosynthesis are described in [73W, 86Wl]. 4.4.2.4.1 Hydrogen burning The net effect of H burning is the transformation of hydrogen to helium in stars. For stars of masses M< 1.3... 1.5 Mo (depending on initial composition), hydrogen burning proceeds by the proton-proton chain (pp chain), while in stars of higher massesthe CNO cycle takes over. The pp chain The reactions involved in the pp chain and their parameters are given in Table 2. The electron capture on 7Becan be calculated using the weak interaction theory and the local physical conditions of the solar plasma [89B2]: r(7Be+e-)=5.54~10-p(p/~,)T~o~5[1+0.004(T,-16)]

[s-l],

(81)

where peis given by eq. (24), and T6 in units of lo6 K. Without neutrino energy loss, the total energy released is the same for all three chains: Q=26.731 MeV. However the neutrino energy loss is different in each chain (seeTable 2). Therefore, one obtains as effective Q values:

QefvPP1) = Q- 2q,(p+p) = 26.20 MeV, Qeff(PPw = Q- q,(p+p) - qJ7Be) = 25.603 MeV, Qeff(PPIII) = Q- q,(p+p) - q,(‘B) = 19.753 MeV. The energy production from the pp chain depends on whether the conditions for 3He equilibrium are achieved in the stellar interior. For T6< 8, 3He cannot be assumed to have reached equilibrium [68C2]. The energy generation rate from pp1 is then calculated by using the effective

Table 2. Reaction parameters for the pp chain [89B2]. Sois the cross section factor at zero energy, Q is the energy release, q, is the average neutrino energy loss obtained from the neutrino spectrum. No.

1 2 3

Reaction

‘H(p, e+v,)‘H ‘H(P, y)3He 3He(3He,2p)4He

4 5 6

7Li (p, a)4He

7 8 9

7Beb Y)*B

*B(e+v,)*Be* sBe*(a)4He

4” WV ppI-chain 1.442 5.494 12.858 ppII-chain 1.586 0.862 0.384 17.347 ppIII-chain 0.137 17.980

0.265

0.862 0.384

SO

[keV barn] 4.07.10-22 2.50.10-4 5.15.10’3 5.40*10-i seeeq. (81) 5.20.10+’ 2.43.10-*

6.710

Landolt:Bb;mstein New Series VU3b

Ref. p. 1201


77

reaction 3H + 3He+v,, with yields p= 1.O69.1O-5rpp [erg cmY3s-l],

(82)

since the pp reaction is immediately followed by the 2H(p, y)3He reaction, where rppis the rate of the pp reaction given by [88Cl]. Since the reaction 3He(3He,2p)4He liberates 12.858 MeV, the energy generation rate of the pp1 chain can be written as p.s= 1.O69.1O-5~,,+2.06lO-~

r33

(83) where r33is the rate of the 3He + 3He reaction given by [88Cl]. Analytical approximations of the energy generation rate by the pp chain are given in [82Ml]. The CNO tri-cycle

The reaction involved in the CNO tri-cycle and their parameters are given in Table 3. Note that the ratio of the S’,,factor of the “N(p, c()12Cand “N(p, y)160 reactions is about 1OOO:l.Therefore, the ON cycle only operates for every 1000 operations of the main CN cycle. This implies that the ON cycle makes a small contribution to the total energy production, but is important for the nucleosynthesis of the I60 and 170 isotopes. It is clear from Table 3 that the net result of the CN cycle is similar to the pp chain: 4p + 4He+2e++2v+26.731

MeV.

The two electron neutrinos produced are of relatively low energies. Thus, most of the liberated energy is retained in the stellar interior. The slowest reaction in the CN cycle is 14N(p,y)150, since 14Nhas the highest Coulomb barrier and this reaction proceeds via electromagnetic interaction, while strong interaction is involved in the “N(p, CX)‘~C reaction. Table 3. Reaction parameters for the CNO tri-cycle. The entries are explained in the caption to Table 2. The values of q, are according to [89B2], while those of 5”’ are taken from [88R2] (see[89B2] for comparison). T’,* is the half lifetime of the radioactive nuclei.

No.

Reaction

4” WV]

ZeV barn]

CN-cycle

7 8 9 10

1.944 2.221 0.7067 7.551 7.297 2.754 0.9965 4.965 ON-cycle 12.128 0.601 2.762 0.9994 1.193

11 12 13

5.609 1.650 3.980

12C(p, yY3N

13N(e+v,)13C 13C(p, yY4N 14Np, yY50

150(efv,)‘5N

15N(p,Q2C

1.40 598 5.50 3.32 122 6.5.104 6.4.10’ 7.50 64.5 1.70

tri-cycle


1.4.10’ 110 1.0.104

78


log T6 -

[Ref. p. 120

Fig. 4. Energy generation rate as a function of temperature for the pp chain and the CNO cycle. Both curves decreasewith decreasing temperature are due mainly to the effect of the Coulomb barrier. Near T6~18, the CNO cycle starts to be dominant. This changeover depends, however, on the abundances of the CNO nuclei present in the star. The CNO cycle is reponsible 3 for the nuclear energy production in stars of M31.5M0.

The total energy generation rate of the CNO cycle should be calculated by including all relevant reaction rates, at least in the CN cycle, and this requires the numerical solution of the time-depen-

dent reaction network [68C2, 73A, 77C, 82Wj to obtain the abundance of the involved nuclei (see subsect. 4.4.2.4.7). Analytical approximations of the energy generation rate of the CNO bi-cycle operating in equilibrium can be found in [68C2]. The temperature dependenceof the energy generation rate of the CNO cycle is shown in Fig. 4 along with that of the pp chain. Clearly, the CNO cycle dominates at T, > 18, and its significantly steeperrise, compared with spp,is due chiefly to the high Coulomb barrier of the CNO nuclei. Note that both curves in Fig. 4 exhibit low gradients at high temperatures, since the Coulomb barriers no longer influence the energy production. We note in passing that the saturation behavior of the CNO cycle is encountered during the main sequenceevolution of massive, very metal-poor stars ([91B2], for details).

Ne-Na-Mg and Mg-Al cycles

As indicated in Table 3, the CNO tri-cycle is completed by the reaction ‘*O(p, a)15N.However, the study of [79L] and [8Ow] has shown that the ‘*O(p, y)19Freaction is also important in the range 0.02 < Tg< 0.7. The resulting nucleus “F may react with protons in two different ways: lgF(p, a)160 or “F(p, y)*ONe.The nucleus *ONerepresentsthe link to th Ne-Na cycle. The Ne-Na-Mg cycle contains the following reactions (P-decay lifetimes are indicated): *ONe(p, y)21Na(e+v,; 22.48 s)*‘Ne 2’Ne(p, y)**Na(e+v,; 2.6 a)**Ne **Na(p, y)*‘Mg(e+v,; 3.86 s)22Na **Na(p, y)23Mg(e+v,; 11.32 s)23Na Land&-Biimstein New Series VI/3b

Ref. p. 1201


79

The reaction 23Na(p,y) represents another link to the Mg-Al cycle. This cycle contains the following reactions: 24Mg(p, y)*‘Al 25Al(e+v,; 7.17 s)*‘Mg 25Al(p, y)26Si(e+v,; 2.23 s)*~AI”

26Alm(e+v,; 6.34 s)26Mg(p, Y)*~A~

27Si(e+v,; 4.14 s)~~A~ 27Si(p, y)**P(e+v,; 0.26 s)28Si

A remarkable feature in the Mg-Al cycle is the existence of two separate nuclear speciesof 26A1 produced by the samereaction 25Mg(p,Y)~~AI.26Alcan be produced either in its ground state 26A10 or in its isomeric state 26Alm.The half-life of the Of isomeric state is 6.34 s, while that of the 5+ ground state is 7.3.105years. The decay of the isomeric state leads to 26Mg,while the ground state may lead to 26Al(p, y)27Si.Consequently, this reaction is critical for the survival of 26A1at the completion of the Mg-AI cycle [88R2]. These cycles are clearly important for the nucleosynthesis of the elements between 20Neand 27A1.The Ne-Na cycle leads to the formation of the so called Ne-E (highly enriched 22Ne)found in meteoritic samples.The Mg-AI cycle seemsto be the source of production of 26A1,whose decay leads to the 26Mg/27A1anomaly also found in some meteorites. It is emphasized that the production of 26A1is a rather complicated issue, becauseof the many sites responsible for its production. It can be produced in AGB stars, in novae, and in massive stars (during hydrogen burning, neon shell burning, and supernovae phases). The astrophysical relevance of 26A1lies in its decay, which leads to the remarkable 1.8 MeV y-ray line. The recent observations [93Dl] by COMPTEL (on board of the COMPTON Observatory) provided the first detailed map of this y-line emission of our galaxy. This map shows that the 1.8-MeV line emission along the galactic plane extends over 60 degreesin longitude, and that the flux distribution is inhomogeneous. The COMPTEL observations seemto exclude a smooth and centrally peaked source population, such as novae [93D2]. It is interesting to note that if the CNO burning occurs at unusually high temperatures in excess of 10’ K, like in novae and supernovae [76W, 78G], accreting neutron stars [78T2], or supermassive stars [73F, 74F, 80F], then the CNO cycle operates on a time scale shorter than the lifetime of P-unstable nuclei, like 13N.In this case,the CNO cycle is said to be P-limited by the B-decay lifetime of the proton-rich nuclei 140and “0 and not by the rate of 14N(p,y)150.Note that the production of Land&-Bihstein New Series VI/3b


80

[Ref. p. 120

I40 proceeds via 13N(p,y)140(efv,)14N. The operation of this hot CNO cycle leads to a new nucleosynthesis process called rp-process([81w], for details). New investigation of the rp-process has been recently presentedby [94T]. 4.4.2.4.2 Helium burning The most important reactions for the energy production during this burning phase are: 4He(2g)‘2C (Q= 7.275 MeV) 12C(ct,y)160 (Q= 7.162 MeV) ‘60(a,y)20Ne (Q = 4.730 MeV). Further reactions important for nucleosynthesis are given in [85Al]. During the core He burning of massive stars (M > 10 Mo), neutrons are liberated by the 22Ne(a,n)25Mgreaction. This neutron source leads to efficient s-processing of nuclei in the mass range A = 65.. .90, where A is the mass number. This so-called “weak s-process component” is described in the review paper by [89Kl].

2.01 1.5u ,z xa- 1.0-

;; k

0.5 -

s O-0.5 -1.0 a

0

I

0.2

I

I

0.4 79-

0.6

I

0.8

J

I.0

Fig. 5a. Ratio, log R, between the reaction rate for r80(a, y) 22Neas obtained from the new compilation by [94K] and the previous one according to [88Cl]. Fig. 5b. Reaction rates ratio for r3C(a,n) I60 (solid line), and 22Ne(a,n) 25Mg(dashed line). The solid and dashed lines represent the ratio between the rate determined by [93D3] and that according to [88Cl], respectively. Land&B6mstein New Series VV3b

Ref. p. 1201


81

Table 4. Reaction rates in [cm” s-l mol-‘1 for some important reactions during He burning in stars, according to [8X2] and [88Cl]. A comparison with some newly measured reaction rates are given in Figs. 5a and 5b. Note that the two rates listed for the ‘*C(a, y) reaction differ by a factor of = 2.67.

0.09 0.10 0.12 0.14 0.16 0.18 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

12c(G“9)

‘*cc& Y)

[85C2]

[88Cl]

13C(a,n) [88Cl]

‘*o(w) [88Cl]

22Ne(ct,n) [88Cl]

2.45E-21 2.46E - 20 l.O9E- 18 2.21E- 17 2.63E - 16 2.11E- 15 1.26E- 14 4.45E - 13 6.60E- 12 5.60E- 11 3.23E- 10 1.41E-09 4.96E - 09 1.48E-08 3.89E-08 9.18E-08 1.98E-07 3.98E - 07 7.49E - 07 1.34E-06 2.28E - 06 3.73E- 06 5.90E- 06

9.19E-22 9.23E-21 4.08E - 19 8.30E- 18 9.85E - 17 7.92E- 16 4.74E- 15 1.67E- 13 2.48E- 12 2.10E- 11 1.21E- 10 5.27E- 10 1.86E-09 5.56E-09 1.46E-08 3.44E - 08 7.43E - 08 1.49E- 07 2.81E-07 5.02E-07 8.56E-07 1.40E- 06 2.22E-06

2.25E- 15 2.58E - 14 1.44E- 12 3,58E- 11 5.08E- 10 4.78E - 09 3.30E - 08 1.58E-06 3.01E-05 3.20E - 04 2.28E-03 1.23E-02 5.30E- 02 1.91E-01 5.87E-01 1.58EfOO 3.80E+OO 8.31E+OO 1.68E+ol 3.16E+01 5.61E+Ol 9.49E+Ol 1.54E+02

8.84E-21 6.92E - 20 1.47E- 18 1.94E- 17 1.54E- 15 9.42E- 14 2.58E- 12 9.73E- 10 4.99E - 08 8.28E- 07 6.78E - 06 3.47E - 05 1.28E-04 3.70E- 04 8.92E - 04 1.87E-03 3.52E-03 6.05E - 03 9.68E-03 1.46E- 02 2.10E-02 2.90E - 02 3.86E-02

1.76E-31 8.66E-29 9.50E - 25 9.93E-22 2.63E- 19 1.87E- 17 5.30E- 16 2.37E- 13 1.86E- 11 5.62E- 10 9.13E-09 9.53E-08 7.14E-07 4.12E-06 1.94E-05 7.72E - 05 2.67E - 04 8.23E-04 2.30E - 03 5.88E- 03 1.40E- 02 3.13E-02 6.60E - 02

The abundance of **Ne available for the s-processis enriched by the transformation of 14Nto 22Ne, at helium ignition, via the reaction chain: The last reaction in this chain has to compete with the 22Ne(a,y)26Mg reaction. Another neutron source leading to the synthesis of the heavy nuclei with A = 90.. .209 by the s-process(the so-called “main s-processcomponent”) is due to: This type of s-processing occurs during the thermal pulsation of the AGB stars (see [89Kl, 90Kl], for details). The current experimental situation for the reactions ‘*O(n, y), 13C(a,n) and 22Ne(a,n) is summarized in Figs. 5a and 5b, where their rates are compared with those of [88Cl], (seeTable 4). It is seenthat the new rates are clearly larger than the previous ones. Therefore, these improved rates will increase the efficiency of the s-processnucleosynthesis. Recent calculations of the s-processin massive stars (M 2 15 M,), which investigate this issue and discussthe sensitivity of the s-processto the stellar model computations, are given by [94K]. The energy generation reate of the triple-alpha processis: s3,=5.1~10” Ti3p2 Xi exp(-44.027/T,)


[erg g-l s-l].

82


[Ref. p. 120

where the reaction rate as given by [88Cl] has been used, and the screening factor (see subsect. 4.4.2.4.5) has been omitted for simplicity. In the vicinity of T, = 1.O,sg,may be approximated by s,,=3.86.10-’

p2 X’, Ti'

[erg g-l s-l].

(85)

This shows the extreme temperature dependenceof the triple-alpha process. Note that for Tg< 0.08, the rate of the triple-alpha reaction should be modified as given in [88Cl]. The energy generation rate due to the ‘%(a, y)r60 reaction without screening factor is: E= 1.44.10r7 X(‘“C) X, pN,(o u),+, a [erg g-l s-l],

(89

where the Maxwellian average cross section (N,(a u)) is given by [88Cl]. Note, however, that the rate of this reaction is still uncertain by a factor of 2 to 3, as indicated in Table 4. The energy generation rate of the “jO(c(,y)*ONereaction can be obtained in a similar way as in eq. (86). The total energy production from He burning should be calculated by adding at least the contribution of the principal reactions listed at the beginning of this subsection. Note that general instructions for handling these reaction rates are given by [75F]. 4.4.2.4.3

Carbon burning

The most important reactions during this burning phase are: 12C(12C,a)20Ne (Q = 4.621 MeV), 12C(12C,p)23Na (Q = 2.242 MeV), which proceed at about equal branching (see [SSCl]). Most of the 23Nais transformed to 20Nevia 23Na(p,cc)‘ONe,and also to 24Mgvia 23Na(p,y)24Mg.Therefore, the most abundant nuclei resulting from C burning are: 20Neand 24Mg, besides 160 left over from He burning. Many other reactions required for nucleosynthesis calculations are summarized in [85Al], which indicate that neutrons are produced via

21Ne(p, y)22Na(e+v,)22Ne(a, n)25Mg(n, y)26Mg Whether these neutrons lead to efficient s-processing is not clear yet (see [91A] for recent calculations). 4.4.2.4.4

Advanced burning phases and nuclear statistical equilibrium

Neon burning

After carbon burning, the composition in the core of a massive star consists mainly of 160,*ONeand “Mg. The separation energy of the a-particles of these nuclei is 7.16, 4.73 and 9.32 MeV, respectively, with the smallest value belonging to 20Ne.Therefore, Ne burning starts (at Tg > 1) by photodisintegration of Ne which is dominated by the 5.63 MeV level of this nucleus [68C2]: y+20Ne + 160+a, followed by a-capture on the remaining 2oNe, 20Ne+a + 24Mg+y. The net effect of this rearrangement is: 2 20Ne -+ 160+24Mg+4.587 MeV. This means that a total energy production of 1.10.lOI erg/g results from Ne burning. Land&-Bknstein New Series VU3b

Ref. p. 1201


83

Also 28Siis produced during Ne burning via 24Mg(a, y)**Si. Hence, the most abundant nuclei after this burning phase are: I60 24Mgand 28Si.Secondary reactions important for the nucleosynthesis during Ne burning are given in [85T]. Oxygen burning

The basic reactions in this caseare: 160(160, a)28Si(Q=9.593 MeV) 160(160, P)~IP (Q= 7.678 MeV) 160(“j0, n)31S(e+v,)31P(Q = 1.50 MeV) The branching factors of these reactions are given in [88Cl]. Other important reactions are: 3’P(p, a)28Si(a, Y)~*S, 28Si(y, a)24Mg(a, ~)*~Al(a, p)30Si, 32S(n,y)33S(n, a)30Si(a, y)34S, **Si(n, y)29Si(a, n)32S(a, p)35C1, 29Si(p, y)30P(e+v,)30Si. The chief products of hydrostatic 0 burning are: 28, 3Osi 32, 33, 34~, 35~1, 36, 38Ar 40, 42~a, 46Ti 5SOCr. The nuclei 28Si,32Sconstitute about 90% of the final composition [86Wl]. ’ It should be mentioned that the heavy nuclei produced by the s process during the previous evolutionary phases (essentially during core He burning) are destroyed by photo-disintegration reactions occurring during 0 burning [76A]. Thus, it seemsthat only few nuclei heavier than nickel survive 0 burning. Another point is the increase of the neutron excessq = l-2 Y, (Y, is the number density of the electrons divided by the baryon density) due to electron capture reactions like: 33S(e-v,)33P(p,n)33S, 35Cl(e-v,)35S(p, n)35C1, 37Ar(e-v,)37C1. Another feature of 0 burning is the formation of “quasiequilibrium clusters” consisting of nuclei in equilibrium with respect to electromagnetic and strong interactions [86Wl]. As an example, the rate of 28Si(n,y)29Siis balanced by the inverse rate 29Si(y,n)?Si, and similarly 29Si(p,Y)~OP is balanced by 3oP(y,p)29Si.Thus, in this casethe nuclei 28Si,29Si,3oPwould be in equilibrium with one another. This feature is even more pronounced during Si burning, as outlined below. Silicon burning

An extensive study of this rather complicated burning phase has been made by Woosley et al. [73W] and Thielemann and Arnett [85T]. No fusion of 28Si+28Sioccurs, since the high temperatures (T9> 3.0) required to overcome the Coulomb barrier lead to photodisintegration of the nuclei into a-particles, neutrons and protons. Consequently, almost all nuclei are linked by these light particles and photodisintegrations. This will finally lead to the state of nuclear statistical equilibrium (NSE), where global equilibrium for strong and electromagnetic interactions can be assumed, but not for the weak interaction processes,like electron capture. However, before NSE is reached, “quasiequilibrium clusters” (QEC) are formed that are not in equilibrium. A dividing line between two QEC is the proton magic number .Z= 20 [85T]. Thus, there is a “bottle-neck” between two QEC with 12 d 2 < 20 (light QEC-group), and 22 d 2 G 28 (heavy QEC-group), respectively. There are many reactions which bridge the bottle-neck as proposed by [85T]. In this work, the Si burning is described as a three-step process: (a) transformation of **Si into 3oSi,(b) build-up of the light QEC and (c) bridging Z = 20 to form the heavy QEC and to finally reach the NSE. Land&-BBmstein New Series VI/3b

84


[Ref. p. 120

The first step depends on the neutron excess q, with a large y favoring the formation of neutronrich nuclei. During the second and the third steps, electron-capture processes are very important and

lead to a continuous increase of q, since Y, decreases.The final value of q reached at the end of Si burning is rather important for the nucleosynthesis during this burning phase. The calculations of

[85T] suggest q = (6.. .8).10-*, which corresponds to Y, = 0.47.. .0.46. Si burning leads finally to the formation of iron-group nuclei. An example of the resulting abundances from hydrostatic Si burn-

ing is given in Fig. 6, which shows that nuclei are produced in the range A = 50.. .60.

1U'

M,=16Mo lo4 0 lo3 10210 -

0

110-l1o-z-

10-3 c 0 I 20

30

I

I

40 50 Atomic number A -

I 60

70

Fig. 6. Abundances resulting from hydrostatic Si burning when Si drops below 0.01 by mass according to [85T] for helium cores of M,=4,8, 16 MO, which roughly correspond to main sequencemassesof 15, 25, 45 MO, respectively. In the low-mass core, more electron capture occurs on nuclei in 0 and Si burning; hence a larger neutron excessq is obtained. Larger q leads to the production of more neutron-rich nuclei. Land&-BBmstein New Series VI/3b

Ref. p. 1201


85

Nuclear statistical equilibrium

In many situations (like in the early phase of core collapse of massive stars, in the interior regions of exploding white dwarfs, and during explosive Si burning type II supernovae), temperatures are achieved in excessof 5.10’ K. Under these conditions, one can use the method of nuclear statistical equilibrium (NSE) to calculate the composition of matter. A general description of this method is given in [SOE](seealso [86Wl, 85H2]). Basically, one considers a mixture of nuclei, electrons, nucleons and photons in thermodynamical equilibrium at a given (T, p, Y,). The variable Y, is required, since one cannot assume equilibrium for the weak interaction processes.If the nuclei and the free nucleons are treated as Maxwell-Boltzmann gases,then the equilibrium composition can be calculated by means of the nuclear saha equation: 3/2(1 -A)

where p is the density (in g cme3)and Y,,, Y,,, Y, are mass fractions divided by the mass number of the nuclei, neutrons and protons, respectively. BzA is the ground-state binding energy of a nucleus (2, A), NA is the Avogadro number, and mZA(T)is the nuclear partition function (see[80E] for calculating this quantity). Notice that eq. (87) is obtained by using the reasonable approximations m,=m,=m,andm,-Am,, where m, is the atomic massunit. The equilibrium abundances are obtained by solving eq. (87) iteratively, imposing the constraints of massconservation (summation is over all nuclei included in the calculation) Y”+ Yp+C AiYi= 1, I and charge conservation y,+c

ziyi=

Ye.

63)

(W

Typical abundances resulting from the NSE calculations are shown in Fig. 7.

Fig. 7. Typical abundances by mass fraction, X, resulting from nuclear statistical equilibrium (NSE) calculations as a function of neutron excessq for T= 3.5109 K and p= IO’ g crne3.Adapted from [85H2]. Land&-Biirnstein New Series VU3b

86


4.4.2.4.5

[Ref. p. 120

Screening factors

For the high temperatures and densities achieved in the deep stellar interiors, the atoms are fully ionized. The nuclei are then embeddedin a sea of free electrons, which tend to cluster in the area of a nucleus and act as a screening potential, which reduces the repulsive Coulomb force of the nuclei. This shielding effect easesthe penetration of the Coulomb barrier of the reacting particles and requires a correction of the thermonuclear reaction rates. This can be done [54S, 69S] by multiplying the unscreenedrate by a screening factor,f, whose value depends on T, p and composition. The calculation off suitable for the conditions of the dense stellar plasma has been performed by De Witt et al. [73D] and Graboske et al. [73G] in terms of a screening function HJO) at zero separation of the reacting nuclei, so that f= ewW,,(O)).

m In the calculation of this function, three casesmay be distinguished: weak screening (Coulomb interaction energy small with respect to the kinetic energy), intermediate screening (Coulomb interaction energy comparable to the kinetic energy), strong screening (Coulomb interaction energy large with respect to the kinetic energy). According to [73D, 73G], these casescan be separated by using the quantity A,, defined as: A,, = 2 2, z, A,,

(914

where A,= 1.88.10* p”’ T-3'2,

CW

and Z,, Z, are the charge numbers of the reacting nuclei. The rms charge average .??isgiven by l/2

.z=

1

ii

z:$+oz

1 ,

i

z=czi

(921

2, I

I

where X, is the mass fraction of the nucleus of type i, Ai is its mass number, and 0 denotes the electron degeneracyfactor: O= F-,,,(y,)lF,,,(y,), where the F’s are the Fermi-Dirac integrals (seeeq. 53). The meaning of 0 is that for a degeneracyparameter y, > 1 (strong degeneracy), the electrons at the bottom of the Fermi distribution cannot participate in screening, and thus 0 will finally vanish in the limit of very large q,, The behavior of 0 versus y, is shown in Fig. 8.

8. Electron degeneracyfactor 0 appearingin eq. (92) versusthe electrondegeneracyparameterqe.For everylarge q,, 0 approacheszero, while it is closeto .O 1.0 up to ~~‘-2.0 (weak screening,see subsect. Fig.

4.4.2.4.5). Land&-Bihstein New Series V1/3b


Ref. p. 1201

87

The combined results for the screening function are then as follows: (i) Weak screening (Ai2 < 0.1): f&(O)=Z

(93)

2, z, A,,

where zcan be evaluated using O= 1.0 as a good approximation in this case(seeFig. 8). (ii) Intermediate screening (0.1 6 Al2 < 2.0): H,,(O)=0.380

ylb[(Z,+Z2)1+b-Z;+b-Z;+b]Abg,

lgZ’b-‘X,IAi q,,=

236-222(1-b)

(944

PW

’

where b = 0.860. (iii) Strong screening (Al2 > 5.0): H12(0)= 0.624 z”3 Af3Hf2,

(95)

HT2: = [(Zl +z,> 5’3-Z;‘3-Z;‘3]+0.316 +0.737 [(z,+z2)2’3-

[(Z,+Z2)4’3-Zf’3-Z;‘3](&)1’3

Z;‘3 - Z;‘3] z- ‘(Aopo)-2’3,

where p0is given by eq. (23). In the transition region between intermediate and strong screening (2.0 < A12S5.0), it is recommended [73G] to use H,,(O) = min[Hi2 (intermediate), H,2 (strong)]. Note that the strong screening factor given above is only valid for one component plasma. A generalization for two-component plasma is given by Itoh et al. [791]. This modification is important, for example, for carbon ignition in strongly electron-degenerateC-O cores. 4.4.2.4.6

Neutrino loss rates

During the advanced evolutionary phases of stars, where temperatures in excess of lo* K are achieved, neutrino energy loss rates have to be taken into account. These rates are due to pair, photo, plasma and bremsstrahlung processes. Recent computations concerning these processes based on the Weinberg-Salam theory of the electro-weak interactions are given in [8732, 8911.The results of [891]are briefly summarized in the following. Photoneutrino process

e

photo

=

A(1

-

’

qphoto)

fphoto’

(96)

A=0.5 [(C;+C;)+n(C~+C;2)],

(97)

B= (C,- c’,>+n 3 M,), since the envelope convection penetrates below the H-He discontinuity. When the He-shell source surrounding the contracting C-O core is closer to the H-He discontinuity, the H-shell reignites and the thermally pulsating A GB phase (TP-AGB) is reached. Several review papers about LMS and IMS are given by [83I, 8411, 8512, 86C2, 88R1, 9111.A detailed discussion of the standard solar model including the solar neutrinos is given by [89B2, 93833,where non-standard solar models are also presented. The main sequenceand subgiant phases of 0.7 to 4 M, are described in [79M]. A set of evolutionary sequencesand isochrones in this mass range has been presented by [SSVl, 85V2]. An extensive study of the RGB phasesis given in [78S]. A grid of sequencesfor the HB phases has been provided by [87Sl, 87S3] and recently by [91Cl]. Sequencesfor 1.. .3 M, from the main sequenceto the AGB phase are given by [86L, 88B3]. A grid of post-AGB models has been calculated by [83Sl, 86W3]. Recent interesting calculations dealing with the fading of massiveAGB remnants and the validity of the core-luminosity relation have been presented by [90Bl, 91Bl]. Model computations that extend to the white dwarf configurations are given in [8412,8511,911]. Landolt-Bijmstein New Series VV3b

90

4.4.3 Model computations

[Ref. p. 120

The LMS are defined as those that develop electron-degenerate helium cores after the core Hburning phase. This is found ([8411]) for stars of initial massesof 0.8...1.0 < M/M, c 2.0...2.3, where the mass limits depend on initial chemical composition and the treatment of convection. In these stars, helium ignition becomesunstable and leads to the so-called heliumflash, since energy is produced more rapidly than it can be transported (by conduction) outward. Details about this phenomenon are given in [8411]and referencestherein. The IMS ignite helium under nondegenerate (or moderately degenerate) conditions, and develop C-O cores following helium exhaustion at the center. This places an upper limit of about 7.. .8M, on the initial mass [8411]. LMS may also develop electron-degenerate C-O cores after helium exhaustion, so that they behave qualitatively like IMS in the samenuclear burning phase. MS with initial massesabove 8 Mo evolve through the carbon and subsequent burning phases quiescently, and degenerate conditions are achieved in their interiors toward the end of the quasistatic evolution (see Fig. 1). Among the MS, a subclass with 8...12 MO is distinguished. General comments on the evolution of these stars are given in subsect.4.4.3.7. Plenty of evolutionary models have been performed in recent years for the three groups of stars mentioned above. A review of these calculations is clearly beyond the scope of this work. Only some general results will be summarized below. Observational tests of the stellar evolution theory are discussedin the IAU symposium no. 105 [84M]. Tests for evolutionary sequencesusing the color magnitude diagram of globular clusters are reviewed in [88Rl].

4.4.3.4

Low- and intermediate-mass stars

After central H burning, LMS and IMS evolve to the red giant branch (RGB) when H burning in a shell surrounding the He core takes over. As the mass of the He core increasesand envelope convection (the so-calledJirst dredge-up) develops, the star climbs the RGB. At this stage, it is expected that the surface abundances will be strongly modified from their initial values. Recent up-dated calculations in this context have been performed by [94E], where the predicted surface abundances of stars in the massrange 1.7.. .15 Mo have been compared with the observed data of red giant stars. After He ignition on the RGB, a low-mass star evolves back down and reaches the horizontal branch (HB). At this stage, He burns in a convective core (if present) while H is still burning in a surrounding shell. Further evolution in the HR diagram proceeds towards higher IT,,. These so-called blue loops are not extended in the LMS in contrast to the IMS (seeFig. 12a and 12b). Note that the blue edges of such loops depend on the mass, composition and physical assumptions used in the model computation (see[95E] for a recent discussion). Near central helium exhaustion, the star evolves back to cooler TeK,the H-shell source dies out, and a He-shell source is formed that moves outward (in mass) toward the H-He discontinuity. The star then evolves at higher luminosity and this phase is called early-asymptotic-giant branch (EAGB). At this stage, the so-called second dredge-up may occur (for stars with M> 3 M,), since the envelope convection penetrates below the H-He discontinuity. When the He-shell source surrounding the contracting C-O core is closer to the H-He discontinuity, the H-shell reignites and the thermally pulsating A GB phase (TP-AGB) is reached. Several review papers about LMS and IMS are given by [83I, 8411, 8512, 86C2, 88R1, 9111.A detailed discussion of the standard solar model including the solar neutrinos is given by [89B2, 93833,where non-standard solar models are also presented. The main sequenceand subgiant phases of 0.7 to 4 M, are described in [79M]. A set of evolutionary sequencesand isochrones in this mass range has been presented by [SSVl, 85V2]. An extensive study of the RGB phasesis given in [78S]. A grid of sequencesfor the HB phases has been provided by [87Sl, 87S3] and recently by [91Cl]. Sequencesfor 1.. .3 M, from the main sequenceto the AGB phase are given by [86L, 88B3]. A grid of post-AGB models has been calculated by [83Sl, 86W3]. Recent interesting calculations dealing with the fading of massiveAGB remnants and the validity of the core-luminosity relation have been presented by [90Bl, 91Bl]. Model computations that extend to the white dwarf configurations are given in [8412,8511,911]. Landolt-Bijmstein New Series VV3b


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Some results concerning the luminosities and final massesof AGB stars are shown in Figs. 10a and lob. Fig. 10a shows the stellar luminosity L,, at the onset of the thermal pulsation (TP) versus initial mass. No general agreement is achieved among the calculations shown in this figure. According to [88B3], the He-shell flashes in stars of metallicity 2=0.02 start at lower L,, than

4.50

Boothroyd and Sockmann -----Lottonzio I Y= 0.2) ... .. ......... Lotton& (y=o.3)

/ ’

0 z= 0.001 z-

4

/’

4.25 l

7,

/’

/’

A’

0.02

I 4.00

-6.0

2 -5.5 Y? 2 m

2 3.75 E ” .z

-6.5

-5.0

2 E

-4.5 2 -4.0 I

3.5c

-3.5 3.25 -3.0 3.oc

1

0.4

2

b

4

3

M.-

,

I

I

I

I

1

2

3

4

5

Mi-

5Mra 6

I

M,

6

Fig. 10a. Stellar luminosity L,, at the onset of He shell flashes versus initial mass Mi according to [88B3] (solid

lines); dotted and short-dashed lines are from [87L]; long-dashed line is from [831]for Z= 0.02. The luminosity region for carbon stars is also shown. Adapted from [88B3]. Fig. lob. The core mass wnp at the onset of He shell flashes, and the final-initial mass (Mr- M,) relations. IR is according to [831].The triangles downward are theoretical values according to [86L]. The solid lines are Mr values, WK-A, WK-B, according to [83w] from galactic white dwarfs; W is according to [84w] from the massdistribution of galactic nuclei of planetary nebulae (NPN). The AM, AM’ lines are drawn by [88B3] through the data of Aaronson and Mould [85A2] for the Magellanic clouds (LMC, SMC). This figure is adapted from [88B3]. Land&Bbmstein New Series VU3b

9.2

[Ref. p. 120


2.1

i

2.0

3

1.9

" 3

1.8 1.7

M=2.5Mo

1.4L

4.10

a

I

I

I

I

4.05

4.00

3.95

3.90 -

-I ”

u=l.O

I

I

3.85 3.80 log (Terrin K)

I

I 3.70

3.75

I 3.65

3

M=5Ma

-0.51

4.3

b

I 4.2

I 4.1

I 4.0 -

I I 3.9 3.8 log ( T&in K)

I 3.7

I 3.6

:

Fig. lla. Evolutionary tracks of a 2.5 A4, star in the HR diagram, according to [91L]. The numbers over the tracks denote different initial chemical compositions, seeTable 5 and text. Fig. llb. Evolutionary tracks in the Mb,,,- Tendiagram of a 5 M0 star calculated from the main sequence through core He exhaustion according to [70H]. The labels S, Y, Z represent the initial chemical composition, seeTable 5 and text.

found in the models of [83I]. The calculations by [87L] show strong dependenceof L,, on the initial He abundance Y, and on the initial mass. According to [88B3], the reduction of LTP allows a large production of the carbon stars suggestedby the observations. The formation of these stars is still a matter of debate, and requires the so-called third dredge-up, i.e. mixing of carbon produced in the Land&-Biknstein New Series VU3b

44.3 Model computations

Ref. p. 1201

93

He-shell during thermal pulses to the surface. This dredge-up seemsto be favored in metal-poor stars with initial 2 = 0.001, but its occurrence depends on the value of the mixing length parameter, the envelope mass, the opacities and the treatment of convection and semiconvection in the outer stellar layers. For a discussion of these issues,see[88Bl, 9111and referencestherein. Other computations dealing with this problem are given by [88H2, 89H2], who concentrate on the production of the heavy elements by the s-processnucleosynthesis. These models have also been used by [90Kl] for a detailed study of the s-process. In Fig. lob, the final mass Mr, and the mass of the hydrogen exhausted core wnp are given versus the initial mass at the time of the first pulse. It is seenthat wnp is approximately independent of the initial massfor Z= 0.02 and for the 1.. .3 Mo stars. However, a strong dependenceon the massis found for Z=O.OOl. The estimate of [831] of MHTpfor the 1...3 Mo stars (line IR in Fig. lob) yields higher value than in the other computations. According to [88B3], this is due to the interpolation formula of [831] obtained on the basis of the more massive stars. The comparison with the curves labeled WK-A, WK-B and W inferred from the observations of galactic white dwarfs shows agreement with the observed Mr-M, relations for low-mass stars. This means ([88B3]) that the mass loss rates due to Reimer’s formula seem to be sufficient in this case. However, for the higher masses, additional mass loss (the so-called superwind) should be invoked for a better agreement with the observed data. Another issue in the study of the LMS and IMS is the effect of the initial composition on the internal evolution and duration of the burning phases.To illustrate this, two independent computations for 2.5 Mo [91L] and 5.0 Mo [70H] are shown in Figs. 1la and b and Table 5. Although these computations are two decadesaway from each other, they show qualitatively similar features, which may be summarized as follows: (i) The tracks of the low-metal stars (sequences1 and Z) are brighter and bluer due to the lower opacities. (ii) The tracks of the He-poor stars (sequences3 and Y) are much fainter. This is due to the effect of reducing the mean molecular weight as a consequenceof the decreasedinitial He abundance. (iii) The initially He-poor stars have the longest lifetime, since they evolve at the lowest central temperatures T,. Consequently, they have the longest red giant branch (RGB), since the top of the RGB is determined by the ignition of the triple-alpha reaction, which is delayed owing to the low T,. The metal-poor stars, on the other hand, have the highest T, at the bottom of the RGB, hence the shortest lifetime. These examples show that not only the variation of initial metallicity may be important, but also that of the initial helium. This feature may be important for the photometric evolution of galaxies.

Table 5. Lifetimes (in years) of the core H-burning phase, t, and ttota,,respectively up to central He exhaustion, for the 2.5 Mo star [91L] and 5.0 Mo star [70H] with different initial chemical compositions. Sequence

&I,

Z

hI

t total

1 2 3

0.30 0.30 0.20

M= 2.5 Ma 0.01 0.02 0.01

4.1455.108 5.0382.10* 7.4394.108

-

0.30 0.30 0.20

M= 5.0 MO 0.030 0.015 0.030

5.1025.10’ 5.1067.10’ 1.1857.10*

7.441I.107 7.1642.107 1.6251.10’

S Z Y Landolt-Bdrnstein New Series VI/3b

94 4.4.3.5


[Ref. p. 120

Massive stars

A general overview of the evolution of MS up to the core carbon-burning phase is given in [86C4]. Intercomparison of evolutionary sequencesfor MS is presented in [88Dl, 9OC2]. Important and still controversial issues in MS evolution are mass loss and convection. The treatment of mass loss in model computations has up to now been based on empirical formulations in terms of the macroscopic parameters of the stars (L, M, T,J (see [86C4] for an overview and [9ON] for a recent work). This treatment of mass loss does not always assure consistency between the type of the star and the mass loss rate assignedfor the evolutionary stage. A possible way out is to use the radiation-driven wind theory [89K2]. This theory is a rather developed one, allowing the calculation of the terminal velocity of the stellar wind and the obtaining of the mass loss rates as a function of metallicity. However, the radiation-driven wind theory is still mainly restricted to hot stars, and has not yet been implemented in stellar evolution calculations. Several features from various computations with parameterized massloss rates are as follows: (i) The decreaseof stellar mass leads to a less rapid increase of T, than in the case without mass loss. Consequently, the mass of the convective core decreasesmore rapidly in the course of evolution, although the core massfraction is larger in mass-losing stars. (ii) Due to the smaller convective core, the luminosity is lower, which tends to increase the lifetime. (iii) Mass loss may reduce the extension of intermediate convective or semiconvective zones at the top of the H-burning shell. Eventually, these zones are not completely suppressedby massloss, so that a careful description of the chemical structure in these layers remains important in following the subsequentevolutionary phases. (iv) A slight main sequencewidening results when moderate massloss rates are used. For very large mass loss rates, material processedin the interior layer is exposed to the surface. The resulting lower surface hydrogen abundance may lead to a narrower main sequencefor stars more massive than = 60 MO. (v) The mass of the helium core (hydrogen exhausted core) at the end of core H burning is smaller when massloss is included. Qualitatively similar features are also obtained when mass loss is combined with over-shooting. This phenomenon is not yet well understood. The simplest way of treating over-shooting is to assumean overshoot distance A = aH,, where HP is the pressure scale height above the edge of the convective core as obtained by the Schwarzschild criterion for convection (eq. 14). In other words, this treatment contains the free parameter a which has to be adjusted in someway. The approach currently used [84B, 86M, 92821is to choose an a for which the models fit the envelope of the main sequenceband for cluster and associations. In the recent computations of Schaller et al. [9282] with the new OPAL opacities (subsect. 4.4.2.3), CI= 0.20 has been adopted. This value has been suggestedas an upper limit in the recent work of Stothers and Chin [91Sl]. These authors argue even for zero core overshooting. The main results of model computations with mass loss and overshooting are as follows (more details in [86C4]): (i) The increase of the convective core’s mass depends crucially on the parameter 01,and leads to several consequences:higher luminosity on the main sequence,larger H-burning duration, possible suppression of intermediate convective or semiconvective zones, wider main sequencefor massesup to = 60 M,. (ii) The He-burning lifetime may not be affected appreciably by overshooting, but may increase slightly [86C4]. However, Schaller et al. [9232] pointed out that this lifetime is also sensitive to the algorithm used to determine the change of chemical composition and the mass of the convective core in the stellar models.

Land&Biirnstein New Series VI/3b

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(iii) Mass loss in combination with overshooting favour the formation of Wolf-Rayet (WR)stars. With more mixing, the material processed by nuclear reactions in the interior layers may appear at the surface even with moderate mass loss rates. Several works [81V, 86C3, 86C4, 87A, 89L3] deal with the general properties of WR stars. The processof their formation is complicated and their progenitors are not only single stars, but they are also produced by masstransfer in binary systems[8OV, 82D, 92D2]. There is observational evidence for a direct link between WR stars and O-type stars. On the basis of their galactic distribution, Conti et al. [83C] proposed stars of masses2 40 M, as progenitors. A lower limit of 30 Mo has been suggestedby Humphreys et al. [85Hl], and about 80% of the WR stars may descend from stars of masses2 80 Mo. The statistics within 2.5 kpc of the sun give a number ratio of WR/O stars of 0.36 * 0.15 [83C] with a lower limit of = 0.1. For WR stars, seesubsect. 5.2.1.2 in this volume. The predictions of evolutionary calculations for that ratio, which is roughly equal to t,,lt, (helium to hydrogen lifetime) are still uncertain. Convective overshooting appears to reduce t,,lt,. It is found [86C4] to be 0.06 to 0.10, smaller than suggestedby observations. The new computations of [9282] yield = 0.10 for stars between 7 and 40 Mo and initial metallicity Z-O.02 as well as for Z=O.OOl. In the mass range 40 to 120 Mo, the situation is different: for Z=O.OOl, t&,=0.09 to 0.10, while for Z=O.O2 it is 0.10...0.16 with “standard” mass loss, but 0.14...0.34 with arbitrary increased mass loss rates by a factor of two during the post main sequencephases.The latter higher values are a consequenceof the lower luminosities during He-burning. It is emphasizedthat the new OPAL opacities influence the formation of WR stars in particular, and this process seemsto be very sensitive to the mass loss rates and the initial composition adopted in the model computation.Presently, it appears that the effect of core overshooting may have been overestimated in the former calculations based on the LAOL opacities. In Fig. 12a, the evolutionary tracks are shown for a grid of stellar models in the mass range 0.80.. .120 Mo according to [9282]. In these computations, the Schwarzschild criterion for convection is used, and parametrized core overshooting by 0.20 HP is assumed. The OPAL opacities according to [92R] have been adopted. Mass loss is also included in these computations basically according to the semi-empirical formula of [90N] (see [9282] for further details). For the sake of comparison, Fig. 12b shows the evolutionary tracks of stellar models with M= 1.7.. .15 Mo according to [94E]. In these computations, similar assumptions have been used, but overshooting is not taken into account, and the OPAL opacities of [921]were utilized. The comparison of Figs. 12a and 12b indicates that the blue loops of the stars with M= 3.. .9Mo are less extended in Fig. 12a. This is mainly due to the effect of core overshooting. In other words, the location of the IMS in the H-R diagram during the core He burning is rather sensitive to this effect. It may also depend on the efficiency of envelope overshooting (see[93B]). Thus, the evolution of the IMS during core He burning is still model dependent. Note, however, that some observations (see[84S]) seemto require the more extended loops, as in Fig. 12b. Another feature is seenin Fig. 12a. For the stars of M > 12 M,, no blue loops are found, while the loops occur again for stars of M 2 40 Mo. There is, however, a major difference in the evolution of these very massive stars as compared with the IMS. The former exhibit large mass loss by stellar wind. As mentioned above, mass loss in combination with overshooting leads to a wider main sequenceand favors the formation of WR stars. This is basically the reason for the behavior of the tracks of the stars above 40 MO seenin Fig. 12a. Note that the sharp decreasein luminosity for these stars is due to the heavy mass loss assumed in these computations during the so-called “WNE” phase (complete loss of the H-rich envelope). This mass loss is based on the semi-empirical formula by [89L1]. In summary, the evolution of very massive stars still needs more work, since the description of mass loss is still based on semi-empirical formulation and the treatment of convection is still under debate.

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-12

120Mo

6

[Ref. p. 120

v -

6OM, 4OMo

-

-10

-8

-6 4

I % 3 . B

2

2

1

Y=i 0.300 Z: 0.020 04 07 09 En

4

81

BZ 83

IIIIIII

-1

b

88

I

I

I

I

I

4.6

4.4

4.2

a

0 4.6

65

I 4.4

6

I

-

4.0 log ( Tefrin K 1

-

I I 4.0 3.8 log ( TeffinK)

I 4.2

I

I

3.8

3.6

I 3.6

: t

Fig. 12a. Evolutionary tracks in the HR diagram according to [9282] for the indicated masses,calculated with Schwarzschild criterion for convection, and with a core overshooting parameter LY= 0.20 HP,The hatched areas indicate the slow phasesof nuclear burning. Seetext. Fig. 12b. Evolutionary tracks in the HR diagram for the indicated masses calculated [94E] with the Schwarzschild criterion for convection, but without including overshooting. The initial chemical compositon is (X, 2)=(0.70, 0.02). The open circles represent the results of [9382] for the main sequencewidth. The filled circles indicate the positions beyond which the first dredge-up ceasesto change the surface abundances. Note that the tracks of the 3. ..9 A4ostars exhibit more extended blue loops as compared with those in Fig. 12a.

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4.4.3.6 The progenitor of SN 1987A In the context of massive star evolution, especially with sub-solar initial composition, the progenitor of the famous and very well studied supernova (SN 1978A) in the Large Magellanic Cloud (LMC) was a surprise in many respects.This progenitor has been unambiguously identified as a blue supergiant (BSG) of spectral type B3 and luminosity class Ia under the number 202 and declination - 69” in the Sanduleak catalog of the brightest stars in the LMC (SK - 69 202). At the time of explosion, it had log LIL, = 5.0 and log T,, = 4.19 as average values [84H]. The initial mass of this star is estimated as 19+3 Mo with a favorable value of = 20 M, [89A2]. Thus, SN 1987A has shown that a massive BSG star can lead to supernova explosion of type II, in contrast to the former common belief that these supernovae originate from red supergiant (RSG) stars. There are also other constraints: the detection [89F, 91C2] of densegas near the supernova suggests mass loss during a RSG stage which ended several lo4 years before the explosion. From the analysis of the light curve of SN 1987A [88Hl, 88W1, 89Hl], the mass of the H-rich envelope is estimated to be = 10 M,, or even smaller. This implies that a progenitor of = 20 Mo has lost = 4 Mo during its evolution, since its He core mass is = 6 M,. This is consistent with the value inferred from the light echo observation by [91C2]. The circumstellar matter around SN 1987A has a large abundance of nitrogen compared with the solar value [89F], and helium seemsto be also enhanced in the supernova [89E]. Thus, the obervations of SN 1987A and the analysis of its light curve indicate that the progenitor performed a red-blue evolution several lo4 years before the explosion. The point is then to understand this behavior within the framework of the theory of massive star evolution, There are calculations without mass loss [87H2] for stars of 15...20 Mo and LMC average metallicity (2 = l/4 Z,), which yield only BSG evolution. These models are not consistent with the observational requirements that massloss is not negligible and with the final red-blue evolution. The calculations with rather large mass loss and with core overshooting above the convective core [87M], and without overshooting [88W3], finally lead to BSGs. However, the mass of the envelope was strongly reduced = 1 Mo. Therefore, these computations are also not consistent with the analysis of the light curve mentioned above. The computations of [SSS]were performed with the Schwarzschild criterion for convection including mass loss for a 21 Mo star. These authors found that the star performs a red-blue loop during the contraction phase towards carbon ignition retaining = 9 M, of H-rich envelope and with L and TeKbeing consistent with SK- 69 202. However, this behavior was found only with artificial mixing of He in the envelope to enhance its abundance (by mass) to about 0.40. The problem here is to understand the physical reason of this helium enhancement and its timing, namely at the end of core He burning. In this context, the role of rotation has been emphasized. The role of mixing in SK - 69 202 has been considered by [89Bl], also in connection with possible binary evolution. Another class of models [88Wl, 88W2, 89L2, 89w] are based on the Ledoux criterion for convection and include semiconvection. These models are able to construct an evolutionary scenario resembling the progenitor of SN 1987A (details in the referencesabove). However, the problem here is to find a common way to describe the effectivity of the semiconvective diffusion, which is simply parametrized. Recent computations [91El, 91E3] based on a new model of semiconvection [92Sl] did not lead to a BSG at the time of explosion. These computations show that the blue loops in the H-R diagram are rather sensitive to the shape of the hydrogen profile near the edge of the helium core, and to the used opacities in the atmospheric layers, below lo4 K. To summarize, the peculiar behavior of the star SK - 69 202 in the LMC is not simply explained by just the lower metallicity of the LMC. Many restrictive conditions such as enhanced helium in a still massive envelope or reduced convection may be invoked in order to find an evolutionary scenario consistent with the observed properties of that star. The question arises whether the theory of massive star evolution with variable composition is still far from being understood, or the SK - 69 202 star may have been a peculiar case. As a final comment in connection with SN 1987A, the neutrinos observed by the detectors of Kamiokande II [87Hl] and IMB [87Bl] have confirmed the basic assumption that the energy of the Land&-Biirnstein New Series VU3b


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[Ref. p. 120

explosion stems from the gravitational energy release of the forming remnant, and the bulk of this energy = 3.1053erg is emitted by neutrinos. In addition, the comprehensive observations of SN 1987A at wavelengths from radio to gamma rays have provided so far the most complete picture about the death of a massive star. For supernovae, seealso subsect. 5.1.4.1.

4.4.3.7

Late evolutionary phases

In connection with Fig. 13a, we describe the main features of the evolution for stars in the mass range M= 1.. .7 M, in the Tc- p, diagram. In this diagram, the dashed line separates roughly the regions of nondegenerate and degenerate electrons. The evolution proceeds first with increasing T, - p’,” in the nondegenerate region. This behavior resembleshomologous contraction as described by [90K2]. Each contraction phase brings the center closer to the region of degeneracy. The classification of the stars introduced above (LMS, IMS and MS) can be clearly seen in Fig. 13a. After core H burning, the LMS develop degenerate He cores, while the IMS develop degenerate C-O cores after core He burning. In constrast, a massive star of M= 15 Mo evolves through C burning under nondegenerateconditions. The common evolution of the central values indicated in Fig. 13a implies that the corresponding cores have similar massesand their mechanical structures are nearly independent of the details of the star’s envelope. This is a remarkable effect of the electron degeneracyachieved in these cores. The formation of a degeneratecore does not imply that the star has reached the end of its evolution. This holds only if the shell source ceasesto increase the massof the core (more details are given below). In this case, the core would cool down at a constant p, (see Fig. 13a) to the white-dwarf state. However, continuous shell burning increasesthe mass of the core to a certain limit where the next burning phase occurs, but under strongly degenerate conditions. This leads to the He flash in the LMS when the core mass exceedsthe critical value of = 0.45&f, [8411, 9OK2]. The effect of the He flash on the ensuing evolution is not completely settled. In the case shown in Fig. 13a, which resembles the results of many computations (see [8411] for an overview), the central temperature rises during the flash until the electron degeneracyis removed. Further evolution proceeds similarly to the more massive stars, which do not encounter the He flash. This type of evolution has also been found in the recent up-dated computation by [94E] for a 2 M, star having solar initial composition. The final evolution of the LMS to the white-dwarf state may resemble that of the 0.80 Mo star displayed in Fig. 13a, which has been computed with the assumption of mass loss from the surface [741]. Note that the resulting final mass depends on many factors as described in connection with Fig. lob. The IMS (in the range up to M= 8 Mo) develop degenerate C-O cores of masses below =1.0&V, [88N]. The central evolution of these cores after core He burning occurs in a region of the T,-- p, diagram (seethe path of the 7 M, star in Fig. 13a), where the neutrino lossesbecome high enough (seeFig. 9b) to cool the central region. Their further evolution is characterized by a possible bifurcation either to the white-dwarf state or to the carbon flash, as indicated in Fig. 13a. This branching depends on whether the core mass M, can increase to approach the Chandrasekhar masslimit MC,,[seeeq. (106)]. The behavior of M, is determined by several factors: (a) M, can remain below Mc,, due either to mass loss or to the initial mass being smaller than Mch. In the former case, the envelope of the star is not massive enough for J4, to increase by shell burning. The star in both casescools down to become a C-O white-dwarf. If, however, this star is a member of a binary system, then it may accrete enough material that its core mass approaches Mch. The resulting carbon flash (or deflegration) representsthe canonical model for the type I supernovae [90T]. (b) With M, < Mch initially, and assuming that the envelope of the star is massive enough, MC can grow (by shell burning) to MCh. In this case,the central evolution will be qualitatively similar to the path of the 7 Ma star shown in Fig. 13a toward the carbon ignition line, and the star will underLand&-Biirnstein Series VU3b

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[Ref. p. 120

explosion stems from the gravitational energy release of the forming remnant, and the bulk of this energy = 3.1053erg is emitted by neutrinos. In addition, the comprehensive observations of SN 1987A at wavelengths from radio to gamma rays have provided so far the most complete picture about the death of a massive star. For supernovae, seealso subsect. 5.1.4.1.

4.4.3.7

Late evolutionary phases

In connection with Fig. 13a, we describe the main features of the evolution for stars in the mass range M= 1.. .7 M, in the Tc- p, diagram. In this diagram, the dashed line separates roughly the regions of nondegenerate and degenerate electrons. The evolution proceeds first with increasing T, - p’,” in the nondegenerate region. This behavior resembleshomologous contraction as described by [90K2]. Each contraction phase brings the center closer to the region of degeneracy. The classification of the stars introduced above (LMS, IMS and MS) can be clearly seen in Fig. 13a. After core H burning, the LMS develop degenerate He cores, while the IMS develop degenerate C-O cores after core He burning. In constrast, a massive star of M= 15 Mo evolves through C burning under nondegenerateconditions. The common evolution of the central values indicated in Fig. 13a implies that the corresponding cores have similar massesand their mechanical structures are nearly independent of the details of the star’s envelope. This is a remarkable effect of the electron degeneracyachieved in these cores. The formation of a degeneratecore does not imply that the star has reached the end of its evolution. This holds only if the shell source ceasesto increase the massof the core (more details are given below). In this case, the core would cool down at a constant p, (see Fig. 13a) to the white-dwarf state. However, continuous shell burning increasesthe mass of the core to a certain limit where the next burning phase occurs, but under strongly degenerate conditions. This leads to the He flash in the LMS when the core mass exceedsthe critical value of = 0.45&f, [8411, 9OK2]. The effect of the He flash on the ensuing evolution is not completely settled. In the case shown in Fig. 13a, which resembles the results of many computations (see [8411] for an overview), the central temperature rises during the flash until the electron degeneracyis removed. Further evolution proceeds similarly to the more massive stars, which do not encounter the He flash. This type of evolution has also been found in the recent up-dated computation by [94E] for a 2 M, star having solar initial composition. The final evolution of the LMS to the white-dwarf state may resemble that of the 0.80 Mo star displayed in Fig. 13a, which has been computed with the assumption of mass loss from the surface [741]. Note that the resulting final mass depends on many factors as described in connection with Fig. lob. The IMS (in the range up to M= 8 Mo) develop degenerate C-O cores of masses below =1.0&V, [88N]. The central evolution of these cores after core He burning occurs in a region of the T,-- p, diagram (seethe path of the 7 M, star in Fig. 13a), where the neutrino lossesbecome high enough (seeFig. 9b) to cool the central region. Their further evolution is characterized by a possible bifurcation either to the white-dwarf state or to the carbon flash, as indicated in Fig. 13a. This branching depends on whether the core mass M, can increase to approach the Chandrasekhar masslimit MC,,[seeeq. (106)]. The behavior of M, is determined by several factors: (a) M, can remain below Mc,, due either to mass loss or to the initial mass being smaller than Mch. In the former case, the envelope of the star is not massive enough for J4, to increase by shell burning. The star in both casescools down to become a C-O white-dwarf. If, however, this star is a member of a binary system, then it may accrete enough material that its core mass approaches Mch. The resulting carbon flash (or deflegration) representsthe canonical model for the type I supernovae [90T]. (b) With M, < Mch initially, and assuming that the envelope of the star is massive enough, MC can grow (by shell burning) to MCh. In this case,the central evolution will be qualitatively similar to the path of the 7 Ma star shown in Fig. 13a toward the carbon ignition line, and the star will underLand&-Biirnstein Series VU3b

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9.oc

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” carbon ignition ” \,

0.7: 8.5C

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\

helium ignition

-I

1 r,/kT=lO

--XT

In\

\

cbmmon ! C-Ocore !

/71 i

i

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< 2.25

6.75 6.50

’

’

-1

’

*--?

0

4

c3.5 5

7

6

8

9

10

log (@n g/cm31 -

a

I _

3

2

1

to white dwarf state

main seqience contraction

“?C

J

) e+e-pair

_._”

3

4

5

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6,--I-

7 -4,El :..-I-...

9

Fig. 13a. Evolution of the central temperature T, (in K) and density p, (in g cm-3) for stars of massesM= 1,2, 7 and 15 M, stars according to [741].The dashed lines represent ignition lines for H, He and C-burning, defined by equating the neutrino lossesto the nuclear energy generation rate. The dashed-dotted line labeled E,lkT= 10, where sr is the Fermi energy of the electron gas, represents roughly a separation between the degeneracy and nondegeneracy of the electron gas. The numbers indicated in the figure are stellar masses. Fig. 13b. Evolution of the central temperature T, (in K) and density p, (in g cmm3)for helium cores of masses M= 2.2, 2.8, 3.0, 3.3, 6 and 8 Mo (seetext). The dashed-dotted line labeled $ = 10 is similar to the dashed line in Fig. 13a.The ignition lines (dotted) are explained in the caption to Fig. 13a.Adapted from [88N].

100


[Ref. p. 120

go explosive carbon ignition. The massrange in which this type of evolution occurs is not well established, and may comprise (4.. .8 MO). However, there are indications (see[84Wj) that at least galactic stars of M 3 5 M, may loose their entire envelopes before reaching the carbon flash. This would have the severeconsequencethat the TP-AGB phase may not be reached at all in these stars. The abovediscussionshowsthat the basic featuresof the late evolution of the IMS (M= 2.3.. .8 Mo) is the competition betweenthe decreasein the star’smassby massloss and the increasein the massof the degenerateC-O core toward Mch. Fig. 13b can be considered as complementary to Fig. 13a and shows the central evolution of helium cores of massesM,=2.2, 2.8, 3.0, 3.3, 6 and 8 Mo according to [88N]. These massescorrespond roughly to initial massesof M= 8, II, 12, 13,20 and 25 M,, respectively. In this diagram, the line labeled with I/J= 10 separatesroughly the regions of degenerate and nondegenerate electrons. The dotted lines representing approximate ignition lines for C, Ne, 0 and Si burning are explained in the caption to Fig. 13a. The late evolution of the above helium cores is rather complex and sensitive to the stellar mass. This complexity stemsfrom the interplay between the electron degeneracy, the neutrino energy losses and the electron capture processes.The many details of such evolution will not be described here (see[88N, 86W1, 86W2]). Only the main basic features will be outlined in the following according to the massranges of the helium cores. (i) M,=2.2...2.7 A&, (M,= 8...10 Mo): After C burning, these stars develop degenerate 0-Ne-Mg cores of massesbelow the critical mass = 1.37 M, for neon ignition [88N]; hence they do not ignite neon. Instead, these cores evolve with increasing core mass (due to C shell burning) toward higher densities (Fig. 13b). As a consequence of the increasing densities, the Fermi energy of the electrons becomessufficiently high to exceedthe threshold for the electron capture reactions on 20Ne(e-,v)20F(e-,v)200and 24Mg(e-,v)24Na(e-,v)24Ne, as indicated in Fig. 13b. The resulting decreasein the electron pressure triggers a collapse phase in these stars. This collapse phase occurs in a 0-Ne-Mg core still containing nuclear fuel. Therefore, nuclear burning may continue during infall, in contrast to the collapse phase of the more massive cores (M, 2 3.3 M,, seebelow), which develop an iron core exhausted of nuclear fuel. (ii) M,=2.7...3.2 M,, (M, = lo...12 Mo): In this mass range, the stars develop partially degenerate 0-Ne-Mg cores of masses1.37.. . 1.5 Mo. Central neon ignition would then be possible in these cores. However, a temperature inversion occurs in the central region due to neutrino energy losses,which are faster at high densities (seeFig. lob). Therefore, neon ignites off-center and under sufficiently degenerate conditions to lead to Neshell flash [88N], which in turn ignites 0 burning. It is then crucial for the final fate of these objects how the burning shell behavesduring the ensuing evolution, which is highly sensitive to the mass of the core. In the computation by [88N], it is argued that the propagation of the burning shell is due to gravitational contraction. This contraction cannot be halted by the pressure of the degenerate electrons, becauseof the electron capture reactions in the burning layers, which reduce Y, and the Chandrasekhar mass[seeeq. (106)]. The net effect is that the burning shell reachessuch high densities that the 0 burning becomesexplosive. If the burning shell is quenched at earlier stage by neutrino cooling, then a degenerate0-Ne-Mg core is left unburned. This brief discussion shows already that the late evolution of stars in the mass range 8.. .12 Mo is extremely sensitive to the massof the 0-Ne-Mg core formed after C burning. The evolution in this mass range is basically determined by the interplay between neutrino energy losses,electron degeneracy and electron capture processes.The neutrino losses lead to a temperature inversion in the central region, so that the nuclear burning occurs off-center. This nuclear shell burning becomes unstable, since it occurs in a region of high electron degeneracy, similar to the He flash in low mass stars described above. Finally, the electron capture processeslead to a decreaseof the electron pressure and acceleratethe evolution, which is then determined by the propagation of the nuclear shell burning toward the center of the star. Land&-Biknstein New Series VU3b

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(iii) M, > 3.3 Mo, (M, 2 13 Mo): Stars in this mass range can be considered as typical massive stars. They ignite neon at the center under nondegenerate conditions, and evolve with increasing temperatures (seeFig. 13b) through the 0 and Si burning phases.After Si burning, these stars form cores composed of iron group nuclei of massesclose to the Chandrasekhar mass,which are exhausted of nuclear fuel. The advanced stagesof massive (nonrotating) stars are described in several works [86N, 86W2, 88N, 88W4,93w]. Various general features may be pointed out: (a) The final location of a massive star in the HR diagram is determined already at the end of core carbon burning, since the remaining evolutionary lifetimes (Table 6) are shorter than the Kelvin-Helmholtz time of the H-rich envelope. (b) The relatively short evolutionary time from carbon burning on is due to the dominant neutrino energy lossesaccelerating the evolution and to the decreaseof nuclear energy production. (c) Silicon burning leads to the formation of the iron group nuclei (subsect. 4.4.2.4.4) which have maximum nuclear stability. At this stage, a massive star develops an electron-degenerate iron core consisting of iron group nuclei, which is surrounded by successiveburning shells of Si, 0, C, He, and H resembling an “onion-skin” structure. The ensuing evolution of the star is characterized by the gravitational collapse of the iron core. At the onset of this core collapse, the central temperature and density are T, = 10” K, p, = lOlo g cmm3, respectively. Presupernova evolutionary models (see [SSWl]) yield an average (over the core) value of the electron concentration (Y,) = 0.45 resulting from electron capture processesmainly during Si burning. Another important parameter is the entropy in the core which is found to be (1.Ok 0.20) k per nucleon (k is the Boltzmann constant) for stars of = 20 Mo. The critical mass of the core which can be supported by the pressure of relativistic and extremely degenerateelectrons against gravity is the ChandrasekharmassMch, given by MCh= 5.76 (Ye)’ MO,

(109

with (Y,)=O.45, Mc,, = 1.17 Mo. However, the finite entropy of the core leads to an increase of Mc. by [82B]: Mc,=5.76

(107)

(Y,)‘( 1+( G)‘),

where the electron entropy s, is about half of the total entropy [82B]. Hence, Mc,, should be about 1.3 M,. According to [88Wl, 88N], stars of 15.. .25 Mo seem to develop iron core masses of 1.4...1.61 M,. Table 6. Properties of nuclear burning phasesof a 20 Mo star according to [89A2]. The products of

the burning phases represent only the most abundant nuclei. The quantities p,, T,, t, L,, and L, are the central density, temperature, burning time, photon luminosity and neutrino luminosity, respectively. Note that energy lossesdue to neutrinos dominate when the star reachesthe carbon burning phase. Fuel H He C Ne 0 Si

Ashes 4He 14N 12c

‘I60

2oN;, 24Mg 160,24Mg 28si

32~

Fe-group 50 G A c 60


T,

t

k cm-‘1

4

4

W9Kl

[al

[&+I

krg/sl

5.6 9.4.102 2.7.10* 4.0.106 6.0.lo6 4.9(7)

0.04 0.19 0.81 1.70 2.10 3.70

1.0.107 9.5.105 3.0.102 0.38 0.50 2 days

2.7.103* 5.3.103*

15 M,) already lose a significant fraction of their mass prior to Roche lobe overflow by stellar wind. Mass loss at these high rates has important consequences,as it influences the evolution of the components as well as the chemical composition of the interstellar environment. In the case of binary systemswhere both components have high effective temperatures (T,,, > 3.104K) the mass loss can also have an important impact on the orbital evolution [90Hl]. Even independent on the existence of a Roche lobe overflow stage, loss of matter and angular momentum determine the evolution of massive binary systems. Land&-Biirnstein New Series VV3b

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[Ref. p. 120

The supernovae stagesof stars will not be described here. The physics of type II supernovae is broadly discussedin several reviews [86W2, 88B2, 89A2, 89H1, 90B2, 9OCl]. Concerning the explosive nucleosynthesis in supernovae the reader is referred to the work of Thielemann et al. [9OT]. The nucleosynthesis resulting from the integrated yields of stellar models in the mass range 12...40 Mo has recently been presented by [93w]. In this work, the evolutionary phasesup to the iron core collapse are considered, and the effect of the ‘%(a, ?)I60 reaction is investigated along with two models of semiconvection. Finally we mention the challenging issue regarding the connection between the various types and subtypes of supernovae (Ia, Ib, Ic, II-P, II-L) and their stellar progenitors. This issue is a complicated task because of the various explosion mechanisms leading to these supernovae types. Recent overviews describing the current situations have been presented by [91B3,91w].

4.4.3.8

Binary stars

The evolution of binary stars can be calculated in the same way as for single stars, taking into account the interaction between the two components, implying changes in mass and angular momentum. This interaction is determined by the concept of the critical Roche lobe [59K]. It is assumedthat either component of the binary system evolves independently of its companion as long as it is smaller than its Roche lobe. The presenceof the Roche limit as an upper limit to the size of the components is the most important factor governing the evolution of binary systems.The systems evolve from detached (D) to semi-detached (SD), possibly contact systems (C) and again to detached systems, or mergers, or systems with common envelopes. Excellent general reviews on close binary evolution can be found in [68P, 71P, 77T]. For reviews on the evolution of low-mass and intermediate-mass close binaries, we refer to [8513,71P], and for the evolution of massive close binaries, we refer to [79Z, 81D, 82D, 86D]. Concerning model computations, the systemsare divided in three groups according to the evolutionary phase where the mass transfer starts, hence depending on the orbital separation A of the binary components, their massesMi and M2, and their massratio q (= M,lM,) [67K]. Case A. The primary fills its Roche limit before the end of core hydrogen burning (point B in Fig. 14). Case B. The primary fills its Roche limit after core hydrogen exhaustion, before the onset of helium burning (between points B and E in Fig. 14). Case C. The primary fills its Roche limit only after the end of core helium burning (point F in Fig. 14). Evolutionary computations have been carried out for two general assumptions: (1) The conservative case:total mass and total angular momentum are considered as constant: all the matter leaving the primary is accreted by the secondary; (2) Nonconservative evolution: only a fraction j?of the matter expelled by the primary owing to Roche lobe overflow is accreted by the secondary, and a fraction (1-p) leaves the system, taking away a fraction a of the angular momentum [67K]. Massive close binaries (M> 15 M,) already lose a significant fraction of their mass prior to Roche lobe overflow by stellar wind. Mass loss at these high rates has important consequences,as it influences the evolution of the components as well as the chemical composition of the interstellar environment. In the case of binary systemswhere both components have high effective temperatures (T,,, > 3.104K) the mass loss can also have an important impact on the orbital evolution [90Hl]. Even independent on the existence of a Roche lobe overflow stage, loss of matter and angular momentum determine the evolution of massive binary systems. Land&-Biirnstein New Series VV3b

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3.6 3.4 3.2 I -6 7 3.0 " ?2.* 2.6

2.2 4.3

k.2

4.1

4.0 -

3.9

3.8

3.7

3.6

3.5

3.4

Log(T,,,in K)

Fig. 14. Evolutionary track of a 7-Mo-star according to [67K]. A-B: H burning in the convective core; B-C: core exhaustion, transition to a H-burning shell; C-D: core contraction, star expansion; D-E: outer convection zone, H-burning shell, He-burning core; E-F: exhaustion of the core. Rsoche: Roche limit; Rz,, and RE;,: maximum radius during the H-burning and He-burning phase, respectively. Model calculations of binaries depend on the evolutionary phase where the mass transfer starts, hence on the orbital separation. Case A: The primary fills its Roche limit before the end of core H burning (point B). Case B: The primary fills its Roche limit after core H exhaustion, before the onset of He burning (between B and E). Case C: The primary fills its Roche limit after the end of core He burning (point F). 4.4.3.8.1

Orbital elements: their variation due to mass exchange

The orbital angular momentum J may be expressedas a function of the orbital separation A and the massesMI and AI2 as [92 Dl].

with c.~the angular velocity. The critical Roche radius R, can be expressed as a function of the orbital separation and the massratio q (Ml/M,) [69H]. R -E = 0.37771+ 0.20247 log qf 0.01838 log q*+ 0.02275 log q3 A forq > 0.1, R R = 0.37710+ 0.2131 log q - 0.00800 log q*+ 0.00660 log q3 A forq < 0.1. Landolt-Bbmstein New Series VU3b

(109)

Ref. p. 1201

103


3.6 3.4 3.2 I -6 7 3.0 " ?2.* 2.6

2.2 4.3

k.2

4.1

4.0 -

3.9

3.8

3.7

3.6

3.5

3.4

Log(T,,,in K)

Fig. 14. Evolutionary track of a 7-Mo-star according to [67K]. A-B: H burning in the convective core; B-C: core exhaustion, transition to a H-burning shell; C-D: core contraction, star expansion; D-E: outer convection zone, H-burning shell, He-burning core; E-F: exhaustion of the core. Rsoche: Roche limit; Rz,, and RE;,: maximum radius during the H-burning and He-burning phase, respectively. Model calculations of binaries depend on the evolutionary phase where the mass transfer starts, hence on the orbital separation. Case A: The primary fills its Roche limit before the end of core H burning (point B). Case B: The primary fills its Roche limit after core H exhaustion, before the onset of He burning (between B and E). Case C: The primary fills its Roche limit after the end of core He burning (point F). 4.4.3.8.1

Orbital elements: their variation due to mass exchange

The orbital angular momentum J may be expressedas a function of the orbital separation A and the massesMI and AI2 as [92 Dl].

with c.~the angular velocity. The critical Roche radius R, can be expressed as a function of the orbital separation and the massratio q (Ml/M,) [69H]. R -E = 0.37771+ 0.20247 log qf 0.01838 log q*+ 0.02275 log q3 A forq > 0.1, R R = 0.37710+ 0.2131 log q - 0.00800 log q*+ 0.00660 log q3 A forq < 0.1. Landolt-Bbmstein New Series VU3b

(109)

104


[Ref. p. 120

It is also possible to use simplified forms of these equations [71P]: R --lL = 0.38 + 0.2 log q A

for 0.3 < q < 20, RR A -

0.46224 M, (Ml + M2)“3

(112)

for q > 0.3. The rate of change A of the orbital separation A can in a general way be given by [8332] (113)

For conservative evolution (p = l), this reducesto (114)

If k c 0 and Mr /M2 < 1 the orbit expands; if M, I M2 > 1 the orbit shrinks. The time scale involved with the mass transfer, the dynamical time scale or Kelvin-Helmholtz time scale,can be estimated as t,,=

k, =

E L pot = -.GM2 RL

3.107M2 RL

years,

(115)

(116)

with M, R, L in solar units, M the mass,R the radius, L the luminosity. A. Conservative evolution

The total massremains constant, (M, + M2) = constant.

The orbital angular momentum J remains constant, log P = 1.5 log A - 0.5 log (M, + M2) - 0.936.

(117)

A is the semi-major axis in solar radii, P the period in days, M, and M2 are the massesof primary and secondary in solar masses.

B. Nonconservative evolution

A fraction /I of the mass lost by the primary leaves the system and carries away a fraction of the angular momentum 6JIJ. Ml is the mass of the donor, i.e. the mass losing star; M2 is the mass of the receiver, i.e. the mass accreting star; the subscript i denotes the initial situation; the massesare expressedin MO.

Land&-Bdmstein New Series VY3b


Ref. p. 1201

105

(a) We consider first stellar wind mass loss (Jeansmode). The period and the distance of the components may be calculated as

(118) (119)

(b) Mass loss via Lagrangian point L, (binary star starts filling its outer critical surface) AJ = 1.750A2

with o the angular velocity; all quantities are cgs. (c) For all other situations, a free parameter can be introduced to describe angular momentum losses. A possible way to handle this is to assumethat during the mass transfer, the angular momentum depends on the mass as J-M* or

with a a parameter to be fixed. These integral espressionsare equivalent to the differential expression, originally introduced by [67Pl] dlog J = CIdlog M. Until recently, only the detailed structure of the initial primary was calculated in computations of close binary evolution; the changing mass of the secondary by accretion was just used to derive the variation of the period, the orbital distance and the Roche radius of the primary. For nonconservative computations, parameters have to be introduced [79V, 7921 to take into account the fractional masslossesand angular momentum losses. The fractional masscan be expressedas c=

AM (121) Mli+ M2i . The orbital angular momentum transported by material leaving the system can be evaluated using a Jeans’ mode, AJ = CJ

Consequently, the orbital separation A and the period P vary, according to the third law of Kepler as A

-=

Ai

P

-=

pi

(1

-

C2~(~li~2iu4

wI~*)*v4l;+

+

%i)

(1 - C2)(MliM*i)(Mr + (“,M2)3(M,i+

442)

M2)

(122)

(123)

M2i)

An alternative way to deal with nonconservative evolution is given in [90H]. The effects on the stellar wind by Roche geometry are in a crude way taken into account by the assumption that the mass loss rates are inversely proportional to the average effective gravitational acceleration on the stellar surface. Starting from a dimensionless Roche potential, assuming the rotation synchronous with the orbital motion, the effective gravitational acceleration can be determined at different points on the surface of the primary mass M,, and then averaged and noted as gd.The analoguous gravitational acceleration g, for an isolated star can also be estimated; the ratio g,/gd is then considered as Land&-Bdmstein New Series VI/3b


106

[Ref. p. 120

the massloss enhancement causedby tidal and centrifugal effects.A similar expression can be found for the secondary. When the component approaches its Roche lobe, the stellar wind coming from the surface facing this component will make a transition to the Roche lobe overflow [82F]. An estimate for the effect on the mass loss rate of a binary component by the continuum radiation of the companion star can be found in [90Hl]. A relation between angular momentum loss and mass loss can be established as follows. Assuming that the mass loss by stellar wind w is distributed within a rigid spherical shell on the surface of the primary’s surface, the angular momentum is *J,=(iR~+x~)*M,,o+fR,‘~~i~u

(124)

where X, is the distance between the center of the primary and the axis through the center of mass, xLo= (Myif2)

’

with

The first term represents the orbital angular momentum, and the second term represents the rotational angular momentum. The angular momentum carried away by the matter lost by the secondary is then similarly,

The total angular momentum loss from the binary systemis then AJ= G”‘(M, + M2)“’ ~3’2

M2

+A2 CM,

+AMzJ2(

+

4

3 ALP&R,‘+ AM,,R, [(

)I

@M,,v + AMA M2)*

1-

;y;2)-

(126)

The total angular momentum of the systemis J=J,+(I,+I,)w,

(127)

with J, the orbital angular momentum (128)

I1 and I, are the moments of inertia of primary and secondary, respectively, and (1, + 12)o is the rotational angular momentum of the system. One can express the change of the orbital momentum as a function of the changing masses. Introducing the parameters cI=

(4

+I,)0

JO

(129)

and Land&-BBmstein New Series W3b

Ref. p. 1201


107

/j = v,+ 12)w =-----)1 J

(130)

1+;

eq. (127) becomes J= J&l + R)

(131) Combination of the logarithmic derivatives of eqs. (127) and (129) yields an expression for the change of the distance between the components AA -zz A

(B - l/2) - “:I 12 1

p 2

I

(131)

For more details we refer to [90Hl]; the effect of the radiation on the Roche lobes is also discussed there. 4.4.3.8.2

Model computations for low- and intermediate-mass close binaries

Equations governing stellar evolution with mass exchange can be found in [7OZ, 8513,92Dl]. For a description of a computer code for the evolution of the primary component, we refer to [7OP,8513, 92Dl], and for a description of a code for simultaneous evolution, we refer to [88P, 92Dl]. The general picture of the evolution is as follows. When the primary starts filling its Roche lobe, a phase of rapid mass transfer sets in. A large fraction of the mass of the primary is transferred toward the secondary. The initially most massive star (primary) becomesthe less massive one, i.e. the massratio is reversed.After this phase of rapid massloss, a phase of slow massexchange follows where the primary continues to fill its critical volume. In this way, a semi-detached system is produced. During the rapid mass transfer phase, mass is removed from the outer layers. In order to restore hydrostatic equilibrium, the underlying layers have to expand. The energy required for this expansion is removed from the luminosity; hence the luminosity decreases.At the end of the rapid mass transfer, the luminosity increases again. During the slow mass transfer phase, the chemical evolution of the primary occurs in a similar way as for a star without mass loss. In the convective core, the hydrogen burning continues. The star is still larger than the critical Roche lobe; hence the mass loss continues. The companion remains near the zero-age main sequence(ZAMS) for some million years. In that time, the system shows the characteristics of Algol stars: the more massive star, scarcely evolved, is near the ZAMS, while the less massive companion which left the ZAMS fills its Roche volume. The mass exchange stops when the primary shrinks back within its Roche volume.

Case A

Examples of caseA evolution, where only the structure of the primary component is computed, can be found in [66K, 66P, 67K, 67P1, 67P2, 7OZ,]. As an example of a simultaneous computation for a caseA, Table 7 gives a number of relevant evolutionary phases for a system of 9 Mo+5.4&, with an initial period of 1.624days [88P].

Case B

In this case, the primary fills its Roche lobe after core hydrogen exhaustion. Owing to the mass transfer, the period and the orbit of the system change. The luminosity of the primary drops, while that of the accretion component increases.The mass loss of the primary starts slowly and increases Land&-BBmstein New Series VU3b

Ref. p. 1201


107

/j = v,+ 12)w =-----)1 J

(130)

1+;

eq. (127) becomes J= J&l + R)

(131) Combination of the logarithmic derivatives of eqs. (127) and (129) yields an expression for the change of the distance between the components AA -zz A

(B - l/2) - “:I 12 1

p 2

I

(131)

For more details we refer to [90Hl]; the effect of the radiation on the Roche lobes is also discussed there. 4.4.3.8.2

Model computations for low- and intermediate-mass close binaries

Equations governing stellar evolution with mass exchange can be found in [7OZ, 8513,92Dl]. For a description of a computer code for the evolution of the primary component, we refer to [7OP,8513, 92Dl], and for a description of a code for simultaneous evolution, we refer to [88P, 92Dl]. The general picture of the evolution is as follows. When the primary starts filling its Roche lobe, a phase of rapid mass transfer sets in. A large fraction of the mass of the primary is transferred toward the secondary. The initially most massive star (primary) becomesthe less massive one, i.e. the massratio is reversed.After this phase of rapid massloss, a phase of slow massexchange follows where the primary continues to fill its critical volume. In this way, a semi-detached system is produced. During the rapid mass transfer phase, mass is removed from the outer layers. In order to restore hydrostatic equilibrium, the underlying layers have to expand. The energy required for this expansion is removed from the luminosity; hence the luminosity decreases.At the end of the rapid mass transfer, the luminosity increases again. During the slow mass transfer phase, the chemical evolution of the primary occurs in a similar way as for a star without mass loss. In the convective core, the hydrogen burning continues. The star is still larger than the critical Roche lobe; hence the mass loss continues. The companion remains near the zero-age main sequence(ZAMS) for some million years. In that time, the system shows the characteristics of Algol stars: the more massive star, scarcely evolved, is near the ZAMS, while the less massive companion which left the ZAMS fills its Roche volume. The mass exchange stops when the primary shrinks back within its Roche volume.

Case A

Examples of caseA evolution, where only the structure of the primary component is computed, can be found in [66K, 66P, 67K, 67P1, 67P2, 7OZ,]. As an example of a simultaneous computation for a caseA, Table 7 gives a number of relevant evolutionary phases for a system of 9 Mo+5.4&, with an initial period of 1.624days [88P].

Case B

In this case, the primary fills its Roche lobe after core hydrogen exhaustion. Owing to the mass transfer, the period and the orbit of the system change. The luminosity of the primary drops, while that of the accretion component increases.The mass loss of the primary starts slowly and increases Land&-BBmstein New Series VU3b

108


[Ref. p. 120

Table 7. Evolution of a systemof 9 Mo + 5.4 Mo according to [88P], with the Schwarzschild criterion applied. The initial composition is X = 0.70, Y = 0.27, 2 = 0.03. Cox-Stewart opacities have been used. The mass M is in units of solar masses,kis the mass loss rate in solar massesper year, M, is the massof the convective core. Subscripts 1 and 2 refer to primary and secondary, respectively. The data are given on two rows; the first refers to the primary, the second to the secondary. The orbital period is in days, the age in million years. The successivestagesare labeled by the letters A through Q: A ZAMS B start of the Roche lobe over flow from star 1 to star 2 C beginning of the contact phase D minimum massloss rate E deepestcontact F reversal of the massratio G end contact = minimum L, H maximum Tcfl,

I J K L M N 0 P Q

minimum R, minimum L, maximum Te, maximum L, red point secondary blue point secondary minimum M, second contact = reversal of the masstransfer outer critical surface

The age is given in million years; the luminosity L in solar units. X, is the hydrogen abundance, Y, the helium abundance. Both given by mass. Stage A B C D E F G H I J K L M N 0 P

Q

Age Period

Ml M2

0.0000 1.6200 0.1770 1.6200 0.2221 1.4300 0.2241 1.3906 0.2288 1.3500 0.2319 1.3400 0.2383 1.3900 0.2435 1.4906 0.2617 1.9200 0.2734 2.1400 0.3489 2.5100 0.3913 2.5300 14.8271 4.0000 16.1642 4.1300 16.2451 4.1400 16.2505 4.0200 16.2551 3.8000

9.00 5.40 9.00 5.40 8.24 6.16 8.03 6.37 7.54 6.86 7.19 7.21 6.37 8.03 5.83 8.57 4.77 9.63 4.46 9.94 4.07 10.33 4.05 10.35 3.22 11.18 3.17 11.23 3.17 11.23 3.21 11.19 3.30 11.10

$1 M2 O.OOOE+OO O.OOOE+OO -O.OOOE+OO -O.OOOE+OO -O.l20E-03 O.l2OE-03 -0.llOE-03 0.1 IOE-03 -O.l20E-03 O.l20E-03 4.120E-03 O.l20E-03 -0.30E-03 -O.l30E-03 -0.900E-04 0.900E-04 -0.350E-04 0.350E-04 -O.l90E-04 O.l90E-04 -0.900E-06 0.900E-06 -0.410E-06 0.410E-06 -0.390E-07 0.390E-07 -0.380E-07 0.380E-07 -0.340E-07 0.340E-07 O.l60E-04 -O.l60E-04 0.290E-04 -0.290E-04

logT,, loK,’ 4.46 4.24 4.32 4.23 4.22 4.36 4.21 4.37 4.16 4.38 4.11 4.39 3.83 4.41 3.92 4.41 4.06 4.40 4.09 4.39 4.11 4.39 4.11 4.39 4.03 4.33 4.03 4.37 4.03 4.27 4.03 4.25 4.04 4.24

2

lo& logL,

Tl T2

y, r,’2

M=1 Kc2

3.59 2.82 3.78 2.88 3.29 3.75 3.25 3.78 3.04 3.87 2.81 3.93 1.60 4.02 1.97 3.96 2.61 3.82 2.76 3.81 2.91 3.82 2.91 3.82 2.78 4.14 2.78 4.19 2.78 4.22 2.87 4.21 3.02 4.19

0.700 0.700 0.337 0.590 0.329 0.617 0.329 0.622 0.329 0.631 0.328 0.634 0.328 0.640 0.328 0.643 0.328 0.645 0.328 0.644 0.327 0.643 0.327 0.642 0.160 0.057 0.143 0.001 0.142 0.970 0.142 0.970 0.142 0.970

0.298 0.298 0.661 0.408 0.669 0.381 0.669 0.376 0.669 0.367 0.670 0.364 0.670 0.358 0.670 0.355 0.670 0.353 0.670 0.354 0.671 0.355 0.671 0.356 0.838 0.941 0.855 0.997 0.856 0.028 0.856 0.028 0.856 0.028

2.69 1.24 1.66 1.05 1.27 1.39 1.17 1.77 0.98 2.30 0.86 2.33 0.61 2.91 0.47 3.21 0.54 3.27 0.63 3.15 0.73 3.06 0.73 3.06 0.48 1.58 0.46 1.07 0.46 0.00 0.47 0.00 0.48 0.00


Ref. p. 1201

-

109

log (T,ff in Kl

Fig. 15. Evolutionary tracks of the componentsof a systemof 9 M, and 5.4 M, starting from the zero-age-

main-sequence (ZAMS) accordingto [88P].The important stepsof the evolution (capital letters)are given in Table7. until minimum luminosity is attained, then decreasesagain. During this phase of rapid mass transfer, the massloss rates are of the order of 10m5M, per year. The phase of rapid mass transfer is followed by a phase of slow mass transfer. Examples of case B evolution, can be found e.g. in [66K, 66P, 67K, 67P1,69K]. In low mass systems,Mo < Mi < 2.8 Mo, electron degeneracy setsin at the core when the hydrogen shell decreases.Contraction of the core occurs rather slowly, hence there is no phase of rapid expansion of the envelope. The mass of the hydrogen-exhausted core is less than 0.35 Mo; the temperature increase is not sufficient to start He burning. The mass exchange stops by extinction of the H-shell; the star becomesa white dwarf. As an example of evolution of a low-mass close binary system, we refer to the computed 2 MO+ 1 Mo system [67K]. In medium mass systems,2.8 Mo < M, < 14 Mo, the core mass is larger than the Chandrasekhar mass required for the thermal stability of the hydrogen exhausted core. Core contraction occurs very rapidly, and the triple alpha process is started and the corresponding rapid expansion of the envelope leads to a rapid phase of mass transfer. The evolution of a 10 Mo+ 8 Mo system with an initial period of 3.15 days [76Dl] occurs as follows. The hydrogen burning lifetime is of the order of 10 million years, while the time for the mass exchange is merely 10000years. The average mass loss is 5.2. 10e5Mo per year and the maximum value is 3.6. 10m5Mo per year. Helium burning proceeds for 2.8 million years; then a degenerate,nearly isothermal core develops. The star moves to the right in the HRD. A second phase of mass transfer occurs; the star has a CO core of 0.94 Mo and a helium atmosphere of 0.5 Mo; in between is a very thin active helium shell source of 0.21 M, which produces 94% of the total energy. Slow mass loss at a rate of 2. 10m5Mo per year continues during 30000years; the helium shell source is then extinguished; the mass of the remnant is 1.12 M,. Case C

For evolutionary computations according to case C we refer to [89P, 67K]. Lauterborn computed the evolution of a 5 Mo + 2 Mo system, with an initial period of 227 days. The evolution of the priLand&-Bb;mstein New Series V1/3b

110


[Ref. p. 120

mary component is followed from ZAMS to its final stage, a white dwarf of 1 A4,. The companion is at that time a main-sequence star of 6 Mo. The period of the system has then increased to 2.8 years. The caseC sequencewas computed in order to model the systemof Sirius A + B.

4.4.3.8.3

Model computations for massive close binaries

By massivebinaries we mean binaries with initial (ZAMS) mass of the primary beyond 15 M,, i.e., a star losing massby stellar wind. Due to this effect, layers of the initial convective core may appear at the surface; hence the atmospheric hydrogen abundance decreases.For lower-mass stars as well as for massive close binaries, phases of mass exchange can occur during core hydrogen burning, shell hydrogen burning and helium burning. For massive close binaries mass loss by stellar wind already changesthe orbital elements. The effectsof centrifugal and tidal forces and a possible radiation field of the companion star on the mass loss rates were already discussedin subsect. 4.4.3.8.1. The mass loss driven by stellar wind carries angular momentum. It is not easy to determine exactly the angular momentum loss rate, becauseof the nonsynchronism of orbital and rotational motion. This is due to the fact that a transition can occur between orbital and rotational angular momentum. Tidal interaction may lead to spin-up or spin-down of each component. The relationship between mass and angular momentum loss was also examined in subsect. 4.4.3.8.1. The effect of the continuum radiation on the Roche lobe may be important [72S, 76K, 76V, 77V, 78V, 90H]. When the Schwarzschild criterion is applied to determine the boundary of the convective regions, it turns out that the casesB and C cover a wide range in binary periods, and that they are in fact the most common type of evolution, assuming a homogeneous period distribution. The fraction of systemsevolving according to case A is relatively small; for primary massesbelow 10 M,, the fraction is lessthan 10%. For higher massesthis fraction is larger; for O-type stars, the percentage is larger than 25%. However, if overshooting is included, case A becomesmore important, especially for more massive stars. For high masses,only caseA is relevant, and for the highest masses,Roche lobe overflow does not even occur; in the latter case, the stars already move to the left in the early phasesof hydrogen burning, as a consequenceof the high mass lossesby stellar wind. In the casesB and C, the evolution of the primary is not very much affected by whether or not the mass transfer is conservative. In most cases,as soon as the primary starts overflowing its Roche lobe, most of the remaining hydrogen-rich envelope (which may contain up to 80% of the total initial stellar mass) is lost on a dynamical (Kelvin-Helmholtz) time scale.After the mass transfer, little more than the core of the primary remains. This remnant consists mainly of helium and a small amount of heavier elements. In view of the dominating presenceof helium, the subsequent evolution may be described in terms of the evolution of the helium core. A detailed analysis of the effects of angular momentum loss, the orbital evolution, and the influence of radiation on the lobes is given in [90Hl]; a system of 40 M,+25 M, has been studied in the conservative and nonconservative approximation for caseA and caseB evolution. For a comprehensive review on observations and evolutionary computations, we refer to [91v]. Characteristics (masses,radii, luminosities, etc.) of the various types of massive binaries (OB binaries, Wolf-Rayet binaries) can be found in [8OC,80G, 92Dl]. About 40% (36 I~I7) of the O-stars are binaries, mostly with a mass ratio larger than 0.4 [8OG]. The binary frequency of Wolf-Rayet stars seemsto be similar to that of O-stars; hence also = 40%. In some 30% of the cases,these systems contain an O-type star. Binaries with very unequal massesare absent. Most systems(about 2/3) have periods betwen 1 and 10 days; a smaller number have periods between 10 and 100 days. At the end of core hydrogen burning, the central temperature rises beyond lo* K and helium burning starts in the central regions. The triple a process converts three He-nuclei into a 12Cparticle, and secondary a-captures convert C into 0, and some 0 into Ne and Mg. At the end of core hydrogen burning, the star has the chemical composition of a Wolf-Rayet star, first a WN star, later a WC-star. The masses of WR stars range from 4.. ,5 Ma to 40.. .50 M, with an average 16 Mo for the WN stars and 13.5 M, for the WC types. The average mass ratios (WR/OB) are 0.52 for the WN and 0.42 for the Land&-BBmstein New Series VI/3b

110


[Ref. p. 120

mary component is followed from ZAMS to its final stage, a white dwarf of 1 A4,. The companion is at that time a main-sequence star of 6 Mo. The period of the system has then increased to 2.8 years. The caseC sequencewas computed in order to model the systemof Sirius A + B.

4.4.3.8.3

Model computations for massive close binaries

By massivebinaries we mean binaries with initial (ZAMS) mass of the primary beyond 15 M,, i.e., a star losing massby stellar wind. Due to this effect, layers of the initial convective core may appear at the surface; hence the atmospheric hydrogen abundance decreases.For lower-mass stars as well as for massive close binaries, phases of mass exchange can occur during core hydrogen burning, shell hydrogen burning and helium burning. For massive close binaries mass loss by stellar wind already changesthe orbital elements. The effectsof centrifugal and tidal forces and a possible radiation field of the companion star on the mass loss rates were already discussedin subsect. 4.4.3.8.1. The mass loss driven by stellar wind carries angular momentum. It is not easy to determine exactly the angular momentum loss rate, becauseof the nonsynchronism of orbital and rotational motion. This is due to the fact that a transition can occur between orbital and rotational angular momentum. Tidal interaction may lead to spin-up or spin-down of each component. The relationship between mass and angular momentum loss was also examined in subsect. 4.4.3.8.1. The effect of the continuum radiation on the Roche lobe may be important [72S, 76K, 76V, 77V, 78V, 90H]. When the Schwarzschild criterion is applied to determine the boundary of the convective regions, it turns out that the casesB and C cover a wide range in binary periods, and that they are in fact the most common type of evolution, assuming a homogeneous period distribution. The fraction of systemsevolving according to case A is relatively small; for primary massesbelow 10 M,, the fraction is lessthan 10%. For higher massesthis fraction is larger; for O-type stars, the percentage is larger than 25%. However, if overshooting is included, case A becomesmore important, especially for more massive stars. For high masses,only caseA is relevant, and for the highest masses,Roche lobe overflow does not even occur; in the latter case, the stars already move to the left in the early phasesof hydrogen burning, as a consequenceof the high mass lossesby stellar wind. In the casesB and C, the evolution of the primary is not very much affected by whether or not the mass transfer is conservative. In most cases,as soon as the primary starts overflowing its Roche lobe, most of the remaining hydrogen-rich envelope (which may contain up to 80% of the total initial stellar mass) is lost on a dynamical (Kelvin-Helmholtz) time scale.After the mass transfer, little more than the core of the primary remains. This remnant consists mainly of helium and a small amount of heavier elements. In view of the dominating presenceof helium, the subsequent evolution may be described in terms of the evolution of the helium core. A detailed analysis of the effects of angular momentum loss, the orbital evolution, and the influence of radiation on the lobes is given in [90Hl]; a system of 40 M,+25 M, has been studied in the conservative and nonconservative approximation for caseA and caseB evolution. For a comprehensive review on observations and evolutionary computations, we refer to [91v]. Characteristics (masses,radii, luminosities, etc.) of the various types of massive binaries (OB binaries, Wolf-Rayet binaries) can be found in [8OC,80G, 92Dl]. About 40% (36 I~I7) of the O-stars are binaries, mostly with a mass ratio larger than 0.4 [8OG]. The binary frequency of Wolf-Rayet stars seemsto be similar to that of O-stars; hence also = 40%. In some 30% of the cases,these systems contain an O-type star. Binaries with very unequal massesare absent. Most systems(about 2/3) have periods betwen 1 and 10 days; a smaller number have periods between 10 and 100 days. At the end of core hydrogen burning, the central temperature rises beyond lo* K and helium burning starts in the central regions. The triple a process converts three He-nuclei into a 12Cparticle, and secondary a-captures convert C into 0, and some 0 into Ne and Mg. At the end of core hydrogen burning, the star has the chemical composition of a Wolf-Rayet star, first a WN star, later a WC-star. The masses of WR stars range from 4.. ,5 Ma to 40.. .50 M, with an average 16 Mo for the WN stars and 13.5 M, for the WC types. The average mass ratios (WR/OB) are 0.52 for the WN and 0.42 for the Land&-BBmstein New Series VI/3b

Ref. p. 1201


111

WC stars. A number of WR stars have been detected that are single-line binaries, with a very small mass function suggesting they have low-mass companions [82M2]. All massive close binaries will pass a stage where an OB star is present with a core helium-burning companion with atmospheric hydrogen abundance X,, 10 Mo ; and the low massX-ray binaries, LMXRB, with M 1.3 1M, and the required initial separation of the components limit the expectations on the supernova rate to a small fraction of the observed frequency [86W2]. In recent years considerable attention has been given to the possibility that type I SN result from the merger originating at the end from gravitational radiation of two white dwarfs [79Tl, 79W, 8412,84141,the so-called double-degenerate model [SSCl, 8513,].A discussion of the problems connected with the scenarios mentioned earlier can be found in [86Wl]. For more details about mergers and alternative scenarios, see[8414,8513,88L].

4.4.3.8.7

Origin and evolution of massive X-ray binaries (MXRB)

From observations, evidence is found that most and probably all binary X-ray sources contain neutron stars or black holes. A fraction of them are pulsating binary X-ray sources, members of a welldefined class of strong X-ray sources, with relatively hard spectra. They are associated with young luminous stars. They are indicated as type I sources. This group can be subdivided into two subgroups with different characteristics: The standard systems are permanent sources, i.e., the X-rays have a regular periodicity and the optical light output displays the ellipsoidal variations, characteristic of the tidal distortion of the optical companion invoked by the orbiting compact star. The optical companion nearly fills its Roche volume, and the system can show regular eclipses. Several tens of such systems are known, and are easily recognized by their extremely strong emission lines. Periods are short, comprising between 1.4 and 10 days, except for the case4U1224-62, with a period of somewhat longer than a month. The progenitors of these systemsare OB stars. A number of these X-ray sources are pulsating. The pulse periods range between 0.75 and 14 min. Doppler determinations of the X-ray-emitting component and visual observations in some of these sources allow the determination of the orbits of the neutron star and its optical companion. From these orbits, the mass ratios and the massesof the two components can be derived. The determined neutron star massesare of the order of 1.5 Mo, while the massesof their optical companions range from 20 through 40 M,. In the group of transient sources the optical components are Be stars not filling their Roche lobes. Eclipses are mostly absent and there are no regular ellipsoidal light variations. Their masses Land&-BBmstein New Series VI/3b

116


[Ref. p. 120

10” erg, is sufficiently large to disrupt the white dwarf. Under special circumstances, a small remnant may be left when carbon is ignited in a shell [80TI, 80T2, 82N]. This nuclear explosion of a CO white dwarf (total or partial) may probably be identified with a supernova of type I. On the other hand, for 0-Ne-Mg white dwarfs accreting matter, the core density can increase beyond the threshold for electron capture. This leads to electron-capture collapse and formation of a neutron star [80M, 8OS].Another important factor determining the fate of the white dwarf component is the accretion rate. This is probably the most important factor. For small accretion rates hydrogen will be ignited in a strong nuclear flash when the accumulated hydrogen exceedsa certain initial mass. For accretion rates below 10m9Mo per year these flashes are so strong that most (and probably all) of the accreted matter is ejected, hence the white dwarf will not grow in mass. For larger accretion rates (IO-‘... 10m8 M, per year), the flashes are weaker, and much of the accreted matter remains, so the white dwarf becomesmore massive. For accretion rates 4.10-* M, per year, a carbon deflagration occurs. Generally, mass transfer by Roche lobe overflow is required to power LMXRBs, since low-mass stars never exhibit strong stellar winds. The compact object is the most massive component; hence the mass transfer from the lower-mass companion will be stable. Two mechanisms can lead to Roche lobe overflow: angular momentum lossesby gravitational radiation or internal nuclear evolution. The evolutionary history for the low-mass X-ray binaries is not yet completely clear. Various configurations can be examined: Roche lobe overflow from main sequencedwarfs, Roche lobe overflow from low-mass degenerate stars, Roche lobe overflow from nondegenerate helium stars, Roche lobe overflow from red giants. Details on these different scenarios may be found in [8382, 92Dl]. The traditionally most attractive model, a degenerate CO dwarf with a red giant companion filling its Roche lobe, poses problems [86Wl, 86W2]. The limitations on the white dwarf mass (it has to be sufficiently large, > 1.3 1M, and the required initial separation of the components limit the expectations on the supernova rate to a small fraction of the observed frequency [86W2]. In recent years considerable attention has been given to the possibility that type I SN result from the merger originating at the end from gravitational radiation of two white dwarfs [79Tl, 79W, 8412,84141,the so-called double-degenerate model [SSCl, 8513,].A discussion of the problems connected with the scenarios mentioned earlier can be found in [86Wl]. For more details about mergers and alternative scenarios, see[8414,8513,88L].

4.4.3.8.7

Origin and evolution of massive X-ray binaries (MXRB)

From observations, evidence is found that most and probably all binary X-ray sources contain neutron stars or black holes. A fraction of them are pulsating binary X-ray sources, members of a welldefined class of strong X-ray sources, with relatively hard spectra. They are associated with young luminous stars. They are indicated as type I sources. This group can be subdivided into two subgroups with different characteristics: The standard systems are permanent sources, i.e., the X-rays have a regular periodicity and the optical light output displays the ellipsoidal variations, characteristic of the tidal distortion of the optical companion invoked by the orbiting compact star. The optical companion nearly fills its Roche volume, and the system can show regular eclipses. Several tens of such systems are known, and are easily recognized by their extremely strong emission lines. Periods are short, comprising between 1.4 and 10 days, except for the case4U1224-62, with a period of somewhat longer than a month. The progenitors of these systemsare OB stars. A number of these X-ray sources are pulsating. The pulse periods range between 0.75 and 14 min. Doppler determinations of the X-ray-emitting component and visual observations in some of these sources allow the determination of the orbits of the neutron star and its optical companion. From these orbits, the mass ratios and the massesof the two components can be derived. The determined neutron star massesare of the order of 1.5 Mo, while the massesof their optical companions range from 20 through 40 M,. In the group of transient sources the optical components are Be stars not filling their Roche lobes. Eclipses are mostly absent and there are no regular ellipsoidal light variations. Their masses Land&-BBmstein New Series VI/3b

Ref. p. 1201


117

lower than those of standard massive X-ray binaries - range between 10 and 20 Mo. The X-ray flux from a number of objects belonging to this group is not constant, but shows outbursts. The permanent (standard) massiveX-ray binaries and the Be X-ray binaries were formed directly from massiveclose binaries by successiveprocessesof stellar wind masslossesand massexchange, finally leading to a supernova explosion and formation of collapsed objects, neutron stars or black holes. The idea, now generally accepted, is that a massive close binary, consisting of two luminous stars, evolves into an X-ray source, first by mass exchange and, through a final explosion, the compact object is produced [72H]. Detailed computations on the evolution of massive X-ray sources were published by [73T, 75D1, 75D2, 75D3]. At a more advanced stage, the massive star also fills its Roche lobe and loses matter. The period of the system is drastically reduced, and the neutron star spirals in. In this way, a second X-ray stage can be initiated, forming a binary with a very short period. Finally, the secondary also explodes and two separate neutron stars result. After the first supernova explosion, the system remains bound since it is the less massive star that is exploding. The second explosion, however, has a greater probability of disrupting the system, although in a few rare casesthe system remains bound and two neutron stars remain together in a binary pulsar. The evolutionary scenario for standard X-ray sourcesis depicted in Fig. 18. We consider stars with cores larger than = 2.3.. .3 Mo, which evolve directly towards core collapse. The remnant of the primary star at the moment of collapse will be the lessmassive component in the case of conservative evolution or moderate mass loss. Since the explosion of the less massive component will not disrupt the system if the explosion occurs in a symmetric way, and will be unlikely to disrupt even in the caseof an asymmetric explosion. The compact stars in conservatively evolving binary systemswill remain bound in practically all cases[77Dl, 77D2]. To obtain orbital periods of a couple of days with conservative mass exchange, one has to start with rather low initial mass ratios, q-’ < 0.3. However, such a scenario does not seemvery realistic since systems with low q-l grow into deep contact. The reason is that the accretion time scale is larger than the mass loss time scale, so that the receiver also fills its Roche lobe and a contact configuration occurs, with a surrounding common envelope. On the other hand, due to the mass transfer, the distance A in systems with small mass ratios shrinks very much during the transfer, reaching a minimum separation when the massesare equal. For q-l < 0.3, the distance decreasesby a factor 2. So with conservative assumptions it appears impossible to explain the observed postsupernova orbital periods shorter than 10 days. When a common envelope is produced, mass loss from the Lagrangian points L, or L, is expected. In this way, the mass loss has a specific angular momentum much larger than the average orbital angular momentum of the components. A list of well-studied massive X-ray binaries (standard sources and transients) with their main characteristics can be found in [92Dl], for example. For a mass ratio near 1, the specific angular momentum at L, is = 4 times the specific orbital angular momentum if and only if the leaving mass stream has angular momentum equal to that of its actual position in the system (which for L,, for example, assures corotation). Hence dJldM = 4JIM,

(132)

(M is the total mass of the system) or J- M4.

(133)

The conclusion is that systemswith mass ratios smaller than 0.4 will evolve through a common envelope phase. During this phase, mass and angular momentum will be lost. In this way the short orbital periods of some X-ray binaries and WR binaries can be explained [Cen X-3, SMC X-l, CX Cep (P = 1.6 d), CQ Cep (P= 2.14 d)]. Systemswith mass ratios near to 1 may evolve in a conservative way, producing post-supernova binaries with orbital periods of 10 days and longer. Only = 14% of the unevolved short period 0- and B-type spectroscopic binaries have q-l ~0.4. For these systems,mass and angular momentum losses are expected to occur, so very short period WR- and X-ray binaries may be formed. The vast majority of the systemswill evolve in a conservative way, producing after the supernova explosion X-ray systemswith periods larger than 5 days. Land&BBmstein New Series VU3b

[Ref. p. 120


118 20Mo f.0

20Mo t.6.17~1060

EM@ P. 4.56d

EM@ P. 4.56d

5.4M@ f=6.2-IO60

3 2Mo

22.6Mo

f=6.78-10%

P=111,7d

2Mo

He star

2Ma t=11.209~10~0

WRstoge

2Mo

22.6M,

22.6Mo P =10.86d

P=ll.?d

X-ray sfoge

6.3Mo

2Mo

6.3Mo

2Mo t=12.150~1060

7

22.6Mo

8

second X-ray stage

2Mo P.7.87h

9

Fig. 18. Evolutionary scenario for standard X-ray sources.P: period of revolution, t: age. I: start with 20 MO and 8 MO (ZAMS) 2: primary fills its Roche lobe 3: end of the masstransfer stage 4: Wolf-Rayet stage 5: supernova explosion; X-ray stage 6: secondary fills its Roche lobe 7: end of this secondRoche lobe over flow phase, secondX-ray stage 8: supernova explosion 9: neutron stars, X-ray-binary, generation of binary pulsar, such as PSR 1913+ 16.

Be-X-ray binaries are produced by lower mass initial systems,c 20 MO. As an example the simultaneous evolution of a 15 M,+lO M, system, with an initial period of 8 days, is shown in Fig. 19 [84D]. The system becomes semi-detached after about 13 million years, and evolves into a contact phase some 3000 years later. Matter leaves the system; the system again becomessemi-detachedand 15000 years later, after the onset of helium burning, the two components become detached. The final system-a primary of 3.42 iI& and a secondary of 20.5 MO-has a period of 68 days. The accreting component starting from 10 M, finally reached 20.5 M,; it evolved on a track parallel to the ZAMS. When the slow phase of mass transfer setsin, the track bends towards the ZAMS; later Land&-BBmstein New Series VU3b

Ref. p. 1201


15M,+ KIM@ P=8d

119

15M@'lOM@ P=8d

12.7Mo+12.3Mo P=?d

start mass transfer 8.4M,+15.6Mo P =10.4d

start contact phase

3.4Mo+ 20.5Mo P = 68.5d

1.5Mo+17.4Me P=81d

0 end contact phase

supernova explosion

neutron star

08 Be- companion

Fig. 19. Simultaneous evolution of a 15 Mo+Mo system with an initial period of 8 days, according to [84D]. Detailed explanation in the text.

on, the star evolvesjust like a ZAMS star of 20 44,. The helium remnant of the primary has meanwhile continued its evolution and has exploded. The system in this phase could represent a Be-X-ray binary, with a Be component of = 20 Mo and a neutron star companion of 1.5 Mo. As mentioned earlier, conservative assumptions are too simple for an adequate description of interactive evolution of close binary systems,and considerable loss of mass and angular momentum may occur during the mass transfer phase. Moreover, mass loss by stellar wind also has to be taken into account. 4.4.3.8.8

Final evolution of massive X-ray binaries

Tidal synchronization and tidal instability

For sufficiently short periods, tidal forces will be able to circularize and synchronize the orbits in a time scale of a few million years after the supernova event. The X-ray binaries SMC X-l, Cen X-3, Her X-l, with nearly circular orbits, are examples of circularization. The determining factor for the circularization processis the internal viscosity of the stars. Radiative damping of the dynamical tide [77Z] may explain the short time scales which are required for the massive X-ray binaries. If the ratio of orbital and rotational angular moments, after circularization and synchronization [73C],

the system is tidally unstable and the compact star will spiral in onto its companion. The rotational angular momentum is given by Jr,, = k2MoR2

(135)

with M and R the mass and radius of the normal star respectively, w its angular velocity and k the gyration radius. The orbital momentum is (136) Land&-Biimstein New Series V1/3b

Ref. p. 1201


15M,+ KIM@ P=8d

119

15M@'lOM@ P=8d

12.7Mo+12.3Mo P=?d

start mass transfer 8.4M,+15.6Mo P =10.4d

start contact phase

3.4Mo+ 20.5Mo P = 68.5d

1.5Mo+17.4Me P=81d

0 end contact phase

supernova explosion

neutron star

08 Be- companion

Fig. 19. Simultaneous evolution of a 15 Mo+Mo system with an initial period of 8 days, according to [84D]. Detailed explanation in the text.

on, the star evolvesjust like a ZAMS star of 20 44,. The helium remnant of the primary has meanwhile continued its evolution and has exploded. The system in this phase could represent a Be-X-ray binary, with a Be component of = 20 Mo and a neutron star companion of 1.5 Mo. As mentioned earlier, conservative assumptions are too simple for an adequate description of interactive evolution of close binary systems,and considerable loss of mass and angular momentum may occur during the mass transfer phase. Moreover, mass loss by stellar wind also has to be taken into account. 4.4.3.8.8

Final evolution of massive X-ray binaries

Tidal synchronization and tidal instability

For sufficiently short periods, tidal forces will be able to circularize and synchronize the orbits in a time scale of a few million years after the supernova event. The X-ray binaries SMC X-l, Cen X-3, Her X-l, with nearly circular orbits, are examples of circularization. The determining factor for the circularization processis the internal viscosity of the stars. Radiative damping of the dynamical tide [77Z] may explain the short time scales which are required for the massive X-ray binaries. If the ratio of orbital and rotational angular moments, after circularization and synchronization [73C],

the system is tidally unstable and the compact star will spiral in onto its companion. The rotational angular momentum is given by Jr,, = k2MoR2

(135)

with M and R the mass and radius of the normal star respectively, w its angular velocity and k the gyration radius. The orbital momentum is (136) Land&-Biimstein New Series V1/3b

120


with m the mass of the compact star, A the distance of the two components. After substitution of eqs. (134) and (135) in (136) one obtains conditions fork: k2 >

mA2 3R2(M + m)

(137)

For stars with 15 M,<M 4.. .5 days, the envelope of the optical star expands rapidly when its Roche lobe overflow starts; the massloss rate increasesto = 1O-3M, per year. The matter is stored in a thick accretion disk. However, owing to the Eddington limit, not more than = 1O-7Mo per year can be acceptedby the neutron star, hence the larger part of the transferred matter is expelled. The inner part of the disk attains the supercritical Eddington luminosity so that the expulsion of the matter occurs by radiation pressure, most probably in directions perpendicular to the plane of the disk [75S].

References for 4.4 54s 59K 61B1 61B2 62B 63H 66K 66P 67K 67P1 67P2 68Cl 68C2 68K 68P 69H 69K 69s 69W 70G 70H 70P 702 71P 72H 72R 72s

Salpeter, E. E.: Australian J. Phys. 7 (1954) 353. Kopal, Z.: Close Binary Systems,New York: Wiley (1959). Blaauw, A.: Bull. Astron. Inst. Neth. 15 (1961) 265. Boersma, J.: Bull. Astron. Inst. Neth. 15 (1961) 291. Baker, N. H., Kippenhahn, R.: Z. Astrophys. 54 (1962) 114. Huang, S. S.: Astrophys. J. 138 (1963) 471. Kippenhahn, R., Weigert, A.: Mitt. Astron. Ges. 21 (1966) 106. Paczynski, B.: Acta Astron. 16 (1966) 231. Kippenhahn, R., Weigert, A.: 2. Astrophys. 65 (1967) 251. Paczynski, B.: Acta Astron. 17 (1967) 1. Paczynski, B., Ziolkowski, J.: Acta Astron. 17 (1967) 7. Cox, J. P., Giuli, R. T.: Principles of Stellar Structure, Vol. I, II New York: Gordon and Breach (1968). Clayton, D. D.: Principles of Stellar Evolution and Nucleosynthesis, New York: McGrawHill (1968). Kriz, S., in: Coil. On Mass Loss from Stars. Astrophys. SpaceSci. Library 13 (1968) 257. Plavec, M.: Mass Exchange and Evolution of Close Binaries, in: Adv. Astron. Astrophys. 6 (1968) 201. Horn, J., Kriz, S., Plavec, M.B.: Bull. Astron. Inst. Czech. 20 (1969) 193. Kriz, S.: Bull. Astron. Inst. Czech. 20 (1969) 127. Salpeter, E. E., Van Horn, H. M.: Astrophys. J. 155 (1969) 183. Wagoner, R. V.: Astrophys. J. Suppl. 18 (1969) 247. Gunn, J. E., Ostriker, J. P.: Astrophys. J. 160 (1970) 979. Hallgreen, E. L., Cox, J. P.: Astrophys. J. 162 (1970) 933. Paczynski, B.: Acta Astron. 20 (1970) 47. Ziolkowski, J.: Acta Astron. 20 (1970) 2. Paczynski, B.: Annu. Rev. Astron. Astrophys. 9 (1971) 183. van den Heuvel, E. P. J., Heise, J.: Nat. Phys. 239 (1972) 67. Ruderman, M.: Annu. Rev. Astron. Astrophys. 10 (1972) 427. Schuerman, D. W.: Astrophys. SpaceSci. 19 (1972) 351. Landok-Bhxtein New Series VU3b

120


with m the mass of the compact star, A the distance of the two components. After substitution of eqs. (134) and (135) in (136) one obtains conditions fork: k2 >

mA2 3R2(M + m)

(137)

For stars with 15 M,<M 4.. .5 days, the envelope of the optical star expands rapidly when its Roche lobe overflow starts; the massloss rate increasesto = 1O-3M, per year. The matter is stored in a thick accretion disk. However, owing to the Eddington limit, not more than = 1O-7Mo per year can be acceptedby the neutron star, hence the larger part of the transferred matter is expelled. The inner part of the disk attains the supercritical Eddington luminosity so that the expulsion of the matter occurs by radiation pressure, most probably in directions perpendicular to the plane of the disk [75S].

References for 4.4 54s 59K 61B1 61B2 62B 63H 66K 66P 67K 67P1 67P2 68Cl 68C2 68K 68P 69H 69K 69s 69W 70G 70H 70P 702 71P 72H 72R 72s

Salpeter, E. E.: Australian J. Phys. 7 (1954) 353. Kopal, Z.: Close Binary Systems,New York: Wiley (1959). Blaauw, A.: Bull. Astron. Inst. Neth. 15 (1961) 265. Boersma, J.: Bull. Astron. Inst. Neth. 15 (1961) 291. Baker, N. H., Kippenhahn, R.: Z. Astrophys. 54 (1962) 114. Huang, S. S.: Astrophys. J. 138 (1963) 471. Kippenhahn, R., Weigert, A.: Mitt. Astron. Ges. 21 (1966) 106. Paczynski, B.: Acta Astron. 16 (1966) 231. Kippenhahn, R., Weigert, A.: 2. Astrophys. 65 (1967) 251. Paczynski, B.: Acta Astron. 17 (1967) 1. Paczynski, B., Ziolkowski, J.: Acta Astron. 17 (1967) 7. Cox, J. P., Giuli, R. T.: Principles of Stellar Structure, Vol. I, II New York: Gordon and Breach (1968). Clayton, D. D.: Principles of Stellar Evolution and Nucleosynthesis, New York: McGrawHill (1968). Kriz, S., in: Coil. On Mass Loss from Stars. Astrophys. SpaceSci. Library 13 (1968) 257. Plavec, M.: Mass Exchange and Evolution of Close Binaries, in: Adv. Astron. Astrophys. 6 (1968) 201. Horn, J., Kriz, S., Plavec, M.B.: Bull. Astron. Inst. Czech. 20 (1969) 193. Kriz, S.: Bull. Astron. Inst. Czech. 20 (1969) 127. Salpeter, E. E., Van Horn, H. M.: Astrophys. J. 155 (1969) 183. Wagoner, R. V.: Astrophys. J. Suppl. 18 (1969) 247. Gunn, J. E., Ostriker, J. P.: Astrophys. J. 160 (1970) 979. Hallgreen, E. L., Cox, J. P.: Astrophys. J. 162 (1970) 933. Paczynski, B.: Acta Astron. 20 (1970) 47. Ziolkowski, J.: Acta Astron. 20 (1970) 2. Paczynski, B.: Annu. Rev. Astron. Astrophys. 9 (1971) 183. van den Heuvel, E. P. J., Heise, J.: Nat. Phys. 239 (1972) 67. Ruderman, M.: Annu. Rev. Astron. Astrophys. 10 (1972) 427. Schuerman, D. W.: Astrophys. SpaceSci. 19 (1972) 351. Landok-Bhxtein New Series VU3b

4.4.3 Model computations 73A 73C 73D 73E 73F 73G 73s 73T 73W 74C

121

Audouze, J., Truran, J. W., Zimmerman, B. A.: Astrophys. J. 184 (1973) 493. Counselman, C. C.: Astrophys. J. 180 (1973) 307. Dewitt, H. E., Graboske, H. C., Cooper, M. S.: Astrophys. J. 181 (1973) 439. Eggleton, P., Faulkner, J., Flannery, B. P.: Astron. Astrophys. 23 (1973) 325. Fricke, K.J.: Astrophys. J. 183 (1973) 941. Graboske, H. C., Crossmann, A. S., Cooper, M. S.: Astrophys. J. 181(1973) 457. Shakura, N. I., Sungave, R. A.: Astron. Astrophys. 24 (1973) 337. Tutukov, A. V., Yungelson, L. R: Nauk. Inf. 27 (1973) 58. Woosley, S. E., Arnett, W. D., Clayton, D. D.: Astrophys. J. Suppl. 26 (1973) 231. Cruz-Gonzalez, C., Recillas-Cruz, E., Costero, R., Peimbert, M., Torres-Peimbert, S.: Rev. Mex. Astron. Astrofis. 1 (1974) 211. 74F Fricke, K.J.: Astrophys. J. 189 (1974) 535. 741 Iben, I.Jr.: Annu. Rev. Astron. Astrophys. 12 (1974) 215. 75Dl de Loore, C., De Greve, J. P.: Astrophys. SpaceSci. 35 (1975) 241. 75D2 de Loore, C., De Greve, J. P., De Cuyper, J. P.: Astrophys. SpaceSci. 36 (1975) 219. 75D3 De Greve, J. P., de Loore, C., De Cuyper, J. P.: Astrophys. SpaceSci. 38 (1975) 301. 75E El Eid, M. F.: Ph. D. Thesis, University of Darmstadt, FRG (1975). 75F Fowler, W. A., Caughlan, G. R., Zimmerman. B. A.: Annu. Rev. Astron. Astrophys. 13 (1975) 69. 751 Iben, I. Jr.: Astrophys. J. 196 (1975) 525. 75s Shlovskii, I. S.: Astron. Zh. 52 (1975) 911. 76A Arnould, M.: Astron. Astrophys. 46 (1976) 117. 76Cl Canal, R., Schatzman, E.: Astron. Astropys. 46 (1976) 229. 76C2 Conti, P. S.: Mem. Sot. R. Sci. Liege, 6eme Series9 (1976) 193. 76Dl De Greve, J. P., De Loore, C. W. H.: Astrophys. Space.Sci. 43 (1976) 35. 76D2 De Cuyper, J. P., De Greve, J. P., de Loore, C. W. H., Van den Heuvel, E. P. J.: Astron. Astrophys. 52 (1976) 315. 76K Kondo, Y., McCluskey, G. E., in: Structure and Evolution of Close Binary Systems (P. Eggleton, S. Mitton, J. Whelan, eds.), IAU Symp. 73, Dordrecht: Reidel(l976) p.343. 76V Vanbeveren, D.: Astron. Astrophys. 54 (1976) 877. 76W Warner, B., in: Structure and Evolution of Close Binary Systems, (P. Eggleton, S. Mitton, J. Whelan, eds.), IAU Symp. 73, Dordrecht: Reidel(1976) p. 85. 77C Caughlan, G.R., in: CNO Isotopes in Astrophysics (J. Audouze, ed.), Dordrecht: Reidel (1977) p.121. 77D1 De Cuyper, J. P., de Loore, C. W. H., Van den Heuvel, E. P. J.: Astron. Astrophys. 30 (1977) 93. 77D2 De Greve, J. P., de Loore, C.: Astrophys. SpaceSci. 58 (1977) 75. 77H Huebner, W. F., Merts, A. L., Magee, N. H. jr., Argo, M. F.: Astrophysical Opacity Library, Los Alamos Scientific Laboratory Report LA-6760-M (1977). 77P Paczynski, B., Rozyczka, M.: Acta Astron. 27 (1977) 214. 77T Thomas, H.-C.: Annu. Rev. Astron. Astrophys. 15 (1977) 127. 77V Vanbeveren, D.: Astron. Astrophys. 62 (1977) 59. 772 Zahn, J. P.: Astron. Astrophys. 57 (1977) 383. 78G Gallagher, J. S., Starrfield, S.: Annu. Rev. Astron. Astrophys. 16 (1978) 171. 78s Sweigart, A. V., Gross, P. G.: Astrophys. J. Suppl. 36 (1978) 405. 78Tl Takahashi, K., El Eid, M. F., Hillebrandt, W.: Astron. Astrophys. 67 (1978) 185. 78T2 Taam, R. E., Picklum, R. E.: Astrophys. J. 224 (1978) 210. 78V Vanbeveren, D.: Astrophys. SpaceSci. 57(1978) 41. 78W Weaver, T. A., Zimmerman G. B., Woosley, S. E.: Astrophys. J. 225 (1978) 1021. 79D Dearborn, D. S. P., Blake, J. B.: Astrophys. J. 231 (1979) 193. 791 Itoh, N., Totsuji, H., Ichimaru, S., Dewitt, H. E.: Astrophys. J. 239 (1979) 415. 79L Lorenz-Wirzba, H., Schmalbrock, P., Trautvetter, H. P., Wiescher, M., Rolfs, C.: Nucl. Phys. A 313 (1979) 346. Landolt-Biirnstein New Series VU3b

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84D de Loore, C., Sutantyo, W., in: Double Stars, Physical Properties and Generic Relations, IAU Coll. No. 80 (B. Hidayat, Z. Kopal, J. Rahe, eds.), Dordrecht: Reidel (1984) Astrophys. SpaceSci. 99 (1984) 335. 84H Humphreys, R. M., McElroy, D. B.: Astrophys. J. 284 (1984) 565. 8411 Iben, I.Jr., Renzini, A.: Phys. Rep. 105 (1984) 329. 8412 Iben, I.Jr., Tutukov, A. V.: Astrophys. J. 282 (1984) 615. 8413 Iben, I.Jr., Astrophys. J. 277 (1984) 333. 8414 Iben, I.Jr., Tutukov, A. V.: Astrophys. J. Suppl. 54 (1984) 335. 84M Maeder, A., Renzini, A. (eds.): Observational Tests of Stellar Evolution, IAU Symp. 105, Dordrecht: Reidel(l984). 84s Schmidt, E. G.: Astrophys. J. 287 (1984) 261. 84W Weidemann, V.: Astron. Astrophys. 134 (1984) Ll. 85Al Arnett, W. D., Thielemann, F.-K.: Astrophys. J. 295 (1985) 589. 85A2 Aaronson, M., Mould, J.: Astrophys. J. 288 (1985) 551. 85Cl Cameron, A. G. W., Iben, I.Jr.: Astrophys. J. 305 (1985) 228. 85C2 Caughlan, G. R., Fowler, W. A., Harris, M., Zimmerman, B. A.: Atomic Data Nucl. Data Tables 32 (1985) 197. 85Hl Humphreys, R. M., Nichols, M., Messey, P.: Astron. J. 90 (1985) 101. 85H2 Hartmann, D. Woosley, S. E., El Eid, M. F.: Astrophys. J. 297 (1985) 837. 85H3 Habets, G.M.: Ph.D. Thesis, University of Amsterdam (1985). 8511 Iben, I.Jr., MacDonald, J.: Astrophys. J. 296 (1985) 540. 8512 Iben, I.Jr.: Q. J. R. Astron. Sot. 26 (1985) 1. 8513 Iben, I.Jr., Tutukov, A. V.: Astrophys. J. Suppl. 58 (1985) 661. 85K Kiong, D.R.: Astron. Astrophys. 150 (1985) 133. 85L Langer, N., El Eid, M. F., Fricke, K. J.: Astron. Astrophys. 145 (1985) 179. 85s Sybesma,C.: Astron. Astrophys. 142 (1985) 171. 85T Thielemann, F.-K., Arnett, W. D.: Astrophys. J. 295 (1985) 604. 85Vl VandenBerg, D. A., Bell, R. A.: Astrophys. J. Suppl. 58 (1985) 561. 85V2 VandenBerg, D. A.: Astrophys. J. Suppl. 58 (1985) 781. 85X Xiong, D.R.: Astron. Astrophys. 58 (1985) 561. 86Cl Chiosi, C., in: Nucleosynthesis and Chemical Evolution (B. Hauck, A. Maeder, G. Meynet, eds.), Geneva Observatory (1986) p. 199. 86C2 Castellani, V.: Fundam. Cosmic Phys. 9 (1986) 317. 86C3 Conti, P. S., in: Luminous Stars and Associations in Galaxies, IAU Symp. 116 (C.W.H. de Loore, P. Laskardis, eds.), Dordrecht: Reidel(l986) p. 199. 86C4 Chiosi, C., Maeder, A.: Annu. Rev. Astron. Astrophys. 24 (1986) 329. 86D De Greve, J. P., de Loore, C. W. H., in: Luminous Stars and Associations in Galaxies, IAU Symp. 116 (C.W.H. de Loore, P. Laskardis, eds.), Dordrecht: Reidel(1986) p. 339. 86E El Eid, M. F., Langer, N.: Astron. Astrophys. 167 (1986) 274. 861 Iben, I.Jr., MacDonald, J.: Astrophys. J. 301 (1986) 164. 86Kl Kuhful3, R.: Astron. Astrophys. 160 (1986) 116. 86K2 Koester, D., Schonberner, D.: Astron. Astrophys. 154 (1986) 125. 86L Lattanzio, J. C.: Astrophys. J. 311 (1986) 708. 86M Mermilliod, J, Maeder, A.: Astron. Astrophys. 158 (1986) 45. 86N Nomoto, K., Hashimoto, M.: Prog. Nucl. Part. Phys. 17 (1986) 267. 86P Praqntzos, N., Doom, C., Arnould, M., de Loore, C.: Astrophys. J. 304 (1986) 179. 86Sl Sybesma,C.: Astron. Astrophys. 159 (1986) 108. 8682 Sybesma,C.: Astron. Astrophys. 168 (1986) 147. 86V Van den Heuvel, E. P. J., in: The Evolution of Galactic X-Ray Binaries (J. Truemper, W. Lewin, W. Brinckmann, eds.), Nato AS1 Series(1986) p. 107. 86Wl Woosley, S. E., in: Nucleosynthesis and Chemical Evolution (B. Hauck, A. Maeder, G. Meynet, eds.), Geneva Observatory (1986) p. 1. Landolt-B6mstein New Series VI/3b

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86W2 Woosley, S. E., Weaver, T. A.: Annu. Rev. Astron. Astrophys. 24 (1986) 205. 86W3 Wood, P. R., Faulkner, D. J.: Astrophys. J. 307 (1986) 659. 87A Abott, D.C., Conti, P. S.: Annu. Rev. Astron. Astrophys. 25 (1987) 113. 87Bl Binota, R.M. et al.: Phys. Rev. Lett. 58 (1987) 1494. 87B2 Baker, N. H., KuhfuB, R.: Astron. Astrophys. 185 (1987) 117. 87H Hillebrandt, W., Hiiflich, P., Weiss,A., Truran, J. W.: Nature 327 (1987) 597. 871 Itoh, N., Kohyama, Y., Matsumoto, N.: Astrophys. J. 322 (1987) 584. 87L Lattanzio, J. C.: Astrophys. J. 313 (1987) L15. 87M Maeder, A., in: SN 1987A, ES0 Workshop (I. J. Danziger, ed.) Garching/b. Munchen (1987) 251 . 87R Renzini, A.: Astron. Astrophys. 188 (1987) 49. 87Sl Seidel, E., Demarque, P., Weinberg, D.: Astrophys. J. Suppl. 63 (1987) 917. 8732 Schinder, P. J., Schramm, D. N., Wiita, P. J., Margolis, S. H., Tubbs, D. L.: Astrophys. J. 313 (1987) 531. 87S3 Sweigart, A. V.: Astrophys. J. Suppl. 65 (1987) 95. 88Bl Boothroyd, A. I., Sackmann, I. J.: Astrophys. J. 328 (1988) 671. 88B2 Brown, G. E. (ed.): Phys. Rep. 163 Amsterdam: North Holland (1988). 88B3 Boothroyd, A. I., Sackmann, I. J.: Astrophys. J. 328 (1988) 653. 88Cl Caughlan, G. R., Fowler, W. A.: Atomic Data Nucl. Data Tables 40 (1988) 283. 88C2 Conti, P. S., Underhill, A. B., in: 0 Stars and Wolf-Rayet Stars, Monograph Serieson Nonthermal Phenomena in Stellar Atmospheres, NASA SP-497(1988). 88Dl De Loore, C.: Astron. Astrophys. 203 (1988) 71. 88D2 De Greve, J. P., Doom, C.: Astron. Astrophys. Suppl. 74 (1988) 325. 88Hl Hiiflich, P.: Proc. Astron. Sot. Austr. 7 (1988) 434. 88H2 Hollowel, D. Iben. I. Jr.: Astrophys. J. 333 (1988) L25. 88L Livio, M.: Astrophys. J. 329 (1988) 764. 88N Nomoto, K., Hashimoto, M.: Phys. Rep. 163 (1988) 13. 88P Packet, W.: Ph.D. Thesis, Vrije Universiteit Brussel (1988). 88Rl Renzini, A., Fusi Pecci, F.: Annu. Rev. Astron. Astrophys. 26 (1988) 199. 88R2 Rolfs, C., Rodney, W.S.: Cauldrons in the Cosmos, Chicago: University Press(1988). 88s Saio, H., Kato, M., Nomoto, K.: Astrophys. J. 331 (1988) 388. 88W1 Woosley, S.E.: Astrophys. J. 330 (1988) 218. 88W2 Woosley, S. E., Pinto, P. A., Weaver, T. A.: Proc. Astron. Sot. Austr. 7 (1988) 355. 88W3 Wood, P. R., Faulkner, D. J., in: Atmospheric Diagonostic of Stellar Evolution: Chemical Pecularity, Mass Loss, and Explosion, IAU Coll. 108 (K. Nomoto, ed.), Berlin:Springer (1988) p. 410. 88W4 Woosley, S. E., Weaver, T. A.: Phys. Rep. 163 (1988) 79. 89Al Anders, E., Grevesse,N.: Geochim. Cosmochim. Acta 53 (1989) 197. 89A2 Arnett, W. D., Bahcall, J. N., Kirchner, R. P., Woosley, S. E.: Annu. Rev. Astron. Astrophys. 27 (1989) 629. 89Bl Barkat, Z., Wheeler, J. C.: Astrophys. J. 342 (1989) 940. 89B2 Bahcall, J. N.: Neutrino Astrophysics, Cambridge: Cambridge University Press(1989). 89C Cloutman, L. D.: Astrophys. J. Suppl. 71 (1989) 677. 89E Eastman, R. G., Kitchner, R. P.: Astrophys. J. 347 (1989) 771. 89F Fransson, C., Cassatella, A., Gilmozzi, R, Panagia, N., Wamstecker, W., Kirshner, R. P., Sonneborn, G.: Astrophys. J. 336 (1989) 429. 89Hl Hillebrandt, W., Hoflich, P.: Rep. Prog. Phys. 52 (1989) 1421. 89H2 Hollowel, D., Iben. I. Jr.: Astrophys. J. 340 (1989) 966. 89H3 Herzig, K., El Eid, M. F., Fricke, K. J., Langer, N.: Astron. Astrophys. 233 (1989) 462. 891 Itoh, N., Adachi, T., Nakagawa, M., Kohyama, Y., Munakata, H.: Astrophys. J. 339 (1989) 354. 89K1 Kappeler, F., Beer, H., Wisshack, K.: Rep. Prog. Phys. 52 (1989) 495. Land&B6rnstein New Series VI/3b


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89K2 Kudritzki, R. P., Pauldrach, A., Puls, J., Abott, D. C.: Astron. Astrophys. 219 (1989) 205. 89Ll Langer, N.: Astron. Astrophys. 220 (1989) 135. 89L2 Langer, N., El Eid, M. F., Baraffe, I.: Astron. Astrophys. 224 (1989) L7. 89L3 Langer, N.: Astron. Astrophys. 210 (1989) 93. 89P Pastetter, L., Ritter, H.: Astron. Astrophys. 214 (1989) 186. 89R Roxbourgh, I. W.: Astron. Astrophys. 211 (1989) 361. 89W Weiss, A.: Astrophys. J. 339 (1989) 365. 90Bl Blocker, T., Schonberner, D.: Astron. Astrophys. 240 (1990) Lll. 90B2 Bethe, H. A.: Rev. Mod. Phys. 62 (1990) 801. 9OCl Cooperstein, J., Baron, E., in: Supernovae (A.G. Patschek, ed.), New York: Springer Verlag (1990) p. 213. 9OC2 Chin, C.-W., Stothers, R. B.: Astrophys. J. Suppl. 73 (1990) 821. 90Hl Huang, R. Q., Taam, R. E.: Astron. Astrophys. 236 (1990) 107. 90H2 Hillebrandt, W., in: International School of Physics Enrico Fermi on High PressureEquation of State: Theory and Application (S. Eliezer, R.A. Ricci, eds.), Amsterdam: North Holland 1990. 90Kl Kappeler, F., Gallino, R., BUSSO, M., Picchio, G., Raiteri, C.: Astrophys. J. 354 (1990) 630. 90K2 Kippenhahn, R. Weigert, A.: Stellar Structure and Evolution, Berlin: Springer (1990). 90N Nieuwenhuijzen, H., de Jager, C.: Astron. Astrophys. 231(1990) 134. 90T Thielemann, F.-K., Hashimoto, M., Nomoto, K.: Astrophys. J. 349 (1990) 222. 91A Argoragi, J. P., Langer, N., Arnould, M.: Astron. Astrophys. 249 (1991) 134. 91Bl Blocker, T., Schonberner, D.: Astron. Astrophys. 244 (1991) L43. 91B2 Baraffe, I., El Eid, M. F.: Astron. Astrophys. 245 (1991) 548. 91B3 Branch, D., Nomoto, K., Filippenko, A. V.: Comments Astrophys. 15 (1991) 221. 91Cl Castellani, V., Chiefi, A., Pulone, L.: Astrophys. J. Suppl. 76 (1991) 911. 91C2 Crotts, A. P. S., Kunkel, W. E.: Astrophys. J. 366 (1991) L73. 91El El Eid, M.F., Htiflich, P., in: Nuclear Astrophys., 6th Workshop MPAIPS (W. Hillebrandt, E. Miiller, eds.), Garching/b. Mtinchen (1991) p. 96. 91E2 El Eid, M.F., in: Supernovae, 10th Santa Cruz Workshop (S.E. Woosley, ed.), New York: Springer (1991) p. 568. 91E3 El Eid, M.F., Hiiflich, P., in: SN 1987A and other Supernovae ESO/EPIC Workshop (I. J. Danziger et al., eds.), Garching: ES0 (1991) p. 29. 911 Iben, I. Jr.: Astrophys. J. Suppl. 76 (1991) 55. 91L Lattanzio, J. C.: Astrophys. J. Suppl. 76 (1991) 215. 91M Muller, E., in: Late Stagesof Stellar Evolution and Computational Methods in Astrophysical Hydrodynamics (Cde Loore, ed.), Lecture Notes in Physics, Berlin: Springer (1991). 91Sl Stothers, R. B., Chin, C.-W.: Astrophys. J. 381 (1991) L67; Astrophys. J. 383 (1991) 820. 91S2 Seaton, M. J.: J. Phys. B 23 (1991) 3255. 91V Vanbeveren, D.: SpaceSci. Rev. 56 (1991) 249. 91W Wheeler, J. C., in: Supernovae (J. C. Wheeler, T. Piran, S. Weinberg, eds.), Singapore: World Scientific (1991) p. 1. 91Z Zahn, J.-P.: Astron. Astrophys. 252 (1991) 179. 92Dl De Loore, C. W. H., Doom, C.: Structure and Evolution of Single and Binary Stars, Dordrecht: Kluwer Acad. Publ. (1992). 92D2 De Loore, C. W. H., De Greve, J. P.: Astron. Astrophys. Suppl. 94 (1992) 453. 921 Iglesias, C. A., Rogers, F. J., Wilson, B. G.: Astrophys. J. 397 (1992) 717. 92K Kiriakidis, M., El Eid, M. F., Glatzel, W.: Mon. Not. R. Astron. Sot. 255 (1992) lp. 92R Rogers, F. J., Iglesias, C. A.: Astrophys. J. Suppl. 79 (1992) 507. 92Sl Spruit, H.: Astron. Astrophys. 253 (1992) 131. 9282 Schaller, G., Schaerer,D., Meynet, G., Maeder, A.: Astron. Astrophys. Suppl. 96 (1992) 269. 92V van den Heuvel, E. P. J., Rappaport, S. A.: X-Ray Binaries and Recycled Pulsars, NATO AST Series.Dordrecht: Kluwer Acad. Publ. (1992). Land&-Bdmstein New Series VI/3b

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4.4.3 Model computations Bressan,F., Fagotto, G., Bertelli, G., Chiosi, C.: Astron. Astrophys. Suppl. 100 (1993) 674. Diehl, R. et al.: Astron. Astrophys. Suppl. 97 (1993) 181. Diehl, R. et al., in: Second COMPTON Symp. 302, New York: AIP Press(1993) p.147. Drotleff, H. W., Denker, A., Knee, H., SoinC, M., Wolf, G., Hammer, J. W.: Astrophys. J. 414 (1993) 735.

93Sl 9382 9333 93W 94D 94E 94K

Seaton, M. J.: Mon. Not. R. Astron. Sot. 265 (1993) L25. Stothers, R. B., Chin, C.-W.: Astrophys. J. 412 (1993) 294. Sackmann, I.-J, Boothroyd, A. I., Kraemer, K. E.: Astrophys. J. 418 (1993) 457. Weaver, T. A., Woosley, S.E.: Phys. Rep. 227 (1993) 65. de Loore, C. W. H., Vanbeveren, D.: Astron. Astrophys. Suppl. 105 (1994) 21. El Eid, M. F.: Astron. Astrophys. 285 (1994) 915. Kappeler, F., Wiescher, M., Giesen, U., Giirres, J., Baraffe, I., El Eid, M.F., Raiteri, C., Busso, M., Gallino, R., Limongi, M., Chieffi, A., Astrophys, J. 437 (1994) 396. 94T Thielemann, F.-K., Kratz, K. l., Pfeffer, B., Rauscher, T., Wormer, L., Wiescher, M.C.: to appear in Nucl. Phys. A (1994). 95E El Eid, M.F.: Mon. Not. R. Astron. Sot. 275 (1995) 983.

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5 Special types of stars

5.1 Variable stars 5.1.0 Abbreviations and notations Magnitudes U, B, V u, , b, y mvis , mpg , … <M>vis , … M , …

0

(for definitions and details, see sect. 4.2) magnitudes in the Johnson system magnitudes in the Strömgren system visual, photographic, …magnitudes mean value of the absolute visual, …magnitude of a group of stars mean value of the absolute visual, …magnitude of a star, averaged over one cycle of the brightness variation (= intensity mean) or averaged over one cycle of the magnitude variation; in this case, it is explicitly stated "magnitude mean'' used as subscript of colour indices: intrinsic (unreddened) colours

Light curve characteristics P period in [d], unless otherwise noted fundamental period PF first overtone period P1H Q pulsational constant, Q = P ( ρ / ρ )½, with ρ , ρ mean stellar and solar densities, respectively phase φ ampl. amplitude max maximum min minimum of brightness, in general asymmetry parameter of a light curve, ε = (tmax – tmin)/P ε t time in [d], unless otherwise specified time in [d] in which the brightness drops (rises) by n magnitudes tn , t–n Various T R g X, Y, Z ∆X, ∆Y, ∆Z [A/B]


mass in units of solar mass [], unless otherwise specified temperature in [K] radius in units of solar radius [R], unless otherwise specified surface gravity in [cm s–2] mass fraction of H, He and heavier elements, X + Y + Z = 1 deviation of mass fraction from mean cosmic abundance of elements, (X0 = 0.70, Y0 = 0.28, Z0 = 0.02) with A and B being symbols of any two elements, [A/B] = log (NA/NB) – log (NA/NB), N = number of atoms/cm3

128

5.1.1 Variable stars: General remarks

[Ref. p. 131

5.1.1 Definitions and general remarks 5.1.1.1 General catalogues and bibliographies The five-volume 4th edition of the General Catalogue of Variable Stars (1985ff) contains data on variable stars which have been assigned variable-star names until 1982. The first three volumes [85K1, 85K2, 87K] contain data on 28277 variables, the fourth one [90S1] contains reference tables (objects sorted according to right ascension, and according to type of variability, as well as crossreferences with other catalogues), and the fifth one [95S1] lists variables in other galaxies. Supplements to the General Catalogue (name lists of variable stars) appear in the Information Bulletin on Variable Stars of IAU Commission 27 (Budapest): IBVS 2681 (1985), 3058 (1987), 3323 (1989), 3530 (1990), 3840 (1993), 4140 (1995). General concepts of classification are outlined in [84K]. The New Catalogue of Suspected Variables [82K] contains data on 14810 objects to which variable-star names have not yet been assigned up to 1980. A catalogue of 491 variable or suspected variable stars in the solar vicinity is given in [90P]. Catalogues of special types of variables are listed in the appropriate subsections. Bibliographic information of variable and suspected variable stars has been collected by Sonneberg astronomers. The catalogues are available in machine-readable form from the Centre des Données astronomiques de Strasbourg (Internet: cdsarc.u-strasbg.fr). Author

Catalogue

CDS number

Huth, H., Wenzel, W. Roessiger, S., Braeuer, H.-J. Roessiger, S., Braeuer, H.-J.

Bibl. Cat. Var. Stars Part I Bibl. Cat. Var. Stars Part II (Update 1994) Bibl. Cat. Suspected Var. Stars Update

VI/67 VI/68 VI/58

5.1.1.2 Monographs A few monographs on general aspects of variable stars have appeared in recent years. Semi-popular books are Variable Stars by Hoffmeister et al. (3rd German edition: [90H], an English translation of the second edition is [85H]) and Variable Stars by Petit (French edition: [82P], English translation: [87P]). A book showing photoelectric and visual light curves of all types of variables, and supplying condensed information on them, is [95S2]. An atlas suitable for visual studies of bright variable stars is [90S2]. A book covering aspects of observational research in the field with modest means is [86P], another one focussing on long-term monitoring is [94S]. Quite a number of books on special aspects of stellar variability, mainly conference proceedings, are available, which are listed under the appropriate subsections.

5.1.1.3 Notation and classification As in the previous edition, the types of variable stars discussed are those defined in the General Catalogue of Variable Stars and its supplements (subsect. 5.1.1.1). The restructuring and introduction of new classes (pulsating, rotating, cataclysmic and eruptive instead of the earlier "pulsating and rotating" and "eruptive" in the 3rd edition of the GCVS), as well as the introduction of new types of variable stars made it necessary to change the numbering system used in LB VI/2b, which is still given for reference in italic numbers in Table 1. The numbers N of variables among the different types and subtypes given in Table 1, as of 1992, was kindly communicated by N.N. Samus and O. Durlevich, Institute for Astronomy of the Russian Academy of Sciences. Landolt-Börnstein New Series VI/3b

Ref. p. 131]


129

Table 1. Types of variable stars, according to the latest edition of the GCVS. Section

Sect. in LB VI/2b

Class, type or subtype

5.1.2 5.1.2.1 5.1.2.1.1

5.1.2 5.1.2.1

Pulsating variables CEP Cepheids (not specified) DCEP Classical Cepheids DCEPS Classical Cepheids (overtone) CW W Virginis stars BL BOO BL Bootis stars RR RR Lyrae stars

5.1.2.1.2 5.1.2.1.3 5.1.2.2

5.1.2.2

Subtype

CEP(B) DCEP(B) DCEPS(B) CWA, CWB RR(B) see below

RRAB

5.1.2.3 5.1.2.4 5.1.2.5

5.1.2.6 5.1.2.7

5.1.2.8

5.1.2.9 5.1.2.10 5.1.2.11 5.1.2.12

5.1.3 5.1.3.1 5.1.3.2 5.1.3.3 5.1.3.4 5.1.3.5

5.1.2.3 5.1.2.4 5.1.2.4 5.1.2.5

5.1.2.6 5.1.2.7

5.1.2.8

5.1.2.9

5.1.2.10

5.1.2.11


RR Lyrae stars with asymmetrical light curves RRC RR Lyrae stars with almost symmetrical light curves SXPHE SX Phoenicis stars (Dwarf Cepheids) SXPHE(B) DSCT DSCT(B) δ Scuti stars DSCTC δ Scuti stars of small amplitude DSCTC(B) RV RV Tauri stars see below RVA RV Tauri stars with constant mean brightness RVB RV Tauri stars with varying mean brightness M Mira stars (long period variables) SR Semiregular variables see below SRA SR giants of late spectral classes SRB SR giants of late spectral classes with poorly expressed periodicity SRC SR supergiants of late spectral classes SRD SR giants and supergiants of spectral classes F, G, K UU UU Her stars L Slow irregular variable stars (not see below specified) LB Slow irregular variables of late spectral classes (red irregular variables) LC irregular variable supergiants of late spectral classes BCEP β Cephei stars (β Canis Majoris stars) BCEPS PVTEL PV Telescopii variables ACYG α Cygni variables ZZ ZZ Ceti stars see below ZZO hot ZZ Ceti stars and PNNE ZZB helium ZZ Ceti stars ZZA hydrogen ZZ Ceti stars Rotating variables SXARI SX Ari variables ACV α2 Canum Venaticorum variables ELL Ellipsoidal variables R Reflection variables FKCOM FK Comae variables

ACVO

N (in Galaxy)

167+13 418 42 177 1 1823 4131 441 16 101 162 87 24 14 5973 1573 884 910 57 85

573 1662 71 118 10 46 40

27 257 69 4 9

130


Section

Sect. in LB VI/2b


5.1.3.6 5.1.3.7

5.1.2.12

BY PSR

5.1.4 5.1.4.1 5.1.4.1.1 5.1.4.1.2 5.1.4.2

5.1.3.1

5.1.3.2

5.1.4.3 5.1.4.4 5.1.4.5

5.1.3.4

5.1.4.6

5.1.3.5

5.1.5 5.1.5.1 5.1.5.2 5.1.5.3 5.1.5.4 5.1.5.5 5.1.5.6 5.1.5.7 5.1.5.8 5.1.5.9 5.1.5.9.1

5.1.3 5.1.3.7

5.1.3.3

5.1.3.8 5.1.3.6 5.1.3.10

5.1.5.9.2 5.1.5.9.3 5.1.5.9.4

5.1.3.9

Eruptive variables SDOR S Doradus variables WR Wolf-Rayet variables GCAS γ Cassiopeiae variables BE Be stars with quasiperiodic fluctuations RCB R Coronae Borealis stars RS RS Canum Venaticorum stars UV UV Ceti stars (flare stars) FU FU Ori variables I Irregular variables IA Irregular variables of early spectral types IB Irregular variables of intermediate and late spectral types IS Rapid irregular variables IN Orion variables (irregular variables associated with diffuse nebulosity) INT T Tauri stars INS rapidly variable T Tauri stars Eclipsing binaries (see section 6.1) E Eclipsing EA Eclipsing, Algol type EB Eclipsing, β Lyrae type EW Eclipsing, W UMa type X-ray stars (see sections 5.6 and 5.7)

S:

Subtype

BY Draconis variables Pulsars

Supernovae and cataclysmic variables SN Supernovae SN I Type I Supernovae SN II Type II Supernovae N Novae NA Fast novae NB Slow novae NC Very slow novae NR Recurrent novae NL Novalike variables AM AM Her stars UG U Geminorum stars (dwarf novae) UGSS U Gem stars, SS Cyg subtype UGSU U Gem stars, SU UMa subtype UGZ U Gem stars, Z Cam subtype ZAND Z Andromedae stars

Others L:

[Ref. p. 131

Unstudied variables with slow light changes Unstudied variables with rapid light changes

N

108 3

SN IA, B, C SN II-L, II-P see below

DQ see below

UVN see below

4 3 73 109 37 9 8 56 1 194 85 47 23 54 15 29 122 12 39 140 978+468 4 192 29 1

ISA, ISB INA, INB

138, 19, 55 348, 33, 72

IN(YY) 52+8 INSA, INSB 372, 19, 108 882 3142 605 618 74 148 182


5.1.1 Variable stars: General remarks Section

Sect. in LB VI/2b


* Unique variables GAL Variable galaxies BLLAC BL Lacertae objects, see LB VI/3c, sect. 9.5 QSO Optically variable quasistellar objects see LB VI/3c, sect. 9.5 CST Constant objects not studied

131 Subtype

N

42 6 4 2 158 428

References for 5.1.1 82K 82P 84K 85H 85K1 85K2 86P 87K 87P 90H 90P 90S1 90S2 94S 95S1 95S2

Kholopov, P.N. (ed.-in-chief): New Catalogue of Suspected Variable Stars, Moscow: Nauka (1982). Petit, M.: Les étoiles variables, Paris: Masson (1982). Kholopov, P.N., in: Sov. Sci. Rev., Astrophys. Space Phys. 3, Amsterdam: Harwood Academic Publishers/OPA (1984) p. 97. Hoffmeister, C., Richter, G., Wenzel, W.: Variable Stars (transl. of 2nd ed.), Berlin: Springer (1985). Kholopov, P.N. (ed.-in-chief): General Catalogue of Variable Stars, Fourth Ed., I, Moscow: Nauka (1985). Kholopov, P.N. (ed.-in-chief): General Catalogue of Variable Stars, Fourth Ed., II, Moscow: Nauka (1985). Percy, J.R. (ed.): The Study of Variable Stars Using Small Telescopes, Cambridge: Cambridge University Press (1986). Kholopov, P.N. (ed.-in-chief): General Catalogue of Variable Stars, Fourth Ed., III, Moscow: Nauka (1987). Petit, M.: Variable Stars, Chichester: John Wiley (1987). Hoffmeister, C., Richter G., Wenzel, W.: Veränderliche Sterne, 3rd ed., Leipzig: J.A. Barth (1990). Petit, M.: Astron. Astrophys. Suppl. 85 (1990) 971. Samus, N.N. (ed.-in-chief): General Catalogue of Variable Stars, Fourth Ed., IV, Moscow: Nauka (1990). Scovil, C.E.: The AAVSO Variable Star Atlas, 2nd ed., Cambridge, USA: AAVSO (1990). Sterken, C., de Groot, M. (eds.): The Impact of Long-Term Monitoring on Variable Star Research, NATO ASI Series, Dordrecht: Kluwer (1994). Samus, N.N. (ed.-in chief): General Catalogue of Variable Stars, Fourth Ed., V, Moscow: Kosmosinform (1995). Sterken, C., Jaschek, C. (eds.): Light Curves of Variable Stars: A Pictorial Atlas, Cambridge: Cambridge University Press (1995).


132

5.1.2 Variable stars: Pulsating variables

[Ref. p. 153

5.1.2 Pulsating variables 5.1.2.0 Generalities 5.1.2.0.1 Radial and nonradial stellar pulsations [80C, 89U, 92B1, 93S2] Generally, the eigenfunctions of a pulsating star can be separated into a radial and an angular part. In spherical polar coordinates, the latter can be written in terms of spherical harmonics Ylm (θ, φ), where θ is the co-latitude and φ the azimuth angle in the polar coordinate system. l is called the harmonic degree, m the azimuthal order (– l ≤ m ≤ + l). The modes belonging to a given value l are distinguished by the number of nodes n in the radial component of displacement from the center to the surface (note that the number of nodes was designated k in the previous edition), n = 0 for the fundamental mode, n = 1 for the first overtone mode, etc. The radial modes are special cases with l = 0, m = 0, and n = 0, 1, 2, etc., correspond to the radial fundamental (F), radial first overtone (1H), radial second overtone (2H), etc. Radial pulsators like cepheids have n = 0, n = 1, and rarely n = 2. The l = 1 and 2 harmonics are the dipole and quadrupole oscillations. We restrict our discussion to spheroidal modes; the toroidal modes, where the radial part of the eigenfunction vanishes, describe large-scale vortices on the surface (Rossby-modes, r-modes). In the linear theory, where different modes are considered as independent from each other (normal mode analysis), the radial component ξr of a displacement can be written

ξr = ξr,nl (r) Ylm (θ , φ) e iσ nml t , where σnlm denote angular pulsation frequencies. n indicates the number of nodes satisfying ξr,nl(ri) = 0, where i = 1, …, n. For velocities, which can be observed directly, Vsph = A(r) (1, k

∂ 1 ∂ ,k ) Ylm (θ , φ) e iσ nml t . ∂θ sin θ ∂φ

Ylm (θ , φ) = Pl m (cos θ ) eimφ , where Pl m ( x ) denotes the associated Legendre polynomial. k is the ratio of the horizontal to radial velocity amplitudes: k=

GM / R 3 = σ2

F Q I, H 0.116 K 2

where G is the gravitational constant, and Q the pulsational constant (see subsect. 5.1.0). The eigenmode of a (slowly rotating) sphere is characterized by three mode indices: the number of radial nodes n, the number of nodelines m that form great circles through the poles, and the number of nodelines parallel to the equator l-|m|, the total number of surface nodelines being l. The richness of nonradial oscillations is formally due to the degree of freedom in the horizontal wave number represented by l, physically by the fact that not only pressure but also gravity can act as a restoring force. A radial oscillation has only the spectrum of the pressure modes (p-modes); nonradial oscillations can show the spectrum of the gravity modes (g-modes) as well. When linear adiabatic oscillations are considered, the basic equations with proper boundary conditions give a well-posed eigenvalue problem with an eigenvalue σ2. Normalized eigenfrequencies ω 2n = σ 2n (R3/GM) for a given l behave differently for p- and g-modes:

ω 2n → ∞ ω 2n → 0

for n → ∞ (p-mode), for n → ∞ (g-mode).


Ref. p. 153]


133

The amplitude of the radial displacement at the surface for p-modes (for g-modes) is large only at the outer (inner) part of the star. Between the p- and the g-mode spectra, there is a fundamental mode (fmode) whose frequency σ increases slowly with increasing l. It can be regarded as the p- or g-mode without nodes. Table 2. Typical light and radial velocity amplitudes, pulsation and rotation periods, observed phenomena, oscillation modes and number of modes for different types of nonradially pulsating stars [89U, 92B1]: (m-p: multiperiodicity, lp: line profile, rv: radial velocity, var.: variation). Type

∆m [mmag]

White dwarfs 50 (ZZ) Ap stars ≤ 10 (ACV) ro Ap δ-Sct stars (DSCT) Solar-type stars

≤ 50

OB stars (general) β-Cep stars (BCEP) 53 Per ζ Oph

≤ 50

10–3

Radial velocity [m s–1]

Ppuls [h]

103

0.1

< 200

0.1

≤ 5·103 0.1 ≤ 104

ACYG (var. supergiants)

Prot [d]

0.1

Observed phenomena

Oscillation modes

light var.; m-p

low-l g-modes

≥2

Nmodes

10 5

3

≥ 0.5

light var.; m-p light + lp var.

0.1

≥ 10

light + rv var.

3…50

≥ 0.5

low-l high n p-modes low-l p-modes low…high-l p-modes, low-l g-modes

5 103

2 light + rv var., m-p lp var. lp var.

semireg. light + rv var.

l = 2…4 f- or pmodes low-l g-modes l = 5…8 p- and g-modes (or r-modes) low-l p- and g-modes

In a nonrotating, nonradially pulsating star, the (2l+1) solutions which, for a given l, are only distinguished by the index m, do not correspond to separate eigenvalues; their eigenvalues are (2l+1)-fold degenerate. The degeneracy is lifted by rotation; a star of uniform angular frequency Ω shows, for the case of slow rotation, a frequency splitting by

σnlm = σnl – m (1 – C(n,l)) Ω . C is a function of n and l and the equilibrium structure of a star. σnl corresponds to a pulsation which is symmetric with respect to the axis of rotation. Modes with negative (positive) m correspond to wave patterns that propagate in (against) the direction of rotation. The rotation rate can be determined from the observed frequency splitting.


134


[Ref. p. 153

Excitation mechanisms [89U]: In order for an oscillation to be overstable, an excitation mechanism is needed that has to provide an entropy increase or a heat input in the high-temperature phase of the oscillation cycle: (1) κ mechanism: positive temperature dependence of opacity (important in ionization zones of abundant elements) (2) ε mechanism: temperature sensitivity of the nuclear energy generation (3) γ mechanism: the spatial variation of the adiabatic exponent enhances the effect of the κ mechanism; this effect is called the γ mechanism (4) δ mechanism (Cowling mechanism): a superadiabatic region excites high-order g-modes (e.g., superadiabatic stratification of plasma stabilized by horizontal magnetic fields).

5.1.2.0.2 Fourier decomposition technique [81S, 86S3, 90A] Stable light curves of pulsating stars can be described by Fourier decomposition: M

m(t) = ∑ Ai cos (2πi(t – t0)/P + φi). i =1

Ai and φi contain useful information for classificational purposes. They define the amplitude ratios Rij = Ai/Aj and the phase differences φij = jφi – iφj, respectively. An application of this method to DCEP, CW, RR variables in star clusters and the field is given in [88S1].

5.1.2.1 Cepheids – CEP Cepheids are radially pulsating variables of luminosity classes Ib-II with periods in the range 1…135 days, amplitudes from several hundredths to 2m in V, and spectral types F at maximum and G…K at minimum light. Subtype: CEP(B) Objects in this subgroup show the presence of two simultaneously operating pulsation modes (usually the fundamental mode with a period P0 and the first overtone with a period P1). P0 is in the range 2…7 days, the ratio P1/P0 ≈ 0.71. Theoretical models of cepheids with varying mass, Teff, initial chemical composition and different degrees of core overshooting, pulsating in F, 1H and 2H modes, together with theoretical colours UBVRI and coefficients of period-luminosity-colour relations are given in [93C1]. 5.1.2.1.1 Classical Cepheids − DCEP Cepheids of population I. They have periods between 1 and 80 days, spectral types F5 to K0, and are concentrated towards the galactic plane. Subtypes: DCEPS (s-Cepheids) Objects in this subgroup are classical cepheids with light amplitudes smaller than 0.,m 5 , almost symmetrical light curves and periods which are generally shorter than 7 days. At least the objects in the short-period group (P < 3 days) are probably all first overtone pulsators. They also might be in


134


[Ref. p. 153

Excitation mechanisms [89U]: In order for an oscillation to be overstable, an excitation mechanism is needed that has to provide an entropy increase or a heat input in the high-temperature phase of the oscillation cycle: (1) κ mechanism: positive temperature dependence of opacity (important in ionization zones of abundant elements) (2) ε mechanism: temperature sensitivity of the nuclear energy generation (3) γ mechanism: the spatial variation of the adiabatic exponent enhances the effect of the κ mechanism; this effect is called the γ mechanism (4) δ mechanism (Cowling mechanism): a superadiabatic region excites high-order g-modes (e.g., superadiabatic stratification of plasma stabilized by horizontal magnetic fields).

5.1.2.0.2 Fourier decomposition technique [81S, 86S3, 90A] Stable light curves of pulsating stars can be described by Fourier decomposition: M

m(t) = ∑ Ai cos (2πi(t – t0)/P + φi). i =1

Ai and φi contain useful information for classificational purposes. They define the amplitude ratios Rij = Ai/Aj and the phase differences φij = jφi – iφj, respectively. An application of this method to DCEP, CW, RR variables in star clusters and the field is given in [88S1].

5.1.2.1 Cepheids – CEP Cepheids are radially pulsating variables of luminosity classes Ib-II with periods in the range 1…135 days, amplitudes from several hundredths to 2m in V, and spectral types F at maximum and G…K at minimum light. Subtype: CEP(B) Objects in this subgroup show the presence of two simultaneously operating pulsation modes (usually the fundamental mode with a period P0 and the first overtone with a period P1). P0 is in the range 2…7 days, the ratio P1/P0 ≈ 0.71. Theoretical models of cepheids with varying mass, Teff, initial chemical composition and different degrees of core overshooting, pulsating in F, 1H and 2H modes, together with theoretical colours UBVRI and coefficients of period-luminosity-colour relations are given in [93C1]. 5.1.2.1.1 Classical Cepheids − DCEP Cepheids of population I. They have periods between 1 and 80 days, spectral types F5 to K0, and are concentrated towards the galactic plane. Subtypes: DCEPS (s-Cepheids) Objects in this subgroup are classical cepheids with light amplitudes smaller than 0.,m 5 , almost symmetrical light curves and periods which are generally shorter than 7 days. At least the objects in the short-period group (P < 3 days) are probably all first overtone pulsators. They also might be in


Ref. p. 153]


135

the first, fast transition across the instability strip after leaving the main sequence, with noticeable period changes [94B5]. The classification as a DCEPS is most conveniently done by a Fourier decomposition of the light curve. According to [90A], DCEP stars follow the relations:

φ21 = 3.332(±0.035) + 0.216(±0.006) P, φ31 = 1.731(±0.105) + 0.154(±0.019) P. For a definition of φ21 and φ31, see sect. 5.1.2.0.2. If the light curve characteristics of a cepheid deviate by ≥ 0.30 in φ21 or by ≥ 1.5 in φ31, it belongs to the DCEPS class. DCEP(B) (Beat cepheids, double-mode cepheids) Two periods are excited at the same time, the fundamental period P0, and the first overtone period P1. P1/P0 = 0.69…0.81, with a pronounced maximum at 0.71. P0 is usually between 2 and 4 days. Lists are given in [85B1, 88S2]. Observations of 45 beat cepheids in the LMC shows that 30 are pulsating simultaneously in the fundamental and first overtone, with P1/P0 ≈ 0.72, and 15 are pulsating in the first and second overtone, with P2/P1 ≈ 0.80 [95A]. Leavitt variables Stars with log P > 1.8, usually low-amplitude pulsators, follow the DCEP period-luminosity relation [85G2]. These objects are found in the Magellanic Clouds. Similar are the "massive yellow supergiant variables" (e.g. ρ Cas, V509 Cas), described in [93P2]. Generalities: Review articles [87B1, 87F1, 88S2], proceedings [85M1, 89S1, 93N]. Photometric BVRI observations of a large sample of cepheids: [84M]. Photometric JHK observations of a large sample of cepheids: [92L, 92S1]. Photometric observations of a large sample of cepheids in the Geneva system: [94B7]. Period-colour relation of classical cepheids. The colour index is averged in the magnitude scale over the pulsation cycle (= magnitude mean) [90F1]: 0 = 0.438(±0.026) log P + 0.311(±0.025). If intensity means and of the B and V light curves are given, the relation between this and the above colour index is – – 0 = 0.003 + 0.010 ∆V – 0.072 (∆V)2 , with ∆V = amplitude of the light variation in V. Colour excesses EB-V on a uniform scale for 328 DCEP and CW are given in [90F2]. They can also be derived under the assumption that classical cepheids have nearly the same spectral type and colour at maximum light [94F2], an assumption also verified by modelling [93S4]: EB–V (±0.050) = (B–V)max – 0.387(±0.020) + 0.302(±0.031) ∆V – 0.318(±0.027) log P. Period-luminosity and period-luminosity-colour relations for classical cepheids with normal metallicity are given in [87F1, 89W1, 93G1]. Absolute magnitudes are derived from the temporal average of intensity; colour indices are defined accordingly: M M M<J> M

= = = =


– 2.24 log P – 1.16 – 2.90 log P – 1.30 – 3.32 log P – 1.83 – 3.42 log P – 2.14

136


[Ref. p. 153

M = – 3.53 log P + 2.13 ( – ) – 2.11 M = – 3.64 log P + 3.28 <J–K>0 – 3.59 Period-luminosity relations are practically metallicity-independent, while period-luminosity-colour relations are sensitive to Cepheid metallicities [88S5, 93G2]. Theoretical period-luminosity and period-luminosity-colour relations for different chemical compositions are given in [90C2]. A maximum-likelihood statistical parallax of galactic classical cepheids yields for the mean absolute magnitude at log P = 0.8: M = – 3.46 ± 0.33 [91W1]. Period-luminosity-relation based on LMC Cepheids, assuming m–M = 18.5 for the distance modulus of the LMC, and EB-V = 0.10 for the foreground reddening (RI: Cousins system) [91M1]: M M M M

= = = =

– 2.43(±0.14) (log P – 1.00) – 3.50(±0.06) – 2.76(±0.11) (log P – 1.00) – 4.16(±0.05) – 2.94(±0.09) (log P – 1.00) – 4.52(±0.04) – 3.06(±0.07) (log P – 1.00) – 4.87(±0.03)

(σ = 0.36 mag) (σ = 0.27 mag) (σ = 0.22 mag) (σ = 0.18 mag)

Period-radius-relation for 101 classical cepheids assuming fundamental mode pulsation [89G2]: log (R/R) = 0.743(±0.023) log P + 1.108(±0.023). A summary of earlier radius determinations may be found in [88T]. A first overtone pulsator (P1H ≈ 0.71 PF ) will show a radius too large by log R ≈ 0.11 when plotted in the period-radius diagram. If one assumes that DCEP with periods below 9 days are 1H pulsators, P-L relations derived separately for the two modes of pulsation (F and 1H) have a steeper gradient than the one derived from the merged data. The transition from F to 1H pulsation may occur at different periods for stars of different metal abundances [94B1]. Table 3. Period changes [84S]. Average period [d] 4.2 6.0 9.1 16.0 36.0

|∆P|/P within 100 years 0.000035 0.000052 0.000068 0.00023 0.0049

Period changes of long-period cepheids show good agreement with theoretical predictions, while short-period cepheids show somewhat larger variation. In addition to the evolutionary changes, two types of period variations occur [91S2]: (1) light time effects due to orbital motion in binary systems (2) phase jumps (step-wise O-C diagram). Light curve asymmetries: Asymmetry parameters ε of light curves of Galactic and Magellanic Cloud cepheids are given in [93A2]. Radial velocity data: [94B8, 94P2]. Distances and space distributions in the Galaxy: [87B2, 89O2, 93G2, 94P2].


Ref. p. 153]


137

Photometric abundances: [81H1, 86G]. Abundances show a galactocentric gradient of d[A/H]/dr = – 0.07 ± 0.02 kpc–1. Masses: From evolutionary mass-luminosity relation [89C3]: log (L/L) = 0.924 + 3.61 log (/ ). Baade-Wesselink masses [89G1]: / = 6.30 − 6.06 log P + 6.28 (log P)2 . With improved opacities, theoretical masses for beat cepheids and bump cepheids (showing the Hertzsprung progression of a secondary maximum before or after primary maximum) have been reconciled with results based on the above methods [92M3]. Spectra: [84G] (including illustrations). During the pulsational cycle, cepheids may vary by up to 5 spectral subtypes. The spectral type at maximum light is almost independent of period, which could also be verified by modelling [93S4]. Mass losses: [88D] Evolution [85B2, 90C2]: Classical cepheids are the result of normal post-main sequence evolution of intermediate to high mass stars (3…10 ) which are now in the core He-burning stage. Most (≥ 90) of them are expected to be on the second crossing (blue loop) through the instability strip.

5.1.2.1.2 W Virginis stars – CW W Virginis stars are cepheids of population II, with periods between 0.8 and 35 days, and amplitudes between 0.,m 3 to 1.,m 2 in V. Two subtypes: CWA W Virginis variables with periods above 8 days. CWB W Virginis variables with periods below 8 days. This classification is rarely used: see below. Review articles [84W, 85G1, 87B1, 88S2], proceedings [85M1], catalogues [81H2, 85H1]. The CW class is a quite inhomogeneous group of stars covering a wide range of abundances and kinematical properties, which show that part of them do not belong to population II. A short-period group (1 day < P < 3 days) is called "BL Her stars'', the long-period group "W Vir stars''; more detailed subdivisions have been proposed [83D, 85G1]. The long-period extension of the CW stars are the RV Tau stars (subsect. 5.1.2.5). "Type II cepheids'' comprise all variables which have periods longer than one day and which are found in globular clusters, as well as variables in the field which have similar pulsation, kinematic and spectroscopic properties, including RV Tau stars. Kinematics: [84H]. Photometric abundances: [81H2].


138


[Ref. p. 153

Fourier decomposition (see 5.1.2.0.2) and comparison with models: [82C, 86S1, 86P, 87P2] (mainly BL Her stars). A resonance at ≈ 1.5 days corresponds to the 10-day resonance of classical cepheids. Period-luminosity relation (for magnitude means) [95M1]: M M M M

= = = =

– 1.33(±0.20) log P + 0.24(±0.07) – 1.61(±0.18) log P – 0.05(±0.07) – 4.35(±0.27) log P + 3.98(±0.34) – 4.17(±0.48) log P + 3.06(±0.38)

for log P < 1.0 for log P < 1.0 for log P > 1.0 for log P > 1.0

Period-luminosity-metallicity relation (for magnitude means) [94N]: M M 0.52 d ∆S > 3, 0.42 < P < 0.60 d

142 17 65 77 73 69 55

M [86B]

M [86S2]

0.68 ± 0.14 1.09 ± 0.38 0.71 ± 0.21 0.65 ± 0.18 0.78 ± 0.21 0.66 ± 0.20 0.73 ± 0.21

0.73 ± 0.18

Luminosity-metallicity-relation and IR-luminosity-period-relation for field RR Lyr stars, proven to be also applicable to cluster RR Lyr stars, based on the Baade-Wesselink method [90L1, 93S1, 94F1]: M = 0.21(±0.05) [Fe/H] + 1.04(±0.10) M = – 2.95(±0.10) log P – 1.07(±0.10) Arguments for a zero point of M= – 0.97, which also leads to a better distance to the LMC, are given in [94F1]. Period-luminosity-metallicity relation (for magnitude means) [94N]: M M M M M M

= 1.53 – 0.03(±0.09) log P0 + 0.35 [Fe/H] = 1.46 – 0.03(±0.09) log P1 + 0.35 [Fe/H] = 1.08 – 0.52(±0.11) log P0 + 0.32 [Fe/H] = 0.96 – 0.52(±0.11) log P1 + 0.32 [Fe/H] = – 0.95 – 2.40(±0.10) log P0 + 0.06 [Fe/H] = – 1.27 – 2.40(±0.10) log P1 + 0.06 [Fe/H]

(RRAB) (RRC) (RRAB) (RRC) (RRAB) (RRC)

Period-luminosity relation for AHB1 stars [94S3]: M = – 2.00 log P – 0.01

(σ = 0.29 mag)

Grid of pulsational models: [94B3]. Period changes [91L]: Periods should increase if the stars evolve from blue to red in the HRD, or decrease, when they evolve in the opposite direction. For Oosterhoff group I (see Table 5) variables ( = 0.72…0.76 ), evolutionary tracks in the instability strip run first, and slowly, blueward, then redward at slightly higher luminosities; for = 0.68 , all stars in the strip evolve rapidly from blue to red. In a group of stars in a globular cluster, small negative as well as large positive period changes should be observable. For Oosterhoff group II variables, all stars in the instability strip are predicted to evolve redward, producing a large positive period change. Landolt-Börnstein New Series VI/3b

Ref. p. 153]


141

Period changes in stars of different Oosterhoff types in three clusters seem to follow the theoretical predictions. Periods of AHB1 stars are predicted to increase, which is supported by observation [94S3]. RR Lyrae stars in globular clusters As seen in Table 5, globular clusters can be divided into two groups. In group I RRAB stars have a mean period of 0.55 days, and the cluster has a metallicity of 3…4 % solar. In group II RRAB stars have a mean period of 0.65 days, and the cluster has a metallicity of ≤ 2 % solar. The explanation is based on evolutionary tracks on the HB, on condition that the actual pulsation mode in the zone, where both fundamental and first harmonic pulsation is possible, depends on the evolutionary history of the variable in the instability strip [94B6]. Table 5. RR Lyrae stars in globular clusters – Oosterhoff dichotomy [93S3, 94B6]. Cluster type [Fe/H] log <Pab> log Nc/(Nab + Nc)

Oosterhoff I –1.1 –0.27 –0.54 0.16

…–1.7 …–0.26 …–0.45 … 0.36

Oosterhoff II –2.0 –0.20 –0.44 0.45

…–2.2 …–0.18 …–0.415 … 0.62

Table 6. Refined masses of RR(B) variables from pulsational models [91P1, 91S1]. Group

Oosterhoff group I: Oosterhoff group II:

Composition

P0

P1/P0

Mass

[Fe/H]

Z

[d]

(observed)

[]

– 1.4 – 2.2

0.0010 0.0002

0.476 0.540

0.745 0.746

0.62 0.66

5.1.2.3 SX Phoenicis stars (Dwarf Cepheids) – SXPHE SX Phe stars are pulsating subdwarfs with spectral types A2 to F5, which belong to population II or to the old disc population. Several periods between 0.04 to 0.08 days may be operating at the same time, and the brightness amplitude is changing; it may reach 0.,m 7 in V, as is the case for the prototype, SX Phe. Phenomenologically they resemble the DSCT stars (subsect. 5.1.2.4). The short period systems are closely connected with the blue stragglers of population II. Monographs [83W, p. 93], proceedings [90R, 90N1], catalogues [84F, 90R, 90N1, 95G]. Recently, two groups have been isolated [90F3]: SXS The short-period group (22 objects, 15 of which are pulsating blue stragglers in globular clusters). The stars are possibly radial fundamental pulsators ([90R] finds 1st, 2nd, 3rd overtone pulsators). The long-period edge is at 0.08 days. Examples: (1) objects with halo kinematics and low metal abundances: BL Cam, KZ Hya, SX Phe; (2) objects with old disc kinematics and intermediate metal abundances: CY Aqr, DY Peg, BS Tuc.


Ref. p. 153]


141

Period changes in stars of different Oosterhoff types in three clusters seem to follow the theoretical predictions. Periods of AHB1 stars are predicted to increase, which is supported by observation [94S3]. RR Lyrae stars in globular clusters As seen in Table 5, globular clusters can be divided into two groups. In group I RRAB stars have a mean period of 0.55 days, and the cluster has a metallicity of 3…4 % solar. In group II RRAB stars have a mean period of 0.65 days, and the cluster has a metallicity of ≤ 2 % solar. The explanation is based on evolutionary tracks on the HB, on condition that the actual pulsation mode in the zone, where both fundamental and first harmonic pulsation is possible, depends on the evolutionary history of the variable in the instability strip [94B6]. Table 5. RR Lyrae stars in globular clusters – Oosterhoff dichotomy [93S3, 94B6]. Cluster type [Fe/H] log <Pab> log Nc/(Nab + Nc)

Oosterhoff I –1.1 –0.27 –0.54 0.16

…–1.7 …–0.26 …–0.45 … 0.36

Oosterhoff II –2.0 –0.20 –0.44 0.45

…–2.2 …–0.18 …–0.415 … 0.62

Table 6. Refined masses of RR(B) variables from pulsational models [91P1, 91S1]. Group

Oosterhoff group I: Oosterhoff group II:

Composition

P0

P1/P0

Mass

[Fe/H]

Z

[d]

(observed)

[]

– 1.4 – 2.2

0.0010 0.0002

0.476 0.540

0.745 0.746

0.62 0.66

5.1.2.3 SX Phoenicis stars (Dwarf Cepheids) – SXPHE SX Phe stars are pulsating subdwarfs with spectral types A2 to F5, which belong to population II or to the old disc population. Several periods between 0.04 to 0.08 days may be operating at the same time, and the brightness amplitude is changing; it may reach 0.,m 7 in V, as is the case for the prototype, SX Phe. Phenomenologically they resemble the DSCT stars (subsect. 5.1.2.4). The short period systems are closely connected with the blue stragglers of population II. Monographs [83W, p. 93], proceedings [90R, 90N1], catalogues [84F, 90R, 90N1, 95G]. Recently, two groups have been isolated [90F3]: SXS The short-period group (22 objects, 15 of which are pulsating blue stragglers in globular clusters). The stars are possibly radial fundamental pulsators ([90R] finds 1st, 2nd, 3rd overtone pulsators). The long-period edge is at 0.08 days. Examples: (1) objects with halo kinematics and low metal abundances: BL Cam, KZ Hya, SX Phe; (2) objects with old disc kinematics and intermediate metal abundances: CY Aqr, DY Peg, BS Tuc.


142


[Ref. p. 153

SXL The long-period group (20 objects). Periods lie between 0.08 and 0.20 days, the stars show nearly symmetrical light curves and light amplitudes close to 0.,m5 and represent the short-period tail of the RRC population. Example: XX Cyg. The SXL, RRAB and CWB stars show a common period-infrared luminosity relationship: M = – 1.92 log P – 0.74 Period-luminosity-metallicity relation (for magnitude means) [94N]: M M M M

= = = =

0.51 – 2.66(±0.52) log P0 + 0.35 [Fe/H] 0.17 – 2.66(±0.52) log P1 + 0.35 [Fe/H] 0.36 – 2.56(±0.54) log P0 + 0.32 [Fe/H] 0.07 – 2.56(±0.54) log P1 + 0.32 [Fe/H]

(F) (1H) (F) (1H)

Noting that [Fe/H] is correlated to P, and assigning F pulsation to objects with amplitudes AV ≥ 0.,m 25, and 1H pulsation to those with AV ≤ 0.,m 2, yields the period-luminosity relations [95M2]: M M M M

= = = =

– 0.94 – 3.29 log P – 1.27 – 3.29 log P – 1.16 – 3.29 log P – 1.53 – 3.29 log P

(F) (1H) (F) (1H)

Data for SXS objects: Radii [87F2]: 1.6…3.0 R. Pulsation masses [87F2, 90N1]: 1.1 ± 0.3 . This range is consistent with masses derived from double-mode objects. It is also in good agreement with evolutionary masses of population II blue stragglers: 1.0…1.4 , age 1…5 Gyr. Temperatures [87F2]: 7300…6775 K. Absolute magnitudes [85M2, 90N1]: 0.5 < M< 4. Metal abundances over a large range [85M2, 90N1]: – 2.4 < [Fe/H] < – 0.2. Period changes [87F2, 87P1]: (1/P) (dP/dt) = =

(– 17.5…2.4)·10–11 d–1 – 8.6·10–11 d–1

The values lie near those predicted for post-helium flash stars. SXPHE stars show much smaller rotational velocities than DSCT stars [85M2]: sin i ≤ 20 km s–1. 5.1.2.4 δ Scuti stars – DSCT δ Sct stars are radially and non radially pulsating stars of spectral types A0…F5 and luminosity classes III…V, which belong to population I. Periods range between 0.01 and 0.2 days and amplitudes between 0.,m 003 and 0.,m 9 in V. Phenomenologically, they resemble the SXPHE stars (subsect. 5.1.2.3). Subtype: DSCTC This group comprises the low-amplitude amplitude variables (∆m < 0.,m 1). The majority of them belongs to luminosity class V, which are also found in open clusters. Landolt-Börnstein New Series VI/3b

142


[Ref. p. 153

SXL The long-period group (20 objects). Periods lie between 0.08 and 0.20 days, the stars show nearly symmetrical light curves and light amplitudes close to 0.,m5 and represent the short-period tail of the RRC population. Example: XX Cyg. The SXL, RRAB and CWB stars show a common period-infrared luminosity relationship: M = – 1.92 log P – 0.74 Period-luminosity-metallicity relation (for magnitude means) [94N]: M M M M

= = = =

0.51 – 2.66(±0.52) log P0 + 0.35 [Fe/H] 0.17 – 2.66(±0.52) log P1 + 0.35 [Fe/H] 0.36 – 2.56(±0.54) log P0 + 0.32 [Fe/H] 0.07 – 2.56(±0.54) log P1 + 0.32 [Fe/H]

(F) (1H) (F) (1H)

Noting that [Fe/H] is correlated to P, and assigning F pulsation to objects with amplitudes AV ≥ 0.,m 25, and 1H pulsation to those with AV ≤ 0.,m 2, yields the period-luminosity relations [95M2]: M M M M

= = = =

– 0.94 – 3.29 log P – 1.27 – 3.29 log P – 1.16 – 3.29 log P – 1.53 – 3.29 log P

(F) (1H) (F) (1H)

Data for SXS objects: Radii [87F2]: 1.6…3.0 R. Pulsation masses [87F2, 90N1]: 1.1 ± 0.3 . This range is consistent with masses derived from double-mode objects. It is also in good agreement with evolutionary masses of population II blue stragglers: 1.0…1.4 , age 1…5 Gyr. Temperatures [87F2]: 7300…6775 K. Absolute magnitudes [85M2, 90N1]: 0.5 < M< 4. Metal abundances over a large range [85M2, 90N1]: – 2.4 < [Fe/H] < – 0.2. Period changes [87F2, 87P1]: (1/P) (dP/dt) = =

(– 17.5…2.4)·10–11 d–1 – 8.6·10–11 d–1

The values lie near those predicted for post-helium flash stars. SXPHE stars show much smaller rotational velocities than DSCT stars [85M2]: sin i ≤ 20 km s–1. 5.1.2.4 δ Scuti stars – DSCT δ Sct stars are radially and non radially pulsating stars of spectral types A0…F5 and luminosity classes III…V, which belong to population I. Periods range between 0.01 and 0.2 days and amplitudes between 0.,m 003 and 0.,m 9 in V. Phenomenologically, they resemble the SXPHE stars (subsect. 5.1.2.3). Subtype: DSCTC This group comprises the low-amplitude amplitude variables (∆m < 0.,m 1). The majority of them belongs to luminosity class V, which are also found in open clusters. Landolt-Börnstein New Series VI/3b

Ref. p. 153]


143

Monograph [83W, p. 93], review articles [83C, 88K2, 90R, 93B], proceedings [90R, 90B], catalogues [90L2, 94R, 95G]. Period-luminosity and period-luminosity-colour relations (also a summary of previous calibrations) are given in [85T]. Period-luminosity relation for several pulsation modes [85T]: M M M M

= = = =

– 2.88(±0.26) log P – 1.31(±0.28) – 3.34(±0.24) log P – 2.19(±0.28) – 2.96(±0.22) log P – 2.14(±0.28) – 3.09(±0.40) log P – 2.65(±0.51)

(F) (1H) (2H) (3H)

Period-luminosity-(Strömgren) colour relation for several pulsation modes [85T]: M M M M

= = = =

– 3.58(±0.25) log P + 4.92(±1.13) (b–y)0 – 2.88(±0.41) – 3.48(±0.19) log P + 4.48(±1.04) (b–y)0 – 3.07(±0.29) – 3.53(±0.26) log P + 3.34(±1.09) (b–y)0 – 3.33(±0.45) – 3.48(±0.32) log P + 5.38(±1.81) (b–y)0 – 3.87(±0.56)

(F) (1H) (2H) (3H)

Period-luminosity-(Johnson) colour relation for the fundamental mode [92F]: M = – 3.05(±0.13) log P + 2.47(±0.39) (B-V)0 – 2.01(± 0.19) . Period-luminosity-temperature relation [90L2] (reduced period Pr = P/(Pk/P0), with k being the pulsation mode, and (Pk/Pk=0) the expected ratio between averaged theoretical values for radial pulsators): Mbol

= – 3.33 log Pr + 10.65 log Te + 39.67 .

Semi-empirical period-radius relations for several pulsation modes [88T]: log (R/R) log (R/R) log (R/R) log (R/R)

= = = =

0.768(±0.040) log P + 1.178(±0.043) 0.739(±0.038) log P + 1.224(±0.043) 0.803(±0.040) log P + 1.378(±0.050) 0.732(±0.057) log P + 1.354(±0.074)

(F) (1H) (2H) (3H)

Spectral classification: [83O]. UV spectroscopy and line identifications for δ Sct: [91M3]. Pulsation modes: 35% in F; 65% in 1H and 2H [81A]. Period changes [90B]: Evolutionary tracks in the instability strip show almost everywhere an evolution towards larger radii, i.e. longer periods. Near the main sequence, one expects (1/P)(dP/dt) = + 10–10 per year, which is roughly confirmed by observations. For variables with longer periods, one expects (1/P)(dP/dt) = + 2·10–7 per year, while decreasing periods have been observed. Theory: Population I stars of masses 1.4 < / < 3.0, in stages of evolution corresponding to central H burning and shell H burning. Periods and period ratios are in the range appropriate to the lowest radial modes, growth rates of pulsation are very slow (≈ 106 years); driving is due to the κ mechanism in the He II ionization region. Nonlinear models in 3.8 < log Teff < 3.95, 0.6 < log L/L < 2.0: [92M1].


144


[Ref. p. 153

Since DSCT and DCEP stars belong to the same family of population I stars, driven by the same mechanism, Fernie [92F] has derived joint period-luminosity, period-luminosity-colour, and periodradius relations for both groups: = – 2.902(±0.030) log P – 1.203(±0.029) M = – 3.422(±0.026) log P – 2.1 ( – ) – 2.272(±0.027) M log (R/R) = 0.7385(±0.0060) log P + 1.1116(±0.0060). 5.1.2.5 RV Tauri stars – RV RV Tauri stars are radially pulsating supergiants of spectral classes F…G at maximum and G…K at minimum light. The light curves are characterized by the presence of double waves with alternating primary and secondary minima that can vary in depth so that the type of minimum can change. The complete light amplitude may reach 3…4m in V. Periods (between subsequent primary minima) range between 30 and 150 days. Two subtypes: RVA RV Tauri stars with constant mean brightness (example: AC Her). RVB RV Tauri stars with periodically varying mean brightness (examples: DF Cyg, RV Tau). The period of this variation lies between 600 and 1500 days. Review article [87B1]. Photometry and CN abundances, Teff, g, MV: [79D]. Visual light curve of the RVA star R Sct: [86A]. UBV photometry of three RV Tau stars: [93Z]. Optical and infrared photometry: [87G]. 11 objects with dust shells, 12 objects with no dust having temperature ≥ 500 K. IRAS photometry: [86J2, 89R]. IRAS observations yield IR excesses which can be explained by circumstellar dust. Average dust temperatures: ≈ 600…460 K for spectroscopic A subgroup, and ≈ 460…250 K for spectroscopic B subgroup. Dust loss rates: typically 3·10–17 per year. Spectral classification: [79D, 92W2] (See LB VI/2b, Table 12 on p. 214, where spectroscopic subgroups A, B and C are described.) A spectroscopic atlas is given in [89C1]; analysis of near-IR spectra as compared to normal population I supergiants: [91M2]. Multiwavelength studies of selected objects: [92S2, 94S1, 94S2]. Period changes: sudden period decreases have been observed [91P2]. Polarisation: [90N2].


144


[Ref. p. 153

Since DSCT and DCEP stars belong to the same family of population I stars, driven by the same mechanism, Fernie [92F] has derived joint period-luminosity, period-luminosity-colour, and periodradius relations for both groups: = – 2.902(±0.030) log P – 1.203(±0.029) M = – 3.422(±0.026) log P – 2.1 ( – ) – 2.272(±0.027) M log (R/R) = 0.7385(±0.0060) log P + 1.1116(±0.0060). 5.1.2.5 RV Tauri stars – RV RV Tauri stars are radially pulsating supergiants of spectral classes F…G at maximum and G…K at minimum light. The light curves are characterized by the presence of double waves with alternating primary and secondary minima that can vary in depth so that the type of minimum can change. The complete light amplitude may reach 3…4m in V. Periods (between subsequent primary minima) range between 30 and 150 days. Two subtypes: RVA RV Tauri stars with constant mean brightness (example: AC Her). RVB RV Tauri stars with periodically varying mean brightness (examples: DF Cyg, RV Tau). The period of this variation lies between 600 and 1500 days. Review article [87B1]. Photometry and CN abundances, Teff, g, MV: [79D]. Visual light curve of the RVA star R Sct: [86A]. UBV photometry of three RV Tau stars: [93Z]. Optical and infrared photometry: [87G]. 11 objects with dust shells, 12 objects with no dust having temperature ≥ 500 K. IRAS photometry: [86J2, 89R]. IRAS observations yield IR excesses which can be explained by circumstellar dust. Average dust temperatures: ≈ 600…460 K for spectroscopic A subgroup, and ≈ 460…250 K for spectroscopic B subgroup. Dust loss rates: typically 3·10–17 per year. Spectral classification: [79D, 92W2] (See LB VI/2b, Table 12 on p. 214, where spectroscopic subgroups A, B and C are described.) A spectroscopic atlas is given in [89C1]; analysis of near-IR spectra as compared to normal population I supergiants: [91M2]. Multiwavelength studies of selected objects: [92S2, 94S1, 94S2]. Period changes: sudden period decreases have been observed [91P2]. Polarisation: [90N2].


Ref. p. 153]


145

Metallicity [89C2]: – spectroscopic subgroup A [Fe/H] ≈ – 0.6, – spectroscopic subgroups B/C [Fe/H] ≈ – 1.4. No period-luminosity relation is evident; absolute magnitudes range between MV = –1…–3 [89W2, 92W2]. RV Tau models: [88S2, 88K3]. Linear, non-adiabatic radial pulsating models with convection. While [85F, 93T2] interpret the phenomenon of unequal minima as the result of an integer resonance between the fundamental period P0 (= the interval between alternate minima) and the first overtone P1 = P0/2 in low mass stars with thin envelopes (related to protoplanetary nebulae), [90M2] interpret it as the result of period doubling bifurcations caused by a half-integer resonance between the fundamental period P0 (= the interval between adjacent maxima) and the second overtone P2. Evolution: [86J2]. The strong IR fluxes and peculiar power law exponents indicate that the RV Tau stars represent lowmass objects that have recently (≈ 500 years) evolved off the asymptotic giant branch (AGB), where they underwent an episode of more dramatic mass loss (10–5 per year) about 100 times stronger than is currently indicated, the "fossil AGB remnant". The short lifetime and the space density shows that the formation rate of RV Tau stars is 1/10 of that of planetary nebulae. The RV Tau stars are probably the low mass, and in some cases the low metallicity portion of those stars in transition from the AGB to white dwarfs. Because of their previously high mass-loss rates, many will probably become planetary nebulae. Calculations indicate that they should evolve rapidly to higher effective temperatures. Predicted period decreases seem to have been observed [91P2]. 5.1.2.6 Mira Ceti variables – M Mira stars are long-period variable late-type giants with emission lines (Me, Ce, Se) with periods between 80 and 1000 days, and light amplitudes from 2.,m5 to 11m in V. In the infrared K band, amplitudes usually do not exceed 0.,m 9. Objects with amplitudes larger than 1…1.,m 5, but likely smaller than 2.,m 5 in V, are designated M: or SR: . Monograph [86Q], review articles [87B1, 88B], proceedings [89S1]. Collection of visual light curves: [83A, 90V]. Infrared (1…20 µm) light curves: [93L2]. Classification of visual light curves according to the scheme outlined in LB VI/1, subsect. 6.2.2.5.2: [88V]. Parameters [88B]: – – – – – – –

Mass: Period: Radius: Teff: Shock amplitude: Wind velocity: Mass loss rate:

1…2 200…500 d 150…300 R 2800…3000 K 25…35 km s–1 10 km s–1 10–7…2·10–6 per year.

A list of oxygen-rich miras in the Galaxy is given in [92J1]. A list of miras and semiregular variables in the LMC, as well as spectra of C-rich and O-rich miras are given in [90H].


Ref. p. 153]


145

Metallicity [89C2]: – spectroscopic subgroup A [Fe/H] ≈ – 0.6, – spectroscopic subgroups B/C [Fe/H] ≈ – 1.4. No period-luminosity relation is evident; absolute magnitudes range between MV = –1…–3 [89W2, 92W2]. RV Tau models: [88S2, 88K3]. Linear, non-adiabatic radial pulsating models with convection. While [85F, 93T2] interpret the phenomenon of unequal minima as the result of an integer resonance between the fundamental period P0 (= the interval between alternate minima) and the first overtone P1 = P0/2 in low mass stars with thin envelopes (related to protoplanetary nebulae), [90M2] interpret it as the result of period doubling bifurcations caused by a half-integer resonance between the fundamental period P0 (= the interval between adjacent maxima) and the second overtone P2. Evolution: [86J2]. The strong IR fluxes and peculiar power law exponents indicate that the RV Tau stars represent lowmass objects that have recently (≈ 500 years) evolved off the asymptotic giant branch (AGB), where they underwent an episode of more dramatic mass loss (10–5 per year) about 100 times stronger than is currently indicated, the "fossil AGB remnant". The short lifetime and the space density shows that the formation rate of RV Tau stars is 1/10 of that of planetary nebulae. The RV Tau stars are probably the low mass, and in some cases the low metallicity portion of those stars in transition from the AGB to white dwarfs. Because of their previously high mass-loss rates, many will probably become planetary nebulae. Calculations indicate that they should evolve rapidly to higher effective temperatures. Predicted period decreases seem to have been observed [91P2]. 5.1.2.6 Mira Ceti variables – M Mira stars are long-period variable late-type giants with emission lines (Me, Ce, Se) with periods between 80 and 1000 days, and light amplitudes from 2.,m5 to 11m in V. In the infrared K band, amplitudes usually do not exceed 0.,m 9. Objects with amplitudes larger than 1…1.,m 5, but likely smaller than 2.,m 5 in V, are designated M: or SR: . Monograph [86Q], review articles [87B1, 88B], proceedings [89S1]. Collection of visual light curves: [83A, 90V]. Infrared (1…20 µm) light curves: [93L2]. Classification of visual light curves according to the scheme outlined in LB VI/1, subsect. 6.2.2.5.2: [88V]. Parameters [88B]: – – – – – – –

Mass: Period: Radius: Teff: Shock amplitude: Wind velocity: Mass loss rate:

1…2 200…500 d 150…300 R 2800…3000 K 25…35 km s–1 10 km s–1 10–7…2·10–6 per year.

A list of oxygen-rich miras in the Galaxy is given in [92J1]. A list of miras and semiregular variables in the LMC, as well as spectra of C-rich and O-rich miras are given in [90H].


146


[Ref. p. 153

The mira sequence can be extended to longer-period objects (P = 500…1500 days) by including type II OH/IR sources. Since the mass loss rates increase with period, these objects are obscured by circumstellar dust shells, and their masses are estimated to be > 4 [87L]. Pulsational models: [88B]. Pulsational modes have been determined to be first overtone in most cases, yielding masses in the range 0.5 ≤ / ≤ 3 [91T]; Fourier analysis of observed light curves agree well with nonadiabatic linear models if they pulsate in the first overtone [94B4]. However, the modeling of pulsation amplitudes and radial velocities has encountered problems, only fundamental pulsators are able to produce the observed amplitudes [90W1]. Mass loss results from complex interactions between pulsation-induced shocks, which greatly extend the atmosphere, time-dependent thermal relaxation, which determines the thermal structure of the atmosphere, and radiation pressure on dust grains, which transfer momentum to the gas and ultimately drive most of the mass loss. Infrared period-luminosity(-colour) relations for oxygen-rich or probable oxygen-rich objects (spectral types M, S, K or [M] – the square brackets indicate the presence of forbidden lines) and for carbon-rich or probably carbon-rich objects (spectral type C or [C]) in the LMC are given in [89F1], we convert them to absolute magnitudes, adopting m – M = 18.5 (it is argued that, because of different metallicities, galactic miras are fainter by 0.2…0.25, and the constants in the following equations have to be increased by such an amount [87L, 92J1, 92J2]). The formulae are given for the average of the maximum and minimum K-magnitudes (and Jmagnitudes) or Mbol magnitudes, designated with M [89F1]: Period-luminosity relations: = – 3.47(±0.19) log P + 0.98(±0.13), = – 3.30(±0.40) log P + 0.48(±0.18), = – 3.57(±0.16) log P + 1.20(±0.15),

29 O miras 20 C miras all 49 miras

M bol = – 3.00(±0.24) log P + 2.88(±0.57), M bol = – 1.86(±0.30) log P + 0.26(±0.74), M bol = – 2.34(±0.19) log P + 1.39(±0.45),

29 O miras 20 C miras all 49 miras

MK MK MK

Period-luminosity-colour relations: = – 4.58 log P + 2.00 (J–K)0 + 1.21, = – 2.88 log P – 0.14 (J–K)0 – 0.28,

29 O miras 20 C miras

M bol = – 4.32 log P + 2.37 (J–K)0 + 3.16, M bol = – 2.42 log P + 0.18 (J–K)0 + 1.28,

29 O miras 20 C miras

MK MK

Spectral classification of optical spectra: [84C]. IRAS spectra: [89V, 89O1]. Energy distributions of M-type miras can be modelled with a stellar blackbody of T = 2500 K and a dust shell with T = 200…500 K at the inner boundary where silicates are formed. Evolution [90W2]: Observational estimates of mira lifetimes are 6·104 years. Theoretical calculations without mass loss yield 10 times longer lifetimes, and it seems that high mass loss rates are required to terminate the mira stage.


Ref. p. 153]


147

Table 7. Statistical properties of oxygen-rich miras, semiregular and irregular variables [92J1, 92J2, 93J]. Type

Period [d]

Mode

Scale height z0 [pc]

M M SR M SR SR SR SR L

> 400 300…400 300…400 100…300 200…300 150…200 100…150 50…100

F 240 F 240 F 250 F 500…600 F 500 ? ? 1H, 2H 250 ? > 190 multiple? 300?

Surface density Space density Progenitor mass n0 [kpc–3] σ [kpc–2] MS [] 18 100 20 40…60 8

38 210 40 35…60 8

70 130? 160?

150 350? 260?

1.1*) 1.1 1.2 < 1.1 ? ? 1.1? < 1.5 1.1?

*) Possibly progenitors of the following group. 5.1.2.7 Semiregular variables – SR Giants or supergiants of intermediate or late spectral types that show noticeable periodicities of light changes, accompanied or interrupted by different irregularities. Periods range between 20 days and 2000 days (or more), light curve shapes are different or variable, and amplitudes range between several hundredths to several magnitudes (usually 1…2m). Subtypes: SRA Semiregular giants of late spectral classes (M, C, S without or with emission lines) with persistent periodicity showing, as a rule small (< 2.,m5 in V), usually varying amplitudes and light curve shapes. Periods range between 35 days and 1200 days. Many of these stars differ from mira variables only by their smaller amplitudes. SRB Semiregular giants of late spectral classes (M, C, S without or with emission lines) with poorly expressed periodicity (mean cycles range between 20 days and 2300 days), or with alternating intervals of periodic and slow irregular changes, even interrupted by intervals of constant light. Usually every star of this type may be ascribed a certain mean period; in some stars two or more periods are found. Examples: RR CrB, AF Cyg. SRC Semiregular supergiants of late spectral classes (M, C, S without or with emission lines). Amplitudes are of the order of 1m, and periods range between 30 days and several thousand days. SRD Semiregular giants and supergiants of spectral classes F, G, K with or without emission lines. Amplitudes range between 0.,m 1 and 4m, periods between 30 days and 1100 days. Examples: SX Her, SV UMa. Isolated group: UU Her stars (see below). Monograph [86Q], review article [87B1], catalogue [92J2]. SRA/SRB: SRAs are often also called small amplitude red variables (SARVs); the best studied object is EU Del [89P]. The variability with time scales of several tens of days is superimposed on a variability with time scales of several hundreds of days [93P1]. The amplitude of the variation appears to increase Landolt-Börnstein New Series VI/3b

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147

Table 7. Statistical properties of oxygen-rich miras, semiregular and irregular variables [92J1, 92J2, 93J]. Type

Period [d]

Mode

Scale height z0 [pc]

M M SR M SR SR SR SR L

> 400 300…400 300…400 100…300 200…300 150…200 100…150 50…100

F 240 F 240 F 250 F 500…600 F 500 ? ? 1H, 2H 250 ? > 190 multiple? 300?

Surface density Space density Progenitor mass n0 [kpc–3] σ [kpc–2] MS [] 18 100 20 40…60 8

38 210 40 35…60 8

70 130? 160?

150 350? 260?

1.1*) 1.1 1.2 < 1.1 ? ? 1.1? < 1.5 1.1?

*) Possibly progenitors of the following group. 5.1.2.7 Semiregular variables – SR Giants or supergiants of intermediate or late spectral types that show noticeable periodicities of light changes, accompanied or interrupted by different irregularities. Periods range between 20 days and 2000 days (or more), light curve shapes are different or variable, and amplitudes range between several hundredths to several magnitudes (usually 1…2m). Subtypes: SRA Semiregular giants of late spectral classes (M, C, S without or with emission lines) with persistent periodicity showing, as a rule small (< 2.,m5 in V), usually varying amplitudes and light curve shapes. Periods range between 35 days and 1200 days. Many of these stars differ from mira variables only by their smaller amplitudes. SRB Semiregular giants of late spectral classes (M, C, S without or with emission lines) with poorly expressed periodicity (mean cycles range between 20 days and 2300 days), or with alternating intervals of periodic and slow irregular changes, even interrupted by intervals of constant light. Usually every star of this type may be ascribed a certain mean period; in some stars two or more periods are found. Examples: RR CrB, AF Cyg. SRC Semiregular supergiants of late spectral classes (M, C, S without or with emission lines). Amplitudes are of the order of 1m, and periods range between 30 days and several thousand days. SRD Semiregular giants and supergiants of spectral classes F, G, K with or without emission lines. Amplitudes range between 0.,m 1 and 4m, periods between 30 days and 1100 days. Examples: SX Her, SV UMa. Isolated group: UU Her stars (see below). Monograph [86Q], review article [87B1], catalogue [92J2]. SRA/SRB: SRAs are often also called small amplitude red variables (SARVs); the best studied object is EU Del [89P]. The variability with time scales of several tens of days is superimposed on a variability with time scales of several hundreds of days [93P1]. The amplitude of the variation appears to increase Landolt-Börnstein New Series VI/3b

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[Ref. p. 153

towards later spectral types [94P]. Interpretation as "chaotic'' mode switching between fundamental, first and second overtones: [91C]. A statistical study of optical and IRAS properties of both groups yielded the following results [92K]: SRA appear as intermediate objects between mira and SRB variables as concerns periods, temperatures, amplitudes, mass loss rates and the fraction of C-rich stars. SRB form a quite homogeneous group as concerns periods, amplitudes and temperatures. They appear as an extension of miras towards higher temperatures and smaller amplitudes. Nevertheless, a subdivision into two groups appears appropriate: blue SRB: stars without circumstellar dust, higher temperature, smaller period, smaller amplitude, about half as luminous as miras; red SRB: stars having mass loss rates, luminosities and main sequence masses comparable to miras, their temperatures being slightly higher. They appear to be first overtone pulsators. Carbon stars, technetium-enriched stars, and almost all S-stars belong to the red SRB group. Table 8. Separation of O-rich long-period variables into miras and SRBs of two types [92K, 94K]. Group

Miras Red SRB Blue SRB

P [d] > 180 60…200 < 150

V-amplitude [mag]

V – [12 µm] colour [mag]

[12 µm] – [25 µm] colour [mag]

>2 ≥1 9 >8 4.3: (2) for log Teff < 4.1:

log P [d] = – 0.200 Mbol – 2.503 log Teff + 9.135 log P [d] = – 0.339 Mbol – 2.951 log Teff +10.407

Empirical period-luminosity-colour relation for B to G supergiants [80M]: log P [d] = – 0.345 Mbol – 3 log Teff +10.60 .

5.1.2.12 ZZ Ceti stars – ZZ ZZ Ceti stars are non-radially pulsating white dwarfs with periods between 30 s to 25 min and amplitudes between 0.,m 001 and 0.,m 2 in V. Usually, a star shows a superposition of several periods. Subtypes: ZZO ZZ Ceti stars of spectral type DO (continuous spectrum) or variable planetary nuclei (also called PG1159 variables). Example: GW Vir (= PG1159-035). ZZB ZZ Ceti stars of spectral type DB (helium WDs). Example: V777 Her. ZZA ZZ Ceti stars of spectral type DA (hydrogen WDs). Example: ZZ Cet. Monograph [89U], review articles [88W, 89K], proceedings [89W3], catalogue [89U]. Additional information is found in subsect. 5.5.3.3. The ZZ Cet stars are nonradial pulsators, with several periods acting at the same time (F, 1H, 2H, …, g-modes). The modes are often split into close pairs by slow rotation. Periods can be extremely stable; instable ones are probably caused by interactions of various periods (beating of closely spaced frequencies).


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[Ref. p. 153

For a given spectral type, the amplitude of variability increases with luminosity (II – Ib – Iab – Ia), the ACYG variables proper being the most variable [80M]. For the Ia supergiants, the amplitudes have a local maximum for the early B stars and level off at the A and F stars (enhanced variability is observed for G to M stars, but these objects are rather classified as SRC or SRD stars, see subsect. 5.1.2.7). Type of variability [91V]: Cyclic variations are not strictly periodic, they suggest a combination of non-radial pulsation and rotational modulation. Instability strip and maximum light amplitude [91V]: Most of the high-mass-losing supergiants (Ie, Ieq) and hot SDOR-type stars at minimum (or quiescent) state have large light amplitudes (0.,m 1…0.,m 4), however, it is not clear if these variations are small-scale SDOR-type eruptions. In the spectral range O6 to F5, variations in supergiants up to 0.,m 12 are observed; among the B supergiants, there is no object with variations less than 0.,m 05. F supergiants at the blue side of the cepheid instability strip are constant. Theoretical period-luminosity-colour relation for fundamental mode pulsators [90S1]: (1) for log Teff > 4.3: (2) for log Teff < 4.1:

log P [d] = – 0.200 Mbol – 2.503 log Teff + 9.135 log P [d] = – 0.339 Mbol – 2.951 log Teff +10.407

Empirical period-luminosity-colour relation for B to G supergiants [80M]: log P [d] = – 0.345 Mbol – 3 log Teff +10.60 .

5.1.2.12 ZZ Ceti stars – ZZ ZZ Ceti stars are non-radially pulsating white dwarfs with periods between 30 s to 25 min and amplitudes between 0.,m 001 and 0.,m 2 in V. Usually, a star shows a superposition of several periods. Subtypes: ZZO ZZ Ceti stars of spectral type DO (continuous spectrum) or variable planetary nuclei (also called PG1159 variables). Example: GW Vir (= PG1159-035). ZZB ZZ Ceti stars of spectral type DB (helium WDs). Example: V777 Her. ZZA ZZ Ceti stars of spectral type DA (hydrogen WDs). Example: ZZ Cet. Monograph [89U], review articles [88W, 89K], proceedings [89W3], catalogue [89U]. Additional information is found in subsect. 5.5.3.3. The ZZ Cet stars are nonradial pulsators, with several periods acting at the same time (F, 1H, 2H, …, g-modes). The modes are often split into close pairs by slow rotation. Periods can be extremely stable; instable ones are probably caused by interactions of various periods (beating of closely spaced frequencies).



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Period changes [88W, 91K]: Depending on radius shrinking and core cooling; the latter causes effects which are observable in the hotter objects. Table 10. Period changes in ZZ Ceti stars. Object

Period P [s]

PG1159-035 (DOV) 516 G117-B15A+RY Mon (DA) 215

Period change log P/(dP/dt) [year]

Theoretical expectation log P/(dP/dt) [year]

5.83 8.75 ± 0.12

6 9.1…9.5

Theory: The variable white dwarfs of types ZZB and ZZA have partial ionization zones of He and H in their surface layers, and cooling white dwarfs will pass through these two instability strips where the κmechanism is operating. A similar mechanism was proposed for the ZZO stars (partial ionization of C and O), but details are still unclear. Cox [93C2] suggests pulsations in a thin CO convection shell for all three types. Asteroseismological properties of chemically stratified DA and DB white dwarf models are given in [91B, 92B3]. Table 11. Observed properties of pulsating white dwarfs [88W]. Subtype – subgroup

Spectrum

ZZO – PNNV

He II, C IV nebula He II, C IV, O VI absorption with narrow emission core He I pure absorption H pure absorption

ZZO – DOV

ZZB – DBV ZZA – DAV

log g

log (L/L)

Te [K]

P [s] Fractional ampl. (typical range) (typical range) (>1000) 1500 (300…850) 500

6

3…4

> 105

7

2

> 105

8

– 1.2

25000

8

– 2.8

12000

0.01 ( 50 at which the stars become unstable and lose so much matter that the expansion is stopped and the evolutionary tracks reverse when the helium core contains 70% of the stellar mass [87L2]. HRdiagrams of the Magellanic Clouds with the HD-limit drawn are presented in [89G]. Mass loss rates (P Cyg): several 10–1 per year. Ejection velocities: typically 100 km s–1, in rare cases higher. Table 34. Observed properties of well-studied LBVs [89H2]. Parent galaxy

Star

T(min) [K]

Galaxy

η Car P Cyg AG Car S Dor R71 R127 Var C Var A

27000 19000 25000 20000…25000 13600 30000 20000…25000 3500

LMC

M33

T(max) [K]

9000 8000 9000 8500 7500…8000 8000

Mbol [mag] – 11.3 – 9.9 – 10.1 – 9.8 – 8.8 – 10.5 – 9.8 – 9.5

& [ / year] 10–3…10–1 2·10–5 3·10–5 5·10–5 5·10–5 6·10–5 4·10–5 2·10–5

5.1.5.2 Wolf-Rayet variables – WR Wolf-Rayet variables are stars with broad emission features of He I, He II, and either C II…C IV, O II…O V, or N III…N V. They display irregular light changes with amplitudes of up to 0.,m 1 in V, which are probably caused by non-stable mass outflow from their photospheres. Monograph [87J], review articles [87A1, 87V2, 88M], catalogue [92L].


Ref. p. 193]

5.1.5 Variable stars: Eruptive variables

185

Short timescale variations seem to be ruled out, longer variations are certainly present, but there is no clarity about existing periodicities, except those which are connected with the binarity of WR stars (a high percentage of WR stars are binaries). Microvariability of 7 objects, presumably due to continuum variations, which are caused by temperature effects in the pseudo-photosphere (variable mass loss) [87V1]. Polarisation changes: [88M, 88P2]; generally found in binaries. WR+O binaries show a relatively broad dip centered at phase 0.0, when the O star is behind the WR star and its wind [87L3]. Among the single WR stars the rms scatter increases towards cooler WR subtypes [87L3] (up to 0.03 and 0.015 mag for WN and WC systems, respectively). More details are found in subsect. 5.2.1.2. 5.1.5.3 γ Cassiopeiae variables – GCAS γ Cas variables are irregularly variable, rapidly rotating Be III…V stars with mass outflow from their equatorial zone. The formation of equatorial rings or discs is sometimes accompanied by a brightness decrease. Light amplitudes may reach 1.,m 5 in V. Monograph [87J], proceedings [87S1]. More details are found in subsect. 5.2.1.4. Long-term variability: Often connected with spectroscopic shell episodes.

5.1.5.4 Variable Be stars – BE BE - variables are spectroscopically classified Be stars showing small-scale light variations which are not related to shell events. In some cases, the variations are quasiperiodic. Monograph [87J], review articles [83C, 87P, 88S3], proceedings [87S1], catalogue [rapid variables: 87P]. The Be stars are discussed in subsect. 5.2.1.4. Here, we focus on the aspects of photometric variability. Rapid variability [87P, 88V, 90B1, 90B2]: About 50% of the Be stars seem to vary from night to night, with an amplitude of 0.,m 1 or greater. Well-determined periods are in the range 0.3 to 2 days, it appears that some periods are stable over many years. Photometric multiperiodicities like in the BCEP stars are not evident. Light curves have generally double-wave forms (two unequal maxima or minima per cycle). Amplitudes are typically between 0.,m 01 to 0.,m 1, and commonly change on a time scale of months. Light curves: [86B, 89C, 92B, 94M]. Survey of bright Be stars: [87S2, 94M] About 50% out of 86 objects showed short- or intermediate-term variability, which is more evident in stars of earlier type. A long-term monitoring of 7 stars yielded quasi-periodic oscillations, sometimes followed by fading events. Landolt-Börnstein New Series VI/3b

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[Ref. p. 193

Theories [87P, 90B1, 90B2]: (1) Non-radial low order (l = 2) g-mode pulsations. (2) Rotation of a star with an oblique dipole magnetic field, causing photospheric temperature differences ("starspots''), also indicated by a correlation between projected rotational velocity and photometric period. (3) Duplicity (ellipsoidal variables – often ruled out by the lack of radial velocity variations). (4) Circumstellar material – inhomogeneities in an equatorial disc (problems with the stability of some periods observed).

5.1.5.5 R Coronae Borealis stars – RCB R CrB stars are hydrogen-poor, helium-rich stars of high luminosity and of spectral type Bpe to R, which are simultaneously eruptive and pulsating variables. They show non-periodic fadings by 1…9m in V, which last for several weeks to several hundred days. Superimposed on these changes, pulsations with amplitudes of up to several 0.,m 1 and periods between 30…100 days are superimposed. Subgroup: Hot RCB stars [91P4] (1) Their visual light curves display RCB-like variations. (2) Their photospheres appear extremely H-deficient, and have Teff > 9000 K, comparable to the hydrogen-deficient He stars. (3) They have infrared excesses indicating the presence of circumstellar material. Examples: MV Sgr, V348 Sgr, DY Cen The group is possibly connected with the hotter group of PVTEL variables (subsect. 5.1.2.10). Monographs [86Q, 87J], catalogues [90L1;90M1 – 40 objects and 15 finding charts]. Visual light curves of R CrB from 1843 to 1990 are given in [91A]. Photometry: Long-term photometry, spectroscopic characteristics of RCB and related cool HdC stars (showing similar pulsations, but no fadings) are given in [90L1]. Optical spectroscopy: [90L1]. UV spectroscopy: [88H2]. Luminosity: Mbol ≈ – 5, M/L-ratio: ≈ 104. Effective temperatures: [90G2]. Atmospheric and abundance analysis: [94P1].


Ref. p. 193]


187

Table 35. Properties of selected R CRB stars [90G2, 90L1, 91P4]. Object

DY Cen* W Men R CrB UW Cen RY Sgr

V [mag] 12.78 13.8 5.83 9.11 6.40

(B–V)0 [mag]

Teff [K]

P [d]

0.35 0.6 0.6 0.6

8120, 14000** 3.8…5.5 6900 175.4, 36.9 6000 45 5950 42.8 5170 37.74, 55.25

R/R

Mbol [mag]

> 25 61

– 5.6 – 4.86

*) Hot RCB star [91P4]. **) Values from two sources. Theories: (1) Evolutionary tracks [87W1]: RCB stars evolve on a nuclear timescale from the red giant region towards higher effective temperatures. Homogeneous models with a mass range of 0.85 ≤ / ≤ 0.90 cross the RCB region in the HRD. Only about 104 years are spend in this upper horizontal part. Inhomogeneous models (merging of a He and a CO white dwarf) are also possible. (2) Pulsations [87W2, 88S2, 90G1]: The above models are unstable against linear nonadiabatic pulsations. The so-called "f-mode" (for a discussion see subsect. 5.1.2) is instable for most models. The blue edge of the instability strip lies at ≥ 10000 K. The periods of the "f-modes" of different models lie between 400 d for Teff = 5000 K and 10 d for Teff = 10000 K. The period decrease of the pulsations of RY Sgr of dP/dn = –1.4·10–3 per cycle is reproduced in model calculations of ≈ 7000 K RCB-stars evolving towards higher temperatures. (3) Light fadings [88F, 90P]: Models with expanding "flat" or "spherical" graphite dust clouds (exp ≈ 30 km s–1) were shown to represent the observations well. A cloud with 1.5·1022 g can cause a fading of about 5m. Further models with conical ejection and detailed dust condensation models are available, yielding masses of the "puffs" between 3·10–9 and 8·10–8. A synthetic light curve of the events of the last 140 years is presented in [94P2].

5.1.5.6 RS Canum Venaticorum stars – RS RS CVn stars are close binary systems with Ca II H and K emission. The enhanced chromospheric activity is linked to quasiperiodic light variability. Periods are close to the orbital period, and the amplitude is typically 0.,m 2 in V. They can also be counted among the rotating variables, and depending on inclination, they may also be eclipsing systems. The original definition of Hall [76H] assumes a main sequence or subgiant primary of spectral type F to G and an evolved secondary, usually an early K subgiant. Monograph [87J], review articles [92R1, 93E], catalogues [88S1, 92L, 93S2]. See also subsect. 6.1.2.8. Photometric effects caused by stellar magnetic activity, generally a "photometric wave'' which is superimposed on the eclipsing binary light curve, which takes several years to travel across all phases. The migration rate is slowest for the short-period systems, because tidal interaction has led to a higher degree of synchronisation of orbital and rotation periods [81R]. Landolt-Börnstein New Series VI/3b

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Light curves: [92R2]. Periods, determination and changes: [90N]. UV spectroscopy: [94L]. Quiescent X-ray fluxes: [93D1]. Line profiles of Ca II H+K and Hα: [94F]. Kinematics and age: [92E]. Modelling of coronae and chromospheres of RS CVn systems: [90L2]. See also Table 15 in subsect. 5.1.3.6 (BY Dra stars). X-ray observations in different wavelength bands point towards two-temperature-structure: T = 2·106 K and 1.6·107 K [88P1, 93D2].

5.1.5.7 UV Ceti stars (flare stars) – UV UV Cet stars are eruptive variables, dwarf stars of spectral type K or M with Balmer emission lines. They show sudden flares with amplitudes in the range between several 0.,m1 to 6m in V (larger in ultraviolet). The rise to maximum occurs in a fraction of a minute, the decline to minimum takes several minutes and can last up to an hour. Subgroup: UVN Eruptive Orion variables of spectral type K or M with Balmer emission lines. These stars are associated with diffuse or gaseous nebulae, and, compared to UV stars, they are characterized by earlier spectral types, larger luminosity and slower development of flares. The UVN stars are a possible subgroup of the INB variables (subsect. 5.1.5.8; irregular variations superimposed by flares). Monographs [86M, 86R, 91P1, 87J], review articles [84M, 89P, 90M3, 91H], proceedings [90M2, 95G]. Catalogues of flare stars in special regions: Solar neighborhood: [91P2: 88 + 21 objects; 92L: 133 objects]; Pleiades [82H]; Orion [91N; 491 objects]; Cygnus [90T; 96 objects]


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189

Table 36. Relative number of flare stars in the Orion Nebula region, the Pleiades and in the solar vicinity [89M]. Mpg

Fraction of stars

interval

Orion

Pleiades

Field

0.03 0.09 0.18 0.76 ? ? ? ?

0.41 0.67 0.63 0.79 ?

0.02 0.03 0.05 0.15 0.42

4.5 … 5.5 5.5 … 6.5 6.5 … 7.5 7.5 … 8.5 8.5 … 9.5 9.5 …10.5 10.5 …11.5 11.5 and fainter

Table 37. Flare star properties [92L].

Luminosity L/L

2500…4500 0.0003…0.1

Radius R/R

0.13…0.80

Mass/

0.06…0.80

Effective temperature Teff

Age Flare luminosity Lf(U) Flare energy Ef

[K]

[years] [W] [J]

108…109 1025…1022 1020…1028

Table 38. Typical parameters of stellar flares from broadband photometry [86R]. Rise time Rise time/decay time ratio log (peak power Lp) log (average power L ) log (total energy E) log ( L /Lquiet star) Mean colours at maximum: U–B B–V Time distribution

[min] Lp in [W] L in [W] E in [J]

[mag] [mag]

0.1…10 1…0.01 19.5…24.5 (B) 18.5…21.0 (B) 20.5…26.8 (B) –1.9…–3.4

*) 20.0…35.0 (U) 18.8…21.3 (U) 20.6…27.0 (U)

*) *)

+ 0.3 ± 0.4 – 0.9 ± 0.3 Poisson-type with strong deviation within ∆t < 10 min

*) Systematically larger values for more luminous stars. Spectra: Nearby flare stars (samples are shown in [91P2]) are mostly of types dKe and dMe. Activity seems to cease with age, but examples of M-type flare stars with halo characteristics are known. Chromospheric emission: H I Balmer lines, Ca II H+K, Mg II hk prominent, well above the continuum, weak emission cores on Na I D doublet and Ca II IR triplet.


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[Ref. p. 193

Spectroscopy of Orion flare stars: Outburst [88C2]: spectral behaviour is similar to strong outbursts of dMe flare stars of the solar neighbourhood. Minimum [91C]: Ca II H and K and Balmer emission; weak-line T Tau stars. Binarity [91P2]: Many flare stars in the solar neighbourhood are members of spectroscopic binaries with periods of a few days. Magnetic fields [91P2]: B = 2.5…5.2 kG.

5.1.5.8 FU Orionis variables – FU The so-called fuors are characterized by a brightness increase of about 6m in several months. After this, the brightness remains constant for decades, or a slow decline by 1…2m sets in. Spectral types at maximum range from Ae to Gpe (with Hα emission). After outburst, an emission spectrum gradually develops, and the underlying absorption spectrum changes to a later spectral type. The fuors are probably one of the evolutionary stages of the Orion variables of T Tauri type (subsect. 5.1.5.9). All presently known fuors are coupled with cometary reflection nebulae. Monograph [87J], review articles [89H1, 90R], catalogue [89H1]. Herbig [89H1] proposes a subgroup, the exors (named after the prototype EX Lupi), which mimic the fuors at a smaller scale, showing sudden flareups at irregular intervals. The average properties of both groups are indicated in Table 39. Table 39. Properties of fuors and exors. Type

No. of observed outbursts

Amplitude [mag]

Rise time [d]

Duration of max. [d]

Spectrum at max.

fuor exor

one several

4…6 3.5…5

120…3500 80…700

? 150…1800

F-G supergiant T-Tau

Models [90R]: Accretion disc model for fuors; initial trigger of outburst poses problems. See also section 5.3.6.

5.1.5.9 Irregular variables – I If no additional designation is available, the irregular variables belong to the poorly studied group of variables with unknown light curve characteristics or spectral types. The classification has not changed since 1982. Literature on photometric properties of I stars is scarce. Light and colour curves of Is stars which exhibit sudden light fadings ("antiflares'') are shown in [91K] and their position in the HRD – up to 2m above the main sequence – is shown in [91P3]. Evidence for rotational modulation in T Tauri stars has been given, e.g. in [86V]. Sample UBV light curves of the INT stars DF Tau and T Tau are shown in [82Z]. Colour characteristics of irregular variables of all types, including T Tau stars, show a nonmonotonic dependence between brightness V and colour indices (B–V) and (U–B): Stars are blue at maximum and minimum, and redder at intermediate magnitude [86Z]. A detailed discussion of pre-main sequence stars and the properties of


Ref. p. 193]


191

T Tau stars is given in subsect. 5.3.4.2, while the groupings of photometrically and spectroscopically identified young stars is given in LB VI/2b subsect. 6.2.3.3. Catalogue containing UBV, spectroscopic (emission line strengths, radial and rotational velocities) as well as bibliographic information: [88H1]. T Tau stars: Results of UBVRI photometry: [92C, 94H]; UBVRIJHKL and uby photometry: [93G]. Herbig Ae/Be stars: UBVR photometry: [93S1, 94H]. The following subtypes are in use: (1) IA Irregular variables of early spectral types. Poorly studied irregular variables of early spectral type (O to A). (2) IB Irregular variables of intermediate and late spectral types. Poorly studied irregular variables of intermediate (F to G) or late (K to M) spectral type. (3) IS Rapid irregular variables, having no connection with diffuse nebulae, which show light changes by 0.,m 5…1.,m 0 during several hours or days. There is no strict boundary between rapid irregular and Orion variables. Subgroups: ISA Rapid irregular variables of early spectral type (O to A). ISB Rapid irregular variables of intermediate (F to G) or late (K to M) spectral type. (4) IN Orion variables (irregular variables associated with diffuse nebulosity). These eruptive variables are connected with bright or dark diffuse nebulae or are found in the vicinity of such nebulae. Some may show cyclic light variations due to axial rotation. The Orion variables are stars that evolve towards the main sequence (in the HR diagram, they populate the region between the main sequence and the subgiants). The brightness variations may reach several magnitudes. For a number of variables in the Orion Nebula region, periodic light variations due to rotation were discovered, with a bimodal period distribution with maxima at 2.2 and 8.5 days [92A]. Subgroups: INS If rapid light changes (up to 1m in 1…10 days) occur, the letter S is added. INA Orion variables of early spectral types (B to A, Ae), which are characterized by occasional Algollike fadings. If rapid brightness oscillations are present, a variable is classified as INSA. INB Orion variables of intermediate or late spectral types (F to M), with or without emission lines. F-type stars may show Algol-like fadings similar to those in INA stars, K to M stars may show flares (similar to those in UVN stars, subsect. 5.1.5.6) along with irregular light variations. If rapid brightness oscillations are present, a variable is classified as INSB.


192


[Ref. p. 193

INT – T Tauri stars. These variables are usually found in diffuse nebulae. The class is assigned because of the following (spectroscopic) criteria: spectral types Fe to Me, presence of emission lines of Fe I 404.6, 412.3 nm, emission lines of [SII] and [OI], and an absorption line Li I 670.7 nm. If the variable is not connected with a nebula, the letter N is dropped. An overview of T Tau star variability is given in [89K, 93B]. T Tau stars are catalogued in [92L]. IN(YY) Some of the Orion variables show the presence of an absorption component on the long-wavelength side of the emission lines in their spectra (matter infall). Prototype: YY Ori. Based on spectroscopic and photometric evidence, the following classification of T Tauri stars is presently in use: CTTS (classical T Tauri stars) – pre-main sequence stars, having enhanced magnetic activity and being surrounded by discs from which they accrete matter. Spectral types are K1 and later, the equivalent width of the Hα emission line is > 1 nm. WTTS (weak T Tauri stars) – pre-main sequence stars, having enhanced magnetic activity without active accretion discs. Spectral types are K1 and later, the equivalent width of the Hα emission line is < 1 nm. ETTS (early-type T Tauri stars) – pre-main sequence stars with light variations whose cause is still unclear. Spectral types range from A0…K0. An overlapping class of objects are the Herbig Ae/Be stars – pre-main sequence stars of spectral types B, A (and sometimes F). Long-term photometry of Herbig Ae/Be stars leads to a classification into three groups [93S1]: P0: long-term periodic phenomena with periods of more than 1 year and amplitudes of 0.,m 4…4.,m 0 in V. P1: middle-scale quasicyclic variability with periods less than 10 days and amplitudes of 0.,m 05…0.,m 5 in V. P2: short-period and quasicyclic variability with periods less than 10 days and amplitudes of 0.,m 05…0.,m 5 in V. The brightness variations are interpreted by Keplerian rotation of various mass concentrations in accretion discs and similar structures. Long-term photometry of the three groups of T Tauri stars also leads to a classification into three types of variability, caused by different mechanisms [94H]: Type I: Variability through cool spots. This is seen most clearly in WTTS, but is also present in some CTTS and ETTS. Cyclic variations, typically a few tenths of a magnitude in V with periods of 0.5 to at least 18 days are present. Light curve shapes can change on timescales of weeks, periods can be stable over months and years. The V, R and I light curves are similar in phase and shape; stars redden as they fade. The brightness variations are caused by rotational modulation of a cool spotted star. In B and U, more random scatter is observed, which is probably caused by flare activity. Type II: Changes in veiling continuum (variable accretion). This is seen in CTTS; it is rare or absent in WTTS and ETTS. Irregular variations on timescales of hours or more are typically less than lm in V. The V, R and I light curves are correlated, stars redden as they fade. More random scatter is observed in B and U, where the amplitudes can be up to 3.,m 8. The brightness variations are caused by variations in mass accretion rate; the rotation of the star causes changing patterns of hot spots on its surface (typically T = 10000 K and areas of up to 3% of the stellar surface). Landolt-Börnstein New Series VI/3b


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Type III: Unknown origin, probably variable circumstellar obscuration. This is seen in ETTS. Generally irregular variations of timescales of days or weeks. Aperiodic minima tend to be asymmetric with faster decline and slower recovery. Changes with timescales of years in mean light level are seen in at least one case. The V, R and I light curves are correlated; stars redden as they fade. During deep minima, they show colour reversals (become blue as they fade). The Hα equivalent width increases, shell lines may strengthen, photospheric spectra remain unchanged. The degree of linear polarisation is anti-correlated with brightness.

References for 5.1.5 76H 81R 82H 82Z 83C 84M 86B 86J 86M 86Q 86R 86V 86Z 87A1 87A2 87J 87L1 87L2 87L3 87O 87P 87S1 87S2 87V1 87V2 87W1 87W2 88C1

88C2 88F 88H1

Hall, D.S., in: Multiple Periodic Variable Stars, IAU Coll. 29 (W. Fitch, ed.), Dordrecht: Reidel (1976) p. 287. Rodonò, M., in: Photometric and Spectroscopic Binary Systems (E.B. Carling, Z. Kopal, eds.), Dordrecht: Reidel (1981) p. 285. Haro, G., Chavira, E., Gonzales, G.: Bol. Inst. Tonantzintla 3 (1982) No. 1, p. 3. Zajtseva, G.V.: Tr. Astron. Inst. Sternberg 52 (1982) 45. Cox, A.N., in: Astrophysical Processes in Upper Main Sequence Stars (B. Hauck, A. Maeder, eds.), Sauverny: Geneva Obs. (1983) p. 1. Mirzoyan, L.V.: Vistas Astron. 27 (1984) 77. Balona, L.A., Engelbrecht, C.A.: Mon. Not. R. Astron. Soc. 219 (1986) 131. Johnson, H.R., Querci, F. (eds.): The M-type Stars, NASA SP-492, Paris/Washington: CNRS/NASA (1986). Mullan, D.J.: p. 455 in [86J]. Querci, F.: p. 1 , as well as Querci, M., p. 113, in [86J]. Rodonò, M.: p. 409 in [86J]. Vrba, F.J., Rydgren, A.E., Chugainov, P.F., Shakovskaya, N.I., Zak, D.S.: Astrophys. J. 306 (1986) 199. Zaitseva, G.V.: Astrophys. 25 (1986) 626. Abbott, D.C., Conti, P.S.: Annu. Rev. Astron. Astrophys. 25 (1987) 113. Appenzeller, I.: p. 55 in [87L1]. Jaschek, C., Jaschek, M.: The Classification of Stars, Cambridge: Cambridge University Press (1987). Lamers, H.J.G.L.M., De Loore, C.W.H. (eds.): Instabilities in Luminous Early Type Stars, Dordrecht: Reidel (1987). Lamers, H.J.G.L.M.: p. 99 in [87L1]. Lamontagne, R., Moffat, A.F.J.: Astron. J. 94 (1987) 1008. Osaki, Y.: p. 39 in [87L1]. Percy, J.R.: p. 49 in [87S1]. Sletteback, A., Snow, T.P. (eds.): Physics of Be Stars, IAU Coll. 92, Cambridge: Cambridge University Press (1987). Stagg, C.: Mon. Not. R. Astron. Soc. 227 (1987) 213. van Genderen, A.M., van der Hucht, K.A., Steemers, W.J.G.: Astron. Astrophys. 185 (1987) 131. Vreux, J.M.: p. 81 in [87L1]. Weiss, A.: Astron. Astrophys. 185 (1987) 165. Weiss, A.: Astron. Astrophys. 185 (1987) 178. Coyne, G.V., Magalhaes, A.M., Moffat, A.F.J., Schulte-Ladbeck, R.E., Tapia, S., Wickramasinghe, D.T. (eds.): Polarized Radiation of Circumstellar Origin, Vatican City State: Vatican Observatory (1988). Carter, B.D., O'Mara, B.J., Ross, J.E.: Mon. Not. R. Astron. Soc. 231 (1988) 49. Fadeyev, Yu. A.: Mon. Not. R. Astron. Soc. 233 (1988) 65. Herbig, G.H., Bell, K.R.: Lick Obs. Bull. 1111 (1988).


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88H2 Holm, A.V., Doherty, L.R.: Astrophys. J. 328 (1988) 726. 88M Moffat, A.F.J.: p. 607 in [88C1]. 88P1 Pasquini, L., Schmitt, J.H.M.M., Pallavicini, R., in: Activity in Cool Star Envelopes (O. Havnes et al., eds.), Dordrecht: Kluwer (1988) p. 241. 88P2 Piirola, V., Linnaluoto, S.: p. 655 in [88C1]. 88S1 Strassmeier, K.G., Hall, D.S., Zeilik, M., Nelson, E., Eker, Z., Fekel, F.C.: Astron. Astrophys. Suppl. 72 (1988) 291. 88S2 Saio, H., Jeffery, C.S.: Astrophys. J. 328 (1988) 714. 88S3 Smith, M.A., in: Pulsation and Mass Loss in Stars (R. Stalio, L.A. Willson, eds.), Dordrecht: Kluwer (1988) p. 251. 88V van Vuuren, G.W., Balona, L.A., Marang, F.: Mon. Not. R. Astron. Soc. 234 (1988) 373. 89C Cuypers, J., Balona, L.A., Marang, F.: Astron. Astrophys. Suppl. 81 (1989) 151. 89D Davidson, K., Moffat, A.F.J., Lamers, H.J.G.L.M. (eds.): Physics of Luminous Blue Variables, IAU Coll. 113, Dordrecht: Kluwer (1989). 89G Garmany, C.D., Fitzpatrick, E.L.: p. 83 in [89D]. 89H1 Herbig, G.H., in: Low Mass Star Formation and Pre-Main Sequence Objects (B. Reipurth, ed.), ESO Conf. Workshop Proc. No. 33, Garching: ESO (1989) p. 233. 89H2 Humphreys, R.M.: p. 3 in [89D]. 89K Kuhi, L.V., Cram, L.E., in: FGK Stars and T Tauri Stars (L.E. Cram, L.V. Kuhi, eds.), NASA SP-502, Paris/Washington: CNRS/NASA (1989) p. 99. 89M Mirzoyan, L.V., Ambaryan, V.V., Garibdzhanyan, A.T., Mirzoyan, A.L.: Astrophys. 31 (1989) 567. 89P Patterson, B.R.: Solar Phys. 121 (1989) 299. 90B1 Balona, L.A., in: Confrontation between Stellar Pulsation and Evolution (C. Cacciari, G. Clementini, eds.), Astron. Soc. Pacific Conf. Ser. 11 (1990) p. 245. 90B2 Balona, L.A., Cuypers, J.,in: Angular Momentum and Mass Loss for Hot Stars (L.A. Willson, R. Stalio, eds.), Dordrecht: Kluwer (1990) p. 181. 90G1 Gautschy, A., Glatzel, W.: Mon. Not. R. Astron. Soc. 245 (1990) 597. 90G2 Goldsmith, M.J., Evans, A., Albinson, J.S., Bode, M.F.: Mon. Not. R. Astron. Soc. 245 (1990) 119. 90L1 Lawson, W.A., Cottrell, P.L., Kilmartin, P.M., Gilmore, A.C.: Mon. Not. R. Astron. Soc. 247 (1990) 91. 90L2 Linsky, J.L., in: Active Close Binaries (C. Ibanoglu, ed.), Dordrecht: Kluwer (1990) p. 757. 90M1 Milone, L.A.: Astrophys. Space Sci. 172 (1990) 263. 90M2 Mirzoyan, L.V., Pettersen, B.R., Tsvetkov, M.K. (eds.): Flare Stars in Star Clusters, Associations and the Solar Vicinity, IAU Symp. 137, Dordrecht: Kluwer (1990). 90M3 Mirzoyan, L.V.: p. 1 in [90M2]. 90N Nelson, E.R., Zeilik, M.: Astrophys. J. 349 (1990) 163. 90P Pugach, A.F.: Sov. Astron. 34 (1990) 646. 90R Reipurth, B.: p. 229 in [90M2]. 90T Tsvetkov, M.K., Tsvetkova, K.P.: p. 105 in [90M2]. 91A American Association of Variable Star Observers: R Coronae Borealis Light Curves 18431990, AAVSO Monogr. 4 (1990), Cambridge/MA: AAVSO. 91C Carter, B.D., O'Mara, B.J.: Mon. Not. R. Astron. Soc. 253 (1991) 47. 91H Haisch, B., Strong, K.T., Rodonò, M.: Annu. Rev. Astron. Astrophys. 29 (1991) 275. 91K Koval'chuk, G.U., Pugach, A.F.: Kin. Fis. Neb. Tel 7, No. 2 (1991) 33. 91N Natsvlishvili, R.S.: Astrofizika 34 (1991) 107 (not available in Astrophys. 34). 91P1 Pettersen, B.R.: Mem. Soc. Astron. Ital. 62 (1991) No. 2. 91P2 Pettersen, B.R.: p. 217 in [91P1]. 91P3 Pugach, A.F., Koval'chuk, G.U.: Kin. Fis. Neb. Tel 7, No. 2 (1991) 43. 91P4 Pollacco, D.L., Hill, P.W.: Mon. Not. R. Astron. Soc. 248 (1991) 572. 92A Attridge, J.M., Herbst, W.: Astrophys. J. 398 (1992) L61. 92B Balona, L.A., Cuypers, J., Marang, F.: Astron. Astrophys. Suppl. 92 (1992) 533.


5.1.5 Variable stars: Eruptive variables 92C 92E 92L 92R1 92R2 93B 93D1 93D2 93E 93G 93S1 93S2 94F 94H 94L 94M 94P1 94P2 95G

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Covino, E., Terranegra, L., Franchini, M., Chavarría-K., C., Stalio, R.: Astron. Astrophys. Suppl. 94 (1992) 273. Eker, Z.: Astrophys. J. Suppl. 79 (1992) 481. Lang, K.L.: Astrophysical Data − Planets and Stars, Berlin: Springer (1992). Rodonò, M., in: Evolutionary Processes in Interacting Binary Stars, IAU Symp. 151 (Y. Kondo, R.F. Sistero, R.S. Polidan, eds.), Dordrecht: Kluwer (1992) p. 71. Rodonò, M., Cutispoto, G.: Astron. Astrophys. Suppl. 95 (1992) 55. Bouvier, J., Cabrit, S., Fernández, M., Martin, E.L., Matthews, J.M.: Astron. Astrophys. 272 (1993) 176. Dempsey, R.C., Linsky, J.L., Fleming, T.A., Schmitt, J.H.M.M.: Astrophys. J. Suppl. 86 (1993) 599. Dempsey, R.C., Linsky, J.L., Schmitt, J.H.M.M., Fleming, T.A.: Astrophys. J. 413 (1993) 333. Elias II, N.M., Mutel, R.L., in: The Realm of Interacting Binary Stars (J. Sahade, G.E. McCluskey, Y. Kondo, eds.), Dordrecht: Kluwer (1993) p. 335. Gahm, G.F., Gullbring, E., Fischerström, C., Lindroos, K.P., Lodén, K.: Astron. Astrophys. Suppl. 100 (1993) 371. Chevchenko, V.S., Grankin, K.N., Ibragimov, M.A., Melnikov, S.Yu., Yakubov, S.D.: Astrophys. Space. Sci. 202 (1993) 121 and 202. Strassmeier, K.G., Hall, D.S., Fekel, F.C., Scheck, M.: Astron. Astrophys. Suppl. 100 (1993) 173. Fernández-Figueroa, M.J., Montes, D., De Castro, E., Cornide, M.: Astrophys. J. Suppl. 90 (1994) 433. Herbst, W., Herbst, D.K., Grossman, E.J., Weinstein, D.: Astron. J. 108 (1994) 1906. La Dous, C., Giménez, A.: Chromospherically Active Binary Stars, IUE-ULDA Access Guide No. 5, ESA SP-1181 (1994). Mennickent, R.E., Vogt, N., Sterken, C.: Astron. Astrophys. Suppl. 108 (1994) 237. Pollard, K.R., Cottrell, P.L., Lawson, W.A.: Mon. Not. R. Astron. Soc. 268 (1994) 544. Pugach, A.F., Koval'chuk, G.U.: Astron. Reports 38 (1994) 219 = Astron. Zh. 71 (1994) 250. Greiner, J., Duerbeck, H.W., Gershberg, R.E. (eds.): Flares and Flashes, IAU Coll. 151, Berlin: Springer (1995).

Acknowledgement We thank Drs. D. Baade and C. Mendes de Oliveira (European Southern Observatory), and W. Gieren and N. Vogt (P. Universidad Catolica de Chile) for useful comments. H.W.D. acknowledges financial support from the Deutscher Akademischer Austausch-Dienst (Bonn-Bad Godesberg) and the hospitality of the Grupo de Astrofísica of the P. Universidad Catolica de Chile, Santiago, where the manuscript was brought into its final form.


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5.3 Protostars, pre-main sequenceobjects

[Ref. p. 200

5.3 Protostars, pre-main sequenceobjects The basic concepts of star formation theory and of the early evolution of stars as outlined in Landolt-Bornstein Volume VI/2b are still valid today. However, much new observational data gathered since 1981 and more sophisticated numerical modelling have resulted in a wealth of new information and in more reliable conclusions concerning all details. The aim of this section of LB VU3b is, therefore, to update and supplement the information given in Section 5.3 of LB VI/2b with the new results obtained during the past decade. In view of the large amount of new data, it would not have been practicable to list all these new results in detail. Hence, for each topic the new information is summarized qualitatively and references to tables, catalogs, and reviews containing the detailed data are given. In order to facilitate the joint use of LB VIRb and LB VI/3b, the notations, designations, and order of the subsections introduced in LB VI/2b are retained throughout this section.

5.3.1

Definitions

Most of the definitions and notations listed in Volume VI/2b are still in use. An exception is the empirical definition of the T Tauri Stars, which has been modified by Bastian et al. [83B]. According to the more precise (and by now widely accepted) definition of these authors, T Tauri stars (TTSs) are: “Stellar objects associatedwith a region of obscuration; in their spectrum they exhibit Balmer lines of hydrogen and the Ca II H and K lines in emission, the equivalent width W of Ha being at least 5A. There is no supergiant or early-type (earlier than late F) photospheric absorption spectrum.” Objects in star formation regions that fit the above definition qualitatively, but that have W (Hrx) 0.1 pc. Typical molecular shell massesseemto be of the order of 0.1 M,. Examples of molecular PN maps include NGC 6853. 6720,2346 [88Z], Rodriguez [89IAU#131] p. 129. Dust is often concentrated in the outer regions of a PN but is also known to coexist with H+, M. J. Barlow [93IAU#155] p. 163. Much effort has been made in trying to identify dust-emission features, seeRoche [89IAU# 13l] p. 117. Silicate dust indicates an oxygen-rich progenitor AGB star, while carbon grains form in envelopes of carbon stars. However, some PN show both O-rich and C-rich dust features [9OZ].

5.4.8

Morphologies and structures of planetary nebulae

The beautiful appearance of many PN has inspired numerous studies of their structures. Complicated shapes appear, yet PN often display notable symmetries. We try to understand these features in terms of post-AGB stellar evolution. The ejected envelope is rarely a homogeneous shell of uniform density. Its properties depend on latitude in a spherical coordinate system in the sense that a shell is thicker in the equatorial zone than at the poles. Furthermore, it is often lumpy. The slowly moving main massof the ejectedenvelope is eventually subjectedto a rapidly moving fast wind. Land&-Bhstein New Series V1/3b

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5.4 Planetary nebulae

[Ref. p. 215

See[87Bl] for a discussion of how the regular structures of many PN can be explained. Forms and kinematics of bipolar and butterfly nebulae are of special interest, both observationally and theoretically [88W, 8911,[90M2] p. 520; Schwarz [93S] p. 223. On possible relationships between nebular morphology and binarity, [86Z, 90B], and also subsect. 5.4.14. Many nebulae are double- or even multiple-shell structures. Some, such as NGC 1535 or NGC 7009, have prominent outer shells; others, such as NGC 6543 and NGC 6853, display faint outer haloes [74K], Chu [89IAU#131] p. 105, [92B, 93P2]. Nebular kinematical properties are also important and must be considered in the construction of PN models: [84Sl, 84821,R. Weinberger [89IAU#l31] p. 93. High-velocity knots and filaments are sometimesfound [93B]. Abel1 78 shows a distinctive nonisotropic ejection pattern [89P]. With CCD detectors and narrow band-pass filters, one can obtain monochromatic images in the diagnostic lines [011], [0111] 5007,4363, [NII] 6584, 5755, [SII] 6717, and 6730 to assessspatial variations of temperature and electron density throughout the nebula, topics which have been reviewed in [89R, 9OPl].

5.4.9

Theoretical models of nebular structure and evolution

Evolutionary models for spherically symmetrical PN are given in [87S, 89B3, 89S]. Most PN are aspherical in shape, however. It appears possible to model most of them with a generalized interacting stellar wind model [87Bl, 89Z, 9211.Seesubsect. 5.4.14. Static theoretical models intended to represent specific PN are used to predict line intensities for comparison with observations. By this means, we may deduce plasma diagnostics and chemical compositions [82H, 87C2, 94H]. Irregularities such as filaments and “condensations” are difficult to handle. Furthermore, a static nebular model may not accurately depict an evolving PN [79T].

5.4.10

Classifications of planetary nebulae

M. Peimbert [78P] proposed a classification schemeinvolving 4 types: type I (He-, N-rich progenitor star, mass up to 8 M,; type II (disk population); type III (high velocity); and type IV (halo population). In recent usage,type I is most often cited.

5.4.11

Chemical compositions of planetary nebulae

The enhancements or depletions of He, C, N, and 0 give clues to the nuclear processesin the late stagesof evolution of the progenitor stars. Other elements, such as Ne, Cl, and Ar, reveal the chemical composition of the interstellar medium at the time and formation locale of the progenitor star. Abundances of metals such as Ca and Fe reveal depletion due to grain formation. Along with novae, Wolf-Rayet stars, and supernovae (SN), PN act to modify the composition of the interstellar medium (ISM). The ISM enrichment per PN in units of 0.001 solar massesis estimatedatH(-13),He(+l3),C(+0.7?),N(+l.4),0(-4.2)[89A]. Abundance determinations are far more difficult for PN than for stars. Methods include theoretical models (seesubsect. 5.4.9), use of models to derive ionization correction factors (ICFs) [81S2, 87Al], measurement of fluxes at several points in an extended PN, and use of empirical ICFs [89B2, 91Bl]. For some metals, resonance absorption lines in PNN can be measured [84P2]. For reviews and summaries, [77T, 83A, 84A, 88G, 8902, 90A, 90H, 9OP1, 9lK4, 9lP2, 93A], R. Clegg Land&-BBmstein New Series VV3b

Ref. p. 2151


209

[89IAU#131] p.139, [93IAU#155] p. 549. Table 1 gives mean abundances for several types of planetary nebulae, including C-rich, N-rich, Peimberts types I and II+III, as well as for an extensive sample of many such objects. Numerous attempts have been made to establish correlations; He/H and N/O ratios, for example, are strongly correlated with the mass of the residual PNN core [9OK3, 91K2]. Studies of individual PN show striking results: Abel1 30 and Abel1 78, for example, show large chemical composition differences between H-depleted interior regions and outer strata [83J]. The abundance of C varies from highly C-depleted PN [87C3, 9OP2,90Ml] to C-rich objects [88K]. Table 2 gives logarithmic abundances on the scale log N(H)= 12.00 for several well-observed objects, including some examples of N-rich objects.

5.4.12

Magellanic Clouds and other galaxies

The Magellanic Clouds permit us to observe a large number of PN at virtually the same, rather well known distance, so that properties such as luminosities can be compared directly. Their remoteness does not permit us to study detailed structures, however. For surveys of this topic, see[78S, 8051; on photometry and dynamics, see[85D2, 88M2,90Ml]; for spectrophotometric surveys, see[88M3, 89B4,9 1M 11; for theoretical PN models, see[87A2,91D]; on abundance patterns for MCs and the galaxy, see[90H], R. Clegg [93IAU#l55] p.549. For other galaxies of the local group, see[78D, 80D, 83F, 84M, 86511. For a discussion of PN in galaxies beyond the local group, seeH. Ford et al. [89IAU#131] p.335, [89Jl, 8952,9OJ],Hui and Ford [93IAU#155] p.533.

5.4.13

The transitional stage, AGB to PN

The focus of much of present-day research on stellar evolution and PN is on the transition from a highly evolved AGB star to a PN, a process that may differ in detail from star to star. In any case,it is difficult to treat theoretically [831, 89L]. For most AGB stars destined to evolve into a PN, a dense C-O core is developed, although massive progenitors, 8 . . . 10 M,, may have C, Ne, Mg cores. Burning of H and He occurs in shells in a complicated scenario. In the most massive stars, C burning can also happen. Much of the time H burns quietly, but occasionally He flashes take place and C and s-type elements get dredged to the surface. Three types of dredge-up have been identified: [80Bl, 8 lR], I. Iben Jr. [93IAU#155] p.587, P. Lattanzio [93IAU#155] p. 235. As the star evolves, the outer envelope expands, pulsations can occur, and the star becomes a Mira variable. Solid grains form in the atmosphere. They are accelerated by radiation pressure and drag the gas along [91B3]. The mass loss rate increases;it may amount to 10m7to 10m4MO per year depending on the mass of the core. Wind velocities may exceed PN expansion velocities by two orders of magnitude, M. Perinotto [89IAU#131] p. 293. Eventually, the envelope becomes disconnected from the core and pulsations stop. There now exists an OH-IR star or its C-rich analogue. Sometimescircumstellar shells can emit a pseudo-supergiant spectrum with perhaps anomalous C, N abundances, and strong IR emission from dust. The superwind ceaseswhen the H mass falls below a critical value. What happens next can be quite complicated [841]. Finally, radiation from the core (now a PNN) dissociates molecules, heats and ionizes the gas, causing it to fluorescence. The AGB phase, lasting lo5 . . . lo6 years, depends on the core mass;the Mira phase lasts an order of 200 000 years; the OH/IR phase, about 50 000 years; and the proto - PN phase, about 10 000 years. Landok-Bhstein New Series VI13b

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5.4.14


[Ref. p. 215

Binary stars and planetary nebulae

A number of planetary nebular nuclei have close companions [9OB],H. Bond [89IAU#13 l] p. 251. A number of wide PNN binaries are also known, e.g. NGC 246. Axially symmetric PN may have or have had companions, often of low mass.Bipolar or “butterfly” PN may originate from systemswith relatively massivesecondaries,M. Livio [93IAU#155] p. 279. Accretion disks may also play a role.

5.4.15

Central stars of planetary nebulae (PNN)

From observed properties of Planetary Nebulae Nuclei (PNN), J. Kaler [89#IAU131] p. 229, we may trace the evolution of the hot core of a defunct star that eventually will become a white dwarf. The track depends on the core mass, M,,, usually 0.56Mo < M,,, < 1.22 Mo [91K2]. Theoretical tracks enable us to predict L, R, and thus L and T,, as a function of time: [71P, 81S1, 86w], D. Schonberner [93IAU#155] p. 415. For comparisons of observations with theory, seee.g. [87HI], S. Pottasch [89IAU#131] p. 481. We must find stellar luminosity, L*, and effective temperature, T,, Measured quantities include ‘Vmagnitude, colors, or flux distribution, and the nebular HP flux from which we may compute the UV stellar flux beyond the Lyman limit. To get the luminosity we must know the distance and bolometric correction, which depends on T,,. Uncertainty in distance provides difficulties. Since Zanstra’s pioneering work [27Z], variations on his methods and alternative techniques have been employed in studies of energy balance (Stoy method): [33S, 76K, 83P, 91Kl], relative ionic concentration: [80N, 87Al], near UV fluxes 120...300 nm: [90G], and model atmospheres (seesubsect.5.4.3, item 7). Extensive tables of Zanstra temperatures have been given in papers such as those cited above. Limitations on accuracy are imposed by effects of optical depth (the nebula may be optically thick in He11 but not in HI), by stellar winds, and by deviations of the stellar flux from that of a black body. Seee.g. [86H]. Earlier low-dispersion studies of the spectra of the central stars of planetary nebulae are summarized in [76AJ. On high dispersion, optical region, seee.g. [89IAU#131], p. 273. On high-dispersion UV spectroscopy, see[90F].

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5.4.16

211


Tables of some basic data

Table 1. Elemental abundances log N in different types of planetary nebulae We give logarithmic abundances on the scale log N(H) = 12.00. In the average planetary nebula, the O/H ratio is smaller than the solar value. Accordingly, we define N-rich as log N/O > - 0.2 and Crich as log C/O > 0.1. “Total” refers to the total sample. Note, however, that if T, fluctuations are significant, the abundances of C, N, 0, etc. will be increased by varying amounts depending on ((T,-F)*)lT* [67Pl, 85D1, 862, 93L2]. Types

He

C

N

0

Ne

S

Cl

Ar

Ref.

N-rich C-rich Total Type-I Types-II, III Solar

11.13 11.01 11.04 11.07 11.01 10.94

8.67 8.89 8.74 8.72 8.82 8.56

8.74 8.20 8.38 8.60 8.07 8.05

8.64 8.65 8.64 8.66 8.66 8.93

8.04 8.05 8.01 8.05 7.99 8.09

7.1 7.10 7.03

5.46 5.24 5.31

6.64 6.39 6.48

7.21

5.5

6.56

89A 89A 89A 9OPl 9OPl 89G

Table 2. Abundances log N in individual nebulae The abundances are all given on the scale log N(H) = 12.00. Nebula

He

C

N

0

Ne

S

Cl

Ar

Ref.

NGC 6302 “) NGC 6537 NGC 2440 NGC 6741 b, NGC 6853 Me 2-l NGC 7027 “)

11.26 11.27 11.04 11.04 11.04 11.01 11.00 11.04 11.02 11.03 11.03 10.97 10.99

8.00 7.6 8.58 9.08 8.88 8.80 8.93 8.78 9.10 8.90 8.62 8.79 8.34

8.92 8.95 8.82 8.70 8.48 8.21 8.26 8.18 8.27 8.18 7.90 7.78 7.63

8.70 8.23 8.7 8.73 8.92 8.73 8.66 8.49 8.69 8.70 8.30 8.56 8.51

7.99

6.80

5.59

6.63

8.02 8.20 8.43 8.17 7.95 7.99 8.07 8.08 7.70 7.85 7.89

6.6 7.0

5.2 5.39

7.13 7.00 6.85 6.95 7.20 6.45 7.18

5.29 5.45 5.28

6.6 6.6 6.52 6.41 6.40 6.30 6.45 6.30 6.00 6.78 6.08

81Al 85F 81S2 85C 84B1 81A2 93H 90K2 90M3 87C2 94H 82H 89B3

NGC 3918 d, IC 2165 “) NGC 7662 NGC 1535

“) Other elements:Na = 6.57, Si = 6.9, K= 5.32, Ca = 5.36. b, Other elements:Na = 6.5, Mg = 7.4, K = 4.6, Ca = 5.5. “) Otherelements:Na=6.48, Mg=7.45, Si=6.74,P=6.5, K=5.21, Ca=5.59. d, Other elements:Mg = 7.18, Si = 7.0, Fe = 5.57. ‘) Other elements:Si = 6.5, K = 4.8, Ca = 5.07.

Land&-Bhstein New Series V1/3b

4.95 6.26

212


[Ref. p. 215

Table 3. Properties of some individual planetary nebulae

(1) Listing: New General Catalogue (NGC), Index catalogue (IC) or discovery designation A = Abell, J = Jonckhere, Hu = Humason. (2) Ex = excitation class as defined in [56A] p. 66. (3) D”= angular diameter in arc set [92A, 67P2]. (4) F(H/I) = H/I flux in erg cm-’ s-i as received at the earth’s surface and corrected for atmospheric but not interstellar extinction [92Cl]. (5) N, = number of electrons/cm3 (6) t = T,/lOOO (7) Extinction factor C= log I(HP) lli(Hp), where Z(HP) is the HP flux as corrected for interstellar extinction and Ir(H/I) is the measured H/3 flux in col. (4). (8) d=distance in kiloparsecs: K denotes a value by Kudritzki’s method [891AU#131] p.273, M: from nebular modelling, E: distance from expansion rate of nebular shell; others are adopted from essentially [74C] or [88Ml]. For NGC 7009, E and K methods are very discordant: d = 2.5 kpc according to K. (9) I’= magnitude of PNN, mostly [85S]. (10) Spectral classesfrom [89IAU#131] p.273, [92A, 76A]. (11) T(PNN) in units of 1000K; K (Kudritzki), M (nebular models), other values are Stoy or Zanstra temperatures. (1) Nebula

(2) Ex

(3) D”

(4) (5) (6) -log F(H/?) log A’, t

(7) C

(8) (9) d[kpc] V

(10) sp.

NGC 40 IC 351 NGC 1535 J 320 IC 418 NGC2022 A 12 IC2165 NGC2392 NGC2440 NGC 3242 NGC4361 NGC 6543 NGC6572 NGC 6741 NGC 6826 IC 4997 “) NGC 7009 NGC7027 Hu 1-2 IC5217 NGC 7662

2 8 7 5 3 10

36 7 18 7 12 20 37 8 45 33 37 42 19 12 8 26 1.5 28 14 5 7 15

10.66 11.42 10.45 11.40 9.57 11.13 11.54 10.90 10.41 10.50 9.79 10.53 9.61 9.82 11.34 9.96 10.53 9.80 10.12 11.21 11.17 9.99

0.7 0.28 0.05 0.31 0.32 0.38 0.75 1.34 0.64 0.44 0.21 0.0 0.18 0.37 1.30 0.04 0.35 0.17 1.43 0.61 0.55 0.19

2.3 7 2.7K 9 l.OM 5.3 1.2 3.0 2.7K 2.3 2.OK 1.3 1.4 1.5E 1.6 2.4 2.4M? 0.5E l.lE 4.3 3.6 1.8

WC8 cant 03 em 07f cant

8 8 9 7 10 5 5 8 5 5 6 10 10 6 8

3.3 1.07 3.5 1.2 3.3 1.09 3.6 1.25 4.1 0.96 2.9 1.21 2.8 1.21 3.6 1.34 3.3 1.42 3.8 1.35 3.7 1.13 3.0 2.0 3.9 0.81 4.0 1.04 3.7 1.2 3.2 0.97 <notes> 3.7 1.4 4.5: 1.4: 3.9 1.8 3.6 1.1 3.5 1.3

11.8 14.77 12.2 14.44 10.17 14.9 19: 14.99 10.53 18.9 12.10 13.18 11.31 12.88 14.7 10.69 14.3 11.5 16.32 16.1 15.5 13.2

(11) T*[lOOOK]

cant 06f sd0 sd0 Of+ WR Of+ WR cant 04f Of+ WR cant cant cant? Of+ WR sd0

32 60 58K 70 29M 69 111 140M 47K 166M 68K 75 47 50M 157M 37 55M 75 160M 87 68 120M

“) IC 4997: Different diagnostic criteria suggestthat this PN consistsof a geometricallythin shell with log iV,= 7.0,surroundedby a muchthicker outer shellwith log N, = 4.

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213

Table 4. Principal or representative lines of elements in planetary nebulae. Wavelengths are in [A] unless otherwise indicated; forbidden lines are denoted by [. . .]. For these lines, N denotes a nebular-type transition, A an auroral-type transition, and TA a transauroral-type transition. Quasi-forbidden lines are denoted ...I. H Hz He1

He11

CI c II c III CIV NI

[N II

N II [N III N III N III] N III] N IV NV PO’11 0 II

P III

0 III

0 III] [O III] 0 IV P Iv] ov OVI F Iv] Ne II

INeIII

[Ne III] We Iv] W VI W Iv] WI

P&t II Land&Bb;mstein New Series VU3b

Lya, Balmer, and Paschenseries.Brackett /34.0512 pm, Bry 2.165 pm, Pfundcl (n = 6 to n = 5) 7.457 pm 2.12 pm {S(l) (l-0)); 2.42 pm {Q(3) (l-o)}; 2.41 pm {Q(l) (1-O)) 7065,4713, etc., 23P-33S,etc. 10830,3889, etc., 23S-23P, etc. 5015, 3965, etc., 2%3’P, etc. 5876,4471, etc., 23P-33D, etc. 6678,4922, etc., 2lP-3lD, etc. 5048,4427, etc., 2’P-4’S, etc. In the near IR: 2’S -2lP 2.058 pm and transitions of type: 3’S, ‘P, ‘D, 3P,3D -+ n’s, ‘P, ‘D, IF, 3S,3P,3D, 3F etc. Paschen4686, 3202, etc., (3-n), etc. Balmer a, 1640(2-3), 9345 (5-8), etc. 10124,6560, etc., (4-5) etc., 10420(6- 13) etc. 9850,9824 (N) 3919,3921,4267,2325,2328, 1335, 1336 4647,4650,5696,4187; C III, 1906, 1909,2297 5801,5812,4659, 1548, 1550 7442,7468 5198,520O(N) 3995,4982,4172,4181,4433,4530,4552,5667,5676,5680 6548,6583, (N), 5755 (A), 3063,307l (TA) 4097,4103,4634,4641,4642 (Bowen fluorescent cycle), 4379 1747, 1749, 1750,1752,1754 57.31 pm 1483,1487,1718 1239,1242 8446,7254,6046,7002, 1302, 1305, 1306 6300,6364 (N), 5577 (A), 63.2 pm 3882,4070,4072,4154,4304,4348,4367,4369,4661,4676 3726,3728, (N), 7319,7330, (A), 2470 (TA) 2808,2819,2836,3023, 3047,3122,3133,3299,3312,3341,3429,3444,3754,3757,3760, 5592 (Bowen fluorescent cycle) 1661,1666 4959,5007 (N), 4363 (A), 2321 (TA), 88.38 pm, 51.81 pm 1402, 1405, 1406,1410, 1413,3381,3385,3403 25.87 pm 1371,5112 1032, 1038 3962,3997 (N) 3335,3569,3694,3113,4392,4428,4182 12.8 pm 3869,3967 (N), 3342.5 (A), 1814 (TA) 4714,4716,4724,4726 (A), 2422,2424 (N), 1602 (TA) 3346,3426 (N), 1575 (TA), 24.25 pm 3242,3362 (N) 4571,2852 4562

214


[Ref. p. 215

Table 4. (cont.) 4481,2796,2804,2929 4.488 pm 2784,2929 (N), 5.608 pm

Mg II CMg Iv] Pk Yl Si II Si III Si IV [Si VI] [Si VII]

3856,3862,5041,5056,6347,5979,6371,2334,2350 1883,1892 1394,1403 1.963 pm 2.486 pm

[P 113

11883 (N), 7876 (A), 4669 (TA)

[SII ts III

7726 (A) 6716,673l (N), 4069,4076 (TA), 10287,10320,10336,10371 9069,953l (N), 6312 (A), 18.7 pm 10.52 pm

[S III] 1s Iv] [Cl II] [Cl III] [Cl IV [Ar II] [Ar III] [Ar Iv] [Ar VI [Ar VI] CK IYI [KYI

(A)

8579,9124 N 5518,5538 (N), 8434,550O (A), 3353 (TA) 7503,8046 (N), 5323 (A) 6.98 pm 7136,775l (N), 5192 (A), 3109 (TA), 8.99 pm 4711,475O (N), 7171,7267,7263 (A), 2854,2869 (TA) 6435,7005 (N), 4625 (A), 2784,2692 (TA) 4.53 pm (detection ?) 6102 (N) 4122,4163 (N) 5604,6228 (N)

[K VII 0 VI tMn VI

6166,6219 (N)

[Fe II] [Fe III] Fe Yl [Fe VI] [Fe VII]

4244,4287,5159,5262,5334 4607,4658,4702,4881,5270,5412 3891,3896,4181,4227,4229 5146,5278,5335,5424,5427,5639,5677 3587,4893,4989,5159,5721,6087 (blend [Cay)

5309,6087 (N)

7378,7412, 6.64 pm [Ni II] mi 1111 7890

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215

References for 5.4 General References and Review Articles

For an overall account of PN see:Pottasch: Planetary Nebulae [84Pl] Progress reports are given in International Astronomical Union (IAU) Symposia, the two most recent of which are: [89IAU#13 l] Planetary Nebulae (S. Torres-Peimbert, ed.) IAU Symp, No. 131, Dordrecht: Kluwer Academic Publ. (1989). [93IAU#155] Planetary Nebulae (R. Weinberger and A. Acker, eds.) IAU Symp. No.155, Dordrecht: Kluwer Academic Publ. (1993). Somebrief summaries are: [85K, 89K2,9OPl, 94K]. Relationships between PN and late-stellar evolution stages have been discussed in several recent books and symposia, e.g. [90M2,91A, 93S].

Special References

272 28B 33s 35B 54M 56A 56s 62M 67Pl 67P2 71P 73L 74C 74K 76A 76K 77T 78D 78K 78L 78P 78s 79T 80Bl 80B2 80D 805 80N 80s 81Al

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87s Schmidt-Voigt, M., Koppen, J.: Astron. Astrophys. 174 (1987) 211. 872 Zeippen, C. J. et al.: Astron. Astrophys. 188 (1987) 251. 88C Clegg, R., Harrington, H.: Mon. Not. R. Astron. Sot. 239 (1988) 869. 88Dl Dinerstein, H. L. et al.: Astrophys. J. 327 (1988) L27. 88D2 Dopita, M. et al.: Astrophys. J. 327 (1988) 639. 88G Guiterrez-Moreno, A., Moreno, H.: Publ. Astron. Sot. Pacific 100 ( 1988) 1497. 88K Kaler, J.: Publ. Astron. Sot. Pacific 100 (1988) 620. 88L Likkel, L. et al.: Astron. Astrophys. 198 (1988) Ll. 88M1 Mallik, C., Peimbert, M.: Rev. Mex. Astron. Astrofis. 16 (1988) 111 88M2 Meatheringham, S. et al.: Astrophys. J. 327 (1988) 651. 88M3 Monk, D. et al.: Mon. Not. R. Astron. Sot. 234 (1988) 583. 88P Payne, H. et al.: Astrophys. J. 326 (1988) 368. 88V Viotti, R., Vittore, A., Freidjung, M. (eds.): Physics of Formation of Fe11 lines outside of LTE, Dordrecht: Reidel(l988). 88W Webster, B. L. et al.: Mon. Not. R. Astron. Sot. 235 (1988) 533. 882 Zuckerman, B., Gatley, I.: Astrophys. J. 324 (1988) 501. 89A Aller, L.: Am. Inst. Phys. Conf. Proc. 183 (1989) 224. 89Bl Bachiller, R. et al.: Astron. Astrophys. 210 (1989) 366. 89B2 Barker, T.: Astrophys. J. 340 (1989) 921. 89B3 Bobrowsky, M., Zipoy, D.: Astrophys. J. 347 (1989) 307. 89B4 Boroson, T., Liebert, J.: Astrophys. J. 339 (1989) 844. 89B5 Burke, V. et al.: Mon. Not. R. Astron. Sot. 236 (1989) 353. 89B6 Butler, K., Zeippen, C.: Astron. Astrophys. 208 (1989) 337. 89C Ciardullo, R. et al.: Astrophys. J. 344 (1989) 715. 89F Ford, H. et al. in: IAU Symp. No.131, (1989) 335. 89G Grevesse,N., Anders, E.: Am. Inst. Phys. Conf. Proc. 183 (1989) 1. 89H Huggins, R., Healy, A.: Astrophys. J. 346 (1989) 201. 891 Icke, V. et al.: Astron. J. 97 (1989) 462. 89Jl Jacoby, G.: Astrophys. J. 339 (1989) 39. 8952 Jacoby, G. et al.: Astrophys. J. 344 (1989) 704. 89Kl Kaler, J. B., Jacoby, G. H.: Astrophys. J. 345 (1989) 871. 89K2 Khromov, G.: SpaceScienceReview 51(1989) 339. 89L Lattanzio, J. C., in: Evolution of Peculiar Red Giants (H. R. Johnson, B. Zuckerman, eds.). Cambridge: Cambridge University Press(1989) p. 161. 89M Masson, C.: Astrophys. J. 336 (1989) 294. 8901 O’Dell, C., Opal, C.: Astrophys. J. 341 (1989) L79. 8902 Osterbrock, D. E.: Astrophysics of Gaseous Nebulae and Active Galactic Nuclei, University ScienceBooks, Mill Vally, CA. (1989). 89P Pismis, P.: Mon. Not. R. Astron. Sot. 237 (1989) 611. 89R Rubin, R.: Astrophys. J. Suppl. 69 (1989) 897. 89s Stasinska, S.: Astron. Astrophys. 213 (1989) 274. 89W Weinberger, R.: Astron. Astrophys. Suppl. 78 (1989) 301. 892 Zijlstra, A. et al.: Astron. Astrophys. 217 (1989) 157. 90A Aller, L. II.: Publ. Astron. Sot. Pacific 102 (1990) 1097. 90B Bond, H., Livio, M.: Astrophys. J. 355 (1990) 568. 90F Feibelman, W., Bruhweiler, F.: Astrophys. J. 357 (1990) 548. 90G Grewing, M., Neri, T.: Astron. Astrophys. 236 (1990) 223. 90H Henry, R. G. C.: Astrophys. J. 356 (1990) 229. 90J Jacoby, G. et al.: Astrophys. J. 356 (1990) 332. 90Kl Keenan, F. P., Aggarwal, K. M.: Astrophys. J. 350 (1990) 262. 90K2 Keyes, C. et al.: Publ. Astron. Sot. Pacific 102 (1990) 59. 90K3 Kaler, J. B., Jacoby, G. H.: Astrophys. J. 362 (1990) 491. Land&-B6rnstein New Series V1/3b

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90Ml Meatheringham, S. et al.: Astrophys. J. 361 (1990) 101. 90M2 Menessier, M. O., Omont, A. (ed.): From Miras to Planetary Nebulae, Montpelier: Edition Frontiers (1990). 90M3 Middlemass, D.: Mon. Not. R. Astron. Sot. 244 (1990) 294. 9OPl Peimbert, M.: Rep, Prog. Phys. 53 (1990) 1559. 9OP2 Pena, M. et al.: Astron. Astrophys. 237 (1990) 454. 90Z Zhang, C., Kwok, S.: Astron. Astrophys. 237 (1990) 479. 91A Aller, L. H.: Atoms, Stars, and Nebulae, Cambridge: Cambridge University Press(1991). 91Bl Barker, T.: Astrophys. J. 371 (1991) 217. 91B2 Berrington, K. A. et al.: J. Phys. B 24 (1991) 3467. 91B3 Bowen, G. H., Willson, L. A.: Astrophys. J. 375 (1991) L53. 91D Dopita, M., Meatheringham, S.: Astrophys. J. 367 (1991) 115. 91Kl Kaler, J. B., Jacoby, G. H.: Astrophys. J. 372 (1991) 215. 91K2 Kaler, J. B., Jacoby, G. H.: Astrophys. J. 382 (1991) 134. 91K3 Keenan, F. et al.: Astrophys. J. 371 (1991) 636. 91K4 KBppen, J. et al.: Astron. Astrophys. 248 (1991) 197. 91L Lame, N., Ferland, G.: Astrophys. J. 367 (1991) 208. 91M1 Meatheringham, S., Dopita, M.: Astrophys. J. Suppl. 75 (1991) 407. 91M2 Middlemass, D. et al.: Mon. Not. R. Astron. Sot. 251 (1991) 284. 91Pl Pequinot, D., Petitjean, P., Bonisson, C.: Astron. Astrophys. 251 (1991) 680. 91P2 Perinotto, M.: Astrophys. J. Suppl. 76 (1991) 687. 91s Smits, D. P.: Mon. Not. R. Astron. Sot. 251 (1991) 316. 92A Acker, A., Ochsenbein, F., Stenholm, B., Tylenda, R., Marcout, J., Schohn, C.: Catalogue of Galactic Planetary Nebulae, European Southern Observatory and Strasbourg (1992). 92B Balick, B. et al.: Astrophys. J. 392 (1992) 582. 92Cl Cahn, J. II., Kaler, J. B., Stanghellini, L.: Astron. Astrophys. 94 (1992) 399. 92C2 Ciardullo, R., Jacoby, G.: Astrophys. J. 388 (1992) 268. 92F Ferland, G. V.: Astrophys. J. 389 (1992) L63. 921 Icke, V., Balick, B., Frank, A.: Astron. Astrophys. 253 (1992) 224. 92K Keenan, F. P. et al.: Astrophys. J. 389 (1992) 443. 92s Schwarz, H. E., Corradi, R. L. M., Melnick, J.: Astron. Astrophys. 266 (1992) 639. 92T Tayal, S. S.: J. Phys. B 25 (1992) 2639. 93A Amnuel, P. R.: Mon. Not. R. Astron. Sot. 261 (1993) 263. 93B Balick, B. et al.: Astrophys. J. 411 (1993) 778. 93H Hyung, S., quoted in: [93IAU#155] p.76. 93Kl Keenan, F. P. et al.: Physica Scripta 48 (1993) 129. 93K2 Keenan, F. P., Conlon, E. S.: Astrophys. J. 410 (1993) 426. 93K3 Keenan, F. P. et al.: Astrophys. J. Suppl. 88 (1993) 169. 93Ll Liu, X., Danziger, J.: Mon. Not. R. Astron. Sot. 262 (1993) 699. 93L2 Liu, X., Danziger, J.: Mon. Not. R. Astron. Sot. 263 (1993) 256. 93M Mendez, R. H., et al.: Astron. Astrophys. 275 (1993) 534. 93Pl Pena,M. et al.: Rev. Mex. Astron. Astrofis. 279 (1993) 175. 93P2 Papamastorakis, J. et al.: Astron., Astrophys. 279 (1993) 536. 93s Schwarz. H. E. (ed): Mass Loss in AGB and Beyond, ES0 Conference Proceedings No.46 (1993). 932 Zhang, C. Y., Kwok, S.: Astrophys. J. 88 (1993) 137. 94H Hyung, S.: Astrophys. J. Suppl. 90 (1994) 119. 94K Kwok, S.: Publ. Astron. Sot. Pacific 106 (1994) 344.

Land&-Bdmstein New Series VI/3b

Ref. p. 2211

219

5.5 White dwarfs

5.5 White dwarfs (WD) 5.5.1

see LB VI12b

5.5.2

Luminosity function, space density

A new luminosity function for DA stars has been determined using the Palomar-Green survey [86G] by Fleming et al. [86F] and extended to cool WD by Liebert et al. [88L]. It has established the strong decline below M, = 16?0, indicative of a finite galactic age. Predictions can be made by means of models of galactic evolution, and the age of the galactic disk can be estimated [9OY, 92yJ. The relative distribution of well-observed WD (Table 1 in LB VI/2b) is still usable, although the total number contained in the third edition of the Villanova Catalogue [87M] has been increased from 600 to 1300 WD. A fourth edition is in preparation. The spacedensity of single white dwarfs has been determined [9Ow] as 0.005 WD/pc3 down to MbO,= 15. The corresponding birth rate is lo-l2 WD/pc3 per year. Since many WD are hidden in binaries, the total space density and birth rate are about two times higher [91W3]. The total mass of WD in the local column is of the order of 4Mo. The fraction of cooled-down invisible WD depends on the history of star formation and is of the order of 25% [9OWJ

5.5.3

Spectral types

5.5.3.1

Spectral classification

A partly new classification has been introduced that takes into account the detection of carbon and/or metals as trace elements in many stars that formerly belonged to the spectral class DC with only continuous spectra [83S]. Pulsating variables are indicated by addition of V, e.g., DAV (ZZ-Ceti stars, 11000. . .13000K, = 20 known), or DBV (GD358, = 25000K, 6 known) or the DOV (PC 1159, GW Vir, > lOOOOOK,15 known). Mixed compositions are indicated by a combination of main letters, e.g., DBA (helium with traces of hydrogen, He/H 104... 106,15 known), DAB (only 2 known), DBZ, DQZ with metal traces (many known). WD with detected magnetic fields indicated by letter P (lo%), if with unknown spectral features: DXP (very few known). Table 1. Primary classification. (seealso Table 2 in LB VI/2b, p. 374.)

Type

Description

DA

HI only, no He or 5000 . . . 70000 metals present HeII, He1 50000 . . . 80000 or H present He1 only, no 12000 . . . 30000 H or metals carbon, atomic 7000 . . . 12000 or molecular metal lines only 5000 . . . 10000

DO DB

DQ DZ

Land&-Bihstein New Series VU3b

T WI

Composition

Examples

N

pure hydrogen

> 800

He/H variable

40 Eri B He 3 HZ21

= 30

He/H > lo4

GD190

= 80

He/C variable

G47-18

= 30

mainly He, with metals

vMa2

= 20

220

5.5 White dwarfs

[Ref. p. 221

A temperature index from 1...9, giving 504OOK/T,is sometimes added mainly for DA and DB stars, e.g., DA3 for T,, = 15000K. PG1159 stars are immediate progenitors of WD, some of them are fully degenerate [91W4]. The hottest star is H1504 with T = 170000K [91W2].

5.5.3.2 seeLB VI/Zb 5.5.3.3 Variable DA (or ZZ Ceti) stars and other pulsating white dwarfs. Asteroseismology Additional instability strips to the DAV stars (seeLB VI/2b) have been found for variable DB stars and hot PG1159 (GW Vir), DOV stars. The variability is traced back to nonradial pulsations caused by mode trapping in compositionally stratified atmospheres [81W]. Modelling is described extensively in [90T] and [91B]. Observations of the amplitude variations are pursued continuously with the Whole Earth Telescope [9ON] in order to achieve high-resolution power spectroscopy. New results in [h]. White dwarf evolution causesa change of period which has been detected [91K2].

5.5.4

Catalogues, observation lists

Table 2. White dwarf observation list. (Addition to Table 3 of LB VI/2b, p. 375) IUE: International Ultraviolet Explorer AJ: Astronomical Journal MC: Multichannel scans ApJ: Astrophysical Journal S/N: Signal-to-noise ratio ApJS: Astrophysical Journal Supplement Sp: Spectra uuby: Stiimgren colors Author

Observation

Remarks

Ref.

Greenstein, J.L. Greenstein, J.L. Greenstein, J.L. Liebert, J. Green, R.F., Schmidt, M., Liebert, J. Sion, E.M., Kenyon, S.J., Aanestad, P.A. Wegner, G., Swanson, S.R. Wegner, G. Fontaine, G., Bergeron, P., Lacombe, P., Lamontagne, R., Talon, A.

MC CCD, high S/N CCD, high S/N Blue star survey from Palomar SP

396 northern WD 140 northern WD 84 northern WD 448 WD spectrosc. classified 18DZ,4DC

ApJ 276(1984)602 ApJ 304(1986)334 ApJ 360(1990)662 ApJS 61(1986)305 ApJS 72( 1990)707

UV Sp.IUE uvby uvby

182 WD 180 northern WD 71 northern WD

ApJS 75( 1991)507 AJ 88(1983)109 AJ 90(1985)1094

5.5.5

Atmospheres, HR diagram

Spectroscopic analysis with model atmospheres has been continued with higher sophistication (e.g.NLTE) for hot DO and DA0 [85W, 91W2], for DB [83W, 8401, DBA [91Wl], DA [92B], DAV [84w]. DQ, DC [82K] and DZ [86Z, 8721, seealso [g, j]. The results presented in LB VI/2b - narrow massdistribution, equal massesfor DA and non-DA stars - are essentially unchanged. Land&-BBmstein New Series VV3b

5.5 White dwarfs

5.5.6

221

Radii, masses

Table 3. Spectroscopically determined data for

DA white dwarfs [84W]. Updated Table 5 of LB VI/2b, p. 377. Mean radius Mean gravity Mean mass Mean density

i?=0.013 R, S = lo8 cm ss2 ==0.58 A4, p=106gcmp3

The mass distribution is narrow [9OW, 92B]. Gravitational redshifts agree now with predictions [87K, 91W5]. Masses of white dwarfs in binaries are as given in Table 6 of LB VI/2b, p.378, however, for 40 Eri B the massis larger, 0.53 k O.O4M, [91Kl].

5.5.7

Interior, envelopes

Evolutionary calculations for carbon /oxygen WD give mass-radius relations for finite temperatures [86K, 92w]. For crystallization and cooling below the Debye temperature, see[fl. Binary remnants can consist of helium [911]. The envelope structure and composition depends on convection, diffusion, mixing, gravitational settling, accretion and winds. Many recent results in [h], [i] and [j].

5.5.8

Evolution, age

Essentially like Vol.V1/2b. Recent additions: Mass loss and initial-to-final mass relations have been established [87W, g]. Birth rates of planetary nebulae and WD agree, if binary evolution is taken into account [89W]. Cooling rates have been recalculated [f, 92w], according to which the red deficit seemsto be due to the finite age of the galactic disk [88L, 9OY, 92w]. Incorporation of WD results provide several constraints on models of galactic evolution [g, 9OY, 92yl.

References for 5.5 Main Catalog

McCook,G. P., Sion, E. M.: Third edition of Villanova Catalogue [87M]. Review articles and proceedings

a b : ;

Angel, J. R. P., Borra, E. F., Landstreet, J. D.: Astrophys. J. Suppl. 45 (1981) 457 (magnetic WD). Weidemann, V.: IAU Transactions XIX A (1985), p. 497 (1981-1984). Sion, E. M.: Publ. Astron. Sot. Pac. 98 (1986) 821 (WD evolution). Weidemann,V.: A Decade of UV Astronomy with IUE. Proc. Celebratory Symposium GSFC, ESA SP-281,Vol.1 (1988) p.l7(WD). Koester, D., Chanmugam, G.: Rep. Progr. Phys. 53 (1990) 837. D’Antona, F., Mazzitelli, I.: Annu. Rev. Astron. Astrophys. 28 (1990) 139.


222

: i j

5.5 White dwarfs Weidemann, V.: Annu. Rev. Astron. Astrophys. 28 (1990) 103. Proceedings of the IAU Coll. No.114, Hanover (G. Wegner, ed.) Lecture Notes in Physics, Heidelberg: Springer Vol. 328 (1989). Proceedings of the Seventh European Workshop on White Dwarfs (G. Vauclair, E. Sion, eds.) NATO AS1 C 336, Dordrecht: Kluwer (1991). White Dwarfs: Advances in observation and Theory (M. A. Barstow, ed.) NATO AS1 C 403, Dordrecht: Kluwer (1993).

Papers

81W Winget, D. E., Van Horn, H. M., Hansen, C. J.: Astrophys. J. 245 (1981) L33. 82K Koester, D., Weidemann, V., Zeidler-K. T., E. M.: Astron. Astrophys. 116 (1982) 147. 83s Sion, E. M., Greenstein, J. L., Landstreet, J. D., Liebert, J., Shipman, H. L., Wegner, G. A.: Astrophys. J. 269 (1983) 253. 83W Wickramasinghe, D. T., Reid, N.: Mon. Not. R. Astron. Sot. 203 (1983) 887. 840 Oke, J. B., Weidemann, V., Koester, D.: Astrophys. J. 281 (1984) 276. 84W Weidemann, V., Koester, D.: Astron. Astrophys. 132 (1984) 195. 85W Wesemael,F., Green, R. F., Liebert, J.: Astrophys. J. Suppl. 58 (1985) 379. 86F Fleming, T. A., Liebert, J., Green, R. F.: Astrophys. J. 308 (1986) 176. 86G Green, R. F., Schmidt, M., Liebert, J.: Astrophys. J. Suppl. 61 (1986) 305. 86lS Koester, D., Schonberner, D.: Astron. Astrophys. 154 (1986) 125. 862 Zeidler-K. T., E. M., Weidemann, V., Koester, D.: Astron. Astrophys. 155 (1986) 356. 87K Koester, D.: Astrophys. J. 322 (1987) 852. 87M McCook, G. P., Sion, E. M.: Astrophys. J. Suppl. 65 (1987) 603. 87W Weidemann, V.: Astron. Astrophys. 188 (1987) 74. 872 Zeidler-K. T., E. M.: Astron. Astrophys. Suppl. 68 (1987) 469. 88L Liebert, J., Dahn, C. C., Monet, D. G.: Astrophys. J. 332 (1988) 891. 89W Weidemann, V.: Astron. Astrophys. 213 (1989) 155. 90N Nather, R. E., Winget, D. E., Clemens, J. C., Hansen, C. J., Hine B. P.: Astrophys. J. 361 (1990) 309. 90T Tassoul, M., Fontaine, G., Winget, D. E.: Astrophys. J. Suppl. 72 (1990) 335. 90W Weidemann, V., in: Baryonic Dark Matter (eds. Lynden-Bell and Gilmore) NATO AS1 C 306, Dordrecht: Kluwer (1990) p.87. 90Y Yuan, J. W.: Astron. Astrophys. 224 (1990) 108. 91B Bradley, P. A.: Winget, D. E.: Astrophys. J. Suppl. 75 (1991) 463. 911 Iben, I. jr.: Astrophys. J. Suppl. 76 (1991) 55. 91Kl Koester, D., Weidemann, V.: Astron. J. 102 (1991) 1152. 91IS2 Kepler, S. 0. et al. (29 authors): Astrophys. J. 378 (1991) L45. 91Wl Weidemann, V., Koester, D.: Astron. Astrophys. 249 (1991) 389. 91W2 Werner, K.: Astron. Astrophys. 251 (1991) 147. 9 1W3 Weidemann, V.: in [i], p. 67. 91W4 Werner, K., Heber, U.: Astron. Astrophys. 247 (1991) 476 91W5 Wegner, G., Reid, I. N., McMahan, R. K. jr.: Astrophys. J. 376 (1991) 186. 92B Bergeron, P., Saffer, R. A., Liebert, J.: Astrophys. J. 394 (1992) 228. 92W Wood, M. A.: Astrophys. J. 386 (1992) 539. 92Y Yuan, J. W.: Astron. Astrophys. 261 (1992) 105.

Landolt-BBmstein New Series VU3b

Ref. p. 2351

5.6.3 Pulsating X-ray sources

223

5.6 Compact objects 5.6.1 and 5.6.2

see LB VI/3c

5.6.3

Pulsating X-ray sources

5.6.3.1

General properties

Numerous observations since the early days of X-ray astronomy have demonstrated the great variety of intensity variations in the X-ray emission of binary systemsaccommodating a compact object. The observed variations are due to orbital motion in the binary system, periodical pulsations, and stochastic fluctuations. Impulsive outbursts have also been measured. In addition, most of the X-ray binaries emit a persistent X-ray flux that is variable over longer time scalesdue to long-term changes in the mass accretion rate onto the compact object. To date, 193 X-ray binaries are known. Two classesof X-ray binaries can be distinguished: high-mass X-ray binaries (HMXB) and low-mass X-ray binaries (LMXB). A catalogue of their system parameters has been compiled by van Paradijs [94P]. For X-ray binaries seealso subsect. 6.1.3.1. HMXB contain luminous young (< 10’ years) and massiv ( > 10 M,) companions, usually with an 0- or B-type spectrum. The compact object is a highly magnetized (= lOi G), rotating neutron star that emits pulsed X-rays with a quite hard spectrum and sometimes with an additional soft component. In most cases,periodic eclipsescan be observed in the X-ray light curve. Together with Doppler shifts of both the pulse period and lines in the optical spectrum, this reveals the binary character of HMXB and enables mass determination. The ratios of X-ray to optical luminosities range from 10e3to 10. HMXB are members of a young galactic disk population. LMXB have star-like, faint optical counterparts (Mv = + 2) with massesof less than = 1 M,. The optical spectra of LMXB are devoid of normal stellar absorption features and instead show emission lines typical for the optical emission of accretion disks. LMXB are bright X-ray sources (L, > 1O34 erg/s) accreting matter from the companion through Roche lobe overflow. The luminosity ratios L,IL,,, range from lo2 to 104.The X-ray spectra are rather soft (kT = 5 keV). In the X-ray light curve of many of the LMXB, no eclipsesor dips are observed from which the parameters of the orbital motion in the binary system could be derived. LMXB usually show no pulsations in their X-ray emission. The compact object in the binary is most likely a neutron star with magnetic fields of strengths ranging from about lo* G to 10” G. For the brightest LMXB, quasi-periodical oscillations of their X-ray emission have been measured, and about 40 LMXB are X-ray bursters (seesubsect. 5.6.4). The majority of the 125 known LMXB [94P] are permanently X-ray active. About 40 sources,however, are transients, i.e., they emit their X-ray radiation episodically rather than permanently. Their active periods typically last for several months. The transient behavior can be recurrent within intervals of years. LMXB are concentrated towards the galactic bulge region; 17 of them are found in globular clusters. Their location outside of active star-forming regions identify them as members of an old galactic star population. There are a few exceptions to this scheme:the companion in the HMXB Her X-l is not really massive (= 2 A4, [89N]), and in three LMXB, pulsations have been detected (GXl + 4 [76W, 71L], 4U1626-67 [78J], and lE2259 + 586 [83F]). Pulsating X-ray emission has not only been detected from accretion-powered neutron stars in binary systemsbut also from isolated, rotationally powered radio pulsars (seesubsect 5.6.3.1.3). 5.6.3.1.1

Periodic pulsations in HMXB

Periodically pulsating binary X-ray sourcescan be classified into three categories [85B]: (1) Binaries with early-type massive companions with the subclasses[86C3, 86S2] Lmdolt-BBmstein New Series VI/3b

224


[Ref. p. 235

(a) short pulse-period systems(high X-ray luminosity) (SMC X-l, Cen X-3, LMC X-4), (b) long pulse-period systems(moderate X-ray luminosity) (Vela X-l, GX 301-2,4U1538-52, etc.). (2) Binaries with Be-star companions (sometimestransient) (4UOl15+63, A0535+26, GX 304-1, etc.). (3) Binaries with medium and low masscompanions (Her X-l, GX 1+4,4U1626-67, etc.). The sources in classes(la) and (3) are thought to be powered preferrentially by mass accretion via Roche-lobe overflow, whereas those in classes(lb) and (2) are considered to be powered by mass accretion via stellar wind capture. The pulse-averagedenergy spectra of most of the pulsating sources can be represented by power law spectra with a high energy cut-off [83w]. The photon indices Tof the power law spectra range between 0.8 s F d 1.5. Some sources, like 4U1258-61 and X Per, show fairly soft X-ray spectra [83WJ.The high energy cut-off is measured at about 10.. .20 keV for most of the sources.Above the break point, the spectra are well represented by exponential spectra with e-folding energiesbetween lOand30keV. The low-energy spectra of the pulsating sources are affected by photoelectric absorption which is attributed to interstellar matter and, in some ceases,to circumstellar matter. The absorption features in the spectra of several sources change with time, depending primarily on the orbital phase, and sometimessporadically due to clumpiness of stellar winds [86N, 90H1,92H]. In the spectra of the majority of the pulsating sources, an iron emission line is detected between 6 and 7 keV. For most sources,the centroid of the iron line is consistent with a 6.4 keV fluorescence line with an equivalent width 2 100 eV [85N]. In the spectra of some sources, an absorption edge of iron at = 7.3 keV was also detectable [840, 86N, 86S3, 89L]. The compact object in pulsating X-ray binaries is in most casesconsidered to be young and highly magnetized neutron stars. Observational evidence of the neutron star magnetic field, derived from the measurement of a line feature in the hard X-ray spectrum of Her X-l, was first reported by Trtimper et al. [78T]. This line was interpreted as a cyclotron absorption line at = 38 keV, corresponding to a surface magnetic field of the neutron star of I=4.10” G [82v]. There is evidence of similar features at = 11.5 keV and 23 keV in the pulsed spectrum of 4UO115+ 63, which are attributed to the fundamental and first harmonic components of the cyclotron resonance [79W, 83w]. Further, there are indications of cyclotron line features reported for the sources lE2259 + 586 [88S] and 4Ul538-52 [9OC]. In Table 1, the properties of newly detected pulsating X-ray binaries are listed together with previously reported sources,for which new parameters could have been determined. Already from early satellite measurements in the 1970s many of the periodically pulsating X-ray sources were found to show secular variations of the pulse period. A general spin-up tendency with rates of -PIP = 10-2...10-6 a-’ has been observed [83R]. However, pulse-period measurementsperformed in the last decade reveal a wide variety of pulse-period changes, including spin-down episodes as well as long time intervals with no change of period [89N]. For 16 pulsating X-ray sources, the pulse-period was monitored over the last decade using measurements with the satellites Einstein Observatory, Hakucho, EXOSAT, Tenma, and Ginga. Their pulse-periods as a function of time are given in Figs. la-p. For another five sources, only few measurements of the pulse-period are available. Their estimated secular variations -k/P are: -4.10m4 a-’ for V 0332+53 [85Sl], -7.10-5 a-l for IE 1048.1-5937[86Sl, 89N], 2~10-~a-l for EXO 2030+375 [89P], - 8.10m4a-’ for 4U 1907-09 [84Ml, 87C], and > - l.10e3 a-’ for GX 304-I [77H, 77M], respectively. For the rest of the 30 pulsating sources,only a measurement of the pulse-period itself exist.

Land&-Blirnstein New Series VI/3b

$5 FE $-5 e; lur %a5

Table 1. Basic properties of pulsating X-ray sources. Pulsating X-ray source Catalogue name A 0535 - 668 v 0331+530 1E 1048-593 2259+586 2s 1553-542 0532- 664 GS 1843+00 EXO 2030+375 2137+57 GS 1843 - 024 A 0535+262 a,b, 1833-076 1258-613 “) A 1118-616 b, GPS 1722 - 363 4u 1907+097 1223 - 624 “)

Synonym

GXl09.1-1.0 LMC X-4

Cep X-4

Set X-l GX304-1

GX301-2

Pulse period

Orbital period

P[sl

Ref.

PWI

0.069 4.37 6.44 6.98 9.26 13.5 29.5 41.8 66.2 94.8 104 111 272 405 413 438 696

82s 83Sl 8582 83F 83Kl 83K2 88Ml 85P 88M2 88M3

16.66 34.25

X-ray luminosity

Optical counterpart

Ref.

Lx [erg/s1

Ref.

Name

Ref.

Spectral class

Ref.

805 85Sl

1.1039

78Wl BQ Cam

83H

B2 III-IVe Be Be

81C 86Cl 86Sl

so.03 30.6 f 2.2 1.408

83F 83Kl 83K2

45.6.. .47.5

89P

111

87T

133

86C2

zz

2.1034 5.1035

86Sl 87Kl

6.1038

78W2

Be 07 III-V

83Kl 78H

I.1038

89P

Be

89P

2.1037

HDE 245770

1.1036

MMV star Hen 3-640

BO III-Ve

88M4 5.1036

89T 83T 76W

8.38 41.50

“) Newly determined orbital period. “) In LB VI12c (1982), p.25, a negative declination was erroneously given. ‘) Recently identified optical counterpart.

80M 82W

8.1035 3.1036

84Ml Wray 977

815

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80s

[Ref. p. 235


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t I 2000

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I I 4000 6000 TO-2,440,000

8000

Fig. 1.1 Pulse-period histories for 16 pulsating X-ray sources [89N]. The lo error bars are given only for data points with poor accuracy; otherwise, the error bars are smaller than the symbols. JD:Julian Date.

Ref. p. 2351

227


1

A0635+28

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228 5.6.3.1.2


[Ref. p. 235

Quasi-periodic oscillations (QPO) and noise in LMXB

With the improved sensitivity as well as the high energy and time resolution of the X-ray detectors onboard the satellites EXOSAT and Ginga, it has become possible in the last decade to investigate the intensity fluctuations in the emission of variable X-ray sources in the sub-second range. In searching for millisecond pulsars, van der Klis et al. [85K2] found a single broad peak in the power spectrum of the X-ray light curve of the bright galactic bulge source GX5-1 and not the expected sharp maximum indicative of a strictly periodic pulsation. The dominant intensity variation of this source is therefore characterized by a range of frequencies; the source is said to oscillate quasi-periodically. Furthermore, the centroid frequency of the QPO peak was found to vary in time, thereby correlating strongly with the changing X-ray intensity. In addition, a low-frequency noise component was present in the data. The study of the chaotically appearing temporal variations of the X-ray flux of LMXB by means of power spectral analysis revealed a great variety of broad and variable components in the power spectra of individual sources as well as among different sources [84M2, 84S, 85K1, 85K2, 85M, 86HlJ. It is generally assumed and substantiated by some evidence [89Kl] that the aperiodic variations underlying all of these changing power spectral components are of a stochastic nature. The confusing complexity of the temporal features can be unravelled by connecting the power spectral data with the variable X-ray spectrum. It turns out that the structure of the correlated temporal and spectral variability is best disclosed by ordering the data of a given source into an X-ray colorcolor diagram that yields characteristic patterns [87Hl, 90H2]. Thereby, an X-ray color is defined as the hardness ratio of the X-ray spectrum in predefined energy bands. Studying the brightest LMXB, it was found that two classesof objects with statistically fluctuating X-ray emission can be distinguished according to the patterns in their color-color diagrams [89H]. 5.6.3.1.2.1

Z-sources

Spectrally varying low-mass X-ray binaries, which trace a Z-shaped pattern in the X-ray color-color diagram, are called Z-sources (Fig. 2). To date, six bright LMXB have been identified as sources of Z-type, all of which show quasi-periodic oscillations. According to three distinct states of spectral and power spectral behavior, three different branches of variability are distinguished in the colorcolor pattern: the horizontal branch, the normal branch, and the flaring branch. In varying, the sources always follow the Z-pattern without jumping between the branches. In a given branch, the sourcesmove irregularly up and down for hours to days before proceeding to the adjacent branch. There is no evidence that a source spends more time at a particular section of the pattern. When passing from one branch to the other, the X-ray spectrum and the temporal characteristics of the intensity fluctuations change. For each branch, characteristic structures of the power spectrum have been observed: three different QPO peaks and three different broad-band noise components. Two of the latter, the very low frequency red noise component (VLFN: 0.01.. .O.1 Hz) and the flat power law high-frequency noise (HFN) with a cut-off frequency between 25 Hz and more than 100 Hz, are omnipresent. The occurrence of the different components in the power spectra of the observed Z-sources are listed in Table 2. Observations of the sources in the different states of variability have yielded the following phenomenology: Horizontal branch (HB)

Sources varying in the horizontal branch of the Z-shaped X-ray color-color diagram show highfrequency quasi-periodic oscillations (HB-QPO) of 15.. .55 Hz, the centroid frequency of which is strongly positively correlated with the X-ray intensity. The QPO peak is of a Lorentzian shape. Its width coriesponds to a coherence time of 1 cycle. The fractional rms amplitude of HB-QPO range between 2 and 7% (1.. .20 keV). Land&-B6rnstein New Series W3b

Table 2. Power spectral components in Z-sources. l

detection, - no detection

Source 1617-155 1642-455 1702-363 1758-250 1813-140 2142+380

ScoX-I GX340+0 GX349+2 GX5-1 GX17+2 Cyg X-2

Any branch

Horizontal branch

Normal branch

Flaring branch

VFLN

HB . . . . .

NB . . . . . .

FB . . . . .

. . . . . .

“) Very broad peaks were reported.

HFN . . . . . .

QPO . . . .

LFN . . . . .

QPO . 1.) . . .

QPO

Ref.

.

86M, 86P, 87K2,89H 88P1,89H 88P2,89H 86E, 87K3,87K4,88D, 88M5,89H 87S, 88L, 88P3,89H, 90P 86H2,86H3,8684,87H2,87K3,87N, 88D, 88M6,89H

- “1 . -

[Ref. p. 235


230

I37

cyg x-z

I23I1-l-

0.70-

r*-

2 0.65B

-3_

g 0.60-

10

0.55-

10

0.501 0.750 0.775 a

-4_

-5

0.800 0.825 Soft colour

0850

0.875

0.900

IO

b

10“

I

I

lo-'

lo-'

I

I

1 IO Frequency

10L Hz IO3

Fig. 2. X-ray color-color diagram and power spectrum of Cyg X-2 [89H]. a Color-color diagram with the Soft

Color=CR(3.2...4.7 keV)/CR(0.9...3.2 keV) and with the Hard Color=CR(6.4...19.1 keV)/CR(4.7...6.4 keV), where CR denotes the count rate in a given energy band. b Power spectra of intensity variations of Cyg X-2 corresponding to individual branches as indicated. Spectra are vertically offset for clarity. Solid curves are functional fits.

The HB-QPO peak is always accompanied by low-frequency noise (LFN), which is best described by a flat power law with exponential cut-off. The cut-off frequency is lower than 15 Hz. The LFN is not always monotonic, increasing towards smaller frequencies. The rms amplitude ratio of LFN and HB-QPO is about 1 and the strength of the LFN seemsto be correlated to that of the QPO in individual sources. All Z-sources show VLFN and HFN in the horizontal branch state, and there their X-ray spectra are hard. In HB-NB transitions the LFN diappears suddenly on time scales as short as about loos, whereas the HB-QPO sometimes survives the transition in a reduced form and coexists with the NB-QPO.

Normal branch (NB) Sourcesin the state of the normal branch show a QPO peak (NB-QPO) at approximately 6 Hz. The centroid frequency of NB-QPO hardly varies along the NB and its coherenceand its strength is similar to that seenin the HB. The X-ray spectrum softens towards the end of the NB, thereby pivoting around a point between 5 keV and 10 keV. There is only a weak, if any, correlation between X-ray intensity and QPO frequency. The luminosities in the NB are thought to be close to the Eddington luminosity. When a source passesfrom the normal branch to the flaring branch, the QPO sometimes survives, but its centroid frequency changes gradually from about 6 Hz to about 10 Hz. Again, the QPO is accompanied by VLFN and HFN. LFN is absent. Land&-Bbmstein New Series W3b

Ref. p. 2351


231

Flaring branch (FB)

Whereas in all Z-sources VLFN and HFN noise components are present in the flaring branch state, only some of them also show an FB-QPO. Its peak frequency varies strongly from = 10 Hz to = 20 Hz, when the source moves up the FB. If present, the FB-QPO smoothly merges with the NB-QPO in the NB-FB transition zone. The QPO frequency correlates strongly to the X-ray intensity as soon as the source rounds the corner from NB into the FB. Up the flaring branch, the QPO becomes wider and finally dissolves into the broad HFN component. Again, no LFN is observed. The physical processesgoverning the spectral and power spectral behavior of Z-sources are not yet fully understood. According to the observed luminosity, the most likely quantity determining the changing properties of the sources in different states seemsto be simply the mass accretion rate which increasesmonotonically from HB to FB, but which is not linearly related to the X-ray intensity. A further key to understanding the underlying processescould be provided by the sudden phase transition observed when the source moves from the horizontal to the normal branch. Summarizing the model ideas presented to date, the phenomena suggestthe following scenario: In the horizontal branch at a moderate accretion rate, the plasma of a thin accretion disk interacts turbulently with the magnetosphere of the spinning neutron star. Plasma inhomogeneities (“clumps”) are produced at the magnetospheric boundary which, in general, are instationarily accreted, causing noisy intensity fluctuations as typical for the LFN. At the polar cusps, clumps can enter the magnetosphere more readily than at other points. A given clump which circulates with the Keplerian frequency vkwill periodically pass the magnetic poles rotating with the neutron star’s rotation rate vns, with the beat frequency vbeat =]vk-vNs]. In terms of a shot noise interpretation, each accreted clump entering the magnetosphere at the poles contributes an oscillating shot to the resulting intensity fluctuation. The modulating frequency vbeatis then the centroid frequency of the QPO. This scenario has been formulated as the modulated-accretion magnetospheric beat frequency model by Alpar and Shaham [85A] and Lamb et al. [85L]. As the mass accretion rate increasesclose to the Eddington limit towards the end of the HB, the dramatic HB-NB phase transition may indicate that the inner disk becomesunstable and blows up, finally embedding the whole neutron star’s magnetosphere. The interface between the radiation pressure-supported disk torus and the magnetosphere is probably not as turbulent as in the HB state. Therefore, matter might be accreted more smoothly than in HB, yielding a reduced LFN and HB-QPO. The fact that the HB-QPO frequency is nearly the samein all Z-sources suggeststhat it is determined by some hardly varying parameters like the Eddington luminosity. At the Eddington limit, the strong radiation pressure causes all dynamical time scales of the accretion to be slowed down. This could explain the reduced frequency of the NB-QPO. Further, the embedding of the X-ray source by cold disk torus material causes a softening of the emerging X-ray spectrum by Comptonization, as observed in the NB. A transition to super-Eddington accretion may explain the NB-FB transition, producing matter outflow and a lower scattering optical depth, which would agreewith the spectral hardening along the flaring branch. Finally, it has to be noted that the discussion of the interaction between the neutron star’s magnetosphere and the inner accretion disk and its instabilities is still sketchy. The outlines of the models have been developed by many authors. A comprehensive description can be found in van der Klis [89K2] and Hasinger [91H], with referencestherein. 5.6.3.1.2.2

Atoll sources

There are low-mass X-ray binaries which show a distinctly different pattern in the X-ray color-color diagram than Z-sources. They display an often fragmented structure with a considerable intrinsic scatter, which consists either of an upward-bended branch or of an isolated clump of color states or of both (Fig. 3). According to a frequent geometrical arrangement of this pattern, these LMXB are called atoll sources.A first description of the characteristics of atoll sources was given by Hasinger and van der Klis [89H]. Landolt-BBmstein New Series VI/3b

232


4U 1636-53

0.70 0.75

[Ref. p. 235

IO3

I 0.80

a

I I 0.85 0.90 Soft colour

I 0.95

1o-J

1.00 b

lo-’

lo-’ 1 Frequency

10

IO’ Hz

Fig. 3. X-ray color-color diagramand power spectrumof atoll source4U1636-536[89H]. a Color-color diagram with the Soft Color=CR(2.9...4.5 keV)/CR(0.9...2.9 keV) and with the Hard Color=CR(6.1. ..20.5 keV)/CR(4.5...6.1keV), whereCR denotesthe count rate in a given energyband. Filled circlescorrespondto the bananastate,opencirclesto the island state.b Powerspectraof intensity variations of 4U1636-536correspondingto the differentstates,asindicated.Spectraarevertically offsetfor clarity. Solid curvesare functional fits. Studying the correlation between the power spectral shape and the X-ray spectral state while the sourcesare moving through the color-color pattern, the following phenomenological description of the different statescan be given: Banana state (B)

The banana state is characterized by a strong correlation between power spectral and the X-ray spectral behavior of the varying source. The power spectrum is dominated by a very low frequency noise component (VLFN) with a power law slope near unity (“llfnoise”). It has a rms amplitude of 2.. .3%. Additionally, sometimes a high-frequency noise (HFN) can be observed. Its characteristics range between strictly “red” noise and a broad peak spreading over a decade in frequency. In most cases,it is more reminiscent of the LFN than the HFN component in Z-sources, although there is no formal evidence that they are related. The shape of the power spectrum gradually changeswhen a source moves from the lower left end of the banana branch (LB) to the upper right end (UB), in the sensethat the VLFN component becomes stronger and the HFN weaker. Atoll sources being observed recurrently in the banana state show banana branches with the same curvature at about the sameplace in the color-color diagram. Island state (I )

Sourcesin the island state show only little correlation and slow motion in the color-color diagram. Their power spectra are dominated by HFN. Little or no VLFN is observed. It is not clear that Land&-B6rnstein New Series VV3b

Ref. p. 2351

233


Table 3. Power spectral components in atoll sources [89K2]. l

detection, - no detection

Source

Banana state

1636- 536 1705-440 1728- 169 1728- 337 1735-444 1744-265 1758-205 1811-171 1820-303

Branch . . . . . . . .

4u 4u GX9+9 GX354-0 4u GX3+1 GX9+ 1 GX13+1 4u

VLFN

Island state HFN

Branch

VLFN

HFN

. . . . . . .

. . . .

.

. . . .

island states always appear at a fixed position with respect to the banana branch. Island states usually occur at the lowest X-ray intensity level. Thereby, it is noticeable that sources in the island state often show regular X-ray bursting. Seven of the nine atoll sources studied are X-ray bursters when they are in the island state (see subsect. 5.6.4). X-ray bursts sometimes also occur in the banana state, but there they tend to be shorter and less regular than in the island state. In one source, 4U1636-536 (Fig. 3), a transition from the island state to the banana state has been observed [89H]. During the transition, the power spectrum changed from an “island-like” continuity to a “banana-like” shape, and the X-ray intensity increased in correlation to the position in the color-color diagram. It is possible that the distinction between island state and banana state is based on an observational selection effect. The move of a source through the island state may be so slow that, in general, the duration of a single observation is too short to follow the source through the transition into the banana branch. In successiveobservational periods, the source is then found already in the banana branch. The atoll behavior of LMXB is not understood. It can be stated that atoll sources are usually fainter than Z-sources. The fact that those atoll sources for which orbital periods have been measured show shorter periods than those measured for Z-sources may indicate that Z-sources contain evolved companion stars, while atoll sources do not. This could explain the different accretion rates in the two classesof quasi-periodically oscillating binaries. It is remarkable that the power spectra of atoll sources do not contain QPO peaks. Possibly, a beat frequency mechanism as in Z-sources cannot work becauseof a weaker magnetic field of the atoll neutron star. 5.6.3.1.3

X-ray emission of radio pulsars

A number of radio pulsars has been detected at X-ray wavelengths. Table 4 gives an overview as well as information about optical and gamma ray detections. The X-ray emission of the three young objects (Crab, SNR 0540-69, and MSH 15-58) is characterized by sharp pulses, a high degree of modulation (= lOO%),and power law spectra. The optical and gamma ray pulsations found in some of the objects show a similar behavior. This radiation is attributed to magnetospheric emission from relativistic particles. The pulsed X-ray emission of the older objects shows sinusoidal light curves with a low degree of modulation (= 15%.. .20%) and indications for thermal spectra. This emission is interpreted in terms of thermal radiation from the neutron star surface. Table 4 also contains the Geminga pulsar, the first “radio-quiet” pulsar detected so far. 5.6.3.2 and 5.6.3.3 see LB VIl2c, p. 26ff Land&-BBmstein New Series VU3b

Table 4. Basic properties of rotationally powered neutron stars [95B3]. Detection of flux in different energy bands. p = detection of pulsed flux; d = detection of unpulsed flux R: at radio wavelengths 0: at optical wavelengths Xs: at soft X-rays (- 1 keV) X,: at hard X-rays (- 100 keV) y,: at medium energy y-rays (- 10 MeV) yh: at high energy y-rays (a 500 MeV) P: period E: pulsar braking power L:(P): combined pulsed and unplused X-ray luminosity of the pulsar in the energy band (0.1.. .2.4)keV qrse(P): X-ray luminosity of the pulsed flux of the pulsar Lx(P+N): X-ray luminosity of the pulsar and the surrounding synchrotron nebula D: distance B: dipolar magnetic field strength of an orthogonal rotator for a neutron star radius of R= 10 km and a moment of inertia of the neutron star of I= 1O45g cm2. Name

Detection

R 0 0531+21 Crab 0540- 69 SNRlLMC MSH 15-58 1509-58 0833 - 45 Vela 1951+32 CTB 80 1706-44 G343.1-02.4 1823- 13 1957+20 ms-Pulsar

2334+61 G114.3+03 0656+ 14 0630+ 17 Geminga 1055- 52 0435 -47 ms-Pulsar rr 1929+10 2 k 0950+8 $i 0823+26 m 0: 2% !s F 5

PPPP p p p d P

P

t; d

p p

d d

P

p

P P P

log &P”‘=(P) log IJp+N)

log (; $)

P

D

log B

b&l

b&l

[w&l

W&l

[al

[IO-‘5s~s-‘]

Fpc]

[G]

38.65 38.17

36.0 36.3

36.0

150.23 37.25

34.3

89.29 39.53 102.45 101.45

32.7 33.4 33.2 33.9

34.3 31.7 33.0

37.6 37.2 35.3 33.4 34.0

3.10 3.22 3.19 4.05 5.03 4.24 4.33

420.96 479.06 1540.19 124.68 5.85 93.04 74.95

2.00 49.4 4.40 0.50 2.50 1.82 4.12

12.58 12.70 13.19 12.53 11.69 12.49 12.45

33.40 50.37

PP p p P

P

d d

log ,x’“‘(P)

Xs X, Y, Y,, bsl

P p

P

log E

P

P P P

P P t;

p P

P P

36.84 36.57 36.53 36.45

1.60 35.20 495.24 384.87

34.79 34.58

31.3

9.18

33.0 32.5

4.61 5.05 5.53 5.73 8.88 6.49 7.24 6.69

p

237.09 34.51

31.7

P

197.10 5.75 226.51 253.06 530.66

32.5 30.5 30.1 28.9 30.0

34.48 34.40 33.59 32.75 32.66

31.7 29.6 31.5 30.1 29.5

1.7.10-5 191.91 55.03 10.97 5.83 1.2.10-4 1.16 0.23 1.72

1.53 2.46 0.76 0.15 1.53 0.14 0.17 0.12 0.38

Ref.

95B1 93Fl 83S2,90T 900, 94K 95s 95B2 93F2

8.22 92F, 92K 12.99 12.67 12.21 12.03 8.93

93B1, 95B4 92F2 93H, 94B3 930 93B2

11.71 94Y 11.39 11.99

94M 93s


235

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85Kl van der Klis, M., Jansen, F. A.: Nature 313 (1985) 768. 85K2 van der Klis, M., Jansen, F., van Paradijs, J., Lewin, W. H. G., van den Heuvel, E. P. J., Triimper, J. E., Sztajno, M.: Nature 316 (1985) 225. 85L Lamb, F. K., Shibazaki, N., Alpar, M., Shaham, J.: Nature 317 (1985) 681. 85M Matsuoka, M., in: Cataclysmic Variables and Low-Mass X-ray Binaries, (Lamb, D. Q., Patterson, J., eds.), Dordrecht: Reidel Publ. Comp. (1985), p 139. 85N Nagase, F.: Adv. SpaceRes. 5 (1985) 95. 85P Parmar, A. N., Stella, L., Ferri, P., White, N. E.: Int. Astron. Union Circ. No. 4066 (1985). 85Sl Stella, L., White, N. E., Davelaar, J., Parmar, A. N., Blissett, R. J., van der Klist, M.: Astrophys. J. 288 (1985) L45. 8582 Smale, A. P., Charles, P. A., Corbet R. H. D., Seward, F. D.: Int. Astron. Union Circ. No. 4083 (1985). 86Cl Corbet, R. H. D., Charles, P. A., van der Klist, M.: Astron Astrophys. 162 (1986) 117. 86C2 Corbet, R. H. D., Smale, A. P., Menzies, J. B., Branduardi-Raymont, G., Charles, P.A., Mason, K.O., Booth, L.: Mon. Not. R. Astron. Sot. 221 (1986) 961. 86C3 Corbet, R. H. D.: Mon. Not. R. Astron. Sot. 220 (1986) 1047. 86E Elsner, R. F., Weisskopf, M. C., Darbro, W., Ramsey, D. B., Williams, A. C., Sutherland, P. G., Grindlay, J. E.: Astrophys. J. 308 (1986) 655. 86Hl Hasinger, G., Langmeier, A., Sztajno, M., Triimper, J., Lewin, W. H. G., White, N. E.: Nature 319 (1986) 469. 86H2 Hasinger, G., in: NATO AS1 Ser.C. The Evolution of Galactic X-ray Binaries (Trtimper, J., Lewin, W.H.G., Brinkmann, W., eds.), Dordrecht: Reidel Publ. Comp. (1986) p. 139. ‘86H3 Hasinger, G., Langmeier, A., Sztajno, M., Triimper, J., Lewin, W. H. G., White, N. E.: Nature 319 (1986) 469. 86M Middleditch, J., Priedhorsky, W. C.: Astrophys, J. 306 (1986) 230. 86N Nagase, F., Hayakawa, S., Sato, N., Masai, K., Inoue H.: Publ. Astron. Sot. Jpn. 38 (1986) 547. 86P Priedhorsky, W., Hasinger, G., Lewin, W. H. G., Middleditch, J., Parmar, A., Stella, L., White, N. E.: Astrophys. J. 306 (1986) L91. 86S1 Seward, F. D.: Charles, P. A., Smale, A. P.: Astrophys. J. 305 (1986) 814. 8682 Stella, L., White, N. E., Rosner, R.: Astrophys. J. 308 (1986) 669. 86S3 Sasto, N., Hayakawa, S., Nagase, F., Masai, K., Dotani, T., Inoue, H., Makino, F., Makishima, K., Ohashi, T.: Publ. Astron. Sot. Jpn. 38 (1986) 731. 8684 Stella, L. Chiapetti, L., Chiapi, A. L., Maraschi, L., Tanzi, E. G. Treves, A., in: Proc. Marcel Grossman Meet. 4th (Ruffini, R., ed.), Amsterdam: North-Holland Publ. (1986), p, 861. 87C Cook, M. C., Page, C. G.: Mon. Not. R. Astron. Sot. 225 (1987) 381. 87Hl Hasinger, G.: Astron. Astrophys. 186 (1987) 153. 87H2 Hasinger, G., in: IAU Symp. No.125. The Origin and Evolution of Neutron Stars (Helfand, D.J., Huang, J.-H., eds.), Dordrecht: Reidel Publ. Comp.( 1987),p. 333. 87Kl Koyama, K., Hoshi, R., Nagase, F.: Pub]. Astron. Sot. Jpn. 39 (1987) 801. 87K2 van der Klis, M., Stella, L., White, N., Jansen, F., Parmar, A. N.: Astrophys. J. 316 (1987) 411. 87K3 van der Klis, M., Hasinger, G., Stella, L., Langmeier, A., van Paradijs, J., Lewin, W. H. G.: Astrophys. J. 319 (1987) L13. 87K4 van der Klis, M., Jansen, F., van Paradijs, J., Lewin W. H. G., Trtimper, J., Sztajno, M.: Astrophys. J. 313 (1987) L19. 87N Norris, J. P., Wood, K. S.: Astrophys. J. 312 (1987) 732. 87s Stella, L., Pat-mar,N. A., White, N. E.: Astrophys. J. 321 (1987) 418. 87T Tanaka, Y.: IAU Symp. No.125. The Origin and Evolution of Neutron Stars (Helfand, D.J., Huang, H., eds.), Dordrecht: Reidel Publ. Comp. (1987) 161. 88D Dotani, T., Mitsuda, K., in: Physics of Neutron Stars and Black Holes (Tanaka, Y., ed.), Tokyo: Univers. Academ. Press(1988), p. 143. Landolt-Bhxtein New Series VV3b


237

88L Langmeier, A.: PhD Thesis, Ludwig-Maximilians-Universitat Mtinchen (1988). 88Ml Makino, F., and the Ginga Team: Int. Astron. Union Circ. No. 4587 (1988). 88M2 Makino, F., and the Ginga Team: Int. Astron. Union Circ. No. 4577 (1988). 88M3 Makino, F., and the Ginga Team: Int. Astron. Union Circ. No. 4661 (1988). 88M4 Makino, F., and the Ginga Team: Int. Astron. Union Circ. No. 4679 (1988). 88M5 Mitsuda, K., Dotani, T., Yoshida, A., in: Physics of Neutron Stars and Black Holes (Tanaka, Y., ed.), Tokyo: Univers. Academ. Press(1988), p.133. 88M6 Mitsuda, K., in: Physics of Neutron Stars and Black Holes (Tanaka, Y., ed.), Tokyo: Univers. Academ. Press(1988) 117. 88Pl van Paradijs, J., Hasinger, G., Lewin, W. H. G., van der Klis, M., Sztajno, M., Schulz, N., Jansen, F.: Mon. Not. R. Astron. Sot. 231(1988) 379. 88P2 Ponman, T. J., Cooke, B. A., Stella, L.: Mon. Not., R. Astron. Sot. 231 (1988) 999. 88P3 Penninx, W., Lewin, W. H. G., Zijlstra, A.A., Mitsuda, K., van Paradijs, J., van der Klis, M.: Nature 336 (1988) 146. 88s Shinoda, K., Koyama, K., Nagase, F., Ogawara, Y., Kawai, N., in: Physics of Neutron Stars and Black Holes (Tanaka, Y., ed.), Tokyo: Univ. Academ. Press(1988), p. 67. 89H Hasinger, G., van der Klis, M.: Astron. Astrophys. 225 (1989) 79. 89Kl van der Klis, M., in: NATO AS1 Ser.C. Timing Neutron Stars (dgelman, H., van den Heuvel, E. P. J., eds.), Dordrecht: Kluwer Academ. Publ. (1989), p. 27. 89K2 van der Klis, M.: Annu. Rev. Astron. Astrophys. 27 (1989) 517. 89L Leahy, D. A., Matsuoka, M.: Astrophys. J. 355 (1989) 627. 89N Nagase, F.: Publ. Astron. Sot. Jpn. 41 (1989) 1. 89P Parmar, A. N., White, N. E., Stella, L.: Astrophys. J. 338 (1989) 373. 89T Tawara, Y., Yamauchi, S., Awaki, H., Kii, T., Koyama, K., Nagase, F.: Publ. Astron. Sot. Jpn. 41 (1989) 473. 90C Clark, G. W., Woo, J., Nagase, F., Makishima, K., Sakao, T.: Astrophys. J. 353 (1990) 274. 90Hl Haberl, F., White, N. E.: Astrophys. J. 361 (1990) 225. 90H2 Hasinger, G., van der Klis, M., Ebisawa, K., Dotani, T., Mitsuda, K.: Astron. Astrophys. 235 (1990) 131. 90P Penninx, W., Lewin, W. H. G., Zijlstra, A.A.: Astron. Astrophys. 240 (1990) 317. 90T Trussoni, E., Brinkmann, W., egelman, H., Hasinger, G., Aschenbach, B., Ferrari, A.: Astron. Astrophys. 234 (1990) 403. 91H Hasinger, G., in: Particle Acceleration near Accreting Compact Objects (van Paradijs, J., van der Klis, M., Achterberg, A., eds.), Amsterdam: North-Holland Publ. (1991), p. 23. 92Fl Fruchter, A. S., Bookbinder, J., Garcia, M. R., Baylin, C. D.: Nature 359 (1992) 303. 92F2 Finley, J. P., ogelman, H., Kiziloglu, 0.: Astrophys. J. 394 (1992) L21. 92H Haberl, F., Day, C. S. R.: Astron. Astrophys. 263 (1992) 241. 92K Kulkarni, S. R., Phinny, E. S., Evans, C. A., Hasinger, G.: Nature 359 (1992) 300. 93Bl Becker, W., Trtimper, J., bgelman, H.: Int. Astron. Union Circ. No. 5805 (1993). 93B2 Becker, W., Trtimper, J.: Nature 365 (1993) 528. 93Fl Finley, J. P., ogelman, H., Hasinger, G., Tri.imper, J.: Astrophys. J. 410 (1993) 323. 93F2 Finley, J. P., Ggelman, H.: Int. Astron. Union Circ. No. 5787 (1993). 93H Halpern, J. P., Ruderman, M.: Astrophys. J. 415 (1993) 286. 930 ogelman, H., Finley, J. P.: Astrophys. J. 413 (1993) L31. 93s Sun, X., Trtimper, J., Dennerl, K., Becker, W.: Int. Astron. Union Circ. No. 5895 (1993). 94K Kanbach, G., et al.: Astron. Astrophys. 289 (1994) 855. 94M Manning, R., Wilmore, P.: Mon. Not. R. Astron. Sot. 266 (1994) 635. 94P van Paradijs, J., in: X-ray Binaries (Lewin, W. H. G., van Paradijs, J., van den Heuvel, E. P. J., eds.), Cambridge: Cambridge Univ. Press(1994), p. 58. 95Bl Becker, W., Aschenbach, B., in: The Lives of Neutron Stars (Alpar, A., Kilizoglu, U., van Paradijs, J., eds.), Dordrecht: Kluwer Academ. Publ. (1995) p. 47. 95B2 Becker, W., Brazier, K. T. S., Trtimper, J.: Astron. Astrophys. 298 (1995) 528. Land&-BBmstein New Series V1/3b

5.6.4 X-ray bursters

238

[Ref. p. 246

95B3 Becker, W.: PhD. Thesis, Universitat Mtinchen (1995). 95B4 Becker, W., Brazier, K.T.S., Tri.imper, J.: Astron. Astrophys. (1995), in press. 950 ogelman, H., in: The Lives of Neutron Stars (Alpar, A., Kilizoglu, U., van Paradijs, J., eds.), Dordrecht: Kluwer Academ. Publ. (1995) p. 101. 95s Safi-Harb, S., ogelman, H., in: The Lives of Neutron Stars (Alpar, A., Kilizoglu, U., van Paradijs, J., eds.), Dordrecht: Kluwer Academ. Publ. (1995), p. 53 95Y Yancopoulos, S., Hamilton, T. T., Helfand, D. J.: Astrophys. J. 429 (1994) 832.

56.4

X-ray bursters

5.6.4.1 General properties X-ray burst sources form a subset of the class of low-mass X-ray binaries. To date, 42 X-ray burst sourcesare known [93L], 10 of which are located in globular clusters. Some of the burst sourcesemit X-ray bursts rather continuously, others only at times. The bursts are characterized by a sudden rise of the X-ray flux, typically by at least one order of magnitude within a rise time of about Is, followed by a decay, generally to the original flux level, with time scalesup to 1 min or more. Outside the activity periods and between successivebursts, the sourcesemit a persistent X-ray flux. Thereby, the ratio of the persistent flux level and the average burst peak flux range from about 0.01 to 0.3, whereas the total energy in the persistent flux is about a factor of 100 higher than the total energy in the bursts. Among the burst sources, 13 are transient X-ray sources,i.e., they do not emit X-rays continuously but rather episodically. Recently, in 10 of the X-ray bursters, quasi-periodical oscillations (QPO) have been detected during the X-ray bursts as well as in the persistent emission. All but three of the bursts sourcesshowing QPO are of atoll type, two of the remainder are of Z-type (seesubsect. 5.6.3.1.2)and the Rapid Burster (seesubsect.5.6.4.3) does not belong to either of these classes[89H]. The observation of a persistent X-ray flux from low-mass X-ray binaries indicates that matter is continuously accreted onto the neutron star via an accretion disc. The accretion of matter leads to the emission of an amount of energy equal to Ed = GA4,sI RNs= 180 MeVlnucleon for “canonical” values of MNs= 1.4 Mo and R,, = 10 km. Usually, the accretion flow is not constant, causing the persistent X-ray flux to be variable. In addition to the persistent emission, all burst sources, with the exception of the Rapid Burster, emit X-ray bursts which are characterized by a distinct softening of the X-ray spectrum during the burst’s decay. These bursts are designated as bursts of type 1. They are thought to be the result of a sudden releaseof energy produced by a thermonuclear flash in freshly accreted matter. Critical conditions causing the unstable helium burning may only develop in the accreted surface layer of matter if the accretion rate is larger than a few tenths of the Eddington limit. In the case of spherical accretion by a compact object of mass M the Eddington limit is determined by the equality of gravity of an accreted unit mass element and the repulsive force produced by the X-ray radiation scattered off the electrons of the optically thin plasma:

with the mass absorption coefficient K= crTlmH, where cr= 6.65.10-25cm2is the Thomson cross-section and mH is the mass of an Hydrogen atom, the limiting Eddington luminosity is given by [26E] LEdd= 1.25.103* (M/M,)

erg/s.

On the other hand, the energy liberated in nuclear burning depends on the composition of the fuel. In transforming pure helium into iron-peak elements the total available nuclear energy is Ed = 1.7 MeV I nucleon. The second type of X-ray bursts, for which the spectral development is much less pronounced than in type-l bursts, is known only from the Rapid Burster . Table 1 summarizes the basic properties of the X-ray bursts of known burst sources and some of their binary systemparameters. Landolt-BBmstein New Series W3b


238

[Ref. p. 246

95B3 Becker, W.: PhD. Thesis, Universitat Mtinchen (1995). 95B4 Becker, W., Brazier, K.T.S., Tri.imper, J.: Astron. Astrophys. (1995), in press. 950 ogelman, H., in: The Lives of Neutron Stars (Alpar, A., Kilizoglu, U., van Paradijs, J., eds.), Dordrecht: Kluwer Academ. Publ. (1995) p. 101. 95s Safi-Harb, S., ogelman, H., in: The Lives of Neutron Stars (Alpar, A., Kilizoglu, U., van Paradijs, J., eds.), Dordrecht: Kluwer Academ. Publ. (1995), p. 53 95Y Yancopoulos, S., Hamilton, T. T., Helfand, D. J.: Astrophys. J. 429 (1994) 832.

56.4

X-ray bursters

5.6.4.1 General properties X-ray burst sources form a subset of the class of low-mass X-ray binaries. To date, 42 X-ray burst sourcesare known [93L], 10 of which are located in globular clusters. Some of the burst sourcesemit X-ray bursts rather continuously, others only at times. The bursts are characterized by a sudden rise of the X-ray flux, typically by at least one order of magnitude within a rise time of about Is, followed by a decay, generally to the original flux level, with time scalesup to 1 min or more. Outside the activity periods and between successivebursts, the sourcesemit a persistent X-ray flux. Thereby, the ratio of the persistent flux level and the average burst peak flux range from about 0.01 to 0.3, whereas the total energy in the persistent flux is about a factor of 100 higher than the total energy in the bursts. Among the burst sources, 13 are transient X-ray sources,i.e., they do not emit X-rays continuously but rather episodically. Recently, in 10 of the X-ray bursters, quasi-periodical oscillations (QPO) have been detected during the X-ray bursts as well as in the persistent emission. All but three of the bursts sourcesshowing QPO are of atoll type, two of the remainder are of Z-type (seesubsect. 5.6.3.1.2)and the Rapid Burster (seesubsect.5.6.4.3) does not belong to either of these classes[89H]. The observation of a persistent X-ray flux from low-mass X-ray binaries indicates that matter is continuously accreted onto the neutron star via an accretion disc. The accretion of matter leads to the emission of an amount of energy equal to Ed = GA4,sI RNs= 180 MeVlnucleon for “canonical” values of MNs= 1.4 Mo and R,, = 10 km. Usually, the accretion flow is not constant, causing the persistent X-ray flux to be variable. In addition to the persistent emission, all burst sources, with the exception of the Rapid Burster, emit X-ray bursts which are characterized by a distinct softening of the X-ray spectrum during the burst’s decay. These bursts are designated as bursts of type 1. They are thought to be the result of a sudden releaseof energy produced by a thermonuclear flash in freshly accreted matter. Critical conditions causing the unstable helium burning may only develop in the accreted surface layer of matter if the accretion rate is larger than a few tenths of the Eddington limit. In the case of spherical accretion by a compact object of mass M the Eddington limit is determined by the equality of gravity of an accreted unit mass element and the repulsive force produced by the X-ray radiation scattered off the electrons of the optically thin plasma:

with the mass absorption coefficient K= crTlmH, where cr= 6.65.10-25cm2is the Thomson cross-section and mH is the mass of an Hydrogen atom, the limiting Eddington luminosity is given by [26E] LEdd= 1.25.103* (M/M,)

erg/s.

On the other hand, the energy liberated in nuclear burning depends on the composition of the fuel. In transforming pure helium into iron-peak elements the total available nuclear energy is Ed = 1.7 MeV I nucleon. The second type of X-ray bursts, for which the spectral development is much less pronounced than in type-l bursts, is known only from the Rapid Burster . Table 1 summarizes the basic properties of the X-ray bursts of known burst sources and some of their binary systemparameters. Landolt-BBmstein New Series W3b

Table 1. Basic properties of X-ray burst sources. Source

Persistent properties Ref.

Pulse properties

X-ray flux HO-‘* erplcm%l

Ref.

Rise time

Ref.

[Sl

Duration

Ref.

Peak flux f1O-8 er&rn*sl

Ref.

IS1

0512-401

77Cl

< 1...4.5

89Pl

i 0.4

80C

10

8OC

0.8

8OC

0614+091

78s

3...20

84Wl

5

78s

40...100

3.5

78s

0748 - 676

86G, 87Gl

3...20

86G, 87Gl

6

86G, 87Gl

8...25

78S, 92B 86G, 87Gl

0.3...3.7

86G, 87Gl

0836-429

92A2

1254-690 1323-619 1455-314

86Cl 85V 69C

6 1.7 0.01...0.06

86Cl 89P2 87V

1 4

1516-569

82D

0.6...20

86T

3

1608-522

76Bl

< 16...80

80M2

1636-536

76Sl

7...60

87Ll

1658-298

76Ll

1...5

1702-429 1705-440

82Ml 87L2

1715-321

76B2

Orbital period

Optical counterpart

Ref.

Ref.

Remarks ‘)

in the globular cluster NGCl851 [77Cl]

3.8 h

86Pl

v1055 ori

74D

UY Vol

85W

transient X-ray source [75E]; PRE [86G, 87Gl] transient X-ray source [77Ml]

20 14 7

86Cl 89P2 80Ml

1.1 0.52 100

.86Cl 89P2 80Ml

3.9 h 2.93 h 15.1 h

86Cl 85V 89C

GR Mus

78Gl

V822 Cen

8OV

86T

lo-25

86-r

0.6

86T

16.6 d

76K

BR Cir

92M

s2

80M2

8...30

80M2

2...8

star (m, = 18.2)

87Ml

1...5

820

6...13

820

1...6

820

3.8 h

81P

V801 Ara

77M2

= 30

76Ll

= 0.2

76Ll

7.1 h

84C

V2134 Oph

79D

17 3...100

78L, 84C 82Ml 87L2

= 10 6...20

82Ml 87L2

1.7...2.5 1.3...2.0

82Ml 87L2

3...9

76M

15...150

8lM1, 84Tl

6.7

84Tl

86Cl 85V

Cen X-4; transient X-ray source [69C, 80M1, 8OK] Cir X-l; transient X-ray source [82D] PRE [86T]; QPO [87T, 88Tj recurrent transient X-ray source [78G2, 87021 PRE [89N]; QPO [89H] 4.1 keV absorption line [SSN] 4.1 keV absorption line [84W2]; QPO [89H] transient X-ray source [83C] QPO [910] high/low states period: r= 223 d[86P2] QPO [89H] PRE [84Tl] (continued)

Table 1. (Cont.) Source

Persistent properties Ref.

X-ray flux [10~‘“erg/cm2s]

Ref.

1724-307

77s

2.2

89Pl

1728-337

76L2

20.. .45

84B

Pulse properties Rise time ts1

1.0...2.5

Ref.

Orbital period Duration

Ref.

Peak flux [lo-* erg/cm%]

Ref.

15

80G

4...6

7.8

84B

s 7.8

77s, 80G 84B

ts1

84B

Optical counterpart Ref.

Ref.

in the globular cluster Terzan 2 [77S] PRE [8OH]; QPO [89H] 12 ms pulsations [82S]

1730-335 1731-260

9OSl

8...17

9OSl

10...20

9OSl

2.4

9OSl

1732-304

8lM2

1...3

87Sl

= 10

8lM2

7.4

811

1735-444 1741-293

77Ll 911

30...60

77Ll

4.4

80L

1.5...4.5 < 0.1

80L 911

1742-289

76L3

0.4

76L3

30...40

76L3

1...3

76L3

1742-294

76L3

0.8...4

76L3

3...12

76L3

1...3

76L3

1744-300 1744-265 1745-248

9OS2 87L3 81M3

1 50...150 6 30

9OS2 89H 81M3

= 20 5...15 = 10

9OS2 83Ml 811

1.2 4...8 2...6

9OS2 83Ml 8lM3

1746-370

77L2

5

89Pl

5

8732

0.95

8732

1747-214

85P

12

85P

= 10

89M

1811-171 1812- 12

85F 83M2

= 50 R_=

1.5R,,

, for R,, c 1.5 R,.

The second relation takes into account that for RNs < 1.5 R,, not all photons can escapeto infinity [79vl. Constraints on the mass-radius relation can be obtained by analyzing the spectral behavior of very strong X-ray bursts showing photospheric radius expansion. Such strong bursts usually show a brief precursor in their light curve, during which the radius of the neutron star’s photosphere increasesdue to the radiation pressure of the thermonuclear flash at its base while the temperature decreases.During this expansion phase, the luminosity is very close to its Eddington limit. The end of the precursor signal indicates that the radius of the photospheric plasma has become so large (some 200 km) and its temperature so low (= 0.5 keV) that X-rays are no longer emitted. Then the photospheric radius starts to decreaseslowly while the plasma gets hotter again. X-ray emission will onset, first at low energies,and later on, as the temperature continues to increase up to = 2.5 keV, at higher photon energiesas well. Early during this contraction phase the observed X-ray flux reaches its maximum, while the luminosity is still close to the Eddington limit. The radius decreasestops when the photosphere has shrunk to its pre-burst value. Subsequently, the hot surface of the neutron star cools at a constant photospheric radius which equals the radius of the neutron star. The spectra emitted by the hot neutron star atmosphere show luminosity-dependent deviations from a Planckian shape. Based on model calculations of London et al. [86L], the relation between the Planckian temperature Te, and the measured color temperature T, can be described according to Tel T,,= 1.51 (LlLEdd)0.04[8782]. With the local Eddington luminosity at a photospheric radius R of LEdd= (4mGMhc)(z(R)+ l), where rc=0.2 (1 +x) cm*/g denotes the electron scattering opacity of the atmosphere and X the hydrogen fraction of its matter, the following relations for the expansion and contraction phase, i.e. R > R,,, R > 1.5 R,, and LIL,,, = 1, are obtained 4ncGM L(RL

=

LEcjd

JR)

=

-

K

(14 Land&-Bhstein New Series VI/3b

Ref. p. 2461

243


and

T(R);_= (I-$ 1. 1.514*

As the relativistic Eddington limit is given by 47ccGM =2.50.103* x(1 +X)-l erg/s, ic 0 the$rst constraint for the neutron star’s masscan be written as M=0.48.108 (1+x)

(1- e)-(Y,

( &)2

E,R(R,,,)Mo.

For a given choice of (1 +x> (1.73 for cosmic abundance and 1.Ofor matter free of hydrogen) and of the anisotropy factor &, for which a range of theoretical values between 0.5 and 2.0 is reported [85L], the observables R,,,, F,,,= F(R,,,) and the distance D determine the neutron star mass within the limits of the uncertainties that are usually dominated by the uncertainty in the optical distance measurement. For the cooling phase of a burst with photospheric radius expansion, where R = R,,, it follows that

-1

1.514.4~cR2,,T,4_

, for R,, >I.5

R,,

LEdd(RNs)

1.514.4~~(+~;j)2R2,~~,

for RN, s 1.5R,,

or, if we identify the observed peak flux Fmaxmof the burst with the Eddington limit at R = R,,,, with eq. (la) and

the second constraint on the neutron star’s mass-radius relation results as 2 (1 -RGIRNS)-0.92 =;A Cl- RGIRmax)o.58

M M,

(1 - R,IRN,)o~os =A( &)2( (1 - RGIRmax)o.5*

F t-1I;,,,

“16T_

&)I’“T;~,

,,“,

for RN, > 1.5R,,

W

for RN, G 1.5R,,

(3b)

where A = 1.514c5/41coGMo. By analyzing two bursts with photospheric radius expansion emitted by the low-mass X-ray binary 4U 1746-37in the metal-rich globular Cluster NGC6441, Sztajno et al. [8782] found for the neutron star mass a range of M=(O.19 . ..0.63)&J4., Land&-Blirnstein New Series VU3b


[Ref. p. 246

3 Fig. 1. Mass and radius of the neutron star in the low-mas X-ray binary 4U 174637/NGC6441 derived from the Eddington luminosity and the optical distance estimate (horizontal lines), and from the observed color temperature-flux relation (solid curve) for an atmosphere without hydrogen (X= 0.0) and an assumedanisotropy factor of lb = 1.O.The figure was taken from Sztajno et al. [87S2].

whereby a distance of D = 6.8 . . . 11.1 kpc was applied as it was determined by comparing the reddening-corrected apparent magnitudes of horizontal-branch stars with their absolute magnitudes. The uncertainties of the latter cause the rather large interval of allowed distances. In deriving the mass from eq. (2), use was made of the fact that during maximum photospheric expansion, the redshift correction factor gl -RJR,,, approaches unity. With the measured flux at maximum expansion of log F,,, [erg cm-‘s-l] = - 8.03 f 0.05 and a flux-color temperature relation during the cooling phase at constant radius of l.l6logF-4logT,=-11.18+0.11,withT,in[keVJ, we obtain from eq.(3) the mass-radius relations 2 (1 - RGIRNS)-0.92

(1 - R,lR,,J0.58 A4 MO

= 101.‘9*o.12(1+X)-r,

(1 - RGIR,s)o~os = 10°.36*o.12(1+x)-r, (1 - RGIRmax)o.5s

for R,,

for R,,

> 1.5R,,

c 1.5R,.

The lo and 20 ranges in the mass-radius diagram allowed by these relations and by the above mass interval are indicated in Fig. 1 .

5.6.4.3

The Rapid Burster

The Rapid Burster MXB 1730-335 [76L5], located in the heavily reddened globular cluster Liller 1, is unique among the other galactic X-ray burst sources in producing two very different kinds of Xray bursts (Fig. 2). The Rapid Burster is a recurrent transient source with activity intervals of about 6 months [77G]. During its activity periods, the X-ray light curve is dominated by rapidly repetitive bursts Land&Bhstein New Series VI/3b

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with a considerable range of durations (few secondsto = 12 min) and recurrence intervals of = 10sto = 1 h. Their energetics are characterized by their recurrence behavior: the time interval to the next burst is roughly proportional to the integrated flux of the previous burst. In that, the series of this type of bursts (bursts of type 2) behave like a relaxation oscillator. Type 2 bursts do not show a spectral evolution, as type-l bursts typically do. If their spectra are described by blackbody spectra, the color temperature remains almost constant during the burst event, and the radius of the corresponding emitting area is considerably larger than that of type-l bursts during the cooling phase, i.e. it is larger than the neutron star radius. The Rapid Burster produces type-2 bursts in two different modes when it is active. In mode I, a dozen or more of relatively short bursts are emitted, followed by a strong burst of ten times longer duration. This pattern repeats itself [79M]. In mode II, the burst pattern is almost regular and the burst trains, lasting for tens of minutes, can show quasi-periods of 15.. .30 s with only a few secondsjitter [84K2]. Superimposed onto the type-2 burst pattern and uncorrelated to its time structure, bursts of type 1 arrive once in = 1.5...4 h, as they are emitted by the other burst sources known in our Galaxy. The most common mode of activity of the Rapid Burster is a combination of type-l and type-2 bursts, but there are short episodes with no type-l bursts and, vice versa, ones with only type-l bursts [84K2, 88S33. Whereas type-l bursts are thought to be produced by thermonuclear flashes in layers of accreted matter on the surface of neutron stars, the large blackbody radii of type-2 bursts may indicate that they originate from instabilities in the accretion flow, most likely located inside the first marginal orbits in a Schwarzschild metric [87M2]. The Rapid Burster is a source of quasi-periodic oscillation (QPO). QPO were observed at = 2 Hz during many type-2 bursts and often also during persistent emission between the type-2 bursts [82T, 91L]. To date, no QPO were detected in any type-l burst. The quasi-periodic oscillations of the Rapid Burster cannot be classified as of atoll type, nor is the burster a Z source [93R].

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871 Ilovaisky, S. A., Auriere, M., Chevalier, C., Koch-Miramond, L., Cordoni, J. P., Angebault, L. P.: Astron. Astrophys. 179 (1987) Ll. 87Ll Lewin, W. H. G., Penninx, W., van Paradijs, J., Damen, E., Sztajno, M, Trtimper, J., van der Klis, M.: Astrophys. J. 319 (1987) 892. 87L2 Langmeier, A., Sztajno, M., Hasinger, G., Triimper, J., Gottwald, M.: Astrophys. J. 323 (1987) 288. 87L3 Lewin, W. H. G., van Paradijs, J., Hasinger, G., Penninx, W. H., Langmeier, A., van der Klis, M., Jansen, F., Basinska, E. M., Sztajno, M., Triimper, J.: Mon. Not. R. Astron. Sot. 226 (1987) 383. 87Ml Murakami, T., Inoue, H., Makishima, K., Hoshi, R.: Publ. Astron. Sot. Jpn. 39 (1987) 879. 87M2 Milgrom, M.: Astron. Astrophys. 172 (1987) Ll. 87Sl Skinner, G. H., Willmore, A. P., Eyles, J. C., Bertram, D., Church, M. J., Harper, P. K. S., Pollock, A. M. T., Ponman, T. J., Watt, M. P.: Nature 330 (1987) 544. 8782 Sztajno, M., Fujimoto, M. Y., van Paradijs, J., Vacca, W. D., Lewin, W. H. G., Penninx, W., Triimper, J.: Mon. Not. R. Astron. Sot. 226 (1987) 39. 8783 Stella, L., Priedhorsky, W. C., White, N. E.: Astrophys. J. 312 (1987) L17. 87T Tennant, A. F.: Mon. Not. R. Astron. Sot. 226 (1987) 971. 87V Van Paradijs, J., Verbunt, F., Shafer, R. A., Arnaud, K. A.: Astron. Astrophys. 182 (1987) 47. 88M Makino, F., and the Ginga Team: IAU Circ. No. 5643 (1988). 88N Nakamura, N., Inoue, H., Tanaka, Y.: Publ. Astron. Sot. Jpn. 40 (1988) 209. 88Sl Smale, A. P., Mason, K. O., White, N. E., Gottwald, M.: Mon. Not. R. Astron. Sot. 232 (1988) 647. 8882 Schmidtke, P.: Astron. J. 95 (1988) 1528. 88S3 Stella, L., Haberl, F., Lewin, W. H. G., Parmar, A., White, N. E., van Paradijs, J.: Astrophys. J. 324 (1988) 379. 88T Tennant, A. F.: Mon. Not. R. Astron. Sot. 230 (1988) 403. 89C Chevalier, C., Ilovaisky, S. A., van Paradijs, J., Pedersen, H., van der Klis, M.: Astron. Astrophys. 210 (1989) 114. 89H Hasinger, G., van der Klis, M.: Astron. Astrophys. 225 (1989) 79. 89M Magnier, E., Lewin, W. H. G., van Paradijs, J., Tan, J., Penninx, W., Damen, E.: Mon. Not. R. Astron. Sot. 237 (1989) 729. 89N Nakamura, N., Dotani, T., Inoue, H., Mitsuda, K., Tanaka, Y., Matsuoka, M.: Publ. Astron. Sot. Jpn. 41(1989) 617. 89Pl Parmar, A. N., Stella, L., Giommi, P.: Astron. Astrophys. 222 (1989) 96. 89P2 Parmar, A. N., Gottwald, M., van der Klis, M., van Paradijs, J.: Astrophys. J. 338 (1989) 1024. 89T Tanaka, Y.: Proc. 23rd ESLAB Symp. ESA SP-296/2(1989) 3. 90C Chevalier, C., Ilovaisky, S. A.: Astron. Astrophys. 228 (1990) 119. 9OSl Sunyaev, R. A., Gilfanov, M. R., Churazov, E. M., Loznikov, V., Yamburenko, N. S., Skinner, G. H., Patterson, G. T., Willmore, A. P., Al-Emam, O., Brinkman, A. C., Heise, J., In’t Zand, J. J. M., Jager, R.: Sov. Astron. J. Lett. 16 (1990) 59. 9OS2 Skinner, G. H., Foster, A. J., Willmore, A. P., Eyles, C. J.: Mon. Not. R. Astron. Sot. 243 (1990) 72. 90V Van Paradijs, J., Dotani, T., Tanaka, Y., Tsura, T.: Publ. Astron. Sot. Jpn. 42 (1990) 633. 91C Chevalier, C., Ilovaisky, S. A.: Astron. Astrophys. 251 (1991) Lll. 911 In’t Zand, J. J. M., Heise, J., Brinkman, A. C., Jager, R., Skinner, G. H., Patterson, G. T., Pan, H.-C., Nottingham, M. R., Willmore, A. P., Al-Emam, O., Sunyaev, R. A., Churazov, E. M., Gilfanov, M. R., Yamburenko, N. S.: Adv. SpaceRes. 11 (1991) 187. 91L Lubin, L. M., Stella, L., Lewin, W. H. G., Tan, J., van Paradijs, J., van der Klis, M., Penninx, W.: Mon. Not. R. Astron. Sot. 249 (1991) 300.

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Oosterbroek, T., Penninx, J., van der Klis, M., van Paradijs, J., Lewin, W. H. G.: Astron. Astrophys. 250 (1991) 389. Schoelkopf, R. J., Kelley, R. L.: Astrophys. J. 375 (1991) 696. Aurier, M., Koch-Miramond, L.: Astron. Astrophys. 263 (1992) 82. Aoki, T., Dotani, T., Ebizawa, K., Itoh, M., Makino, F., Nagase, F., Takeshima, T., Mihara, T., Kitamoto, S.: Publ. Astron. Sot. Jpn. 44 (1992) 641. Brandt, S., Castro-Tirado, A. J., Lund, N., Dremin, V., Lapshov, L., Sunyaev, R.: Astron. Astrophys. 262 (1992) L15. Charles, P. A., Naylor, T.: Mon. Not. R. Astron. Sot. 255 (1992) 6p. Moneti, A.: Astron. Astrophys. 260 (1992) L7. Lewin, W. H. G., van Paradijs, J., Taam, R. E.: SpaceSci. Rev. 62 (1993) 223. Rutledge, R. E., Lubin, L. M., Lewin, W. H. G., van Paradijs, J., van der Klis, M.: Bull. Am. Astron. Sot. 25 (1993) 882.

Black holes

The distinction between a neutron star and a black hole as the compact object in an X-ray binary system is not trivial. All of the spectral and timing characteristics of the X-ray emission thought to be characteristic of a black hole can also be found in sources containing a neutron star. None of the information that has been obtained from such objects to date tests general relativity in the strongfield limit. As no stable neutron stars are believed to exist with massesin excessof about 3 Mo (see LB VI/2c, subsect. 5.6.1.2.2 and [74R]), any compact object exceeding this mass limit is provisionally assumedto be a black hole. Therefore, we call a compact object a black hole candidate (BHC) in a strict senseif its mass function as determined from Doppler shift measurements [see LB VI/2c, subsect. 5.6.3.2., eq.(2)] exceeds 3 Mo. There are six sources that satisfy this criterion: Cyg X-l, LMC X-l, LMC X-3, A 0620-00, GS 1124-68,and GS 2023 + 338 (seeTable 1). By comparing the spectral and temporal characteristics of the X-ray emission of these six mass selectedBHCs, certain common properties can be extracted that may indicate the possibility that a binary systemcontains a black hole. These properties are: - ultrasoft spectra, - high-energy power law tail above 20 keV, - often two spectral states: a soft spectrum for the source bright at energies < 10 keV (high state); and a hard spectrum when the source is weak at low energies(low state), - msec-variability and flickering in the hard state. Inspecting the host of known X-ray binaries [94vP], another 16 sources are identified that fulfil at least three of the four listed conditions without showing features like periodical pulsations or X-ray bursts, which would reveal the compact object unambiguously as a neutron star. These 16 sources can also be assumed to be BHCs in a less strict sense.Their properties and those of the six massselected BHCs are summarized in Table 1. Of the 20 BHCs, three are high-mass X-ray binaries (HMXB), whereas 16 BHCs are identified as low-mass X-ray binaries (LMXB). For one source, the character of the binary system is unclear. It is remarkable that 13 of the low-mass BHCs are transient sources, and that six of them show a recurrent transient behavior. Although the list in Table 1 seemsto indicate that BHCs are preferential LMXB, such a conclusion could be rash: of the six BHCs, whose massesare known to exceedthe 3 Mo limit, three are LMXB and the other three are HMXB. Forthcoming detailed studies of the less strict BHCs will almost cerrtainly reveal some of them to be neutron stars in LMXB.

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Oosterbroek, T., Penninx, J., van der Klis, M., van Paradijs, J., Lewin, W. H. G.: Astron. Astrophys. 250 (1991) 389. Schoelkopf, R. J., Kelley, R. L.: Astrophys. J. 375 (1991) 696. Aurier, M., Koch-Miramond, L.: Astron. Astrophys. 263 (1992) 82. Aoki, T., Dotani, T., Ebizawa, K., Itoh, M., Makino, F., Nagase, F., Takeshima, T., Mihara, T., Kitamoto, S.: Publ. Astron. Sot. Jpn. 44 (1992) 641. Brandt, S., Castro-Tirado, A. J., Lund, N., Dremin, V., Lapshov, L., Sunyaev, R.: Astron. Astrophys. 262 (1992) L15. Charles, P. A., Naylor, T.: Mon. Not. R. Astron. Sot. 255 (1992) 6p. Moneti, A.: Astron. Astrophys. 260 (1992) L7. Lewin, W. H. G., van Paradijs, J., Taam, R. E.: SpaceSci. Rev. 62 (1993) 223. Rutledge, R. E., Lubin, L. M., Lewin, W. H. G., van Paradijs, J., van der Klis, M.: Bull. Am. Astron. Sot. 25 (1993) 882.

Black holes

The distinction between a neutron star and a black hole as the compact object in an X-ray binary system is not trivial. All of the spectral and timing characteristics of the X-ray emission thought to be characteristic of a black hole can also be found in sources containing a neutron star. None of the information that has been obtained from such objects to date tests general relativity in the strongfield limit. As no stable neutron stars are believed to exist with massesin excessof about 3 Mo (see LB VI/2c, subsect. 5.6.1.2.2 and [74R]), any compact object exceeding this mass limit is provisionally assumedto be a black hole. Therefore, we call a compact object a black hole candidate (BHC) in a strict senseif its mass function as determined from Doppler shift measurements [see LB VI/2c, subsect. 5.6.3.2., eq.(2)] exceeds 3 Mo. There are six sources that satisfy this criterion: Cyg X-l, LMC X-l, LMC X-3, A 0620-00, GS 1124-68,and GS 2023 + 338 (seeTable 1). By comparing the spectral and temporal characteristics of the X-ray emission of these six mass selectedBHCs, certain common properties can be extracted that may indicate the possibility that a binary systemcontains a black hole. These properties are: - ultrasoft spectra, - high-energy power law tail above 20 keV, - often two spectral states: a soft spectrum for the source bright at energies < 10 keV (high state); and a hard spectrum when the source is weak at low energies(low state), - msec-variability and flickering in the hard state. Inspecting the host of known X-ray binaries [94vP], another 16 sources are identified that fulfil at least three of the four listed conditions without showing features like periodical pulsations or X-ray bursts, which would reveal the compact object unambiguously as a neutron star. These 16 sources can also be assumed to be BHCs in a less strict sense.Their properties and those of the six massselected BHCs are summarized in Table 1. Of the 20 BHCs, three are high-mass X-ray binaries (HMXB), whereas 16 BHCs are identified as low-mass X-ray binaries (LMXB). For one source, the character of the binary system is unclear. It is remarkable that 13 of the low-mass BHCs are transient sources, and that six of them show a recurrent transient behavior. Although the list in Table 1 seemsto indicate that BHCs are preferential LMXB, such a conclusion could be rash: of the six BHCs, whose massesare known to exceedthe 3 Mo limit, three are LMXB and the other three are HMXB. Forthcoming detailed studies of the less strict BHCs will almost cerrtainly reveal some of them to be neutron stars in LMXB.

Land&-B6rnstein New Series V1/3b

Table 1. Basic properties of black hole candidates, based on a compilation prepared by Tanaka and Lewin [94T2]. F, = X-ray flux [erg/cm%] for the energy band [key listed, < . . .> = mean flux value for the highly variable sources, l...lO c-9.2> I...10 -5.9... 1...6 -6.6... I...6

83B 83B - 12.2 - 11.0

G-8.5 I...10 s - 7.9 3...6 -7.o... c-11.3 2...6

-7.6... 1...50

77W 81L 92K

90K 75K 76L

-9.5

83B

X-ray spectrum ~ Type Photon index US+HET 2.2 f 0.1 US+HET 2.3 & 0.1 US+HET Jan...May ‘91 US+HET 2.2...2.6 June...Sept ‘91 power law 1.5...1.8 US+HET 2.1 US+HET US+(HET) ‘83:5.3 (1.5...7keV) ‘92: 2.2.. .2.9 (20.. ,230 keV) US+HET 1.0...2.5

Ref.

High-energy detection >50 keV

Orbital period Ref.

Wol

Ref.

V bag1

Ref.

2.3kO.3 Mx>7 0.14 & 0.05 M,=6 3.18 + 0.16 M,>7.3 3.1 + 0.4 Mx>3.1

83Pl

B3V 16.7...17.5 07...9111 14.5 V616 Mon 12...18 KOV.. .4V 13.5

83C

1.70d

83C

90D

4.22 d

87H

75R

7.75 h

86M

10.4 h

92Ml

~600

92s

Optical counterpart

Ref.

88T

920

Mass function

87H 86M 90H 92R

87H 76B 80M 91D

91Gl

83Wl 90s 84K 92H 86P

c 100

90s

~230

92H

star -17 B= 17...>19.5 AlV...2V 15...17

90K

77M 89C 83P2

1659 - 497

1705-250

GX339-4

N Ophiuchi (1977)

LMXB RT

LMXB T

1740-297

73M 94Tl

77G 77Kl 87s

1741- 322 1755-338

LMXB T LMXB

77K2 77Dl 775

1758-258

LMXB?

90M

1826-238

LMXB T LMXB LMXB

88MI

1846-031 1957+115

89T1 84Wl

H: -7.3...-8 L: -8...-10 0: 500

91s2

-9.3 2...11

84Wl

HET 1.9...2.9 US+HET 2.4 thermal kT=2keV power law = 2.0 power law = 1.7 US+HET thermal kT= 1.7 keV (0.5...10 keV) power law

84W2 91s2 88Ml

88Hl

V821 Ara 15.4... B20.0

79D 85Ml 87R

V2107 Oph B= 16.5... B21.0

78G

85M 1

78G

77Dl

14.8 h

91E

84Wl 84C 84Wl 91s2

s300

4.5 h

84W2

V4134 Sgr 18.5

85M2

9.3 h

87T

V1408 Aql 18.7

77D2

V1357 Cyg 8.9

71R 78C

QZ Vu1 16...>21

880

v404 cyg 12...21

89W 89H

93G

88Ml 89T1 84Wl

93Y 1956+350

Cyg X-l

HMXB

65B

2000+25 1

N Vulpec. (1988)

LMXB T

88M2

LMXB RT

89M 89K

2023+338

H: -7.3 L:-8.2 20 keV)

90B

= 1000

90B

5.6 d

72W

92M2

US+HET 1.9...2.5

89T2 88s

= 300

88s

8.3 h

91c2

92M2

power law 1.3...1.6

92M2 91Sl

= 300

91s3

6.47 d

92C

0.24 f 0.01 Mx>7 M,=16+5

6.26 + 0.31 M,=8...12

72W 82G

92c

254

5.6.5 Black holes

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83Wl White, N. E., Marshall, F. E.: IAU Circ. No. 3806 (1983). 83W2 Wilson, C. K., Rothschild, R. E.: Astrophys. J. 274 (1983) 717. 84C Cook, B. A., Levine, A. M., Lang, F. L., Primini, F. A., Lewin, W. H. G.: Astrophys. J. 285 (1984) 258. 84K Kitamoto, S., Miyamoto, S., Tsunemi, H., Makishima, K., Nakagawa, M.: Publ. Astron. Sot. Jpn. 36 (1984) 799. 84L Liang, E. P., Nolan, P. L.: SpaceSci. Rev. 38 (1984) 353. 84W1 White, N. E., Marshall, F. E.: Astrophys. J. 281 (1984) 354. 84W2 White, N. E., Parmar, A. N., Sztajno, M., Zimmermann, H. U., Mason, K. O., Kahn, S. M.: Astrophys. J. 283 (1984) L9. 85Ml Match, C., Ilovaisky, S. A., Chevalier, C., Angebault, P.: SpaceSci. Rev. 40 (1985) 219. 85M2 Mason, K. O., Parmar, A. N., White, N. E.: Mon. Not. R. Astron. Sot. 216 (1985) 1033. 86M McClintock, J. E., Remillard, R. A.: Astrophys. J. 308 (1986) 110. 86P Parmar, A. N., Stella, L., White, N. E.: Astrophys. J. 308 (1986) 664. 87H Hutchings, J. B., Crampton, D., Cowley, A. P., Bianchi, L., Thompson, I. B.: Astron. J. 94 (1987) 340. 87M Makino, F.: IAU Circ. No. 4342 (1987). 87P Priedhorsky, W. C., Holt, S. S.: SpaceSci. Rev. 45 (1987) 291. 87R Remillard, R. E., McClintock, J. E.: IAU Circ. No. 4384 (1987). 87s Skinner, G. K., Willmore, A. P., Eyles, C. J., Bertram, D., Church, M. J., Harper, P. K. S., Herring, J. R. H., Peden, J. C. M., Pollock, A. M. T., Ponman, T. J., Watt, M. P.: Nature 330 (1987) 544. 87T Thostensen, J. R.: Astrophys. J. 312 (1987) 739. 88B Boney, W. B., Charles, P. A.: IAU Circ. No. 4532 (1988). 88D de Kool, M.: Astrophys. J. 334 (1988) 336. 88Ml Makino, F., and the Ginga Team: IAU Circ. No. 4653 (1988). 88M2 Makino, F.: IAU Circ. Nos.4587,4600 (1988). 880 Okamura, S., Noguchi, T.: IAU Circ. No. 4589 (1988). 88s Syunyaev, R. A., Lapshov, I. Yu., Grebenev, S. A., Efremov, V. V., Kaniovskii, A. S., Stepanov, D. K., Yunin, S. N., Gavrilova, E. A., Loznikov, V. M., Prudkoglyad, A. V., Rodin, V. G., Babushkina, 0. P., Kiselev, S. V., Kuznetsov, A. V., Melioranskii, A. S., Smith, A., Parmar, A. N., Pietsch, W., Dtibereiner, S., Englhauser, J., Reppin, C., Triimper, J., Voges, W., Kendziorra, E., Maisack, M., Mony, B., Staubert, R.: Sov. Astron. Lett. 14 (1988) 327. 88T Treves, A., Belloni, T., Chiapetti, L., Maraschi, L., Stella, L., Tanzi, E. G., van der Klis, M.: Astrophys. J. 325 (1988) 119. 89C Chevalier, C., in: Proc. 23rd ESLAB Symp. on X-ray Astronomy (eds. Hunt, J., Battrick, B.), ESA SP-296(1989) 341. 89H Hurst, G. M., Mobberley, M.: IAU Circ. No. 4783 (1989). 89K Kitamoto, S., Tsunemi, H., Miyamoto, S., Yamashita, K., Mizobuchi, S., Nakagawa, M., Dotani, T., Makino, F.: Nature 342 (1989) 518. 89M Makino, F.: IAU Circ. Nos. 4782,4786 (1989). 89Tl Tanaka, Y., in: Proc. 23rd ESLAB Symp. on X-ray Astronomy (eds. Hunt, J., Battrick, B.), ESA SP-296(1989) 3. 89T2 Tsunemi, H., Kitamoto, S., Okamura, S., Russel-Dupre, D.: Astrophys. J. 337 (1989) L81. 89W Wagner, R. M., Starrfield, S., Cassatella, A.: IAU Circ. No. 4783 (1989). 90B Barr, P., van der Woerd, H.: Astrophys. J. 352 (1990) L41. 90D Dotani, T., Tnoue, H., Murakami, T., Nagase, F., Tanaka, Y., Tsuru, T., Makishima, K., Ohashi, T., Corbet, R. H. D.: Nature 347 (1990) 534. 90H Haswell, C. A., Shafter, A. W.: Astrophys. J. 359 (1990) L47. 90K Kitamoto, S., Tsunemi, H., Pedersen,H., Ilovaisky, S. A., van der Klis, M.: Astrophys. J. 361 (1990) 590. Land&-BBmstein New Series V1/3b

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90M Mandrou, P., and the Granat Team: IAU Circ. No. 5032 (1990). 90s Sunyaev, R.: IAU Circ. No. 5104 (1990). 9lC1 Cowley, A. P., Schmidtke, P. C., Ebisawa, K., Makino, F., Remillard, R. A., Crampton, D., Hutchings, J. B., Kitamoto, S., Treves, A.: Astrophys. J. 381 (1991) 526. 9lC2 Callanan, P. J., Charles, P. A.: Mon. Not. R. Astron. Sot. 259 (1991) 395. 91D Della, Valle, M., Jarvis, B.: IAU Circ. No. 5165 (1991). 91E Ebisawa, K.: PhD Thesis, ISAS, University Tokyo (1991). 91Gl Greiner, J., Egger, R., Hartner, G., Hasinger, G., Pietsch, W., in: Proc. Workshop on Nova Muscae 1991(ed. Brandt, S.), Lyngby (1991) 79. 91G2 Grebenev, S. A., Syunyaev, R. A., Pavlinski, M. N., Dekhanov, I. A.: Sov. Astron. Lett. 17 (1991) 413. 91L Lund, N., Brandt, S., Makino, F., and the Ginga Team: IAU Circ. No. 5161 (1991). 91M Miyamoto, S., Kimura, K., Kitamoto, S., Dotani, T., Ebisawa, K.: Astrophys. J. 383 (1991) 784. 91Sl Syunyaev, R., Kaniovskii, A. S., Efremov, V. V., Aref’ef, V. A., Borozdin, K. N., Gil’fanov, M. R., Churazov, E. M., Kuznetsov, A. V., Melioranskii, A. S., Yamburenko, N. S., Pietsch, W., Ddbereiner, S., Englhauser, J., Reppin, C., Triimper, J., Voges, W., Kendziorra, E., Maisack, M., Mony, B., Staubert, R., Skinner, G. K., Nottingham, M. R., Pan, H., Willmore, A. P., Brinkman, A. C., Heise, J., In’t Zand, J. M., Jager, R.: Sov. Astron. Lett. 17 (1991) 123. 91S2 Syunyaev, R., Gil’fanov, M., Churazow, E., Pavlinski, M., Babalyan, G., Dekhanov, I., Kuznetsov, A., Grebenev, S., Yunin, S., Yamburenko, N., Cordier, B., Lebrun, F., Laurent, P., Ballet, J., Mandrou, P., Roques, J. P., Vedrenne, J., Boucher, L.: Sov. Astron. Lett. 17 (1991) 50. 92Bl Brandt, S., Castro-Tirado, A. J., Lund, N., Dremin, V., Lapshov, I., Sunyaev, R.: Astron. Astrophys. 254 (1992) L39. 92B2 Bazzano, A., La Padula, C., Ubertini, P., Sood, R. K.: Astrophys. J. 385 (1992) L17. 92C Casares,J., Charles, P. A., Naylor, T.: Nature 355 (1992) 614. 92H Harmon, B. A., Wilson, R. B., Finger, M. H., Paciesas,W. S., Rubin, B. C., Fishman, G. J.: IAU Circ. No. 5504 (1992). 92K Kitamoto, S., Tsunemi, H., Miyamoto, S., Hayashida, K.: Astrophys. J. 394 (1992) 609. 92M1 McClintock, J. E., Bailyn, C., Remillard, R.: IAU Circ. No. 5499 (1992). 92M2 Mineshige, S., Ebisawa, K., Takizawa, M., Tanaka, Y., Hayashida, K., Kitamoto, S., Miyamoto, S., Terada, K.: Publ. Astron. Sot. Jpn. 44 (1992) 117. 920 Ogawa, M.: MSc. Thesis, ISAS, Tokyo: Rikkyo University (1992). 92R Remillard, R. A., McClintock, J. E., Bailyn, C. D.: Astrophys. J. 399 (1992) L145. 92s Sunyaev, R., Aref’ev, V., Borozdin, K., Churazov, E., Efremov, V., Gilfanov, M., Kaniovsky, A., Kendziorra, E., Mony, B., Maisack, M., Staubert, R., Dobereiner, S., Englhauser, J., Pietsch, W., Reppin, C., Trtimper, J., Skinner, G. K., Nottingham, M. R., Pan, H., Willmore, A. P., Brinkman, A. C., Heise, J., In’t Zand, J. M., Jager, R., in: Frontiers of X-ray Astronomy (eds. Tanaka, Y., Koyama, K.), Tokyo: Univ. Acad. Press(1992) 697. 93G Grebenev, S., Sunyaev, R., Pavlinsky, M., Churazov, E., Gilfanov, M., Dyachkov, A., Khavenson, N., Sukhanov, K., Laurent, P., Ballet, J., Claret, A., Cordier, B., Jourdian, E., Niel, M., Pelaez,F., Schmitz-Fraysse, M. C.: Astron. Astrophys. Suppl. 97 (1993) 281. 93Y Yaqoob, T., Ebisawa, K., Misuda, K.: Mon. Not. R. Astron. Sot. 264 (1993) 411. 94Tl Tanaka, Y., in: Ginga Memor. Symp. (eds. Makino, F., Nagase, F.), (1994), in press. 94T2 Tanaka, Y., Lewin, W. H. G, in: X-ray Binaries (eds. Lewin, W. H. G., van Paradijs, J., van den Heuvel, E. P. J.), Cambrgide: Cambridge University Press,(1994), p. 126. 94vP van Paradijs, J., in: X-ray Binaries (eds. Lewin, W. H. G., van Paradijs, J., van den Heuvel, E. P. J.), Cambridge: University Press(1994), p. 58

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5.7 X-ray and y-ray sources

5.7 X-ray and y-ray sources 5.7.1

X-ray sources

5.7.1.1 Overview The progress of X-ray astronomy in the last decade is based on the observational results obtained from several satellite-borne experiments. In the early 1980s pictures of some parts of the X-ray sky were taken for the first time with the X-ray telescope onboard the Einstein Observatory, consisting of a Wolter-type mirror system and electronic image detectors working at X-ray energies between 0.5 keV and 4.5 keV. Becauseof the superior sensitivity of the imaging telescope,some 6000 new galactic and extragalactic X-ray sources could be discovered. The subsequent satellite experiments, - EXOSAT, MIR-Kvant, Tenma, and Ginga-, were devoted mainly to pointed observations of individual sources in order to study their spectral and temporal properties. The relevant part of these measurements was performed in the energy range from 2 keV to about 20 keV using non-imaging detector devices. In the middle of 1990, the satellite ROSAT was launched carrying two X-ray telescopes, the main telescopetaking pictures of the X-ray sky in the soft energy band from 0.1 keV to 2.4 keV with a sensitivity improved by a factor of more than 5, and a wide-field camera, an XUV telescopemeasuring in the very soft energy band from 0.025 keV to 0.2 keV. In the first 6 months of its mission, ROSAT carried out an all-sky survey resulting in a qualitative leap in observational X-ray astronomy by detecting more than 60 000 new celestial X-ray sources, out of which 20 000 -30 000 objects are extragalactic. ROSAT’s mission is still going on. With the measurementsof ROSAT, X-ray astronomy has reached the stage where large samples of all kinds of objects can be studied on a wide scale of luminosities and redshifts at photon energies that trace the most energetic processesknown to occur in the universe. Table 1. Classesof observed X-ray sourcesand their typical members. Continuation of Table 1 in LB VI/2c p.33. L, = Isotropic X-ray luminosity for the spectral band given in the preceding column. X-ray luminosity range = general luminosity range of the class as a whole. In some cases,the proposed radiation processesare given in footnotes. Table la. Galactic objects. Object class

Typical object X-ray luminosity

Neutron stars (seesubsect. 5.6.1) Cooling neutron PSR0656+14 stars “)

Spectral band WCI

L,

0.1...1.35

2.1032

Ref.

[erg s- ‘1

93B

“) The tentative identification of a point source (lE161348-5055.1) in the SNR RCW103 could not be confirmed by the more sensitive measurement with ROSAT.


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Table lb. Extragalactic objects. Object class

Blazars BL Lacertae objects OW/HPQ b,

Typical object

MKN 421 3C 279

Diffuse extragalactic emission

X-ray luminosity range “)

X-ray luminosity “) Spectral band [W

L, [erg s- ‘1

Ref.

& [erg s- ‘1

Ref.

0.1...2.4 2...10 0.1...2.4 2...10

12.1045 2. lo4 2.6.1046 (0.6...3.3).1046

91F 81M 92 Ml 89M

5~1042...3~1046 2.1043...8.1045 5.104s...3.1046

92Fl 90G1 920

Energy W’l 1

Surface brightness lphotons cm-*sslsrl] 7

Ref. 92Hl

“) Blazars are suspectedto emit their radiation beamed. The luminosity for beamed radiation is lower than for isotropic luminosity by a factor of l/2(1 -co@), where @is the opening half-angle of the conical radiation beam. b, Optically violently variable and highly polarized quasar. 5.7.1.2 Sky surveys see Table 2. 5.7.1.3 X-ray emission processes see LB VI/2c, p. 36

5.7.2

y-ray sources

5.7.2.1 Overview The high-energy experiment EGRET (Energetic Gamma Ray Experiment Telescope) onboard the Gamma Ray satellite Observatory (GRO), launched in early 1991, recently detected 14 new extragalactic y-ray sources (Table 3). At least 11 of them belong to the class of blazars, i.e., violently variable and highly polarized sources in galactic nuclei showing jets at radio and optical wavelengths. The strong correlation of y-ray emission and blazar characteristics indicates that in extragalactic sources, y-rays are likely to be produced in jets as relativistically beamed radiation. In addition, GRO/EGRET detected two y-ray pulsars at photon energies greater than 100 MeV, and GRO/BASTE (Bursts And Transient Source Experiment) a further pulsar above 1.8 MeV in the Circinus region.

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Table 2. Main surveys and catalogues of X-ray sources. Continuation Energy band NYI

of Table 2 in LB VI/2c, p. 36.

Satellite/ experiment

Catalogue designation

Einstein Obs./IPC

MS

0.3...3.5

835

IO-‘3 . ..3-10-i’ b)

EXOSATKMA

EXO

0.05.. .2.0

230

2*10-13...2~10-12b)

ROSAT/XRT ROSAT/WFC

RX

=60000 = 400

8e10-14. ..4.10-‘3

0.1.. .2.4 0.025.. .0.2

Number of detected sources

Sensitivity “) [erg cm-*s-‘keV-I]

Remarks

Ref.

High galactic latitude lb1> 20” “) High galactic latitude lb1> 20” d, All-sky survey All-sky survey

90G2 89G

it

“) For a power law spectrum with a photon index of l-=2.0 and an interstellar absorption of NH=2.5~10zo cmm2. “) Sensitivity depends on the exposure time of the individual pointed observation. “) Sample of serendipitous sources found in the fields of view of 464 individual pointed observations approximately evenly distributed over the sky at high galactic latitudes covering 820 deg2. d, Sample of serendipitous sources found in the fields of view of 1435 individual pointed observations covering 780 deg2.

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Table 3a. Extragalactic y-ray sources. Object 0202+ 149 0208-512 0235+164 0420-014 0528+134 0537-441 0716+714 0836+710 1101+384 1226+023 1253 - 055 1633+382 2230+114 2251+158

Redshift AfU& PKS PKS A0 PKS

1.03 0.852 0.915 0.691 0.894

PKS s5 s5 MKN 421 3C 273 b, 3C 279 4C 38.41 CTA 102 3c 454.3

2.17 0.031 0.158 0.538 0.81 1.037 0.859

Intensity (> 100 MeV) [10e6 photons cm-%‘] “1 0.3kO.l

Type

Ref.

QSO

92H2 92K 92H2 92H2 92K 92M2 921112 92F2 92M2 93M 92H3 92K 92H4 92H4

Blazar Blazar Blazar

:; 0.8’cO.l 0.34 * 0.09 0.20 f 0.04 0.15+0.04 0.11 f 0.03 0.3+0.1 0.6.. .4.9 “) 1.O-tO.l 1;

Blazar Blazar

QSO Blazar Blazar Blazar Blazar Blazar Blazar

“) Source detectedat energiesgreater than 100 MeV but with intensity not yet established. b, Source previously detected with the satellite COS-B observed at an intensity level 20 times brighter than in the recent GRO/EGRET observation. “) Variable by a factor of 8 during the GROlEGRET observational peroid between June and October 1991. Table 3b. Galactic y-ray sources. Discrete galactic sources

Period [ms]

Ref.

Geminga pulsar PSR 1706-44 PSR 1509-58

237 102 151 (SNR MSH 15-52)

92B2,92H5 92Bl 92F3

5.7.2.2 y-radiation processes see LB VI/2c, p. 42

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References for 5.7 Catalogues a b

The ROSAT/XRT catalogue is in preparation; cf.: Voges, W.: European ISY Symposium, SpaceSciencewith Particular Emphasis on High-Energy Astrophysics, ESA ISY-3 (1992) 9. Pounds, K. A., et al.: The ROAST Wide Field Camera allsky survey of extrem ultraviolet sources.I. The Bright Source Catalogue. Mon. Not. R. Astron. Sot. 260 (1993)77.

Special references 81M Marshall, N., Warwick, R. S., Pounds, K. A.: Mon. Not. R. Astron. Sot. 194 (1981) 987. 89G Giommi, P., Tagliaferri, G., Beuermann, K., Branduardi-Raymont, G., Brissenden, R., Graser, U., Mason, K. O., Murdin, P., Pooley, G., Thomas, H.-C., Tuohy, I.: BL Lac Objects (Maraschi, L., Ulrich, M.-H., eds.), Lect., Notes Phys. 334 (1989) 231. 89M Makino, F., Kii, T., Hayashida, K., Inoue, H., Tanaka, Y., Ohashi, T., Makishima, K., Awaki, H., Koyama, K., Turner, M. J. L., Williams, 0. R.: Astrophys J. 347 (1989) L9. 90Gl Giommi, P., Barr., P., Garilli, B., Maccagni, D., Pollock, A. M. T.: Astrophys. J. 356 (1990) 432. 90G2 Gioia, L. M., Maccacaro, T., Schild, R. E., Wolter, A., Stocke, J. E., Morris, S. L., Henry, J. P.: Astrophys. J. Suppl. 72 (1990) 567. 91F Fink, H. H., Thomas, H.-C., Hasinger, G., Predehl, P., Schaeidt, S., Makino, F., Warwick, R. S.: Astron. Astrophys. 246 (1991) L6. 92Bl Bertsch, D. L., Fichtel, C. E., Hartman, R. C., Hunter, S. D., Kwok, P. W., Mattox, J. R., Nel, I., Sreekumar, P., Thompson, P. J., Fierro, J. M., Lin, Y. C., Michelson, P. F., Nolan, P. L., Schneid, E., Kanbach, G., Mayer-Hasselwander, H. A., von Montigny, C., Pinkau, K., Rothermel, H., Sommer, M.: IAU Circ. No. 5485 (1992). 92B2 Bertsch, D. L., Brazier, K. T. S., Fichtel, C. E., Hartman, R. C., Hunter, S. D., Kanbach, G., Kniffen, D. A., Kwok, P. W., Lin, Y. C., Mattox, J. R., Mayer-Hasselwander, H. A., von Montigny, C., Michelson, P. F., Nolan, P. L., Pinkau, K., Rothermel, H., Schneid, E., Sommer, M., Sreekumar, P., Thompson, P. J.: Nature 357(1992) 306. 92Fl Fink, H. H., Thomas, H.-C., Brinkmann, W., Okayasu, R., Hartner, G.: X-Ray Emission from Active Galactic Nuclei and the Cosmic X-Ray Background (Brinkmann, W., Triimper, J., eds.), MPE Report 235 (1992) 202. 92F2 Fichtel, C. E., Bertsch, D. L., Hartman, R. C., Hunter, S. D., Kwok, P. W., Mattox, J. R., Sreekumar, P., Thompson, P. J., Kniffen, D. A., Chiang, J., Lin, Y. C., Michelson, P. F., Nolan, P. L., Schneid, E., Kanbach, G., Mayer-Hasselwander, H. A., von Montigny, C., Pinkau, K., Rothermel, H., Sommer, M.: IAU Circ. No. 5460 (1992). 92F3 Fishman, G.: Meet. Am. Astron. Sot. (1992). 92Hl Hasinger, G.: X-Ray Emission from Active Galactic Nuclei and the Cosmic X-Ray Background (Brinkmann, W., Trtimper, J., eds.), MPE Report 235 (1992) 321. 92H2 Hartman, R. C., Bertsch, D. L., Fichtel, C. E., Hunter, S. D., Kwok, P. W., Mattox, J. R., Sreekumar, P., Thompson, P. J., Kniffen, D. A., Chiang, J., Lin, Y. C., Michelson, P. F., Nolan, P. L., Schneid, E., Kanbach, G., Mayer-Hasselwander, H. A., von Montigny, C., Pinkau, K., Rothermel, H., Sommer, M.: IAU Circ. No. 5519 (1992). 92H3 Hartman, R. C., Bertsch, D. L., Fichtel, C. E., Hunter, S. D., Kanbach, G., Kniffen, D. A., Kwok, P. W., Lin, Y. C., Mattox, J. R., Mayer-Hasselwander, H. A., Michelson, P. F., von Montigny, C., Nel, I., Nolan, P. L., Pinkau, K., Rothermel, H., Schneid, E., Sommer, M., Sreekumar, P., Thompson, P. J.: Astrophys. J. 385 (1992) Ll. Landolt-B6mstein New Series VU3b

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92H4 Hartman, R. C., Bertsch, D. L., Fichtel, C. E., Hunter, S. D., Kwok, P. W., Mattox, J. R., Sreekumar, P., Thompson, P. J., Kniffen, D. A., Lin, Y. C., Michelson, P. F., Nolan, P. L., Schneid, E., Kanbach, G., Mayer-Hasselwander, H. A., von Montigny, C., Pinkau, K., Rothermel, H., Sommer, M.: IAU Circ. No. 5477 (1992). 92H5 Halpern, J. P., Holt, S. S.: Nature 357 (1992) 222. 92K Kanbach, G., Mayer-Hasselwander, H. A., von Montigny, C., Pinkau, K., Rothermel, H., Sommer, M., Bertsch, D. L., Fichtel, C. E., Hartman, R. C., Hunter, S. D., Kwok, P. W., Mattox, J. R., Sreekumar, P., Thompson, P. J., Kniffen, D. A., Lin, Y. C., Michelson, P. F., Nolan, P. L., Schneid, E.: IAU Circ. No. 5431 (1992). 92Ml Makino, F., Fink, H. H., Clavel, J.: Yamada Conference on Frontiers in X-ray Astronomy (Tanaka, Y., Koyama, K., eds.) Tokyo: Universal Academic Press(1992) p.543. 92M2 Michelson, P. F., Lin, Y. C., Nolan, P. L., Bertsch, D. L., Fichtel, C. E., Hartman, R. C., Hunter, S. D., Kwok, P. W., Mattox, J. R., Sreekumar, P., Thompson, P. J., Kniffen, D. A., Schneid, E., Kanbach, G., Mayer-Hasselwander, H. A., von Montigny, C., Pinkau, K., Rothermel, H., Sommer, M.: IAU Circ. No. 5470 (1992). 920 Okayasu, R.: PhD Thesis (1992), Saitama: University Saitama, Japan. 93B Becker, W., Triimper, J., ogelman H.: Isolated Pulsars (Riper, K. A., Epstein, R. I., Ho, C., eds.) Cambridge: Cambridge University Press(1993) p.104. 93M von Montigny, C., Bertsch, D. L., Fichtel, C. E., Hartman, R. C., Hunter, S.D., Kanbach, G., Kniffen, D. A., Kwok, P. W., Lin, Y. C., Mattox, J. R., Mayer-Hasselwander, H. A., Michelson, P. F., Nolan, P. L., Pinkau, K., Rothermel, H., Schneid, E., Sommer, M., Sreekumar, P., Thompson, P. J.: Astron. Astrophys. Suppl. 97 (1993) 101.

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6.1.0 Double stars: General remarks

263

6 Double stars and star clusters

6.1 Double stars 6.1.0 General remarks For a definition of double stars or binaries, see LB VI/2b, subsect. 6.1.0

6.1.0.1 Classification Progress of research since 1970 made it reasonable, almost inevitable, to organize the treatment of double stars along new, markedly different lines. A new class of objects emerged to primary importance: (a) Systems which contain at least one collapsed component, notably a neutron star or black hole. Although the number of such systems discovered is still only about 150…200, their separate treatment is fully justified, also by the methods of their study which is very much different from that of other binaries. (b) Spectroscopic and eclipsing binaries, while their separate treatment is still justified in various contexts, can be considered as a major, common group, linked by the fact that interaction between the components is not only possible but it actually occurs at certain phases of the binary evolution. There are close binaries where individual, stellar evolution of the component is thus mutually influenced, possibly to a very significant degree. (c) The long-recognized class of visual double stars is virtually identical with that of the wide binaries, characterized by the lack of any significant interaction between the components which evolve essentially as single stars. There is no exact dividing line between close and wide binaries but, except for high-mass binaries, orbital periods of 10…15 years can serve as separation between the two classes. From the observational point of view, increasing resolution of both visual and spectroscopic techniques (see discussion later) generated a number of overlapping cases between these two classes. In this chapter binary and multiple stars are now divided into the following three classes: (1) Wide binaries (subsect. 6.1.1): the visual double stars of the earlier edition, see LB VI/2b, subsect. 6.1.1 (2) Close binaries (subsect. 6.1.2): spectroscopic and eclipsing binaries, see LB VI/2b, subsects. 6.1.3 and 6.1.5 (3) Binary systems with collapsed (compact) objects (subsect. 6.1.3): see LB VI/2b, subsect. 6.1.4 A preliminary remark seems necessary here. Two wide topics of double star astronomy are not treated here in any detail: (1) cataclysmic variable stars, and (2) binaries in star clusters. These topics Landolt-Börnstein New Series VI/3B

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have to be referred to other chapters of this work: subsect. 5.1.4 and sect. 6.2, respectively. On the other hand, there are some obvious connections between these topics and the main field of binary astronomy, and thus in the following treatment, especially dealing with compact objects, occasional cross references will prove necessary.

6.1.0.2 Orbital elements Symbols a P e i Ω

= semi-major axis = orbital period = numerical eccentricity = inclination = position angle of the ascending node

ω = longitude of the periastron t0 = epoch of periastron passage M1 , M2 = masses of the components R1 , R2 = radii of the components

For more details see LB VI/2b, subsect. 6.0.1.2. Observations and the orbital elements derived – Visual binaries, relative motion (referred to brighter component): all orbital elements, but for i the sign remains ambiguous; if distance known, M1+M2 – Visual binaries, motion referred to barycenter: all orbital elements and M1 /M2 ; for i, sign ambiguous; if distance known, M1 and M2 ; sign of i can be determined from radial velocities. – Spectroscopic binaries, one spectrum observed: P, a1 sin i, e, ω, t0 , mass function f(M) = f(M1 , M2 , i). The actual form of f(M) is discussed in subsect. 6.1.3.1.3. – Spectroscopic binaries, two spectra observed: P, a1 sin i, a2 sin i, e, ω, t0 , mass function and M1 /M2 . For a complete solution, knowledge of the inclination i is necessary. – Eclipsing binaries: P, R1 /a, R2 /a, i, e, ω and (if e ≠ 0) t0. For any accurate determination of i, a well observed total-annular eclipse is needed.

6.1.0.3 Masses A particularly important contribution to the physics of stars is the derivation of stellar masses. On a larger scale, individual stellar mass determinations are only possible by using binary systems. The only known other cases are (1) white dwarf masses, using the relativistic redshift, or (2) relying on the surface gravity, as derived from large dispersion spectra, in combination with an estimated radius. The first method is mainly statistical, the second yields hardly more than estimates of masses. (1) Visual double stars yield, in the case of relative orbits, the sum of the masses: M1+M2 = a3(arc)/p3P2 , where a(arc) is the semi-major axis of the relative orbit in angular units, p the parallax (usually both expressed in arcsec), P the period in sidereal years, and the masses in solar masses M . Individual masses are only obtainable, if the "absolute" orbits (referred to the center of mass of the system) are

Landolt-Börnstein New Series VI/3B

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also observed. Owing to the p–3 factor, mass determinations using visual binaries are of lower accuracy, except for the nearest stars. An inversion of the method is the determination of dynamical parallaxes, assuming representative values for M1+M2 and treating the parallax as the unknown quantity. If spectral types and/or colors of the components are known, dynamical parallaxes become superior to the trigonometric ones for distances above 30…40 pc. (2) Mass determinations based on spectroscopic binaries yield the best values, if spectra of both components are observed and the system is eclipsing (preferably complete eclipses). In such cases the inclination in the system and the mass ratio can be derived and the mass function solved uniquely; see LB VI/2b, subsect. 6.1.3.1, especially equ. (3). This method yields the masses of the components independently of the distance of the binary. For the best observed systems a critical discussion, almost exclusively based on spectroscopic and photometric evidence, is to be found in: D. M. Popper, "Stellar masses" [80P]. For some of the best determined system parameters, see also J. Andersen's review of the "Copenhagen program" [87A]. Accuracy obtainable for the best known systems is also discussed by Popper [84P] and in the extensive review by J. Andersen, "Accurate masses and radii of normal stars" [91A]. See also Andersen et al. in [84A].

6.1.0.4 Statistics Among statistical studies concerning the incidence of double and multiple systems as well as the distribution of orbital elements we have to mention: H.A. Abt, "Normal and abnormal binary frequencies" [83A]. Among those systems where binarity is complete or nearly complete, two important groups are to be considered closer: (1) cataclysmic variables, and (2) Wolf-Rayet stars. Novae, dwarf novae, recurrent novae and nova-like objects (cataclysmic variables) are, according to general consensus today, all or at most with very few exceptions binary stars. The typical combination is: white dwarf – late main sequence star (in a few cases: late giant). The accretion of matter in these close pairs from the late-type component onto the white dwarf, usually surrounded by an accretion disk, is the basic mechanism leading to the outbursts. These variables are only mentioned here because of their structural similarity to low-mass X-ray binaries (where the white dwarf is replaced by a neutron star). See subsect. 5.1.4. Contrary to earlier belief, statistical arguments suggest that at least some Wolf-Rayet (WR) stars are single. However, the percentage of binarity may be as high as 80…85%, although using limited criteria, such as the appearance of absorption lines in the spectrum (due to the secondary component), Vanbeveren and Conti [80V], and also Massey [81M] reach only to about 40% duplicity. The great majority of systems show the combination: WR star + O star. The mass-ratio WR/O is about 0.3 to 0.5 and the more evolved WR component has had to suffer very large mass losses. The presence of compact components was also occasionally argued. For WR stars see also subsect. 5.2.1.2. Among brighter stars, studies of statistical properties of binaries have been evaluated, based on the Catalog of Bright Stars, 4th edition (BSC) [82H], by J.L. Halbwachs, concerning visual binaries [83H] and systems with evolved primary components [86H]. It has been suggested that for visual binaries, the intrinsic distribution of log a (semi-major axis of the relative orbit) is constant for a > 30 AU; according to these studies, the proportion of single stars among stellar systems is ≤ 23%. Binary statistics can be fundamentally linked with theories of stellar formation, see Zinnecker [84Z], also [93Z], and Bodenheimer [93B], among others, or the more general review by Shu et al. [87S]. The binary frequency among A-type stars shows a remarkable distribution which has to be mentioned here. Spectroscopic information suggests a dichotomy between A-metallic (Am) stars and normal composition A-stars in the range A4…F1 insofar that the former group may consist not only predominantly but perhaps entirely of binary systems, with orbital periods ranging from a few days


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to maximum 80…100 days. The information stems from radial velocity measurements and, in the first place, the observed equatorial velocities of rotation; a considerable portion of the data is due to H.A. Abt. These periods of rotation are then results of synchronization, and the relatively slow rotation (as compared with the fast-rotating normal A-stars) may be also responsible for the anomalous abundances in the spectra of Am-stars, especially in the presence of mass loss; see [83M] on this point, and for statistical studies of binary frequencies in general, the review by Abt [83A], also the earlier dicussions of Heintz [69H] and Levato [76L]. Multiplicity among solar-type stars (F7 to G9) in the solar neighborhood was studied by Duquennoy and Mayor [91D] based on an extensive CORAVEL radial-velocity survey. In a sample considered unbiased, they found an unimodal binary period distribution with a median period of 180 years, cicularization only for the closest systems (P < 11d) and no maximum in the secondary-mass distribution toward equal masses of the components. Binaries in the third Catalogue of Nearby Stars (CNS3, for a short description see [93J]) are being discussed by Gliese and Jahreiss [88G]. The relative binary frequency (for a definition see LB VI/2b, subsect. 6.1.0.4, p. 384) has been found 63% for distances < 5 pc, and 50% for 5…10 pc. In spite of the unavoidable incompleteness of the catalog, it seems difficult if not impossible to adopt 100% binarity in the solar heighborhood; this is supported by [91D] finding that perhaps 1/3 of solar-type stars may be single (i.e. not having components above 0.01 M ). Wide separations are remarkably frequent: CNS3 contains 65 systems with projected separations > 2000 AU, and 32 systems with separations > 5000 AU; a number of these objects, however, may not form physical systems. The question of multiplicity among pre-main sequence stars, in particular T Tauri variables, promises to shed some light on the problem of binary origin, a process which after all produces the majority of stellar objects. Among several recent investigations dedicated to this problem we mention [92S1, 93R, 93G]; the latter study was based on speckle interferometry (see subsect. 6.1.1.3). The results seem to indicate an excess of binarity as compared to G and K type main sequence stars. This may suggest that pre-stellar fragmention in dense interstellar clouds first produces wide, multiple condensations, most (but not all) of them evolve to binary and (hierachic, ab–c type) triple systems. As to the formation of close binary pairs, fission of fast rotating protostars (or extremely young stars) is a wide-spread, although not generally accepted opinion. A survey of binary candidates among high-velocity, population–II stars, carried out using the ICCD speckle camera (see speckle interferometry, subsect. 6.1.1.3), found among nearly 200 stars of the solar neighborhood no noticeably lower binary frequency than shown by low-velocity main sequence stars [87L]. This study, also the fact that several halo binaries do exist (for instance, µCas) is in conformity with the emerging conviction that population–II systems are not seriously deficient in binaries, as it was earlier assumed. See to this question V. Trimble's review [92T] and the extensive discussion by nine authors in [92H]. The problem of the so-called blue stragglers may also contribute to the question of binarity among population–II stars. These are apparently unevolved stars in the upper main sequence of globular and some very old open clusters and binary mechanisms are repeatedly proposed as explanation of the phenomenon. See several articles in [92S2] Multiplicity among stars within 5 pc The 48 nearest stars contain 66 components, unseen companions (UC) not counted (as yet, none of the UCs proposed earlier is definitively confirmed). Of these 66 stars, 33 are in systems. A sample is given Table 1. Distances up to 5 pc are known, on the average, with an uncertainty of about 1.5 percent (all these are trigonometric parallaxes). In a sample of nearby stars, inconclusive evidence for UCs has been found in the case of Barnard's star, BD36°2147, 61 Cygni, BD5°1668, BD68°496, BD20°2465, and BD43°4305. The search for unseen companions by astrometric methods, that is, study of the primary component's proper motion, is part of a major effort to detect substellar masses. Two kinds of Landolt-Börnstein New Series VI/3B


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objects are sought: planets or planetary systems (M ≈ 10–3 M ) and the so-called brown dwarfs, with an upper bound of the mass usually quoted 0.07 or 0.08 M . This still hypothetical latter group may contain stars of extremely low mass which then bypass the evolutionary phase of nuclear burning. Table 1. Some double and multiple systems within 5 pc, based on Gliese's data (LB VI/2c, subsect. 8.2.5, Table 6). Identification

Distance [pc]

Type of multiplicity

Remark

α Centauri

1.31

visual triple

AB + Proxima (common proper motion)

L726-8 α CMa (Sirius) 61 Cygni BD 43°44

2.58 2.65 3.40 3.45

visual double visual double visual double triple

α CMi (Procyon) BD 59°1915 Krueger 60 BD –12°4523 Ross 614 Wolf 424 G208 -44/45 40 Eridani 70 Ophiuchi G9-38+LP426-40

3.51 3.55 3.95 4.05 4.07 4.35 4.7 4.8 4.9 5.2

visual double visual double visual double spectroscopic double visual double visual double visual double visual triple visual double visual double

companion B white dwarf visual companion A spectroscopic binary companion B white dwarf

companion B white dwarf

The lowest observed stellar masses 0.05 and 0.06 M , probably very faint red dwarfs, are found in the system Wolf 424 [89H]. These low mass companions could be also detected by a very accurate study of the primary component's radial velocity; the necessary accuracy is of the order of 10…20 m/s, in favorable cases 100…200 m/s. This accuracy was achieved when Mayor and Quelnoz found indications of a planetary companion in orbit around the star 51 Pegasi, see for instance [95M]. The only possible brown dwarf candidate (HD 114762) was found by Latham and his collaborators [89L]. The very accurate observations by Campbell et al. [88C] indicate no companions in the range 0.02 to 0.08 M , and the object Gliese 623 with M ≈ 0.08 M is probably another faint red dwarf [89M]. However, the best evidence yet for a brown dwarf (or "failed star") was supplied by direct telescopic observation: an extremely faint companion was found to the M1-type star Gliese 229; see [95K] for a summary. Gliese 229B has an absolute magnitude MV ≈ 18…19 and its mass is estimated at 0.02…0.03 M . Accurate timing of radio pulsars can indicate motions around the barycenter with an accuracy of a few m/s. Recently, around the pulsar PSR 1257+12, the unexpected presence of (at least) two planetary masses has been established [92W].

References for 6.1.0 Monographs Batten, A.H.: Binary and multiple systems of stars, Oxford: Pergamon (1973). Heintz, W.P.: Double stars, Dordrecht: Reidel (1978).


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Colloquia, conferences Astrometric Binaries, conference held in Bamberg, FRG, June 1984 (Z. Kopal, chairman; J. Rahe, co-chairman). Fundamentals of Astrometry, IAU Coll. No. 100 (George Teleki Memorial Colloquium) held in Belgrade, Yugoslavia, September 1987. The Proceedings of the Colloquium have been published in Astrophys. Space Res. 177 (1991). Special references 69H 76L 80P 80V 81M 82H 83A 83H 83M 84A

84P 84Z 86H 87A 87L 87S 88C 88G 89H 89L 89M 91A 91D 92H 92S1 92S2 92T 92W 93B 93G 93J 93R 93Z 95K 95M

Heintz, W.D.: J. R. Astron. Soc. Can. 63 (1969) 275. Levato, H.: Astrophys. J. 203 (1976) 680. Popper, D.M.: Annu. Rev. Astron. Astrophys. 18 (1980) 115. Vanbeveren, D., Conti, P.: Astron. Astrophys. 88 (1980) 239. Massey, P.: Astrophys. J. 246 (1981) 153. Hoffleit, D. (with the collaboration of C. Jaschek): Bright star catalogue, 4th revised edition, Yale University Observatory, New Haven, Connecticut (1982). Abt, H.A.: Annu. Rev. Astron. Astrophys. 21 (1983) 343. Halbwachs, J.L.: Astron. Astrophys. 128 (1983) 399. Michaud, G., et al.: Astrophys. J. 269 (1983) 239. Andersen, J., Clausen, J.V., Jorgensen, H.E., Nordstom, B., in: Observational Tests of Stellar Evolution Theory (A. Maeder, A. Renzini, eds.), IAU Symp. No. 105, Dordrecht: Reidel (1984) p. 391. Popper, D.M.: Astron. J. 89 (1984) 132. Zinnecker, H.: Astrophys. Space Sci. 99 (1984) 41. Halbwachs, J.L.: Astron. Astrophys. 168 (1986) 161. Andersen, J.: Bull. CDS 38 (1987) 59. Lu, P.K., Demarque, P. et al.: Astron. J. 94 (1987) 1318. Shu, F.H., Adams, F.C., Lizano, S.: Annu. Rev. Astron. Astrophys. 25 (1987) 23. Campbell, B., Walker, G.A.H., Wang, S.: Astrophys. J. 331 (1988) 902. Gliese, W., Jahreiss, H.: Astrophys. Space Sci. 142 (1988) 49. Heintz, W.D.: Astron. Astrophys. 217 (1989) 145. Latham, D.W., Mazeh, T. et al.: Nature 339 (1989) 38. Marcy, G.W., Moore, D.: Astrophys. J. 341 (1989) 961. Andersen, J.: Astron. Astrophys. Rev. 3 (1991) 91. Duquennoy, A., Mayor, M.: Astron. Astrophys. 248 (1991) 485. Hut, P., McMillan et al.: Publ. Astron. Soc. Pac. 104 (1992) 663. Simon, M., Chen, W.P. et al.: Astrophys. J. 384 (1992) 212. Saffer, Rex A. (ed.): Blue stragglers, ASP Workshop, Baltimore, Maryland (1992). Trimble, V.: Comments Astrophys. 16 (1992) 61. Wolszczan, A., Frail, D.A.: Nature 355 (1992) 145. Bodenheimer, P., Ruzmaikina, T., Mathieu, R.D., in: Protostars and Planets III (T. Gehrels, ed.), Tucson: University of Arizona Press (1993) p. 367. Ghez, A.M., Neugebauer, G., Matthews, K.: Astron. J. 106 (1993) 2005. Jahreiss, H., Gliese, W., in: Development of Astrometry (I.I. Muller, B. Kolaczek, eds.), Dordrecht: Kluwer Acad. Publ. (1993) p.107. Reipurth, B., Zinnecker, H.: Astron. Astrophys. 287 (1993) 278. Zinnecker, H., McCaughrean, M.J., Wilking, B.A., in: Protostars and Planets III (T. Gehrels, ed.), Tucson: University of Arizona Press (1993) p. 429. Kulkarni, S., et al.: Nature 378 (1995) Nov. 30. Mayor, M., Quelnoz, D.: Nature 378 (1995) Nov. 23.


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6.1.1 Double stars: Visual (wide) binaries

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6.1.1 Visual (wide) binaries 6.1.1.1 Catalogues and collections of data The Index Catalogue of Visual Double Stars (IDS) published 1963 at the Lick Observatory (see LB VI/2b, subsect. 6.1.1.2) is now being replaced by the Washington Double Star Catalog (WDS) established by Charles E. Worley. The catalogue is currently maintained at the US Naval Observatory, Washington D.C., in form of hard disk files containing, as of 1991, about 77000 pairs. A companion Catalog of Observations, also at the US Naval Observatory, contains about 428000 measurements or means of measurements including the 180000 observations entered at Lick Observatory in the IDS; it is complete for published observations since 1927. A short description of both catalogs is by Worley and Douglas [90W], it also gives the address for requesting data (supplied freely at the time this is written). Among various individual catalogues of visual binary and multiple systems be listed: – Salukvadze: A Catalogue of Trapezium-Type Multiple Systems [78S1] – Salukvadze: Trapezium-Type Multiple Systems in T-Associations [78S2] – P. Couteau: Catalogue de 2550 Étoiles doubles CDS. (Contains about 15000 observations.) Available from the author. Lists of interferometric measurements of binary systems, see subsect. 6.1.1.3. A large number of observations is being regularly published by the US Naval Observatory; Sproul Observatory; Observatoire de Nice; Bosscha Observatory, Lembang; Observatorio Universidade de Santiago de Compostella, among others. Catalogue of orbits The fourth and, as yet, last catalogue of orbits has been published 1983 by C. Worley and W. Heintz, Publ. US Naval Obs., 2nd Ser., Vol. 27, pt. 7. (1983). Circulaire d'Information Edited on behalf of Commission 26, Étoiles Doubles, by Paul Couteau (Observatoire de la Cote d'Azur). Contains primarily new orbits computed, occasionally newly discovered visual pairs and interferometric observations. Published trimonthly. In 1993, with No. 118, the editorship has been taken over by J. A. Docobo and J. F. Ling (Observatorio Astronomico "R. M. Aller," Universidade de Santiago de Compostela.) The new Information Circular also brings pieces of general information about visual binaries. Latest issue, as of Oct. 1994, is No. 127.

6.1.1.2 Space astrometry of double stars As preparative work for the HIPPARCOS astrometric mission, the necessary survey of multiplicity has been carried out for the HIPPARCOS Input Catalogue (INCA) Consortium. This catalogue is for the specific purpose of providing the satellite with a reliable target list giving positions, proper motions, magnitudes and colours to the best accuracy available for ground-based observations; the leader of the consortium is C. Turon. Work toward a Catalogue of the Components of Double and Multiple Stars (CCDM) is directed by J. Dommanget. CCDM includes about 63000 systems, identified by DM, AG or SAO numbers. A short description of INCA is given by Turon et al. [92T]. Brosche and Sinachopoulos prepared two lists of wide visual binaries containing about 1960 systems, many of them not physical. The main aim is obtaining scale factors [86B].


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6.1.1.3 New observational techniques Essential progress was achieved during the years 1970-1990 by introducing and applying in larger scale new observational techniques. Most earlier observations have been done visually, by the aid of the filar micrometer, and for wide pairs, photographically, using long-focus instruments. Both methods are still in regular use in several centers: Observatoire de Nice, U.S. Naval Observatory, Washington DC, (26 inch refractor), U.S. Naval Observatory, Flagstaff Station (1.5 m astrometric reflector), Swarthmore College Observatory, among others. (1) To some extent, area photometry (which also measures the magnitude difference between components) has been applied, and for late-type giants and supergiants, the Michelson stellar interferometer still can be used successfully. Michelson and Pease epoch-making observations in 1920, however, could not be followed up owing to difficulties with the required mechanical stability of a larger apparatus and also the atmospherically induced fringe motion. In recent years, however, remarkable results have been achieved in phase-coherent interferometry by using two independently movable siderostats at separations of the order of 5…30 m. Pioneering in this field were studies made with the I2T interferometer at CERGA in France [75L] and with the Mark III Stellar Interferometer at Mt. Wilson, see [94H]. The objectives are: accurate stellar positions, stellar diameters larger than 2 milliarcsec, and binary star orbits in the range 10…20 milliarcsec. A new generation of interferometers is under construction or planned in several places (Flagstaff, Sydney, CERGA's GI2T) capable of measuring angular diameters to a limit of 0.2…0.3 milliarcsec. At CERGA successful measurements have already been reported at separations up to ≥ 60 m [94K]. (2) Lunar occultation methods, based on the Fresnel diffraction pattern of an occultation by the Moon; see, for instance D. Evans [83E]. The majority of this type of observations is being carried out at the McDonald Observatory, Texas, revealing a number of new visual binaries, usually as a byproduct of attempted measurements of stellar diameters. (3) The intensity interferometer, first introduced in the radio astronomy, by Hanbury Brown and R.Q. Twiss, then applied to the optical domain, is not relying on phase coherence but on the correlation of intensity fluctuations in the two beams; the method is described in Hanbury Brown's monograph [74H]. Most measurements are made in Narrabi, Australia and are primarily aimed at the determination of angular diameters of early-type, relatively bright stars. An accuracy of a few milliarcsec can be achieved with no difficulty. In a few cases, close visual duplicity of some bright stars has been detected, so in the case of the spectroscopic binary α Virginis (Spica), with an orbital period of only 4 days [71H], the apparent separation being 0",. 00086. (4) Speckle interferometry can reach the diffraction limit of the telescope by ingeniously circumventing seeing effects. The method was worked out by A. Labeyrie [70L]; see also his later report [78L]. By far the most extensive work on speckle interferometry is carried out at CHARA (Center for High Angular Resolution Astronomy) at Georgia State University, Atlanta, Georgia. A CCD camera for speckle interferometry (ICCD) is frequently used in combination with some of the largest telescopes. The first major catalog of speckle interferometry: – H.A. McAlister, W.I. Hartkopf: "Catalog of interferometric measurements of binary stars." CHARA Contribution No. 1 (1986). The same authors published the Second CHARA Catalog (Contribution No. 2). A few sample quotations of further programs: – Speckle interferometric measurements of binary stars IX. [84M], 400 measurements on 232 stars; – Binary stars unresolved by speckle interferometry III. [84H], 1164 measurements on 156 stars;



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– ICCD speckle observations of binary stars II. Measurements during 1982-1985 from the Kitt Peak 4m telescope [87M1], 2780 new measurements of 1012 double and multiple systems. See also McAlister: "Five years of double star interferometry and its lessons" [83M]. Speckle observations can be used with advantage to follow the motion of very close pairs and derive orbits, usually of very good quality; among the first studies, the Hyades binary 70 Tau has been observed, with a period close to 6 years [88M]. Among statistical studies, supported by speckle interferometry, we mention a survey of a sample of 672 stars from the Bright Stars Catalog [87M2]. The frequency of close visual pairs in the separation range 0",. 04 to 0",. 25 could be raised to a surprisingly high 11 percent. Further programs of speckle interferometry at Pic du Midi, France (A. Labeyrie), also by the CFH telescope, Hawaii; Sternberg Astronomical Institute Moscow; Special Astrophysical Observatory at Zelenchukskaya; European Southern Observatory (G. Weigelt), among others. The average separation routinely achievable by the speckle method is around 0",. 3, but 0",. 026 was already measured (31 Cygni).

References for 6.1.1 Monographs Couteau, P.: L'Observation des Étoiles Doubles Visuelles. Paris (1978). (English translation by A.H. Batten: Observing visual double stars, MIT Press, 1981). Colloquia, conferences Wide Components in Double and Multiple Stars, IAU Coll. No. 97 held in Brussels, Belgium, June 1987. The Proceedings of the Colloquium have been published in Astrophys. Space Res. 192 (1988). Special references 70L 71H 74H 75L 78L 78S1 78S2 83E 83M 84H 84M 86B 87M1 87M2 88M 90W 92T 94H 94K

Labeyrie, A.: Astron. Astrophys. 6 (1970) 85. Herbison-Evans, D., Hanbury Brown, R., et al.: Mon. Not. R. Astron. Soc. 151 (1971) 161. Hanbury Brown, R.: The Intensity Interferometer and its Applications to Astronomy, London: Taylor & Francis (1974). Labeyrie, A.: Astrophys. J. 196 (1975) L71. Labeyrie, A.: Annu. Rev. Astron. Astrophys. 16 (1978) 77. Salukvadze, G.N.: Astrofizika 14 (1978) 57. Salukvadze, G.N.: Astrofizika 16 (1978) 505 and 687. Evans, D.S.: Lowell Obs. Bull. No. 167, 9 (1983) 63. McAlister, H.A.: Lowell Obs. Bull. 9 (1983) 125. Hartkopf, W.I., McAlister, H.A.: Publ. Astron. Soc. Pac. 96 (1984) 105. McAlister, H.A., et al.: Astrophys. J. Suppl. 54 (1984) 251. Brosche, P., Sinachopoulos, D.: Bull. CDS 34 (1986) 39, and 36 (1986) 3; cf. also Astron. Astrophys. Suppl. 65 (1986) 189. McAlister, H.A., Hartkopf, W.I., et al.: Astron. J. 93 (1987) 668. McAlister, H.A., Hartkopf, W.I., et al.: Astron. J. 93 (1987) 183. McAlister, H.A., Hartkopf, W.I., et al.: Astron. J. 96 (1988) 1431. Worley, C.E., Douglass, G.G.: Bull. CDS 38 (1990) 195. Turon, C., Crézé, M., Egret, D., et al.: Bull. CDS 41 (1992) 9. Hummel, C.A., Mozurkewich, N.M. et al.: Astron. J. 108 (1994) 326. Koechlin, E.: announced at 22nd General Assembly of the IAU, Den Haag, The Netherlands (1994).


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6.1.2 Double stars: Close binaries

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6.1.2 Close binaries This class of double stars comprises the earlier classes eclipsing and spectroscopic binaries, for which the observational techniques and methods of orbit calculation are considerably different. Commission 42 of the IAU (Eclipsing Binaries) has been renamed Close Binary Stars or Étoiles Binaries Serrées. Orbital elements for spectroscopic binaries, see LB VI/2b, subsect. 6.1.3.1. For classification of eclipsing systems, see LB VI/2b, subsect. 6.1.5.2. A simple definition of a close binary pair is: a double star where the components, at least in certain phases of their evolution, interact with each other, significantly modifying their evolution in the H-R diagram. For an approximate division between wide and interacting systems, see LB VI/ 2b, p. 382. Systems showing tidal effects, deformation due to the rotation, and the resulting apsidal motion (the rotation of the major axis of the orbit), represent the smallest degree of observable interaction between the components, which, however, can also significantly influence the orbit and the rotation of the components (circularization, synchronization, see below, subsect. 6.1.2.4). The major types of interactions are: – mass exchange between the components, leading to a possible reversal of the mass-ratio of the components (Algol-type evolution); – mass loss from the system; – formation of an accretion disk or ring; – enhanced chromospheric activity; – occurrence of starspot zones and large starspots. Classification of close pairs according to configuration, see LB VI/2b, subsect. 6.1.5.2, is particularly important for identification of one main mechanism of interaction (Roche lobe overflow), cf. also LB VI/2b, subsect 6.1.5.3. It is, however, important to notice that other types of interaction mechanism are recently recognized as important in many cases: accretion from the stellar wind of a giant or supergiant component; hydrodynamic phenomena (jets, shock fronts) in the circumstellar envelope of a massive binary. The last 20…25 years brought not only a very large increase in the number of new orbit determinations, see subsect. 6.1.2.1, but also three lines of significant technical developments which represent a fundamentally new approach to close binary systems: (1) Improved techniques of radial velocity determinations and their frequent application to spectroscopic binary systems. (2) New methods of calculation for eclipsing binary orbits, leading not only to more accurate orbital elements but also to a better modeling of the luminosity distribution on the stellar surface. (3) Satellite observations making it possible to study close binaries in the far and near ultraviolet, inaccessible for earth-bound instruments (about 100 to 300 nm; also 10 to 100 nm, extreme ultraviolet).


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6.1.2.1 Catalogues Eclipsing systems The General Catalogue of Variable Stars (GCVS; 4th edition, Moskow, 1985-1987, editor-in-chief: P.N. Kholopor) contains over 2800 variables classified as eclipsing systems. For at least half of them, only occurrence and type are reliably known; for some of the fainter systems, even the possibility of confusion with RR Lyrae type variables cannot be excluded. Volume 5 of the GCVS was published in 1995 (editor-in-chief: N.N. Samus) and contains the unique material of all known variables in extragalactic systems, including lists of extragalactic supernovae in chronological order, up to SN 1993 ak. A Finding List for Observers of Interacting Binary Stars, 5th edition, by F.B. Wood, J.P. Oliver, D.R. Florkowski and R.H. Koch (Publication of the Department of Astronomy, University of Florida, Vol. 1; Publication of the University of Pennsylvania, Astronomical Series Vol. 12, 1980). It contains over 3500 systems, mainly of eclipsing type with a few basic references. Rocznik Astronomiczny, published annually by the Krakow Observatory, No. 63 for 1992. It contains photometric elements and an ephemeris of the times of minima for over 800 brighter eclipsing systems. A General Catalog of Close Binary Stars, by R.F. Webbink. A working copy of 5 volumes has been deposited with the Library of the U.S. Naval Observatory (1993); target date of completion is the year 2000. Spectroscopic systems Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Systems, by A.H. Batten, J.M. Fletcher and D.G. McCarthy (Publ. Dominion Astrophys. Obs. Vol. 18, 1989). Contains over 1400 systems, for many of them also short summaries of the literature. Catalogues Supplementaires are published, between successive editions of the Dominion Astrophys. Obs. Catalogues, by A. Pédaussaut, J.M. Carquillat and N. Ginestet from the Observatoire de Toulouse et Pic du Midi.

6.1.2.2 New techniques Photoelectric radial velocities This technique applies a movable mask immediately above the stellar spectrum in the telescope, usually corresponding to late (G…K) spectral type. Translation of the mask generates a variable intensity of the transmitted light which is recorded photoelectrically. To obtain the radial velocity of a star, the position of the mask has to be calibrated by radial velocity standards; an internal error as low as 0.5 to 1.0 km s–1 can be achieved in 5…10 min. observation. The method is applicable to late spectral types, both dwarfs and giants, and is well suited to mass production of velocity data for stars brighter than about 10th magn. A wide ranging program on binary stars is being carried out since 1975 by R.F. Griffin (and occasional collaborators) in Cambridge, England, and the orbits are published regularly in the journal The Observatory. The program concentrates on wider systems with relatively slow orbital motion: most periods are between 100 and 3500 days, most radial velocity amplitudes between 3 and 30 km s–1. As of 1994, the orbits of almost 200 systems have been discussed. Synopsis of publications 1…50 is found in [83G2]; synopsis of publications 51…100 in [91G]. A bibliographical index of the first 100 publications is given in the 2nd synopsis. Photoelectric radial velocities are extensively observed at the Iowa State University, but not necessarily concentrated on double stars. See Beavers and Eitter [86B]. About the origin of the method see [91F], and description of the first instrumentation see [67G]. Landolt-Börnstein New Series VI/3B

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Cross-correlation methods Implemented in the hardware, that is, as part of the observing system, the most important advance is the construction of the CORAVEL spectrograph. This is a Cassegrain spectrophotometer which derives the radial velocity by cross-correlation between the stellar absorption lines and a suitable mask located in the focal surface. The determination of the velocity depends only on the calibration of the optics and the domain of measurements can be extended to a substantial part of the wavelength range used. The accuracy from a few 0.1 to about 1 km s–1 can be achieved and a number of very accurately determined orbits, resp. masses of (usually not very close) binary systems was obtained by the CORAVEL (see Andersen's reviews [84A, 87A, 91A]. The CORAVEL spectrograph can also be used for the derivation of stellar rotation and metallicity parameters. CORAVEL was introduced by A. Baranne, M. Mayor, J.L. Poncet [79B]. For cross-correlation methods implemented in the software, that is, the derivation of purely digital radial velocities, see for instance, D.W. Lantham [85L]. The method is in use at the Center for Astrophysics, Cambridge, Massachusetts, and holds the promise of mass production of radial velocities for faint stars, with an accuracy of about ±1 km s–1. The technique of digital stellar radial velocities have been discussed in several articles presented to IAU Colloquium No. 88 [85P] which also contains reviews of numerous other approaches of instrumental problems and applications in studies of galactic structure; for digital correlations, see [85L] and [85W], for CORAVEL, [85M]. Another digital approach, based on synthesis of absorption line profiles, was proposed by Antokhina and Cherepashschuk [94A]. The method includes the effect of stellar wind and is well suited to treat X-ray binaries. Use of absorption cells Highest accuracy of relative radial velocities, with a mean external error as low as 10…20 m/s, can be obtained by placing an absorption cell (containing usually hydrogen fluoride) in front of the spectrograph slit. The method was developed earlier by Campbell and Walker [79C] and later applied by them [88C] and several other research groups to searching for substellar binary components (planets, brown dwarfs). See also Visual Binaries, subsect. 6.1.1. Doppler tomography A very special application of radial velocities is the surface imaging of rapidly rotating stars or close (usually eclipsing) binaries by the aid of the Doppler tomography. Through an analysis of the line profiles in high dispersion spectra, it is possible to reconstruct the intensity distribution over the stellar disk. The method is also applicable, using emission lines, to the study of the structure of stellar chromospheres, or accretion disks; for references see R.W. Hilditch's review [94H]. Calculation of eclipsing binary orbits The traditional method of eclipsing binary orbit calculation using the so-called rectification of the light-curve (Russell's method [52R]) is now almost completely replaced by calculations which make extensive use of digital computers. Here we wish to mention: – methods based on Fourier transformation (Kitamura; Kopal's frequency domain method); – synthetic methods, based on numerical variation of the parameters and least-squares approximation of the light curve (Wood; Wilson and Devinney), programs available upon request; – simplex method of isolation of the best representation in multidimensional parameter space (Kallrath, Linnell).


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Lists of photometric solutions are published tri-annually in the Reports of Astronomy volumes of the IAU general assemblies, as part of the report of Commission 42, compiled by the presidents of the commission. For the time mid-1987 to mid-1990, we find over 200 orbits listed. According to a survey by R.E. Wilson [91W], the currently most frequently used method of light curve analysis is the Wilson-Devinney procedure (44 percent), followed by a method proposed by E. Budding (12 percent) and by the frequency domain analysis by Z. Kopal (6 percent). The Russell-Merrill method, mentioned above and representing 23 percent for the triennium 1975-78, was used only for 1 percent of the cases. The light curve modeling technique is treated in fair detail in E.F. Milone (ed.), Light Curve Modeling of Eclipsing Binary Stars [93M]. The power of light synthesis solutions was first demonstrated on the system MR Cygni [71W]; further developments and some of the physical basis of the method were surveyed by Wilson [94W]. For the methods of Kitamura and Kopal, the monograph [79K] is to be consulted, for the work of Linnell and also Kallrath, the chapters written by these authors in [93M]. Much work has been done on starspot models, that is, considering perturbations in the light curve which may be ascribed to dark or bright areas on the stellar surfaces, see for instance the volume Activity in Red Dwarf Stars (IAU Colloquium No. 71) among the large number of investigations dealing with these effects, where the uniqueness of the solution often remains problematic, we mention only works by Bopp and Evans [73B], Friedemann and Gürtler [75F], and further developments by Rodonò et al. [86R]; see also material presented at the colloquium [92B]. UV studies (rocket and satellite UV, about 100 nm to 300 nm) In addition to contributions from manned satellites and the European Space Agency (ESA) satellites TD-1 and ANS, most of the UV studies on binary systems were conducted by the Orbiting Astronomical Satellites OAO-2 and OAO-C (designated Copernicus) and, in particular, the International Ultraviolet Explorer (IUE). The IUE satellite was launched in January 1972 and operates since under the joint sponsorship of NASA (Goddard Space Flight Center) and ESA (Villafranca del Castillo, Spain). In the field of double-star astronomy, the main problems in the ultraviolet which can be addressed exclusively or with specific advantage by using satellites, are: – spectral classification, and the detection of hot subdwarf and white dwarf companions, – the structure of accretion disks, – mass loss rates, – structure of particular binaries, such as symbiotic stars, WR + OB systems (Wolf-Rayet + hot main sequence stars), and possibly WR-stars with compact companions. General references: – for results with OAO-2, see A.D. Code (ed.) [72C]; – for a summary of research done on single and binary stars with the IUE, see [87K]; – current technical problems and up-to-date information of research are reviewed by NASA Goddard Space Flight Center, in the IUE Newsletters (No. 49, in Dec. 1992). During the last decades it became clear that interstellar space in the extreme ultraviolet (EUV), between about 10 and 75 nm, is much less opaque than previously estimated, at least in certain directions. After promising experiments onboard Apollo-Soyuz and a survey of bright sources based on the EUV camera carried by the ROSAT satellite [93P], with the advent of Extreme Ultraviolet Explorer (EUVE), constructed for NASA by a team around Stuart Bowyer and launched 1992, this wavelength range is now open to detailed studies; a short revue is given in [94B1]. EUVE carried out a first all-sky survey in the wavelength range 100…600 Å listing more than 400 sources [94B2]. Landolt-Börnstein New Series VI/3B

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Most of these objects have been observed in the 100 Å and 200 Å band; in the 100 Å band, the two by far strongest objects are the highly peculiar system HZ 43 (28 counts/s) and Sirius B (12 counts/s), while Sirius A remains apparently undetectable. Furthermore a number of interacting binaries had been recognized at the 0.1…1 counts/sec level, among them Sco X-1, Her X-1, Nova Cygni 1992, Castor C (but not Castor A+B), AM Her (2.3 counts/s), V471 Tau, the W UMa system 44 Boo (probably only component A), Capella A+B, a coronally active pair of giants.

6.1.2.3 Orbital perturbations, apsidal motion (1) In triple systems of ab-c type, the direct method to detect the presence of a third body is to observe the changes of the system velocity of the close pair or using light travel effects (light time effects) which cause periodic phase shifts in an eclipsing orbit. A discussion of an exemplary case (AH Cephei) is given in [89D]. In support of such studies a list of 80 eclipsing binaries in triple systems was given by Chambliss [92C]. (2) In hierarchic triple systems two main kinds of perturbation in the close orbit can be detected: – change of orbital inclination, – apsidal motion (apsidal rotation). The first type of these perturbations is best demonstrated in the case of the eclipsing triple system IU Aurigae where an increase of i, amounting to 0.,° 42 per year has been found [87M]. For wider, visual triples, such as 44i Bootis, orbital perturbations will remain very difficult to detect. (3) Rotation of the apsidal line (major axis) in an eccentric system can be detected spectroscopically by following the nearly linear change (increase) of the orbital element ω; in eclipsing systems one is to observe periodic displacement of the minimum epochs, primary and secondary minimum showing phase shifts opposite to each other. It is important to note that such a perturbation can arise in close binaries without interaction with a third body in the system, due to deviations from the simple, undisturbed Newtonian potential. Most observed cases of apsidal rotation are due to the non-sphericity of the components caused by rotation of the components (oblateness) or tidal interaction between them, the dominant effect being caused by the tidal interaction. A rotation of the apsidal line (analogous to the relativistic perihelium precession of Mercury) is required by General Relativity. To this problem we will return while discussing tests of the relativity, using pulsar timing. For apsidal motion, the first successful treatment has been given by Sterne [39S]; for a detailed review see Z. Kopal's monograph [59K] or a somewhat more elementary treatment by M. Schwarzschild [58S]. The main observed quantity is the ratio of orbital period (P) to the period of apsidal rotation (U), which assumes the form

F I FG 15 f ( e ) + FG ω IJ 1 + q H K GH H ω K d1 − e i

P R = ∑ k2i i U a i

2

5

K

2 2

I JJ , K

i = 1, 2

where q is the mass-ratio of the components taken in the right order, ωK the Keplerian angular velocity, ω the actual angular velocity, and f(e) is a simple function in powers of the eccentricity e. The main result of such a study is obtaining the k2 coefficients which measure the central mass R condensation of the two stars, being proportional to the integral 0 ρ r 7d r , using obvious notation.

z

Since the dependence on the R/a values is very sharp, only eclipsing systems can yield a meaningful


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determination of k2. Furthermore, this data can be comfortably determined only in systems with two similar components--thus assuming that k21 ≈ k22. An algorithm to calculate the P/U ratio and the coefficient k2, well suited to automated on-line computation, has been given by A. Gimenéz and J. García-Pelayo [83G1]. The best-observed system is Y Cygni, with the data Sp. O9.5 + O9.5, P = 2.99 days , U = 48 years, k = 0.008 or log k = –2.1 . All of the well-determined 15…18 cases contain nearly identical components and are detached systems. For the important prototype Algol (β Per), a semi-detached system with very different components, the previously found apsidal motion could not be confirmed [80S]. A comprehensive list of 93 binaries showing apsidal motion and about twice as many candidates, was published by Hegedüs [87H2]. These unexpectedly large numbers may suggest the need of a closer look at some of the systems listed.

6.1.2.4 Tidal evolution in close binaries It was recognized early that tidal interaction in a close binary pair must have a tendency to reduce orbital eccentricity, to circularize the orbit and also to establish synchronism between rotational and orbital period. In both cases, energy dissipation through tidal friction will be minimized. Theory must deal with two effects of the tidal effect: the equilibrium tides (hydrostatic adjustment) and the stars' dynamical response to this adjustment. It is of great importance whether one of the components or both components have a convective envelope. The time scales of circularization resp. synchronization is still a much discussed problem. To the theory of the tides in close binaries several early works by J.-P. Zahn contributed significantly, see in particular [66Z, 75Z]. For early statistical studies of the stellar rotation, see Plavec's review [70P] and Levato [74L], among many. Synchronization is preponderant, but not exclusive, in systems with periods roughly under 5 days, but binary evolution, in particular expansion of a component at relatively recent exchange of mass can create important exceptions: both ß Lyrae and U Cephei show conspicuous deviations from synchronism (the primaries rotate too fast). Circularization seems to take place on a longer time scale than synchronization; the so-called cut-off between circular and elliptical orbits may be near 8 days. Recently, it became evident that pre-main sequence evolution, particularly in the Hayashi phase, plays an important role in establishment of the configuration. Recent works to consult [ 89Z1, 89Z2, 90H] and several articles in [92D]. In the case of RS CVn-type stars, as first pointed out by D.S. Hall, the observed gradual, systematic displacement of the (orbital) phase of strong activity may be an indication of a nearsynchronous, but not completely synchronized rotation, as discussed in some detail in the review article [90H].

6.1.2.5 Circumstellar matter: the "Barr effect" It was noticed by W.M. Barr as early as in 1908 that the orbital element ω (the longitude of periastron) exhibits a singular distribution, greatly preferring the first quadrant and to a lesser extent, the second one [08B]. The reality of the effect was argued convincingly by Struve, see, for instance [48S], and verified by Batten, using the data of his Sixth Catalogue [67B]. The explanation of the effect lies in a specific distortion of the observed radial velocities by gaseous streams in a close, interacting systems. This explanation is supported by the fact that orbits determined from photoelectric radial velocities and referring primarily to wider pairs with very little apparent interaction, do not show the effect, see Griffin's 2nd synopsis paper (1991) [91G]. The Barr effect was the first indication of circumstellar matter existing around binary stars. A modern survey of the field is given in the proceedings of IAU Symposium No. 122 [86A]. Landolt-Börnstein New Series VI/3B

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6.1.2.6 Atmospheric eclipses: Zeta Aurigae type stars Zeta Aurigae type stars are defined as binary systems consisting of a K-M type supergiant and a Btype main sequence star, where the inclinations of the orbit are such that eclipses become possible. Before and after the total eclipse of the B-component or in the case of grazing eclipses, the light of the hot star penetrates the chromosphere of the late supergiant. The additional absorption lines in the spectrum make a unique study of the chromospheric structure possible. In spite of the long periods and apparently detached structure, several of the Zeta Aur type systems show signs of interaction between the components (gaseous streams, circumstellar shock fronts). The known representants of this type of binaries are usually subdivided into two groups although it is questionable whether this division would reflect any deeper physical significance. Binary system

Spectral type

Period

Group Zeta Aurigae Zeta Aur 31 Cygni 32 Cygni 22 Vulpeculae

K5II+B7V K3II+B K5Iab+B8: G3Ib-II+B9

973 10.2 1050 249

with the possible new member: τ Persei

G5III+A2V

and with the little known systems: V381 Scorpii V383 Sco

A5Ia:+? F5Ia:+?

17.9 years 13 years

Group VV Cephei VV Cep

M2pIab+B8

20.3 years

with possible new members: δ Sagittae KQ Puppis

M2II+B9V M2pIab+B

10.2 years 26.7 years

days years days days

4.15 years

The systems AL Velorum (P = 96 d), HR 2554 (P = 195 d) and HR 6902 (P = 385 d) have been proposed as additional members of the Zeta Aurigae group, see [90E, 91S]. The binary δ Sagittae has the spectral combination M2II+B9 but low orbital inclination precludes that eclipses, even atmospheric eclipses occur; the system is not counted among the Zeta Aurigae type stars. For a number of Zeta Aur-type systems the diameters of the giant and supergiant components have been observed by interferometry, see [90D] and further references therein. Counting the extraordinary eclipsing system ε Aurigae (P = 27.1 years) among the Zeta Aurigae type systems is probably not justifiable. The primary component is an F0Ia supergiant but the nature of the companion is unknown: the occulting body is possibly an opaque disk or ring formed of dust particles. The literature of these stars before 1970 is summarized by K.O. Wright [70W]. For early studies of ε Aurigae, see K. Gyldenkerne [70G]. For recent studies in the UV region, see Hack and Stickland [87H1], for a summary of the extensively observed 1982-84 eclipse [85S], also [90G].


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6.1.2.7 Symbiotic stars Variable stars of this type first appeared by showing combination spectra which presented characteristics of a late type spectrum, including the TiO bands, with high excitation emission lines, preeminently He II λ4686Å, also [Fe VII] λ6087Å and lines of equivalent very high excitation. Symbiotic stars are now commonly recognized as binary systems with strongly interacting components where a late-type giant star or mira variable transfers matter to a hotter companion; this accreting component is usually white dwarf, occasionally main sequence star and, in exceptional cases, neutron star. Prototype of the symbiotic stars with accreting main sequence secondary is CI Cygni, with a white dwarf as accreting component, AX Per; both show at irregular intervals novalike outbursts (3 magn). The only known symbiotic with a neutron star component is V 2116 Ophiuchi, the optical counterpart of the X-ray source GX 1+4. See also subsect. 6.2.

6.1.2.8 RS Canum Venaticorum stars An important group of binaries, between systems with merely orbital perturbations and those showing strong interaction between the components, form the RS Canum Venaticorum (RS CVn) stars. These are actually detached systems (see LB VI/2b, subsect. 6.1.5.2) with at least one component in the (early) post main-sequence evolution and the conspicuous activity resides mainly in the surface layers of individual components, in the form of photospheric and chromospheric phenomena, reminiscent of the solar activity but usually on a far larger scale. Local magnetic fields of kilogauss strength or more play an important role in these phenomena and the ultimate explanation may be the restructuring of the sub-surface convection due to the incipient giant evolution. Besides RS CVn, AR Lac, UX Ari and V711 Tau (= HR1099) may be mentioned here. The periods are about 2 to 12 days, the components of the spectral types G or K, with at least one subgiant or even giant member. The Ca II lines are in strong emission, the light curves disturbed. An early definition of the group was attempted by D.S. Hall [72H, 76H] who emphasized a characteristic photometric feature: a wave-like disturbance in the light curve migrating usually towards decreasing orbital phase, with periods around 5…10 years. This may be interpreted as a lack of complete synchronization between orbital and rotational angular velocities or, perhaps more convincingly, a consequence of the differential rotation on the surfaces of the stars, in connection with the shift of the activity centers toward the equator. A further important phenomenon is the occurrence of strong radio bursts or flares in several, perhaps even most, systems of the group; the first radio flares have been found in the case of AR Lacertae [73H, 74G]. The site of these bursts are thought to be in the active regions around star spot groups but origin in the stellar coronas or even in a circumstellar cloud are also conceivable. A recent review of the RS CVn-stars is by Rodonò [92R].

6.1.2.9 Mass exchange. The Algol problem and its essential solution In the most intense form of interaction between components of binary systems, the binaries undergo extensive mass exchange and, in many cases, mass loss from the system, completely transforming the initial configuration. The first major result of theories considering evolution of close binaries undergoing intense mass exchange was the complete clarification of the so-called Algol paradoxon. Algol (ß Persei) is here a prototype of the semidetached systems, consisting of a B8V primary (M ≈ 4.5 M ) and a G-subgiant secondary (M ≈ 1 M ). Why is the less massive component seemingly more evolved, having already left the main sequence? The key to the solution is in the Roche configuration, with the secondary Landolt-Börnstein New Series VI/3B

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filling its lobe, indicating the possibility of mass transfer, through the inner Lagrangian point L1, to the primary. There are hundreds of similar semidetached configurations known as Algols. The evolution of such a system is governed by massive mass transfer from the original primary, evolving faster, to the original secondary; the mechanism is the overflow of the Roche lobe of the original primary, as the star leaves the main sequence. The ensuing mass exchange leads to a reversal of the mass ratio. In typical Algols the mass gaining component, the present primary is still on the main-sequence; its evolution into the subgiant region will probably create a contact configuration with possible reversal of the mass flow. See also subsect. 4.4.3.8. This solution of the Algol paradoxon was suggested by Crawford [55C] and numerically worked out, at least for some selected masses and mass ratios, by Paczynski [67P1], Plavec [67P2] and Kippenhahn et al. [67K, 68K]. These important works were made possible by the rapid development of the calculation of stellar models after 1958. A recent review of the quite extensive literature is by van den Heuvel [92V]; a brief summary has been given by Verbunt [93V]. The hydrodynamical problems of the mass flow are still frequently discussed; see for instance parts of a review by S.N. Shore [92S]. An accretion disk may form inside the Roche lobe of the more massive, mass-gaining component, in some cases (for instance, RW Tauri) spectroscopically convincingly demonstrated; see also a report by Plavec on accretion disks in nondegenerate binary systems [90P]. Most studies of the mass exchange in semidetached systems assume a conservative, that is mass conserving, evolution. The case of substantial mass loss from the entire system can lead to radically different evolutionary history of the binary; this is particularly important for binaries which will have as end configuration a compact object in the system, a white dwarf, neutron star or black hole. We return to these questions later, dealing with X-ray binaries or binary radio pulsars.

References for 6.1.2 Monographs Sahade, J., Wood, F.B.: Interacting Binary Stars, Oxford: Pergamon Press (1978). Eggleton, P.P., Pringle, J.E. (eds.): Interacting binaries, Dordrecht: Reidel (1983). Symposia, colloquia Close binary stars: observations and interpretation (M. Plavec, D.M. Popper, R.K. Ulrich, eds.), IAU Symp. No. 38, Dordrecht: Reidel (1980). Stellar radial velocities (A.G.D. Philip, D.W. Latham, eds.), IAU Coll. No. 88, Schenectady, N.Y.: Davis Press (1985). Interacting binaries. Saas-Fee Adv. Course 22. Lectures by S.N. Shore, M. Livio, E.P.J. van den Heuvel. (H. Nussbaumer, A. Orr, eds.), Berlin, Heidelberg, New York: Springer (1994). Special references 08B 39S 48S 52R 55C 58S

Barr, W.M.: J.R. Astron. Soc. Can. 2 (1908) 70. Sterne, T.E.: Mon. Not. R. Astron. Soc. 99 (1939) 662. Struve, O.: Publ. Astron. Soc. Pac. 60 (1948) 160. Russell, H.N., Merrill, J.E.: Princeton Obs. Contrib. 26 (1952). Crawford, J.A.: Astrophys. J. 121 (1955) 71. Schwarzschild, M.: Structure and Evolution of Stars, Princeton University Press (1958).


6.1.2 Double stars: Close binaries 59K 66Z 67B 67G 67K 67P1 67P2 68K 70G 70P 70W 71W 72C 72H 73B 73H 74G 74L 75F 75Z 76H 79B 79C 79K 80S 81B 81L 81M 81W 83B 83G1 83G2 84A 85L 85M 85P 85S 85W 86A 86B 86B1 86R 87A

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Kopal, Z.: Close Binary Systems, London: Chapman-Hall (1959). Zahn, J.-P.: Ann. Astrophys. 29 (1966) 489. Batten, A.H.: Publ. Dominian Astrophys. Obs. 13 (1967) 119. Griffin, R.F.: Astrophys. J. 148 (1967) 465. Kippenhahn, R., Weigert, A.: Z. Astrophys. 65 (1967) 251. Paczynski, B.: Acta Astron. 17 (1967) 1, 193, 287, 355; see also Comm. Obs. R. Uccle B17 (1967) 111. Plavec, M.: Comm. Obs. R. Uccle B17 (1967) 83. Kippenhahn, R., Kohn, K., Weigert, A.: Z. Astrophys. 66 (1968) 58. Gyldenkerne, K.: Vistas Astron. 12 (1970) 199. Plavec, M, in: Stellar Rotation (A. Slettebak, ed.), Dordrecht: Reidel (1970). Wright, K.O.: Vistas Astron. 12 (1970) 147. Wilson, R.E., Devinney, E.J.: Astrophys. J. 166 (1971) 605. Code, A.B. (ed.): Scientific results from OAO-2, NASA-SP 310 (1972). Hall, D.S.: Publ. Astron. Soc. Pac. 84 (1972) 323. Bopp, B.W., Evans, D.S.: Mon. Not. R. Astron. Soc. 164 (1973) 343. Hjellming, R.M., Blankenship, L.: Nature 243 (1973) 81. Gibson, D.M., Hjellming, R.M.: Publ. Astron. Soc. Pac. 86 (1974) 652. Levato, H.: Astron. Astrophys. 35 (1974) 259. Friedemann, C., Gürtler, J.: Astron. Nachr. 296 (1975) 125. Zahn, J.-P.: Astron. Astrophys. 41 (1975) 329. Hall, D.S., in: Multiple Periodic Variable Stars (W. Fitch, ed.), (1976). Baranne, A., Mayor, M., Poncet, J.L.: Vistas Astron. 23 (1979) 279. Campbell, B., Walker, G.A.H.: Publ. Astron. Soc. Pac. 91 (1979) 540. Kopal, Z.: Language of the stars, Dordrecht: Reidel (1979). Söderhjelm, S.: Astron. Astrophys. 89 (1980) 100. Beer, P. (ed.): Vistas Astron. 25 (1981) 1-233 (Proc. 1980 Conference in Rome). Lewin, W.G.H., Joss, P.C.: X-ray bursters and X-ray sources of the galactic bulge, Space Sci. Rev. 28 (1981) 3. McHardy, I.M., Lawrence, A., Pye, J.P., Pounds, K.A.: Mon. Not. R. Astron. Soc. 197 (1981) 893. Warwick, R., Marshall, N., Frazer, G.W., et al.: Mon. Not. R. Astron. Soc. 197 (1981) 865. Bradt, H.V.D., McClintock, J.E.: Optical counterparts of compact galactic X-ray sources, Annu. Rev. Astron. Astrophys. 21 (1983) 13. Gimenéz, A., García-Pelayo, J.M.: Astrophys. Space Sci. 92 (1983) 203. Griffin, R.F.: Observatory 103 (1983) 273. Andersen, J., Clausen, J.V., Jorgensen, H.E., Nordstom, B., in: Observational Tests of Stellar Evolution Theory, IAU Symp. No. 105 (1984) 137. Latham, D.W., in: Stellar Radial Velocities, IAU Coll. 88 (1985) 21. Mayor, M., in: Stellar Radial Velocities, IAU Coll. 88 (1985) 35. Philip, A.G.D., Latham, D.W. (eds.): Stellar Radial Velocities (IAU Coll. No. 88), Schenectady, N.Y.: Davis Press (1985). Stencel, R.E.: The Recent Eclipse of Epsilon Aurigae, NASA Conf. Publ. No. 2384 (1985). Wyatt, W.F., in: Stellar Radial Velocities, IAU Coll. 88 (1985) 123. Appenzeller, I., Jordan, C. (eds.): Circumstellar matter (IAU Symp. No. 122, Heidelberg), Dordrecht: Kluwer Acad. Publ. (1986). Beavers, W.I., Eitter, J.J.: Astrophys. J. Suppl. 62 (1986) 147. Backer, D.C., Hellings, R.W.: Pulsar timing and general relativity, Annu. Rev. Astron. Astrophys. 24 (1986) 537. Rodonò, M., Cutispoto, G., et al.: Astron. Astrophys. 165 (1986) 135. Andersen, J.: Bull. CDS 38 (1987) 59.


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6.1.3.1 Double stars: X-ray binaries

[Ref. p. 299

87H1 Hack, M., Stickland, D., in: Exploring the Universe with the IUE satellite (Y. Kondo, ed.-inchief), Dordrecht: Reidel (1987). 87H2 Hegedüs, T.: Bull. CDS 35 (1987) 15; see also corrigenda in Bull. CDS 36 p. 23. 87K Kondo, Y, (ed.): Exploring the Universe with the IUE Satellite, Dordrecht: Reidel (1987). 87M Mayer, P., Drechsel, H.: Astron. Astrophys. 183 (1987) 61. 88C Campbell, B., Walker, G.A.H., Wang, S.: Astrophys. J. 331 (1988) 902. 89D Drechsel, H., et al.: Astron. Astrophys. 221 (1989) 49. 89Z1 Zahn, J.-P.: Astron. Astrophys. 220 (1989) 112. 89Z2 Zahn, J.-P., Bouchet, L.: Astron. Astrophys. 223 (1989) 112. 90D Di Benedetto, G.P., Ferluga, F.: Astron. Astrophys. 236 (1990) 449. 90E Eaton, J.A., et al.: Astron. J. 100 (1990) 799. 90G Guinan, E.G., Carrol, S.M., in: Active Close Binaries (C. Ibanoglu, ed.), Dordrecht: Kluwer Acad. Publ. (1990) esp. 21-33. 90H Hall, D.S., Henry, G.V., in: Active Close Binaries (C. Ibanoglu, ed.), Dordrecht: Kluwer Acad. Publ. (1990) p. 287. 90P Plavec, M., in: Active Close Binaries (C. Ibanoglu, ed.), Dordrecht: Kluwer Acad. Publ. (1990) 37. 91A Andersen, J.: Astron. Astrophys. Rev. 3 (1991) 91. 91F Fellgett, B.P.: Observatory 111 (1991) 250. 91G Griffin, R.F.: Observatory 111 (1991) 291. 91S Stickland, D.J.: Observatory 111 (1991) 113. 91W Wilson, R.E., in: Report of IAU Com. 42 (Koch, R.H., ed.). See Reports on Astronomy XXI A (D. McNally, ed.), Dordrecht: Kluwer Acad. Publ. (1991), p. 483. 92B Byrne, P.B., Mullen, D.J. (eds.): Surface Inhomogeneities of Late-Type Stars. Colloquium at the Armagh Obs., N. Ireland, 1990, Berlin: Springer (1992). 92C Chambliss, C.R.: Publ. Astron. Soc. Pac. 104 (1992) 981. 92D Duquennoy, A., Mayor, M. (eds.): Binaries as Tracers of Star Formation. Workshop at Bettmeralp, Switzerland 1991, Cambridge: Cambridge University Press (1992). 92R Rodonò, M., in: Evolutionary Processes in Interacting Binary Stars (Y. Kondo, R.E. Sisterò, R.S. Polidan, eds.), IAU Symp. 151, Dordrecht: Kluwer Acad. Publ. (1992) p. 71. 92S Shore, S.N.: Saas-Fee Lecture Notes (1992). 92V van den Heuvel, E.P.J.: Saas-Fee Lecture Notes (1992). 93M Milone, E.F. (ed.): Light Curve Modeling of Eclipsing Binary Stars, Berlin: Springer (1993). 93P Pounds, K.A. and 55 collab.: Mon. Not. Astron. Soc. 260 (1993) 77. 93V Verbunt, F., in: Annu. Rev. Astron. Astrophys. 31 (1993) 93. 94A Antokhina, A., Cherepashchuk, A.M.: Astron. Zh. 71 (1994) 420. 94B1 Bowyer, S.: Science 263 (1994) 55. 94B2 Bowyer, S., Lieu, R. et al: Astrophys. J. Suppl. 93 (1994) 569. 94H Hilditch, R.W.: Observatory 114 (1994) 214. 94W Wilson, R.E.: Publ. Astron. Soc. Pac. 106 (1994) 921.

6.1.3 Systems with compact objects 6.1.3.1 X-ray binaries 6.1.3.1.1 Introduction and catalogues A large number of low luminosity X-ray sources is known which are, however, not counted as X-ray binaries since their relatively low X-ray luminosity excludes the essential mechanism of accretion on a compact companion in a close binary system. To these stellar sources belong,


282


[Ref. p. 299

87H1 Hack, M., Stickland, D., in: Exploring the Universe with the IUE satellite (Y. Kondo, ed.-inchief), Dordrecht: Reidel (1987). 87H2 Hegedüs, T.: Bull. CDS 35 (1987) 15; see also corrigenda in Bull. CDS 36 p. 23. 87K Kondo, Y, (ed.): Exploring the Universe with the IUE Satellite, Dordrecht: Reidel (1987). 87M Mayer, P., Drechsel, H.: Astron. Astrophys. 183 (1987) 61. 88C Campbell, B., Walker, G.A.H., Wang, S.: Astrophys. J. 331 (1988) 902. 89D Drechsel, H., et al.: Astron. Astrophys. 221 (1989) 49. 89Z1 Zahn, J.-P.: Astron. Astrophys. 220 (1989) 112. 89Z2 Zahn, J.-P., Bouchet, L.: Astron. Astrophys. 223 (1989) 112. 90D Di Benedetto, G.P., Ferluga, F.: Astron. Astrophys. 236 (1990) 449. 90E Eaton, J.A., et al.: Astron. J. 100 (1990) 799. 90G Guinan, E.G., Carrol, S.M., in: Active Close Binaries (C. Ibanoglu, ed.), Dordrecht: Kluwer Acad. Publ. (1990) esp. 21-33. 90H Hall, D.S., Henry, G.V., in: Active Close Binaries (C. Ibanoglu, ed.), Dordrecht: Kluwer Acad. Publ. (1990) p. 287. 90P Plavec, M., in: Active Close Binaries (C. Ibanoglu, ed.), Dordrecht: Kluwer Acad. Publ. (1990) 37. 91A Andersen, J.: Astron. Astrophys. Rev. 3 (1991) 91. 91F Fellgett, B.P.: Observatory 111 (1991) 250. 91G Griffin, R.F.: Observatory 111 (1991) 291. 91S Stickland, D.J.: Observatory 111 (1991) 113. 91W Wilson, R.E., in: Report of IAU Com. 42 (Koch, R.H., ed.). See Reports on Astronomy XXI A (D. McNally, ed.), Dordrecht: Kluwer Acad. Publ. (1991), p. 483. 92B Byrne, P.B., Mullen, D.J. (eds.): Surface Inhomogeneities of Late-Type Stars. Colloquium at the Armagh Obs., N. Ireland, 1990, Berlin: Springer (1992). 92C Chambliss, C.R.: Publ. Astron. Soc. Pac. 104 (1992) 981. 92D Duquennoy, A., Mayor, M. (eds.): Binaries as Tracers of Star Formation. Workshop at Bettmeralp, Switzerland 1991, Cambridge: Cambridge University Press (1992). 92R Rodonò, M., in: Evolutionary Processes in Interacting Binary Stars (Y. Kondo, R.E. Sisterò, R.S. Polidan, eds.), IAU Symp. 151, Dordrecht: Kluwer Acad. Publ. (1992) p. 71. 92S Shore, S.N.: Saas-Fee Lecture Notes (1992). 92V van den Heuvel, E.P.J.: Saas-Fee Lecture Notes (1992). 93M Milone, E.F. (ed.): Light Curve Modeling of Eclipsing Binary Stars, Berlin: Springer (1993). 93P Pounds, K.A. and 55 collab.: Mon. Not. Astron. Soc. 260 (1993) 77. 93V Verbunt, F., in: Annu. Rev. Astron. Astrophys. 31 (1993) 93. 94A Antokhina, A., Cherepashchuk, A.M.: Astron. Zh. 71 (1994) 420. 94B1 Bowyer, S.: Science 263 (1994) 55. 94B2 Bowyer, S., Lieu, R. et al: Astrophys. J. Suppl. 93 (1994) 569. 94H Hilditch, R.W.: Observatory 114 (1994) 214. 94W Wilson, R.E.: Publ. Astron. Soc. Pac. 106 (1994) 921.

6.1.3 Systems with compact objects 6.1.3.1 X-ray binaries 6.1.3.1.1 Introduction and catalogues A large number of low luminosity X-ray sources is known which are, however, not counted as X-ray binaries since their relatively low X-ray luminosity excludes the essential mechanism of accretion on a compact companion in a close binary system. To these stellar sources belong,


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– among binary stars: ß Per and a few related systems (1031 erg/s, in bursts), a significant number of RS CVn stars (1031…1032 erg/s), cataclysmic variables (1032 erg/s); – among single stars: flare stars (1030 erg/s at peak), coronal X-ray emitters (1027…1028 erg/s); – an exceptional state of evolving X-ray sources is represented by super-soft sources of high luminosity, see subsect. 6.1.3.1.2.3. Luminosities closest to the level of binary X-ray sources are those of the peculiar white dwarf binaries HZ 43 and Feige 24 (≈ 3·1034 erg/s) and AM Her, the prototype of a subclass of cataclysmic variables with strong magnetic fields, (1033 erg/s). Yet even the X-ray luminosities of these sources are 2 or 3 order of magnitude below that of the X-ray binaries proper. Cf. subsect. 5.1.4. Catalogues The most comprehensive catalogue of X-ray sources in general (not limited to binary sources) is still: – W. Forman, C. Jones, L. Cominsky et al.: The 4th UHURU Catalogue of X-ray Sources, Astrophys. J. Suppl. 38 (1978) 357-412. The designation is 4U + code for coordinates. Several catalogues of X-ray sources have been published containing binary and other objects discovered by Leicester University Sky Survey Instrument (SSI) on the satellite Ariel 5: – B.A. Cooke et al.: Catalogue of high galactic latitude sources, |b|>10° (2A Catalogue), 105 Xray sources. Notation: 2A + code for coordinates. – R. Warwick et al.: The Ariel (3A) Catalogue of X-ray Sources I, |b|10°, 142 sources. Notation: 3A + code for coordinates. – A Catalogue and Bibliography of Galactic X-ray Sources covering the earlier material up to 1978, can be found in X-ray Astronomy (W.A. Braity, L.E. Peterson, eds.), Pergamon Press (1979). – The latest and by far the most comprehensive list of X-ray binaries can be found in J.A. van Paradijs: Neutron Stars in X-ray Binaries in the volume Neutron Stars: Theory and Observation (J. Ventura, D. Pines, eds.), Kluwer Acad. Publ. (1991). See also H. Ritter's listing of 36 lowmass X-ray binaries [90R]. Further discoveries by the satellites Ariel 5, SAS-3, HEAO 1 and 2 (Einstein satellite), Hakucho, Temna, Ginga, Exosat, ROSAT, and ASCA are referred to using these names or by incidental designation. These satellites worked on the whole field of X-ray astronomy; observations of brighter binary stars by Ginga are summarized by Nagase [89N1], work of ROSAT by Trümper [93T1], and initial results by ASCA are presented in several papers on binary sources in Publ. Astron. Soc. Jpn. 46 (1994) L81-L109. A group of sources in the galactic bulge, not far from the direction of galactic center, are usually designated: GX + code for galactic coordinates. Most of these have to be distant objects (several kpc) and thus they are bright X-ray sources, containing a neutron star and probably a low-mass companion, or, in exceptional cases, such as GX301-2, a massive B or Be star.


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[Ref. p. 299

6.1.3.1.2 Classification of binary X-ray sources 6.1.3.1.2.1 High-mass X-ray binaries (HMXB) This is a very homogeneous class where the mass losing component (mostly via stellar wind) is always a massive, early-type star usually of spectral type O or B. The accreting component is a neutron star or, in a few cases, probably a black hole. Several of the HMXBs exhibit X-ray pulses and this makes good or very good orbital determinations for the compact component possible which, however, enables only estimates of the component masses. (About masses and mass determinations of HMXBs, see binary systems with possible black hole components, subsect. 6.1.3.1.4). Among earlier review articles we mention: Bahcall [78B], Rappaport and Joss [81R, 83R], Joss and Rappaport [84J]. A recent review is by Nagase [89N1]. The best known HMXBs are listed in Table 2. Table 2. High-mass X-ray binaries. (Galaxy and Magellanic Clouds). The table is presented in order of increasing right-ascension. For the main references, see the reviews [81R, 83R, 84J]. Identification

4U0115+63

4U0900–40 4U1223–62 4U1538–52 4U1700+37 4U1907+09

SMC X-1 LMC X-4 LMC X-3 LMC X-1 Vela X-1 Cen X-3 GX301-2

Cyg X-1

Sp. type

Pulse Orbital period [s] period [d]

B B0I O7 B3V O7III

3.6 0.7 13.5

O7 B1Iem B0I O6f ≈ B2 O9.7Iab

Variable star notation

24.3 3.9 1.4

Remarks

X-ray transient

black hole cand. 283 4.83 695

8.96 2.09 35 3.73

5.60

V779 Cen est. mass 30 M QV Nor

V1357 Cyg

no pulses obs. no pulses obs. black hole cand.

Data of 21 binary X-ray pulsars, mostly HMXBs, can be found in Joss and Rappaport's review [84J]. The pulse periods range from 69 ms (A0538–66) to 835 s (4U0352+30 = X Persei). The pulse (obviously rotational) periods are expected to decrease gradually, resulting essentially from gaining angular momentum during accretion (spin-up). Several systems with increasing angular velocities have been observed (e.g. Her X-1, Cen X-3) but others show only seemingly irregular variations of the pulse period. An important group of the HMXBs show early type emission line spectra, mostly O9e…B2e. They tend to be highly variable; some of them are transient sources. Periods are longer (> 20 days) and the orbits seem to be noncircular. Better studied representatives of the group are 4U0115+63, A0535+26, 4U0352+30 (= variable star X Per, orbital period 580 days).

6.1.3.1.2.2 Low-mass X-ray binaries (LMXB) All X-ray binaries which contain manifestly no early-type, massive stellar companion, are considered as belonging to the class of LMXBs. These systems may have ages >108 years and are concentrated (with important exceptions such as Cyg X-2 or Cyg X-3) toward the central bulge of the Galaxy. The number of the LMXBs can be estimated 50 to 75 and in most, if not all, systems the accreting


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285

component is a neutron star. The stellar component is of about solar mass or less. The mechanism of the X-ray emission is most probably Roche-lobe overflow. The class of LMXBs may not be as homogeneous as that of the HMXBs: (1) There exists at least one system which possibly represents an intermediate case between the main groups. Although it is counted as LMXB, it is certainly not a prototype for the low-mass systems. Its characteristic properties are given in Table 3. Table 3. Characteristic properties of binary 4U1656+35. Identification

4U1656+35

Her X-1

Sp. type

Pulse period [s]

Orbital period [d]

Variable star Remarks notation

≈ late A

1.24

1.7

HZ Her

Total mass ≈ 3.5 M

This extensively studied system exhibits several unusual features: 35 day periodicity of on and off X-ray luminosity (probably due to precession of the accretion disk), long periods (years) of inactivity, strong magnetic field (≈ 1012 G) indicated by the presence of cyclotron lines. References: X-ray orbit, Deeter et al. [81D]; cyclotron lines, Trümper [79T]. For questions of evolution, see [92S]. For earlier identifications, see M. Gottwald et al. An atlas of optical counterparts of low mass Xray binaries: I. The northern sample (Max Planck Institut für Physik and Astrophysik, Garching, Preprint, Nov. 1990). The southern declination limit is –22° and the atlas includes 18 identified and 10 unidentified objects, their data see Table 2. By far the most extensive list of LMXBs is in [91V2]. An early classification scheme for galactic bulge X-ray sources, based on the X-ray spectra of these objects up to 28 keV energies, was given by Parsignault and Grindlay [70P]. (2) It is possible, although not generally accepted, that a number of bright sources near the galactic center form a subclass of low-mass systems. Stellar population considerations make it almost certain that these sources are not young and massive objects; yet they may be related to a small group of bright sources near the center of the M31 galaxy. (3) The LMXB systems show a weak concentration toward the galactic plane (z components a few 100 pc to over 1 kpc) and also to the galactic center (most systems within 5 kpc of the center). They do have high space velocities which certainly influenced their observed distribution in the galaxy. The LMXB systems are much less well known than the HMXBs: they are usually faint in the optical and show only in a few cases X-ray pulses or eclipses. An early, tentative explanation of this apparent anomaly has been proposed in terms of thick accretion disks obscuring the central X-ray source. Nonetheless, one important piece of information, the period of the system, can be estimated from modulations of the X-ray light curve. These modulations seem to fall into two categories: – sudden, quasi-periodic reductions of the X-ray intensity (dips) due to structures in the disk, and – smoother variations through radiation scattered into the line of sight by a corona encompassing the whole X-ray source (accretion disk corona or ADC). The periods are of the same order of magnitude as those of cataclysmic variables; for a recent review of this question, see [92P] Two of the systems possibly harboring black hole components (see Table 4), both transients or Xray novae, clearly have visible components on or near the lower main sequence (G or K type). Thus a small number of LMXBs, perhaps 2…5 percent, certainly do not have a neutron star component in the system; these are recognizable by their nonbursting nature, tendency to transient behaviour and very hard spectrum extending over 30 keV.


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[Ref. p. 299

Several LMXBs exhibit quasi-periodic oscillations (QPOs); the best studied case is the perhaps less typical system Cyg X-2. These oscillations are particularly well shown in a "colour-colour diagram" of the source, i.e., high-energy index vs. low-energy index in the X-ray spectrum. The position assumed at any time in this diagram is strongly correlated with the (variable) luminosity of the source. This phenomenon may furnish important information about the structure of the system as well as the neutron star; see the reviews by van der Klis [87V], also by Lamb [89L]. (4) A number of binary pulsars, the majority of them radio pulsars, have been found in globular clusters. About ten are X-ray sources (mostly producing X-ray bursts) which have to be counted as LMXBs. Only one of them has a confirmed optical counterpart, the source 4U2127+11 in M15 [84A]. If the X-ray component is a neutron star, the secondary may be of mass 0.2…0.3 M ; see Naylor and Charles [89N2], Ilovaisky [89I]. Among these sources, 4U1820–30 has the shortest orbital period known, 685 s; the secondary with ≤ 0.1 M is possibly a degenerate helium star, Tan et al. [90T]. 6.1.3.1.2.3 Super-soft sources Following up a few early discoveries by the Einstein satellite observations by ROSAT revealed another class of X-ray sources, named super-soft sources; a number of them (10…15 objects) have been discovered in the Large Magellanic Cloud and the M31 galaxy. Characteristic features are blackbody temperatures of a few times 105 K and relatively high luminosity, 1037 to 1038 erg/s. It seems that the accreting source is in most, but possibly not all, cases a massive CO white dwarf. It is thought that this evolution may lead to a supernova of Type Ia. Practically all X-ray emitting binary sources show (besides regular pulses in some cases) strong and apparently irregular variations on timescales ranging from milliseconds to years. Two types of these variations are particularly important: transient behaviour and bursts. 6.1.3.1.2.4 Variable sources: transients and bursters (1) X-ray transients, sometimes called X-ray novae, are normally, for years or decades, faint or even unobservable X-ray sources which brighten within weeks or months to high luminosity levels, about 1037…1038 erg s–1 In many cases we observe in the optical the outburst of a nova, occurring simultaneously; the observed novae seem to belong, as searches in plate archives indicate, to the subclass of recurrent novae. The transient source 4U0115+53 and possibly a very few others belong to the HMXB class, the majority can be classified as LMXB objects. It is remarkable that two well observed systems are among the 5 or 6 debated candidates for having a black hole component: A0620+00 (V614 Mon) and GS2023+338 (V404 Cyg); the stellar components are on the lower main-sequence. See Table 4 in subsect. 6.1.3.1.4. Apparently, in the optical nova-like brightenings are accompanying the X-ray transient phenomena. Outbursts of V614 Mon ocurred in 1917 and 1975, those of V404 Cyg in 1938, 1956 and 1984. Two further transient X-ray sources which may be structurally similar to SS 433 but show far higher energetic phenomena (relativistic jets leading to so-called superluminal velocities) are discussed together with the black hole candidate systems in subsect. 6.1.3.1.4. (2) The X-ray burst sources or bursters show regular but no periodic outbursts of X-ray luminosity in characteristic intervals of a few hours to about one day. The bursts show a very rapid rise, within 1…5 s and the gain in intensity is 5…10 times of the interburst level; the luminosity then decays more gradually, in 20…30 s (Type I bursts). The burst are quite distinct in the observed energy range of 1.3…19 keV, above these energies, the bursts give place to large but apparently irregular fluctuations. Sources exhibiting Type I bursts are markedly concentrated in the galactic bulge and are almost certainly all LMXBs. Some typical representants of the class are: Landolt-Börnstein New Series VI/3B

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287

– MBX 1636-53, MBX 1728-34, MBX 1735-44 (notation: MBX stands for MIT X-ray source, burster). An apparently unique object is MBX 1730-335, the Rapid Burster only a few degrees distance in the sky from the galactic center. The bursts occur on timescales of seconds to minutes, instead of several hours (Type II bursts). The energy in the bursts seems to be approximately proportional to waiting time between consecutive bursts. The system contains a weakly magnetized (108 G) neutron star. It is to be added that the Rapid Burster also exhibits, with some regularity (3…4 h), Type I bursts. Current models ascribe Type I bursts to thermonuclear flashes, while Type II bursts are thought to result from instabilities in the accretion flow. For a review, see Lewin and Joss [83L]. (3) Among the X-ray sources tentatively classified as LMXBs, there are two extraordinary systems still not yet well understood which deserve a short description: Cygnus X-3 is undetectable in the optical but can be identified as infrared source. It is also a radio emitter and the strongest gamma-ray source in the sky with a possibly pulsed emission of 12 ms period. Both radio and X-ray observations show strong bursts, correlated in the two frequency ranges. During one large burst in 1978, a shower of apparently neutral particles of yet unknown nature reached the earth from the direction of the source. The binary nature is indicated by a 4.8-hmodulation of the X-ray flux ascribed to orbital motion. This short period could be readily interpreted as the stellar component, rendered invisible by heavy circumstellar absorption, being a low-mass object. Never-theless, a new aspect in the study of this system was opened up by the remarkable discovery of a WR-type object, shown by helium emission lines in the IR [92V]. Even if the WR component seems to be somewhat unusual, the system Cygnus X-3 may turn out of crucial importance for the evolutionary relationship of massive luminous helium stars and X-ray binaries. The system may be in the rapid spiral-in phase of the compact object which must be a neutron star in this case. SS 433 is a highly peculiar binary of 13.1 d period, V ≈ 14m (O…B star?), with unprecedented, rapidly moving systems of emission lines in its spectrum; variable star notation (ellipsoidal variable) V1343 Aql. The X-ray radiation is of secondary importance but it indicates the presence of a compact object. The gross behaviour of the strongly Doppler-shifted lines can be predicted on the basis of a kinematic model, cf. Milgrom [79M1], and other authors, e.g.. [79M2]. This model postulates a dense, precessing accretion disk and twin jets moving outward perpendicularly to the disk, thus themselves precessing, at a relativistic speed of 0.26 c; the precession period remains near 164 days. The precessing jets are apparently linked to the structure of the surrounding nebula W50, thus extending over distances of the order of a parsec. Energy supply and collimation of the jets are still badly understood and opinion is also divided about the nature of the compact object in the system. Extensive discussions of SS 433 in Beer [81B], Margon [84M].

6.1.3.1.3 Neutron star masses based on X-ray binaries For both X-ray binaries and binary pulsars, the starting point for mass determinations is the mass function. From the Doppler effect or the light time effect shown by the pulses, an accurate orbit can be determined yielding aX sin i and P. Applying Kepler's 3rd law we obtain for the mass function f(M),

a f

f M ≡

( aX sin i )3 G M23 sin 3 i G MX sin 3 i = = 2 2 2 4 π ( MX + M2 ) 4 π 2 ( q + 1 )2 q P

with q = MX/M2; a2 and M2 refer to the normal star, and aX and MX to the compact object (using AU, year, and M instead of m, s, and kg leads to G ≈ 4π2). The mass function contains 3 unknowns and further equations are needed to reduce this number. These are, as a rule, Landolt-Börnstein New Series VI/3B

288


[Ref. p. 299

– the spectroscopic orbit of the normal component, giving a2 sin i, – the duration of X-ray eclipses, if they occur; see also LB VI/2c, p. 27. Furthermore, in some cases the assumption that the mass losing component fills its Roche critical equipotential supplies an additional relationship. As a rule these supplementary data are of lesser accuracy than the pulse timing observations, thus the neutron star masses derived from X-ray binaries have in all cases a far wider margin of uncertainty than that of the masses obtained from the best determined radio pulsar orbits (see subsect. 6.1.3.2.4). The following graphical representation is a summary given by van den Heuvel [94V, p. 304].

Fig. 1. Neutron star masses for X-ray binaries, from [94V]. Three radio pulsars are also shown for comparison. In the case of PSR 1534+12 the apsidal motion test is not applicable; solution for Her X-1 is still ambiguous.

6.1.3.1.4 Binary systems with possible black hole components (stellar black holes) It is generally agreed that stellar black holes originate in the core collapse of a massive star (M ≥ 20 M on the zero-age main sequence). As of today, stellar black holes can only be detected in binary X-ray sources, both in HMXB and LMXB systems. The high X-ray output indicates the presence of a compact object. Sources with putative black hole components must satisfy the obvious condition that no pulses and no indication of a magnetic field are observed. Basics of identifying possible black holes in an X-ray source are: – the presence of a high-mass component invisible in the spectrum; – peculiar light and spectrum variations, especially in the high-energy range. The mass of the invisible companion can be estimated, not always with high accuracy, from the radial velocity curve and the mass-function of the stellar component and a minimum possible mass can be derived, if we assume a normal or nearly normal mass corresponding the observed spectral type and set i = 90°. For identification as a black hole system, the mass of the invisible component has to be higher than the maximum possible mass (mass limit) of a stable neutron star. This value depends on the behaviour (equation of state) of dense matter and no unique value is known yet; most studies suggest values around 2.5 M . Landolt-Börnstein New Series VI/3B

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6.1.3.2 Double stars: Binary radio pulsars

289

Using the estimated mass of the invisible "secondary" component, five X-ray binaries have been proposed as possibe candidates for a stellar black hole (see Table 4) [91M]. Table 4. Properties of X-ray binaries possibly harboring a stellar black hole. System

Visual sp.

f(M) [ M ]

Minimum mass [ M ]

Remark

Cyg X-1 LMC X-3 A0620-00

O9.7Iab B3V K5V

0.24 2.3±0.3 3.2

≈6 6…10 ≈4

Roche configuration? transient

LMC X-1 V404 Cyg

O7III G…KV

0.14 6.3

≈5 ≈6

transient

Ref.

84L, 73M 83C, 83P 86M, 94M1, 94S 87H, 86P 92C1

It is doubtful that all these systems are harboring a black hole companion but almost certainly some of them do. Among light variations and spectral features, thought to be characteristic of an invisible black hole companion, the most important to be expected are fast, irregular fluctuations of the radiation level (down to ms time scales), corresponding to the strongly perturbed flow in the immediate neighborhood of the black hole; this phenomenon is well known, for instance, in the Cygnus X-1 system. The spectrum is normally very soft in the 1…10 keV region, but sometimes can harden considerably and show significant emission at the 100 keV energies. Several objects have been mentioned as black hole candidates, among others Circinus X-1, Norma X-1, GX 339-4, but only one case may deserve to be included in Table 4 above: Nova Muscae 1991, see [92R]. This is a strong X-ray transient, in many respects similar to A0620– 00. The essential data are: visual sp. K0…4V, orbital period 10.4 h, f(M) = 3.1 M . A.P. Cowley [92C2] reviewed this group of black hole candidates. Moreover, two further sources deserve closer consideration. In recent years two transient X-ray sources have been discovered where high resolution radio observations (VLA) indicated relativistic jets emanating from the sources moving apparently faster than light (superluminal motion) These are GRS 1915+105, see [94M2], and GRO J1665–40, see [95T1]. These galactic "miniquasars" are almost certainly binary systems with accretion and energy considerations strongly suggest the presence of a stellar black hole component. The phenomenon of the apparently superluminal motion was first found in the case of certain quasars (e.g. 3C 273). Explanation of these motions was given in terms of very high velocities in combination with the geometry of the systems by M. Rees [66R]; see also [87P] for a short description.

6.1.3.2 Binary radio pulsars 6.1.3.2.1 Introduction Pulsars are rapidly rotating, strongly magnetized neutron stars with nuclear bulk densities (up to ρ ≈ 1017 kg m–3); they emit rotating beams of radiation, predominantly at radio frequencies which, as they sweep across the earth, are causing the observed pulses. Thus the mean pulse period of a pulsar is assumed to be equal to the rotation period of the neutron star. The physics of neutron stars is treated in subsect. 5.6.1. It is, however, an important attribute of this class of objects that some of them are members of binary stellar systems. These are the main source of our knowledge of structural parameters of the neutron stars, especially their masses as well


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289

Using the estimated mass of the invisible "secondary" component, five X-ray binaries have been proposed as possibe candidates for a stellar black hole (see Table 4) [91M]. Table 4. Properties of X-ray binaries possibly harboring a stellar black hole. System

Visual sp.

f(M) [ M ]

Minimum mass [ M ]

Remark

Cyg X-1 LMC X-3 A0620-00

O9.7Iab B3V K5V

0.24 2.3±0.3 3.2

≈6 6…10 ≈4

Roche configuration? transient

LMC X-1 V404 Cyg

O7III G…KV

0.14 6.3

≈5 ≈6

transient

Ref.

84L, 73M 83C, 83P 86M, 94M1, 94S 87H, 86P 92C1

It is doubtful that all these systems are harboring a black hole companion but almost certainly some of them do. Among light variations and spectral features, thought to be characteristic of an invisible black hole companion, the most important to be expected are fast, irregular fluctuations of the radiation level (down to ms time scales), corresponding to the strongly perturbed flow in the immediate neighborhood of the black hole; this phenomenon is well known, for instance, in the Cygnus X-1 system. The spectrum is normally very soft in the 1…10 keV region, but sometimes can harden considerably and show significant emission at the 100 keV energies. Several objects have been mentioned as black hole candidates, among others Circinus X-1, Norma X-1, GX 339-4, but only one case may deserve to be included in Table 4 above: Nova Muscae 1991, see [92R]. This is a strong X-ray transient, in many respects similar to A0620– 00. The essential data are: visual sp. K0…4V, orbital period 10.4 h, f(M) = 3.1 M . A.P. Cowley [92C2] reviewed this group of black hole candidates. Moreover, two further sources deserve closer consideration. In recent years two transient X-ray sources have been discovered where high resolution radio observations (VLA) indicated relativistic jets emanating from the sources moving apparently faster than light (superluminal motion) These are GRS 1915+105, see [94M2], and GRO J1665–40, see [95T1]. These galactic "miniquasars" are almost certainly binary systems with accretion and energy considerations strongly suggest the presence of a stellar black hole component. The phenomenon of the apparently superluminal motion was first found in the case of certain quasars (e.g. 3C 273). Explanation of these motions was given in terms of very high velocities in combination with the geometry of the systems by M. Rees [66R]; see also [87P] for a short description.

6.1.3.2 Binary radio pulsars 6.1.3.2.1 Introduction Pulsars are rapidly rotating, strongly magnetized neutron stars with nuclear bulk densities (up to ρ ≈ 1017 kg m–3); they emit rotating beams of radiation, predominantly at radio frequencies which, as they sweep across the earth, are causing the observed pulses. Thus the mean pulse period of a pulsar is assumed to be equal to the rotation period of the neutron star. The physics of neutron stars is treated in subsect. 5.6.1. It is, however, an important attribute of this class of objects that some of them are members of binary stellar systems. These are the main source of our knowledge of structural parameters of the neutron stars, especially their masses as well


290


[Ref. p. 299

as the main source of theories of late phases of stellar evolution. We will restrict our treatment to binary radio pulsars here. The number of known radio pulsars is presently well over 700. The increase of the numbers is represented in the major catalogue works: – in 1982, M. Grewing in LB VI/2c, subsect. 5.6.2.3, p. 11, gave 321 pulsars; – in 1990, Lyne and Graham-Smith (see Monographs in the reference list, p. 299) listed 450 pulsars, – while the most recent compilation gives the Catalog of 558 pulsars by J.H. Taylor, R.N. Manchester and A.G. Lyne [93T2]; the catalogue also contains orbits for 24 binary systems. For completing this last catalogue, the authors describe a free access over the Internet to the continually updated computer data base [93T2, p. 567]. The first issue of this remarkable new way of publication is a Catolog of 706 pulsars by Taylor, Manchester, Lyne and F. Camilo, dated 1995 May 3 [95T2]; the list of binary pulsar orbits also increased to 44. Designation of individual pulsars is similar to the method used for X-ray sources: two groups of digits give the right ascension and declination. For indicating an epoch 2000, a prefix J is added, for the epoch 1950, widely used earlier, in recent catologues a prefix B appears. Thus the first pulsar discovered [68H] was PSR 1919+21 or PSR B1919+21 = PSR J1921+2153, the first binary pulsar recognized [75H] was PSR 1913+16 or PSR B1913+16 = PSR J1915+1606. The large majority of the known radio pulsars are single objects. The progenitors of these pulsars were either massive (8…25 M ) single stars or members in a binary system which have been dissociated during the supernova event immediately preceding the formation of neutron stars. During the 1980s, however, a considerable number of binary pulsars have been discovered at the short period end of the distribution (usually under 100 ms), many of them in the ms-range (under 25 ms). A surprising number of these binary and ms pulsars, about 50, possibly as much as 75 percent, have been found in globular clusters and must have been formed and evolved under distinctly different conditions from those for the overwhelming number of single pulsars. Thus we have to consider the binary and ms pulsars a class for itself. The distribution of binarity with the pulse period is the following (as of May 1995, see [95T2]): – millisecond pulsars (1.5…6 ms): 39 pulsars, among them 26 binaries; – millisecond pulsars (6…25 ms): 13 pulsars, among them 12 binaries; – short-period pulsars (30…100 ms): 15 pulsars, among them 10 binaries; – pulsars with period 100 ms…5 s: 639 pulsars, among them 18 binaries. For the whole pulsar population (1995) the fraction of binarity was 66/706 = 9.3 percent. Progenitors The birth of a neutron star is almost certainly connected with the collapse of a stellar mass. This again occurs in most (perhaps not all) cases in a supernova explosion. The majority of supernova outbursts take place in close binary systems during the last phase of stellar evolution. There is general consensus that neutron stars originate in supernovae of Type II, probably also Type Ib and Ic, following the core collapse of a massive star (about 10 M to 20…25 M ); stars more massive than this limit will probably collapse to a stellar black hole. Binarity may play a decisive role in the loss of the hydrogen envelope in progenitors of supernovae Type Ib and Ic. Supernovae of Type Ia, belonging to an older stellar population, originate in a close binary with a massive white dwarf component, pushed over the Chandrasekhar mass limit of 1.4 M by a proper rate of accretion from the companion star. It seems important that present day theory strongly suggests that the exploding white dwarf will be completely destroyed, without leaving a compact object.


Ref. p. 299]


291

Most pulsars or compact components in X-ray binaries have masses around 1.4 M . In view of the above discussion, the closeness of this value to the Chandrasekhar mass limit must be mainly coincidental. It is well known that in supernova events the energy contributions of (1) the neutrino outburst, (2) the kinetic energy of the expanding envelope and (3) the light (photons) show, roughly, the ratio 90:10:1, respectively. It is true, however, that a "silent" collapse (no significant remnant or visible flash) of a massive white dwarf is theoretically possible. The designation "silent collapse" is Nomoto's [86N]; another generally used term is "accretion-induced collapse". Conditions for such type of events are highly specific, moreover, the large binding energy of the resulting neutron star would render its gravitational mass l.2 to 1.25 M , a value not yet found in the most reliable mass determinations. This type of event may be rare or unusual and, since in Type Ia supernovae the complete destruction of the white dwarf is expected, it seems, in summary, a justifiable assumption that most, if not all, pulsars as well as neutron stars in X-ray binaries have been produced in core collapses of massive stars.

6.1.3.2.2 Binary pulsars in globular clusters Both binary and ms-pulsars are strongly concentrated in globular clusters, see Table 5; these objects in clusters are obviously of different origin and follow a different evolution. They play an important role in the dynamical evolution of the clusters themselves. Albeit all sort of clusters may contain binary pulsars, prominently those with so-called collapsed cores, where the stellar density is high enough to make close approaches, and tidal and three-body captures, even collisions are more frequent, contain binary pulsars. In particular, the cluster 47 Tucanae has 11 binary pulsars, and M15 has 8 binary pulsars (and a bright X-ray binary). To illustrate this much discussed point (see, for instance, [86H]) we mention that the binary 2127+11C in M15, consisting of two neutron stars, may have originated in an exchange collision: (neutron star + white dwarf, neutron star) → (neutron star + neutron star, white dwarf), while the first binary pulsar 1913+16, with very similar parameters, resulted in all likelihood in massive binary evolution, see subsect. 6.1.3.3. 6.1.3.2.3 Binary pulsars as probes of General Relativity Very high timing accuracy (a few 100 µs) can be achieved by observing pulses of radiopulsars, in combination with the fact that although the individual pulse profiles are highly variable, averaging 50 to 100 profiles will yield a remarkable stable mean profile, often characteristic of the pulsar. Thus pulsar timing enabled radioastronomers to verify to a considerable accuracy several predictions of General Relativity. At the same time, pulsar binarity gave us some of the best determinations of neutron star masses, in general with much higher accuracy than X-ray pulsars. (See, for instance, [86B].) A total of four relativistic effects are observable by the aid of binary radio pulsars, in cases of favorable combinations of the orbital elements, see for instance [92T] or the Shapiro-Teukolsky monograph [83S]: (a) the rate of the relativistic apsidal rotation, ω& ; (b) obtaining the so-called redshift parameter (order of magnitude: ms), actually a combination of the transverse Doppler effect and the gravitational redshift; (c) the delay due to gravitational bending of the beam in the field of the nonpulsing component, sometimes called Shapiro delay (order of magnitude: 10 µs); (d) the decay of the orbit, the gradual shortening of the orbital period due to the emission of gravitational quadrupole radiation.


292


[Ref. p. 299

Although the latter effect was clearly observed only in the case of the first binary pulsar PSR 1913+16, it is presently considered the only uncontested demonstration of gravitational radiation. The observed value P& = –2.43·10–12 is within about 1 percent of the relativistic prediction [89T]. A later study by Damour and Taylor improved on the agreement somewhat, taking into account the accelerations due to the galactic orbits of the sun and the pulsar [91D]. In the case of this best observed pulsar PSR 1913+16, very accurate values of the component masses became available: 1.386 M (pulsar) and 1.442 M (companion). Relativistic apsidal motion Neutron stars can be considered as point masses and most (but not all) binary pulsars are "clean systems" free of circumstellar matter, thus they furnish excellent testing ground for the apsidal motion required by relativity theory; the binary orbit must be, of course, markedly eccentric. The general relativistic formula for the precession of the major axis in the two-body problem was derived by Levi-Civita [37L], in conventional notation: ∆ω =

6 πG ( M1 + M2 ) rad/period, c 2 a (1 − e 2 )

(alternative forms give deg/year.) The effect is proportional to the sum of masses, for instance, in case of PSR 1913+16, ω& = 4.,° 227 year–1, corresponding to M1 + M2 = 2.828 M ; both components are neutron stars. The system PSR 1855+09 shows, however, a practically circular orbit (e ≈ 10–5) and the determination of masses, based on the Shapiro delay, is less accurate: for the neutron star we 23 obtain the mass 1. 27+−00..15 M , for the secondary ≈ 0.23 M . Here the companion is a low-mass (helium) white dwarf, a characteristic combination for a wide class of systems [91R]. For binaries with no compact component, the deformation effect dominates and only in a few cases seems the isolation of the relativistic effect possible. One of the best candidates is the 10-day eclipsing binary DI Herculis, proposed by Rudkjøbing [59R]. However, Guinan and Maloney found an apparent discrepancy with the relativity theory [85G]; this discrepancy (too slow rotation of the apsidal line) is not yet convincingly explained. The general consensus is, however, that no reformulating of General Relativity will be necessary, and simpler explanations like perturbations from a third body or perhaps an offset rotational axis may ultimately explain the anomalous rate of apsidal motion. 6.1.3.2.4 Neutron star masses from radio pulsars If through relativistic effects additional information is supplied to the usually very accurately determined mass-function (see subsect. 6.1.3.1.3) we may derive the best individual masses for neutron stars. The errors of the numbers quoted below are, if not otherwise indicated, less than 0.01 M :

PSR 1913+16

Mp = 1.36 M

Ms = 1.44 M

2 neutron stars

PSR 19524+12

Mp = 1.36 M

Ms = 1.32 M

2 neutron stars

PSR 2127+11C (in M15)

Mp = 1.35 M

Ms = 1.36 M

2 neutron stars

[89T]


Ref. p. 299]


PSR 1855+09

23 M Mp = 1. 27+−00..15

neutron star + He white dwarf (0.23 M )

PSR 1802-07

Mp + Ms = 1.71 M

neutron star + He white dwarf (≈ 0.35 M )

PSR 2303+46

Mp ≈ 1.4 M

Ms ≈ 1.5 M

293

[91R]

2 neutron stars

(In the case of PSR 1855+09 the orbit is virtually circular, and mass determination is based on the Shapiro delay, see above.) Since the earliest discussion of neutron star masses, these are usually quoted as being of the "canonical" value of 1.4 M . As the few values above suggest, 1.35 M appears a slightly better average. Comparison with neutron star masses derived from X-ray binaries (Fig. 1) may or may not indicate systematic differences. The large scatter and the considerable uncertainty of the X-ray binary masses are, however, likely to be due to difficulties of the measuring procedure and it is doubtful whether the extreme values indicated ( ≤ 1 M for Her X-1, 1.8 M for 4U1700–37) would correspond to physically realistic cases. One may still assume that, apart from the variable quantities of angular momentum and magnetic field strength, all neutron stars are of similar constitution. 6.1.3.2.5 Millisecond pulsars It was realized early that the ultimate energy source of the beamed radiation of rotating (single) neutron stars was the slow breaking down, the spin-down of their rotation. Interaction with the pulsar magnetosphere leads, by not yet well understood processes, to the conversion of the rotational kinetic energy into the energy of the radiated beam. All linear period changes for single pulsars, indeed, increase, P& > 0, P& /P being as a rule 10–15…10–14 s–1; the ratio P/(2 P& ) is defined as the characteristic age of a pulsar and is typically of the order of 107 years. The relationship dE E rad = L = − rot = Iωω& gives the right order of magnitude of the observed radiation; here I is the dt moment of inertia for the neutron star of the order of 1038 kg m2, and ω = 2π/P is the angular velocity. As the increasing pulse period reaches 4 or 5 s, the pulses become too faint to be observed (silent pulsars). The so-called millisecond pulsars (ms pulsars) follow a very different evolutionary history. The first discovered objects are still of the shortest 1.6 ms period: PSR 1937+21 (single) and PSR 1957+20 (close binary, orbital period 9.5 h). The latter displays visible mass outflow from the secondary which has an estimated mass of 0.02 M ; thus, the key object PSR 1957+20 supplied the plausible solution for the problem of the very short periods. The ms pulsars almost certainly result from an extended accretion process in the close system neutron star + normal star, when at a stage the system's evolution made mass exchange (mass flow from the normal star to the neutron star) possible. The pulsar gained mass and angular momentum during this mass flow and this interaction accelerated its rotation. During this spin-up period the system turns to an X-ray binary, in most cases probably to an LMXB. After the accretion process ends, the short-period ms-pulsar remains (it is usually called a recycled pulsar), usually with a lowmass (0.2…0.4 M ) helium white dwarf as companion, see subsect. 6.1.3.3. Table 5 gives 49 binary and ms-pulsars. A table of 24 well studied binary pulsars (with orbital parameters) is given in the recent pulsar catalogue by Taylor et al. [93T2] and 20 further added in [95T2]. All clusters are globulars, no pulsar found in open clusters. Noncluster members are field objects belonging to the disk population. The values of log P& are generally much lower than those of individual pulsars, –19…–15. Magnetic fields, derived from the obliquely rotating dipole model are in the range of 108 to 1011 G. Eccentricities not indicated in the Table 5 are ≤ 0.025; in particular, for Landolt-Börnstein New Series VI/3B

294


[Ref. p. 299

systems with low-mass secondaries orbits are essentially circular, e < 0.01, in several cases e 0.1

2.6 357.8

0.0097 0.068

> 0.25 0.8…1.0

e = 0.27 M4 M13 M13 4

Ter5 NGC5440 NGC6539

)

e = 0.22 e = 0.795

NGC6624 NGC6624 M26 1.81 12.33

1.2·10–4 0.0052

0.06…0.13 0.2…0.4

0.32

0.1322

1.4

NGC6760 e = 0.62 2)


Ref. p. 299]


PSR

Prot [ms]

Porb [d]

f(M) [ M ]

1953+29 1957+20 2127+11A 2127+11B 2127+11C 2127+11D 2127+11E J2145–0750 2303+46 J2317+1439

6.13 1.61 110.66 56.13 30.53 4.65 4.8 16.052 1066.37 3.44

117.35 0.38

0.0027 5.2·10–5

Ms [ M ]

295 Cluster

0.2…0.4 ≈ 0.01

0.34

0.15

1.36

6.839 12.34 2.46

0.0241 0.2463 0.0022

≥ 0.43 ≈ 1.5 ≈ 0.2

Remarks

3

M15 M15 M15 M15 M15

)

e = 0.68 2) 5

) e = 0.66

Notes to individual systems: 1

) 0021–72A and 0021–72B are not located in 47Tuc (discordant dispersion measure). Orbit for 0021–72A not yet confirmed. 2 ) 1913+16 and 2127+11C (in M15), notice similarity of orbital elements and masses. 3 ) 1957+20, companion being disrupted by radiation and/or tidal forces. 4 ) J1713+0747, spin-down age ≈10·109 years. 5 ) J2145–0750, spin-down age ≥12·109 years. J1713+0747 and J2145–0750 seem to be the oldest neutron stars yet observed. 6.1.3.2.6 Secondaries in binary pulsar systems There are three particular systems showing exceptional combinations of the binary components. – PSR 1957+12, a ms-pulsar with two, perhaps three, secondaries of planetary masses, two of them around 3 MEA [92W]. The question whether these objects are survivors of a SN-explosion, or were later formed from debris of the event, is not yet settled. – PSR 1259–63, a field pulsar of relatively short period (48 ms) in a highly eccentric orbit (e = 0.9) around a massive Be star [92S]. Apart from the high eccentricity, this combination corresponds to that of a high-mass X-ray binary (HMXB). The orbital period is about 3.5 years and there seems to be no significant mass flow or accretion in the system except near periastron; the period is somewhat above that of the longest values among X-ray binaries around 2 years (e.g., X Per). It is possible that the neutron star originated in a relatively recent SN-event and that the pulse period is not accretion modified but it is close to the original value of the pulsar's rotation. – Another pulsar, J0045–7319, the only one known in the Small Magellanic Cloud, has also a massive early B-star companion (but not Be-type); the estimated mass, 8…10 M , suggests an unevolved main-sequence object. The orbital period is 51 days, the pulse period with 926 ms relatively long. In spite of the high eccentricity (e = 0.81) no significant interaction ocurrs at periastron. See [94K]. Systems with massive B-type companions seem exceptional. It was pointed out, however, by van den Heuvel already much earlier that O-type systems with a (quiet) compact companion may be considerably more frequent than observed HMXBs. Among the other binary systems, we may distinguish two, perhaps three, classes. Four systems, among them PSR 1913+16, have a high-mass secondary, as suggested by the mass-function. The orbits are eccentric and relativistic effects enabled accurate determination of the masses. These secondaries proved to be neutron stars; all masses are in the range of 1.30 to 1.45 M . In two cases, the secondaries seem to be massive white dwarfs; this could be confirmed by optical observations, see the review by Backer and Kulkarni [90B]. Landolt-Börnstein New Series VI/3B

296

6.1.3.3 Double stars: Evolution leading to compact objects

[Ref. p. 299

The large majority of the companion stars, as Fig. 2 indicates, comprises low-mass stars of an apparently homogeneous class. The masses range from < 0.1 M to about 0.5 M and the companions are in all likelihood helium white dwarfs. The decrease of the masses toward shorter orbital periods may be real and the result of interaction between the stars: slow loss of mass from the helium star (only a small part of which arrives at the neutron star), leading to the ultimate disruption of this component; the example is PSR 1957+21.

Fig. 2. Mass of the secondary components in binary pulsars plotted against the binary period. (Massive B-type secondaries are not shown.) The markings for the range of each star represent assumed values of inclination of i = 90°, 60° and 41.4°, respectively. The pulsar mass itself was taken to be 1.4 M .

6.1.3.3 Binary evolution leading to compact objects There is general consensus among astrophysicists that compact objects, single ones as well as in binary systems, are descendants of massive stars of only a few 106 years lifetime, after core collapse and SN explosion of Type II or Ibc. Supernovae of Type Ia (belonging to an older galactic population) occur as end phase of low-mass binary evolution; this may correspond to the detonation of an unstable, overmassive (M ≥ 1.4 M , Chandrasekhar limit) degenerate object. Such an object could be formed by coalescence, merger of two white dwarfs but a serious difficulty is that no progenitors seem to exist in the form of very close white dwarf double systems. The alternative hypothesis, accretion onto a massive white dwarf which pushes it over the above mentioned mass limit, seems to be more promising although it is surprisingly difficult to find the required orbital and accretion parameters (see, for instance, [90W]) but the recently discovered super-soft X-ray sources, see subsect. 6.1.3.1.2.3, may lead to an acceptable solution of the problem. While the "single-degenerate" origin of Type Ia supernovae in symbiotic systems did not prove promising, the "double-degenerate" configuration of two massive carbon-oxygen white dwarfs forming a very close system may lead, through merger of the components, to a highly instable single object which then collapses to a neutron star; an early proposal was by Iben and Tutukov [84I]. In the case of Type Ia supernovae it is, however, not expected that the outburst would produce a compact object; the collapse may destroy the former white dwarf completely. For a neutron star, 8 M is considered to be minimum mass for a progenitor, albeit some theories propose values as low Landolt-Börnstein New Series VI/3B

296

6.1.3.3 Double stars: Evolution leading to compact objects

[Ref. p. 299

The large majority of the companion stars, as Fig. 2 indicates, comprises low-mass stars of an apparently homogeneous class. The masses range from < 0.1 M to about 0.5 M and the companions are in all likelihood helium white dwarfs. The decrease of the masses toward shorter orbital periods may be real and the result of interaction between the stars: slow loss of mass from the helium star (only a small part of which arrives at the neutron star), leading to the ultimate disruption of this component; the example is PSR 1957+21.

Fig. 2. Mass of the secondary components in binary pulsars plotted against the binary period. (Massive B-type secondaries are not shown.) The markings for the range of each star represent assumed values of inclination of i = 90°, 60° and 41.4°, respectively. The pulsar mass itself was taken to be 1.4 M .

6.1.3.3 Binary evolution leading to compact objects There is general consensus among astrophysicists that compact objects, single ones as well as in binary systems, are descendants of massive stars of only a few 106 years lifetime, after core collapse and SN explosion of Type II or Ibc. Supernovae of Type Ia (belonging to an older galactic population) occur as end phase of low-mass binary evolution; this may correspond to the detonation of an unstable, overmassive (M ≥ 1.4 M , Chandrasekhar limit) degenerate object. Such an object could be formed by coalescence, merger of two white dwarfs but a serious difficulty is that no progenitors seem to exist in the form of very close white dwarf double systems. The alternative hypothesis, accretion onto a massive white dwarf which pushes it over the above mentioned mass limit, seems to be more promising although it is surprisingly difficult to find the required orbital and accretion parameters (see, for instance, [90W]) but the recently discovered super-soft X-ray sources, see subsect. 6.1.3.1.2.3, may lead to an acceptable solution of the problem. While the "single-degenerate" origin of Type Ia supernovae in symbiotic systems did not prove promising, the "double-degenerate" configuration of two massive carbon-oxygen white dwarfs forming a very close system may lead, through merger of the components, to a highly instable single object which then collapses to a neutron star; an early proposal was by Iben and Tutukov [84I]. In the case of Type Ia supernovae it is, however, not expected that the outburst would produce a compact object; the collapse may destroy the former white dwarf completely. For a neutron star, 8 M is considered to be minimum mass for a progenitor, albeit some theories propose values as low Landolt-Börnstein New Series VI/3B

Ref. p. 299]

6.1.3 Double stars: Systems with compact objects

297

as 5 M . Formation of a black hole requires progenitors of 15…20 M , at the least. In any case, these mass values indicate that the evolution toward neutron stars or black holes may involve, at some stages, large mass losses in the binary additionally to the supernova losses; the evolution is nonconservative. It should perhaps be added that the mass-defect due to the difference in the binding energy and corresponding to the final collapse to a neutron star is, according to Zeldovich and Novikov, merely of the order of 0.2 M ; this corresponds to about 3…4·1046 J, most of which will appear in the form of high-energy neutrinos. The origin of Type Ia supernovae in evolved close binary systems is considered as virtual certainty. There is some evidence that at least some of the Type II supernovae also descend from interacting binaries. Possible examples are SN 1993 J and SN 1994 I, where the hydrogen (and helium) lines at an early time disappeared from the spectrum. This can be interpreted in the way that prior to the core collapse the supernova candidate lost most or all of its envelope due to close binary interaction. In theoretical evolutionary sequences describing how some close binary systems may end up with compact components (frequently called "scenarios") several characteristic processes have to be considered. (1) For massive early-type stars, also for stars near the end of giant or supergiant evolution, mass loss due to stellar wind can be significant, as illustrated, for instance by Wolf-Rayet stars; values of 10–5…10–6 M /year are not uncommon. In the case of HMXBs, the accretion onto a disk around the neutron star (and on the neutron star itself) can be powered essentially by the stellar wind of the early-type component. (2) Roche lobe overflow can drive material through the inner Lagrange point L1 (mass transfer) and, under rather specific conditions, through the outer Lagrange points out of the system. An important circumstance is that in case of mass exchange, for the mass losing component, the critical equipotential itself becomes narrower and this will accelerate the process. This phase of evolution can be very critical during the transition of the more massive component from the main-sequence into the subgiant or giant region of the HR-diagram (mass exchange case B). But the critical equipotential could become important not only for secular changes in a close binary system but also for its short term, temporary behaviour. In the case of Her X-1, for instance, a very small decrease of the radius of the subgiant component may make it lose contact with the critical equipotential, which again may stop the accretion flow and the system temporarily ceases to be an X-ray binary. We have evidence that this happened during the years from about 1940 to 1960. (A somewhat similar system is 4U 2129+47 = variable star V1727 Cygni.)

(3) Gravitational quadrupole radiation causes momentum and energy loss from the system, orbital period and semi-major axis decrease monotonously. This effect, however, can introduce significant rapid changes only for the shortest period, 1…2 h only; it may have a prominent role for cataclysmic variables below the so-called period gap. Yet in the case of the first discovered binary pulsar, PSR 1913+16, which has a period of 7h40m, the observed Porb (Table 5) will lead to a substantial orbital degradation only after several 108 years. (4) At certain, rather narrowly specified, phases of close binary evolution, if the mass exchange or loss is very fast, the mass-gaining component could become involved in the extended envelope of its partner. This is the case of spiraling in, also called common envelope evolution. Frictional energy dissipation can reduce the size of the orbit substantially, until contact, even merger of the two stellar nuclei. The extended atmosphere itself may be destructed during the process.


298


[Ref. p. 299

From the many scenarios constructed to explain various systems with compact components, only a few samples will be given here. The following somewhat simplified evolutionary sequence illustrates how a massive binary can evolve to a HMXB, and further perhaps to a neutron star binary of the type of PSR 1913+16; after van den Heuvel [83V]. Star 1

Star 2

Evolution

25 M

10 M

Detached system, period ≈ 5 days; primary fills its Roche lobe; after ≈ 6·106 years, first stage of mass exchange begins

8.5 M helium star

26.5 M

(after ≈ 8·106 years) helium star undergoes core collapse and SN explosion

≈ 1.4 M neutron star (+ accretion disk)

26.5 M

X-ray binary, period ≈ 10 days; accretion powered by stellar wind, later possibly also Roche lobe overflow; large mass-loss from system; compact star may spiral in, period reduced to < 1 day

1.4 M neutron star

12…14 M helium star?

Massive component undergoes core collapse, second SN explosion

1.4 M

1.4 M

If system not disrupted: binary neutron star; More likely case: two neutron stars in independent galactic orbits

Sometimes the helium-star stage above is, tentatively, referred to as the Wolf-Rayet binary. The helium stars will produce in all likelihood a SN of Type Ibc; the second explosion may lead to a SN of Type II. Disruption of the binary in the first SN outburst is less probable, since the site of the explosion is the much less massive star. Investigations into the evolution of the 50…60 LMXBs have to rely on a number of hypothetical elements. Even the structure of these binaries is not completely clear. By definition we may assume in these systems a neutron star (its mass sometimes assumed around 1 M but this is not suggested by any evidence) and a companion of much lower mass, from 0.1 M to perhaps 0.5…0.6 M , which can be a late main sequence star or possibly a low mass helium white dwarf. Due to scarcity of observed eclipses and pulses, orbital parameters are very poorly known besides that for explaining the sustained, strong X-ray radiation some sort of a Roche configuration has to be assumed. Although there is some evidence for faint blue companions of the LMXBs, among the best observed systems Cyg X-2, Sco X-1, and, if we count it as a rather special low-mass system, Her X-1 have manifestly main sequence companions (subgiant in case of Her X-1?). Models for the difficult object 4U1626–67 are compatible with a late M-type secondary as well as 0.1- M large white dwarf, see [80L]. A further important group of 8 very luminous galactic bulge (GX) sources, radiating near the so-called Eddington limit, deserves mentioning. They are lying within 2…3 kpc of the galactic center and may be similar to a more compact group of bright sources around the center of M31, first studied with the Einstein Observatory (HEAO 2), see [79V]. In these objects the neutron star may have a giant "donor", operating by stellar wind. We briefly sample one scenario for LMXBs following, with small modifications, an example given by Verbunt [93V, p. 112]. In an original binary of 7 M + 1 M , the massive star barely Landolt-Börnstein New Series VI/3B


299

satisfies the generally accepted mass requirement for producing a neutron star, instead of a white dwarf. In this system, the massive component can grow, at the top of the giant phase of its evolution, to a radius comparable with 1 AU; its core has about 2 M . The smaller, main sequence star can then spiral in into the extended envelope until its period around the core is 7…9 h; at this point it starts to lose mass due to Roche lobe overflow. The increased mass causes the core to explode as a supernova and one is left with a binary consisting of a neutron star and companion of perhaps 0.5 M , a combination representing well a typical LMXB. The question whether the low-mass companion is a late main-sequence star or a white dwarf (see discussion above) may not be critical if the late star can ultimately turn to a degenerate dwarf (perhaps similar to Procyon B with M ≈ 0.4 M ). The role of common envelope evolution is in many cases fundamental in producing very close pairs with compact components. Theory should be able to point out the conditions and work out the mechanisms of "throwing off" the envelope of a massive stellar component, engulfing the neutron star and forcing it to approach to core (and thereby destroy the hydrogen–helium envelope). Such an evolution might have even started from a wide configuration, with a period of years. An early, thorough discussion of this common-envelope evolution was given by Webbink [84W]. The extreme configuration of a massive star with a neutron star in its center was first considered by Thorne and Zytkov [77T] and these objects, postulated only by theory, are usually referred to as "TZOs"; see the recent review [92C3]. A question of central importance is the origin of millisecond pulsars as well as the evolution of low-mass binary radio pulsars, where the secondary is, as in the case of LMXBs, a low-mass object (M ≤ 0.5 M ). The assumption of an X-ray binary phase, a spin-up by accretion is quite unavoidable (see subsect. 6.1.3.1.2.1). As a plausible hypothesis, it is also generally considered that low-mass radio binaries are descendants of LMXBs. Some problems of statistical nature (birthrates, ages, observed space densities) are, however, still to be solved, see [88K], also [89C]. For a detailed discussion of the origin and evolution of ms-pulsars see, for instance, [93V] and several review articles by van den Heuvel, those in the volume "Neutron stars: theory and observation," listed under symposia in the references, and in particular for ms-pulsars in globular clusters see [92L].

References for 6.1.3 Monographs Lyne, A.G., Graham-Smith, F.: Pulsar Astronomy, Cambridge: Cambridge University Press (1990). Appendix with a catalog of 450 pulsars. Manchester, R.N., Taylor, J.H.: Pulsars, London: Freeman (1977). Smith, F.G.: Pulsars, Cambridge: Cambridge University Press (1977). Symposia, colloquia Pulsars (W. Sieber, R. Wielebinski, eds.), IAU Symp. No. 95, Dordrecht: Reidel (1981). Accretion driven stellar X-ray sources (W.H.G. Lewin, E.P.J. van den Heuvel, eds.), Cambridge: Cambridge University Press (1983). An early classic. The origin and evolution of neutron stars (D.J. Helfand, J.-H. Huang, eds.), Dordrecht: Reidel (1987). High energy phenomena around collapsed stars (F. Pacini, ed.), Dordrecht: Reidel (1987). Physics of neutron stars and black holes, Intern. Symp., Tokyo 1988 (Y. Tanaka, ed.), Tokyo: Universal Academic Press (1988). Neutron stars: Theory and Observation (J. Ventura, D. Pines, eds.), Dordrecht: Kluwer Acad. Publ. (1991). A recent classic. Pulsars as physics laboratories (R.D. Blandford, A. Hewish, A.G. Lyne, L. Mestel, eds.), Philos. Trans. R. Soc. 341 ( 1992) 1-192. X-ray binaries and recycled pulsars (E.P.J. van den Heuvel, S.A. Rappaport, eds.), Dordrecht: Kluwer Acad. Publ. (1992). Landolt-Börnstein New Series VI/3B


299

satisfies the generally accepted mass requirement for producing a neutron star, instead of a white dwarf. In this system, the massive component can grow, at the top of the giant phase of its evolution, to a radius comparable with 1 AU; its core has about 2 M . The smaller, main sequence star can then spiral in into the extended envelope until its period around the core is 7…9 h; at this point it starts to lose mass due to Roche lobe overflow. The increased mass causes the core to explode as a supernova and one is left with a binary consisting of a neutron star and companion of perhaps 0.5 M , a combination representing well a typical LMXB. The question whether the low-mass companion is a late main-sequence star or a white dwarf (see discussion above) may not be critical if the late star can ultimately turn to a degenerate dwarf (perhaps similar to Procyon B with M ≈ 0.4 M ). The role of common envelope evolution is in many cases fundamental in producing very close pairs with compact components. Theory should be able to point out the conditions and work out the mechanisms of "throwing off" the envelope of a massive stellar component, engulfing the neutron star and forcing it to approach to core (and thereby destroy the hydrogen–helium envelope). Such an evolution might have even started from a wide configuration, with a period of years. An early, thorough discussion of this common-envelope evolution was given by Webbink [84W]. The extreme configuration of a massive star with a neutron star in its center was first considered by Thorne and Zytkov [77T] and these objects, postulated only by theory, are usually referred to as "TZOs"; see the recent review [92C3]. A question of central importance is the origin of millisecond pulsars as well as the evolution of low-mass binary radio pulsars, where the secondary is, as in the case of LMXBs, a low-mass object (M ≤ 0.5 M ). The assumption of an X-ray binary phase, a spin-up by accretion is quite unavoidable (see subsect. 6.1.3.1.2.1). As a plausible hypothesis, it is also generally considered that low-mass radio binaries are descendants of LMXBs. Some problems of statistical nature (birthrates, ages, observed space densities) are, however, still to be solved, see [88K], also [89C]. For a detailed discussion of the origin and evolution of ms-pulsars see, for instance, [93V] and several review articles by van den Heuvel, those in the volume "Neutron stars: theory and observation," listed under symposia in the references, and in particular for ms-pulsars in globular clusters see [92L].

References for 6.1.3 Monographs Lyne, A.G., Graham-Smith, F.: Pulsar Astronomy, Cambridge: Cambridge University Press (1990). Appendix with a catalog of 450 pulsars. Manchester, R.N., Taylor, J.H.: Pulsars, London: Freeman (1977). Smith, F.G.: Pulsars, Cambridge: Cambridge University Press (1977). Symposia, colloquia Pulsars (W. Sieber, R. Wielebinski, eds.), IAU Symp. No. 95, Dordrecht: Reidel (1981). Accretion driven stellar X-ray sources (W.H.G. Lewin, E.P.J. van den Heuvel, eds.), Cambridge: Cambridge University Press (1983). An early classic. The origin and evolution of neutron stars (D.J. Helfand, J.-H. Huang, eds.), Dordrecht: Reidel (1987). High energy phenomena around collapsed stars (F. Pacini, ed.), Dordrecht: Reidel (1987). Physics of neutron stars and black holes, Intern. Symp., Tokyo 1988 (Y. Tanaka, ed.), Tokyo: Universal Academic Press (1988). Neutron stars: Theory and Observation (J. Ventura, D. Pines, eds.), Dordrecht: Kluwer Acad. Publ. (1991). A recent classic. Pulsars as physics laboratories (R.D. Blandford, A. Hewish, A.G. Lyne, L. Mestel, eds.), Philos. Trans. R. Soc. 341 ( 1992) 1-192. X-ray binaries and recycled pulsars (E.P.J. van den Heuvel, S.A. Rappaport, eds.), Dordrecht: Kluwer Acad. Publ. (1992). Landolt-Börnstein New Series VI/3B

300


See also: Nagase, F.: Accretion powered X-ray Sources, Publ. Astron. Soc. Jpn. 43 (1989) 1-79. Gelman, H., van den Heuvel, E.P.J. (eds.): Timing neutron stars, Dordrecht: Kluwer Acad. Publ. (1989). Canal, R., Isern, J,. Labay, J.: The origin of neutron stars in binary systems, Annu. Rev. Astron. Astrophys. 28 (1990) 183. Kundt, W. (ed.): Neutron stars and their birth events, Dordrecht: Kluwer Acad. Publ. (1990). van den Heuvel, E.P.J.: Evolution of Close Binaries and the Formation of ms Radio Pulsars, in: Neutron stars: Theory and Observation (J. Ventura, D. Pines, eds.), Dordrecht: Kluwer Acad. Publ. (1991). van Paradijs, J.: Neutron Stars in X-ray Binaries, in: Neutron stars: Theory and Observation (J. Ventura, D. Pines, eds.), Dordrecht: Kluwer Acad. Publ. (1991). Special references Levi-Civita, T.: Am. J. Math. 59 (1937) 225. Rudkjøbing, M.: Ann. Astrophys. 22 (1959) 111. Rees, M.: Nature 211 (1966) 468. Hewish, A.S., Bell, J., et al.:Nature 217 (1968) 709. Parsignault, D.B., Grindlay, J.C., in: X-ray Astronomy (W.A. Parity, L.E. Peterson, eds.), (1970) p. 87-92. 73M Mauder, H.: Astron. Astrophys. 28 (1973) 473. 75H Hulse, R.A., Taylor, J.H.: Astrophys. J. 195 (1975) L51. 77T Thorne, K.S., Zytkov, A.N.: Astrophys. J. 212 (1977) 832. 78B Bahcall, J.: Annu. Rev. Astron. Astrophys. 16 (1978) 241. 79M1 Milgrom, M.: Astron. Astrophys. 76 (1979) L3. 79M2 Margon, B., et al.: IAU Circular No. 3345 (1979). 79T Trümper, J., in: X-ray Astronomy (W.A. Baity, L.E. Petersen, eds.), Oxford: Pergamon Press (1979). 79V Van Speybrock, L., Epstein, A. et al.: Astrophys. J. 234 (1979) L45. 80L Li, F.K., Joss, P.C.: Astrophys. J. 240 (1980) 628. 81B Beer, P. (ed.): Vistas Astron. 25 (1981) 1-233 (Proc. 1980 Conference in Rome). 81D Deeter, J.E., Boynton, P.E., Pravdo, S.H.: Astrophys. J. 247 (1981) 1003. 81L Lewin, W.G.H., Joss, P.C.: X-ray bursters and X-ray sources of the galactic bulge, Space Sci. Rev. 28 (1981) 3. 81M McHardy, I.M., Lawrence, A., Pye, J.P., Pounds, K.A.: Mon. Not. R.Astron. Soc. 197 (1981) 893. 81R Rappaport, S.A., Joss, P.C., in: X-ray Astronomy with the Einstein Satellite (R. Giacconi, ed.), Astrophysics and Space Science Library Vol. 87, Dordrecht: Reidel (1981) p. 123. 81W Warwick, R., Marshall, N., Frazer, G.W., et al.: Mon. Not. R. Astron. Soc. 197 (1981) 865. 83B Bradt, H.V.D., McClintock, J.E.: Optical counterparts of compact galactic X-ray sources, Annu. Rev. Astron. Astrophys. 21 (1983) 13. 83C Cowley, A., et al.: Astrophys. J. 272 (1983) 118. 83L Lewin, W.H.G., Joss, P.C., in: Accretion driven stellar X-ray sources (W.H.G. Lewis, E.P.J. van den Heuvel, eds.), Cambridge: Cambridge University Press (1983), chapter 2. 83P Paczynski, B.: Astrophys. J. 273 (1983) L81. 83R Rappaport, S.A., Joss, P.C., in: Accretion driven stellar X-ray sources (W.H.G. Lewis, E.P.J. van den Heuvel, eds.), Cambridge: Cambridge University Press (1983). 83S Shapiro, S.L., Teukolsky, S.A.: Black Holes, White Dwarfs, and Neutron Stars, New York: John Wiley & Sons (1983). 83V van den Heuvel, E.P.J., in: Accretion driven stellar X-ray sources (W.H.G. Lewis, E.P.J. van den Heuvel, eds.), Cambridge: Cambridge University Press (1983) p. 303. 84A Aurière, M., Le Févre, O., Terzan, A.: Astron Astrophys. 138 (1984) 415.

37L 59R 66R 68H 70P


6.1.3 Double stars: Systems with compact objects 84I 84J 84L 84M 84W 85G 86B 86M 86N 86P 87H 87P 87V 88K 89C 89I 89L 89N1 89N2 89T 90B 90R 90T 90W 91D 91M 91R 91V1 91V2 92C1 92C2 92C3 92L 92P 92R 92S 92T 92V 92W 93T1 93T2 93V

301

Iben, I., Tutukov, A.V.: Astrophys. J. Suppl. 4 (1984) 335. Joss, P.C., Rappaport, S.A.: Neutron stars in interacting binary systems, Annu. Rev. Astron. Astrophys. 22 (1984) 537. Liung, E.P., Nolan, P.L.: Space Sci. Rev. 38 (1984) 353. Margon, B.: Annu. Rev. Astron. Astrophys. 22 (1984) 507. Webbink, R.F.: Astrophys. J. 277 (1984) 355. Guinan, E.F., Maloney, F.P.: Astron. J. 90 (1985) 1519. Backer, D.C., Hellings, R.W.: Pulsar timing and general relativity, Annu. Rev. Astron. Astrophys. 24 (1986) 537. McClintock, J.A., Remillard, R.A.: Astrophys. J. 308 (1986) 110. Nomoto, K.: Prog. Part. Nucl. Phys. 17 (1986) 249. Pakull, M.V., Angebault, L.P.: Nature 322 (1986) 511. Hutchings, J.B., et al.: Astron. J. 94 (1987) 340. Peterson, T.J., Zensus, J.A., in: Superluminal radiation sources (J.A. Zensus, T.J. Peterson, eds.) Cambridge: Cambridge University Press (1987) van der Klis, M.: Quasi-periodic oscillations in low-mass X-ray binaries, in: Origin and Evolution of Neutron Stars (D.J. Helfand, J.-H. Huang, eds.), Dordrecht: Reidel (1987). Kulkarni, S.R., Narayan, R.: Astrophys. J. 335 (1988) 755. Coté, J., Pylyser, E.H.P.: Astron. Astrophys. 218 (1989) 131. Ilovaisky, S.A., in: Proc. of the 23rd ESLAB Symp. ESA-SP 296 (1989). Lamb, F.K.: Binary X-ray Sources, in: Annals N.Y. Acad. Sci. 571 (1989). Nagase, F.: Publ. Astron. Soc. Jpn. 41 (1989) 1. Naylor, T., Charles, P.A.: Mon. Not. R. Astron. Soc. 236 (1989) 1P. Taylor, J.H., Weisberg, J.M.: Astrophys. J. 345 (1989) 434. Backer, D.C., Kulkarni, S.R.: Physics Today 43 (1990) No. 3, p.26. Ritter, H.: Astron. Astrophys. Suppl. 85 (1990) 1179. Tan, J., et al.: Bull. Am. Astron. Soc. 22 (1990) 1148. Wheeler, D.C., Harkner, R.P.: Rep. Prog. Phys. 53 (1990) 467. Damour, T., Taylor, J.H.: Astrophys. J. 366 (1991) 501. McClintock, J.: Ann. N.Y. Acad. Sci. 647 (1991) 495. Texas/ESO-CERN Symp. 1990, Brighton., England Ryba, M.F., Taylor, J.H.: Astrophys. J. 371 (1991) 739. van den Heuvel, E.P.J., in: Neutron stars, theory and observation (J. Ventura, D. Pines, eds.), Dordrecht: Kluwer Acad. Publ. (1991) p.171. van Paradijs, J.A., in: Neutron stars, theory and observation (J. Ventura, D. Pines, eds.), Dordrecht: Kluwer Acad. Publ. (1991) p. 289. Casares, J., et al.: Nature 355 (1992) 614. Cowley, A.P.: Evidence for black holes in stellar binary systems, Annu. Rev. Astron. Astrophys. 30 (1992) 287. Cannon, R. et al.: Astrophys. J. 386 (1992) 206. Lyne, A.G., in: X-ray Binaries and Recycled Pulsars (E.P.J. van den Heuvel, S.A. Rappaport, eds.), Dordrecht: Kluwer Acad. Publ. (1992). Parmar, A.N., in: X-ray Binaries and Recycled Pulsars (E.P.J. van den Heuvel, S.A. Rappaport, eds.), Dordrecht: Kluwer Acad. Publ. (1992) p. 5. Remillard, R.A., McClintock, J.E., Bailyn, C.D.:Astrophys. J. 399 (1992) L145. Sutantyo, W., in: X-ray Binaries and Recycled Pulsars (E.P.J. van den Heuvel, S.A. Rappaport, eds.), Dordrecht: Kluwer Acad. Publ. (1992) p. 293. Taylor, J.H.: Philos. Trans. R. Soc. London A 341 (1992) 117. van Kerkwyk, M.H., et al.: Nature 355 (1992) 703. Wolszczan, A., Frail, D.A.: Nature 355 (1992) 145. Trümper, J.: Symp. Texas/PACOS 1992, Ann. NY Acad. Scci. 688, 260 (1993). Taylor, J.H., Manchester, R.N., Lyne, A.G.: Astrophys. J. Suppl. 88 (1993) 529. Verbunt, F., in: Annu. Rev. Astron. Astrophys. 31 (1993) 93.


302 94K 94M1 94M2 94P 94S 94V 95T1 95T2

6.1.3 Double stars: Systems with compact objects Kaspi, V.M., et al.: Astrophys. J. 423 (1994) L42. Marsh, T.R. et al.: Mon. Not. R. Astron. Soc. 266 (1994) 137. Mirabel, I.F., Rodrigues, L.F.: Nature 371 (1994) 46. Pinney, E.S., Kulkarni, S.R.: Annu. Rev. Astron. Astrophys. 32 (1994) 591. Shabaz, T. et al.: Mon. Not. R. Astron. Soc. 268 (1994) 756. van den Heuvel, E.P.J., in: Interacting binaries. Saas-Fee Adv. Course 22 (H. Nussbaumer, A. Orr, eds.), Berlin, Heidelberg, New York: Springer (1994) p. 263. Tingay, S.J., Jauncey, D.L., et al.: Nature 374 (1995) 141. Taylor, J.H., et al.: unpublished work, distributed electronically, see subsect. 6.1.3.2.1


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6.2

6.2 Star clusters and associations

303

Star clusters and associations

General remarks

Since the publication of LB VI/2b in 1982 the study of star clusters has made a great step forward observationally due to the implementation of fast and linear CCD detectors on new large telescopes and theoretically due to the proliferation of ever more powerful computers. This has led to

(1) considerable progress in our knowledge on clusters in our galaxy reaching far down the main sequence, (2) in depth investigations of clusters in the Large and Small Magellanic Cloud, (3) the recognition that many other galaxies possessvery diverse systemsof globular clusters, (4) much improved modelling of cluster structure and the development of formation theories. The new directions of research and the rapidly growing knowledge of star clusters in the Galaxy as well as in extragalactic systemsrequire a concise rearrangement of this chapter. The new sections and the corresponding ones in LB VU2b can be read off the following synopsis: LB VI/2b 6.2.1 6.2.1 Galactic globular clusters 6.2.1.4, 6.2.1.13 6.2.1.1 Structure and dynamics of globular clusters 6.2.1.12, 6.2.1.14 6.2.1.2 Chemical abundance and relation to galactic structure 6.2.1.8, 6.2.1.9 6.2.1.3 Colour-magnitude diagrams and relation to stellar evolution 6.2.1.10 6.2.1.4 Stellar content of globular clusters 6.2.1.11 6.2.1.5 Interstellar matter in globular clusters 6.2.2 6.2.2 Galactic open clusters 6.2.2.12 6.2.2.1 Formation and dynamics of open clusters 6.2.2.8, 6.2.2.11, 6.2.2.13 6.2.2.2 Galactic structure, abundances and ages 6.2.2.9 6.2.2.3 Stellar content of open clusters 6.2.3 6.2.3 Associations New 6.2.4 Clusters in extragalactic systems General bibliographical and numerical data bases

(1) Large collections of data: Centre de Donnees Stellaires, Strasbourg, France, especially - for comprehensive on-line object searches:SIMBAD data base, - catalogue and basic data of galactic open clusters by Lynga [87L2], - catalogue and basic data of galactic globular clusters by Webbink [SSWl] and in the appendices and tables of the globular cluster conference [k, 19931. Catalogues are generally distributed on magnetic tape, on floppy disk or via e-mail. Another data base for Galactic globular clusters is available in the World Wide Web under http://www.phys.mcmaster.ca (W.E. Harris). (2) Main bibliographical data base: Astronomy and Astrophysics Abstracts, Astronomisches Rechen-Institut Heidelberg; printed version published by Springer-Verlag, Berlin, Germany; online retrieval via STN-International, Karlsruhe, Germany.

6.2.1

Galactic globular clusters

General remarks

Concise reviews of globular cluster research have been given by Zinn [9OZ] and Hesser [93Hl, 95H]. Large collections of basic data (coordinates, integrated properties, structural and physical Landolt-BBmstein New Series VI/3b

304


[Ref. p, 317

parameters, velocities and velocity dispersions) have been published by Webbink [85Wl] and by a group of authors [k, appendices]; see also the older compilation by Madore [80M]. Metal abundancesin the Zinn scaleare listed in [85Z, 88A]. 6.2.1.1

Structure and dynamics of globular clusters

General reviews

Comprehensive treatises are given by Lightman and Shapiro [78L] and by Spitzer [8782]. Seealso the concise review of Elson et al. [87E2] and the reviews in the symposia [a], [d, chapter Iv] and [k]. Structural parameters and masses

Compilations of observed and derived structural parameters: - surface brightness profiles and derived quantities (125 clusters) [95T]; - core radii, concentration classes,central surface brightnesses, total visual luminosities (106 clusters) [87P], (143 clusters) [93T]; - integrated intrinsic UBVRI colours, reddening, spectral types (50 clusters) [88Rl], (135 clusters) [93Pl]; - velocity dispersions and derived parameters (56 clusters) [93P4]; - dynamical masses(147 clusters) [91M2]; - large number of different parameters (154 clusters) [85Wl] and (143 clusters) [k, appendices]. Dynamical evolution

Structural parametersas constraints for dynamical cluster models and evolution: seeespecially [87M2, 93M3] and the results in Table 1. Detailed discussion of cluster evolution until core collapse [9OC4]. Post-collapsecluster evolution [88C4]; seealso the observational results reported in [86D, 91A]. The role of binaries in the dynamical evolution of clusters [91M5, 93M2]. Compact objects and cluster evolution [91Bl, 93P33.

Table 1. Structural parameters and massesof well-observed galactic globular clusters [87M2,93Dl].

f-c rt *h

4 Cluster NGC 104 5139 5272 6205 6341 7089

core radius tidal radius half-light radius projected central velocity dispersion

F&l 47 Tut 0 Cen M3 M 13 M 92 M2

0.48 4.7 1.3 1.5 0.74 1.1

rt

L M;L,

maximum rotation velocity total cluster massin lo6 Mo mean mass-luminosity ratio in solar units

VO

[PC1 &I

[km s-i]

;Ikm s-l]

58 79 190 23 61 53

11.6 16.6 5.3 7.1 6.1 10.4

6.5 8.0 1 6 4 5

3.9 6.9 3.3 3.2 2.0 3.4

0.7 3.9 0.6 0.7 0.4 0.9

1.8 2.9 2.2 3.6 2.4 2.7

Land&-BGrnstein New Series W/3 b


Ref. p. 3171 6.2.1.2

305

Chemical abundances and relation to galactic structure

Reviews

General reviews: [9OZ,90G, 88Bl]. Reviews on chemical inhomogeneities [88N, 9387, 94K]; abundances of CNO elements [91B2], ironpeak elements [91G2].

Metallicity

scales

Zinn-(West-Armandroff) scale: [84Z, 85Z, 88A], Pilachowski scale: [83P, 84Pl]. A comparison of the scales(see Fig. 1) shows a significant number of metal-rich clusters in the Zinn scale and therefore a bimodal metallicity distribution with peaks at roughly [Fe/H] = - 0.6 and - 1.6, where [Fe/H] =log (NFe/NH)I(NFeINH)o.

Relation to galactic structure and evolution

Review [91L2] and conference [j]. The bimodal metallicity distribution (Fig. 1) and the distribution of distances from the galactic plane led to the distinction of two subsystemsamong the galactic globular clusters: a slowly rotating halo and a rapidly rotating (“thick”) disk [9OZ and referencestherein]; seeTable 2. However, other authors compile evidence that the metal-rich clusters rather belong to the Galactic bulge (see[95M]). Further discussion of structure and formation of the subsystemsin [j]. For referenceson the kinematics of the globular cluster system see[91B5]. The implication of the properties of the system of globular clusters on the evolution of the Galaxy is briefly summarized in [9OZ,94D2].

Galaxy

Fig. 1. Comparisonbetweenthe [Fe/H] distribution of galactic globular clustersin the scales of Zinn ([85Z, 0

I -0.4

Land&Bhstein New Series VI/3b

I I I I I -1.2 -1.6 -0.8 -[Fe/HI

I

I -2.0

I

I -2.4

88A], soild line) and Pilachowski([84Pl], dotted line). N is the numberof clustersin bins of 0.2 dex in [Fe/H]. Metallicity [Fe/H] = log (NFeINH)I(NFeIN&.

306


[Ref. p. 317

Table 2. Comparison of the thick disk and halo subsystemsof galactic globular clusters [9OZ, 89A].

[Fe/H] = log(N,,IN,)I(N,,lN,), z distance from the galactic plane Subsystem

Thick disk Halo “) Approximate

6.2.1.3

@I

Mean metallicity [Fe/H]

1100 3000 “)

-0.6 -1.6

Scale height

z-gradient of the metallicity

MC- ‘I

Mean rotation velocity [km s-i]

Mean velocity dispersion [km s-l]

-0.1 (-0.1)

193 43

59 116

value of the effective halo radius.

Colour-magnitude diagrams and relation to stellar evolution

Colour-magnitude diagrams (CMDs)

General discussion of CMDs: [88H2, 92C, 93853. Peterson [86P] has compiled a bibliography of globular cluster CMDs together with their characteristic parameters. The position of the population II main-sequencesis discussedby Sandage[86Sl].

Relation to stellar evolution (see also sect. 4.4)

A large number of evolutionary tracks and isochrones has been published. Tables 3 and 4 give an overview. Critical discussions of the different models: [91Vl], see especially the test of the models using CMDs of globular clusters [88R2]. For the transformation from the theoretical (log L, log T,) plane to the observational (M,, B- V) plane, see[85V2, 87621 and the procedure in [91Ml]. Numerous papers evaluate the horizontal branch (HB) evolution; seethe referencesto HB models in Table 3 and the exemplary application to Ml5 [91D2]. HB types are given by [94L]. Discussion of HB models with special emphasis on the Sandage period-shift effect and Oosterhoff period dichotomy of RR Lyrae stars: [91L4]. Post-asymptotic giant branch evolution is discussed e.g. in [94V, 95B].

Ages of globular clusters

Reviews are given in [SSV,9OVj. For the problem of age calibration seeespecially [89B2]. Ages range between 15 and 19.109years dependent on the parameters of the isochrones and their calibration; seee.g. [90Bl]. Final conclusions are not yet possible. Though the well-studied clusters show a small range in age, there is now increasing evidence that some clusters are up to 30% younger [90B2, 90B3, 93B2]: Pal 12, NGC 288, NGC 362, Ruprecht 106.

Formation of globular clusters and their stellar luminosity functions and mass functions

Scenarios of star formation in globular clusters are given by Lin and Murray [91L5] and Kang et al. [90K]. Seealso the contributions in b]. Luminosity (and/or mass)function (LF, MF) in globular clusters: seethe discussion in [95D]. Landolt-B6mst.h New Series VI/3b

Ref. p. 3171

307


Table 3. Compilation of evolutionary trucks in the (log L, log T,) plane suitable for the interpretation of CMDs of open and globular clusters (for full details seethe references). helium massfraction (for some models Z depending) Y z massfraction of elements heavier than helium CMD colour-magnitude diagram AGB asymptotic giant branch HB horizontal branch MS main sequence RGB red giant branch Description

z

Y

Mass range

Reference

Wol Solar composition Improved grids High mass-loss rates High-mass stars New opacities New opacities Massive close binaries MS to end of He core burning H, He burning AGB evolution MS to first thermal pulse MS to RGB Red clump stars HB evolution HB evolution HB, AGB HB, AGB Blue HB Oxygen enhancement


0.02

0.28

120...0.8 (21 steps) 0.3410.24 0.001...0.04 120...0.8 (5 steps) (18 steps) 120...12 0.3410.24 0.001...0.04 (5 steps) (8 steps) 0.002...0.04 120...15 (0.24) (4 steps) (7 steps) 0.28 0.02 120...0.6 (31 steps) 0.25 100...0.6 0.008 (31 steps) 0.2410.25 0.002/0.01 40...9 (14 steps) 0.24 0.002...0.04 15...3 (2 steps) (5 steps) 0.2310.27 0.002...0.02 9...3 (3 steps) (5 steps) 0.210.3 0.001...0.02 5...1 (3 steps) (c7 steps) 0.210.3 0.001...0.02 5...1 (5 steps) ( 10’Oyears).In this respect Magellanic Cloud clusters are quite different from the Milky Way globular clusters. Exact numbers are difficult to give becauseparticularly for young objects there is a smooth transition to open clusters, which are very abundant in both Clouds [88H3, 86H2]. Crude numbers are 50 globular clusters in the LMC and 20 in the SMC. Most catalogued objects are open clusters. General reviews are given by van den Bergh [9lV3] and Westerlund [9Ow]; seealso the contributions in ij]. Catalogues, atlases, basic data

Catalogues of LMC clusters: [63S, 63L, 66H]; catalogue of catalogues: [88H5]. Catalogues of SMC clusters: [56K, 56L, 86H2]. Identifications and finding charts: LMC [67H]; SMC [76H]. Identifications of individual cluster stars: [75A]. Prominent clusters with approximate agesseeTable 6. Land&-B6mstein New Series VI/3b

312


[Ref. p. 317

OB associations in extragalactic systems

Review of existing data on OB associations in other galaxies [86Hl]. Magellanic Clouds: reviews in [9OW,91Gl]. Massive-star content and initial mass functions for 14 OB associations [94H2]. Aggregates of young stars between the Magellanic Clouds: [91D, with references]. M33: [91W3]. NGC 6822: [92W2].

6.2.4

Clusters in extragalactic systems

6.2.4.1

Open clusters in extragalactic systems

Magellauic Clouds (Large Cloud, LMC, and Small Cloud, SMC)

Seegeneral remarks in subsect.6.2.4.2.1 Catalogues of new clusters: 156 LMC clusters outside the Hodge-Wright atlas [880], 255 LMC clusters [88H5], 213 SMC clusters [86H2]. Total estimated cluster population: LMC 4200, SMC 2000 [88H3]. Discussion of age distribution of LMC clusters [88H4] and SMC clusters [87Hl]. Andromeda galaxy (M31)

Seesubsect.6.2.4.2.2.1. Characteristics of 403 open star clusters and spiral structure [79H]; properties of selectedyoung star clusters and compact OB associations [87H2]. 6.2.4.2 6.2.4.2.1

Globular clusters in extragalactic systems Magellanic Clouds

General properties and reviews, open and globular clusters

The Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) host globular clusters of a large age interval from young (lo7 years) to old (> 10’Oyears).In this respect Magellanic Cloud clusters are quite different from the Milky Way globular clusters. Exact numbers are difficult to give becauseparticularly for young objects there is a smooth transition to open clusters, which are very abundant in both Clouds [88H3, 86H2]. Crude numbers are 50 globular clusters in the LMC and 20 in the SMC. Most catalogued objects are open clusters. General reviews are given by van den Bergh [9lV3] and Westerlund [9Ow]; seealso the contributions in ij]. Catalogues, atlases, basic data

Catalogues of LMC clusters: [63S, 63L, 66H]; catalogue of catalogues: [88H5]. Catalogues of SMC clusters: [56K, 56L, 86H2]. Identifications and finding charts: LMC [67H]; SMC [76H]. Identifications of individual cluster stars: [75A]. Prominent clusters with approximate agesseeTable 6. Land&-B6mstein New Series VI/3b

Ref. p. 3171

313


Table 6. Prominent star clusters of the Large and Small Magellanic Cloud [81V, 89Sl].

‘v

integrated apparent magnitude

B-V integrated colour index

Name (a) LMC clusters NGC 1446 NGC 1711 NGC 1818 NGC 1841 NGC 1850 NGC 1866 NGC 1978 NGC 1984 NGC 1994 NGC 2004 NGC 2100 NGC 2157 NGC 2164 NGC 2173 NGC 2210 NGC 2214 NGC 2257 (b) SMC clusters NGC 121 NGC 152 NGC 330 NGC 416 NGC 419 NGC 458 NGC 465 Ll L 8 (K3)

V

B-V

Age

bagI

bwl

[lO”a]

11.59 10.11 9.70 14.08 8.96 9.73 10.70 9.72 9.83 9.60 9.60 10.16 10.34 12.30 10.94 10.93

0.66 0.12 0.18 0.90 0.12 0.25 0.78 0.02 0.16 0.17 0.16 0.19 0.10 0.84 0.71 0.11 0.69

15000 32 30 12000 21 86 3000 7 7 16 16 24 63 1800 12000 63 15000

11.24 12.92 9.60 11.42 10.61 11.73 11.45 13.32 12.05

0.78 0.65 0.17 0.77 0.67 0.17 - 0.06 0.75 0.68

12000 1300 10 1200 2500 50 10 10000 8000

Integrated photometry and spectroscopy UBV [81v], JHK [90F], Washington photometry [87Gl], IJV-spectra [87C]. Ages, abundances, colour-magnitude diagrams

General compilation of CMDs and ages[89Sl], seeFigs. 2 and 3. Photometric age classification, SWB classes(Searle-Wilkinson-Bagnuolo) [8OS]. Ages of LMC clusters from integrated photometry [88El]. Basic parameters of old clusters and comparison with galactic population II [9235, Tables 6 and 81. Spectroscopic abundances from individual stars

Only few data are available [9 1S3, 9 lo]; an age-metallicity relation is still under debate. Land&-Bihstein New Series VI/3b


314

[Ref. p. 317

1 LMC 20 16-

I

=z

12 -

8-

Fig. 2. Age histogram of LMC clusters (the age is 6.0

6.5

7.0

25

80

8.5

9.0

95

10.0 II

log agehl-

5

given in years, N is the number of clusters in bins of 0.3 of log age) [89Sl].

V.’

LMC 0

-0.2 o-

0.2 f 2% rb 0.4 0.6

0

0 1.01 6.0

I 6.5

I 7.0

I 7.5

I 8.0

I 8.5

%

0

c? O. o" s" 0 I 9.0

00 00

0 I I 9.5 10.0 10

logage[o 1-

Fig. 3. Colour-age diagram of LMC clusters (the age is given in years and the integrated colour-index B-V in mag) [81V, 89Sl].

The central star cluster of the 30 Dor nebulum Detailed discussion and references [94Ml]. Resolution of the central object R136a into a dense star cluster by speckle interferometry and by Hubble Space Telescope observations [94M 11.

[92P]

Masses Dynamical masses for individual clusters: NGC 1866, 1.3.10’ Mo [92Fl] and NGC 1835, about lo6 Mo [90D2]. Masses from M/L ratios [89E, 91M4]. Land&-BBmstein New Series VU3b

Ref. p. 3171


315

Structural parametersand massfunctions Surface brightness profiles [91E, 92E]. Mass functions [91Sl, 93Ml]. Kinematics of the LMC cluster system Analysis of the velocities for 83 clusters [9282]. 6.2.4.2.2 Local Group galaxies 6.2.4.2.2.1 M31 The cluster system of M31 is similar to the cluster system of the Galaxy. Reviews [88F, 88E2, 91H4]. Observational surveys Summary [93F2]. About 500 cluster candidates are known, 300 with high confidence [87B, 85C]; catalogue of 51 halo clusters [91Rl]. A clustering of globular clusters seemsto exist [93A2]. HST observations of 13 clusters [94F]. Magnitudes, colours and abundances Integrated colours from different photometric systems are available for 153 clusters [88E2]; BVR magnitudes and colours for halo clusters [92R2]. Globular cluster luminosity function [92Rl]. Metallicities from low dispersion spectra [91B4]; CN bands are stronger than for galactic clusters at a given age. Kinematics Review [93H]. Radial velocities are available for about 150 clusters [91H4]; they show that the disk-halo distinction is similar to the galactic system. First colour-magnitude diagrams Clusters Gl [88Hl], G219 [91C2]. 6.2.4.2.2.2 M33 The cluster system of M33 is similar to the Magellanic Clouds cluster systems.Reviews [88Cl, 91S2, 93c33. Colours UBV colours are available for 128 clusters [88C2]; there exists a wide spread due to large age differences. Land&-BBmstein New Series VU3b


316

[Ref. p. 317

Kinematics

Review [9383]. The blue clusters follow the disk kinematics; the red clusters show a large dispersion [91S2,91B4]. Metallicities

Metallicities from integral spectra [91B4]. 6.2.4.2.2.3

Other Local Group galaxies

Companions of M31

Integrated spectroscopy for globular clusters in NGC 147, NGC 185, NGC 205 [88Dl]; there exists one intermediate-age cluster in NGC 205. Fornax system

The Fornax systemcontains 6 globular clusters [85B]. Integrated spectra: [89R2]. One cluster resolved; colour-magnitude diagram: [90Dl]. NGC 6822

About 30 globular clusters are known [77H, 79VJ Wolf-Lundmark-Melotte

system

One globular cluster candidate may exist [77A]; colour: [89F]. NGC 3109

10 candidates found [85D]; 23 candidates found [88B2]. 6.2.4.2.3

Galaxies outside the Local Group

General review

Cluster systems have been investigated for about 50 galaxies outside the Local Group; the most important review are given by Harris [91H2] and Richtler [95R]. Cluster frequencies

The specific frequency S is defined by S = N. 10’3.4(Mt+15) Land&-BBmstein New Series VV3b


317

where N= total number of clusters and M, = absolute visual magnitude of the parent galaxy (in case of spiral galaxies the specific frequency is named S* if M, is the bulge magnitude only). For spiral galaxies no dependenceof S on galaxy type can be seen; but S depends on the environment, i.e. whether the host galaxy is located in a sparseor a rich galaxy cluster (seeTable 7). Richest galaxies are central giant ellipticals (M87, NGC 1399, NGC 3311, NGC 4874) with S about 15 to 20. The total number of clusters in these galaxies is about 10000to 15000. Table 7. Mean specific frequencies (S) of clusters in various types of galaxies (N is the number of galaxies observed) [91H2]. For explanation seetext. Galaxy type Sc/Irr Sa/Sb E/SO (small groups) E/SO (Virgo, Fornax) dE

69 0.5 + 0.2 1.2*0.2 2.6kO.5 5.4kO.6 4.8& 1.0

N 4 9 13 15 4

Comments (s*) = 2.1 f0.4 excluding M87, NGC1399 excluding Fornax, M32

Colours and abundances,presently forming clusters In all investigated casesthe mean colour of the cluster system is bluer than the galaxy light by typically 0.3 mag in B- V (metallicity effect?). Integrated spectra are available for clusters in M87 and M49, which confirm a lower metallicity [90M]. Colour gradients are still under debate [91H2, 88C3, 91Wl]. Metallicity gradients are observed in M87 in the Virgo cluster [93L] and NGC 1399 in the Fornax cluster of galaxies [930]. Bright blue pointlike sources are interpreted as presently forming globular clusters; seee.g. the HST discoveries in NGC 1275 (Per A) [92Hl], NGC 7252 [93w] and He 2-10 [94C]. Spatial distribution Rich cluster systemsshow flatter distributions than the underlying galaxy light; poorer systemsare not well constrained [9 1H2]. The M87 globular cluster system is elliptical in shape; the ellipticity increases with galactocentric radius [94M3]. Luminosity function and massspectrum The globular cluster luminosity function seemsto be universal; it can be approximated by a t5-function with a dispersion of 1.3 mag and a peak at Mv = - 7.1 mag [9334]. The mass spectrum of globular cluster systemsand its relation to the luminosity function is discussedin [94Hl, 94M2].

References for 6.2 General references a b

Int. Astron. Union Symp. 113, Dynamics of Star Clusters (Goodman, J., Hut, P., eds.), Dordrecht: Reidel(l985). Int. Astron. Union Symp. 115, Star Forming Regions (Peimbert, M., Jugaku, J., eds.), Dordrecht: Reidel(1987).

Landok-Bhstein New Series V1/3b


317

where N= total number of clusters and M, = absolute visual magnitude of the parent galaxy (in case of spiral galaxies the specific frequency is named S* if M, is the bulge magnitude only). For spiral galaxies no dependenceof S on galaxy type can be seen; but S depends on the environment, i.e. whether the host galaxy is located in a sparseor a rich galaxy cluster (seeTable 7). Richest galaxies are central giant ellipticals (M87, NGC 1399, NGC 3311, NGC 4874) with S about 15 to 20. The total number of clusters in these galaxies is about 10000to 15000. Table 7. Mean specific frequencies (S) of clusters in various types of galaxies (N is the number of galaxies observed) [91H2]. For explanation seetext. Galaxy type Sc/Irr Sa/Sb E/SO (small groups) E/SO (Virgo, Fornax) dE

69 0.5 + 0.2 1.2*0.2 2.6kO.5 5.4kO.6 4.8& 1.0

N 4 9 13 15 4

Comments (s*) = 2.1 f0.4 excluding M87, NGC1399 excluding Fornax, M32

Colours and abundances,presently forming clusters In all investigated casesthe mean colour of the cluster system is bluer than the galaxy light by typically 0.3 mag in B- V (metallicity effect?). Integrated spectra are available for clusters in M87 and M49, which confirm a lower metallicity [90M]. Colour gradients are still under debate [91H2, 88C3, 91Wl]. Metallicity gradients are observed in M87 in the Virgo cluster [93L] and NGC 1399 in the Fornax cluster of galaxies [930]. Bright blue pointlike sources are interpreted as presently forming globular clusters; seee.g. the HST discoveries in NGC 1275 (Per A) [92Hl], NGC 7252 [93w] and He 2-10 [94C]. Spatial distribution Rich cluster systemsshow flatter distributions than the underlying galaxy light; poorer systemsare not well constrained [9 1H2]. The M87 globular cluster system is elliptical in shape; the ellipticity increases with galactocentric radius [94M3]. Luminosity function and massspectrum The globular cluster luminosity function seemsto be universal; it can be approximated by a t5-function with a dispersion of 1.3 mag and a peak at Mv = - 7.1 mag [9334]. The mass spectrum of globular cluster systemsand its relation to the luminosity function is discussedin [94Hl, 94M2].

References for 6.2 General references a b

Int. Astron. Union Symp. 113, Dynamics of Star Clusters (Goodman, J., Hut, P., eds.), Dordrecht: Reidel(l985). Int. Astron. Union Symp. 115, Star Forming Regions (Peimbert, M., Jugaku, J., eds.), Dordrecht: Reidel(1987).

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C

d e f g h

m

Int. Astron. Union Symp. 116, Luminous Stars and Associations in Galaxies (De Loore, C. W. H., Willis, A. J., Laskarides, P., eds.), Dordrecht: Reidel (1986). Int. Astron. Union Symp. 126, Globular Cluster Systemsin Galaxies (Grindlay, J. E., Davis Philip, A. G., eds.), Dordrecht: Kluwer (1988). Int. Astron. Union Symp. 148, The Magellanic Clouds (Haynes, R., Milne, D., eds.), Dordrecht: Kluwer (1991). ES0 Conf. and Workshop Proc. 27, Stellar Evolution and Dynamics of the Outer Halo of the Galaxy (Azzopardi, M., Matteucci, F., eds.), Garching: Europ. Southern Obs. (1987). Astron. Sot. Pacific Conf. Ser. 13, The Formation and Evolution of Star Clusters (Janes, K., ed.), San Francisco: Astron. Sot. Pacific (1991). Proc. Fifth Workshop Inst. d’Astrophys. Paris, Astrophysical Ages and Dating Methods (Vangioni-Flam, E., CassC,M., Audouze, J., Tran Thanh Van, J., eds.), Gif sur Yvette: Editions Front&es (1990). Vulcan0 Workshop on Young Star Clusters and Early Stellar Evolution (Palla, F., Persi, P., Zinnecker, H., eds.), Mem. Sot. Astron. Ital. 62 (1991) 705. Astron. Sot. Pacific Conf. Ser. 48, The Globular Cluster-Galaxy Connection (Smith, G. H., Brodie, J. P., eds.), San Francisco: Astron. Sot. Pacific (1993). Astron. Sot. Pacific Conf. Ser. 50, Structure and Dynamics of Globular Clusters (Djorgovski, S. G., Meylan, G., eds.), San Francisco: Astron. Sot. Pacific (1993). Astron. Sot. Pacific Conf. Ser. 65, Clouds, Cores and Low Mass Stars (Clemens, D.P., Barvainis, R., eds.), San Francisco: Astron. Sot. Pacific (1994). Int. Astron. Union Symp. 164, Stellar Populations (van der Kruit, P.C., Gilmore, G., eds.), Dordrecht: Kluwer (1995).

Special references

56K 56L 63L 63s 66H 67H 75A 76H 77A 77H 78L 79H 79V 80M 80s 81V 825 83F 83P 83V 84L 84Pl

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85C

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89Rl 89R2 89Sl 8982 90Bl

Reimers, D., Koester, D.: Astron. Astrophys. 218 (1989) 118. Rodgers, A. W., Harding, P.: Publ. Astron. Sot. Pac. 101 (1989) 563. Sagar, R., Pandey, A. K.: Astron. Astrophys. Suppl. 79 (1989) 407. Sweigart, A. V., Greggio, L., Renzini, A.: Astrophys. J. Suppl. 69 (1989) 911. Bertelli, G., Betto, R., Bressan, A., Chiosi, C., Nasi, E., Vallenari, A.: Astron. Astrophys. Suppl. 85 (1990) 845. 90B2 Bolte, M.: J. R. Astron. Sot. Canada 84 (1990) 137. 90B3 Buonanno, R., Buscema, G., Fusi Pccci, F., Richer, H. B., Fahlman, G. G.: Astron. J. 100 (1990) 1811. 9OC1 Castellani, V., Chief& A., Straniero, 0.: Astrophys. J. Suppl. 74 (1990) 463. 9OC2 Cayrel, R., in: Physical Processesin Fragmentation and Star Formation (Capuzzo-Dolcetta, R., Chiosi, C., Di Fazio, A., eds.). Dordrecht: Kluwer (1990) p. 343. 9OC3 Cayrel de Strobel, G.: Mem. Sot. Astron. Ital. 61 (1990) 613. 9OC4 Chernoff, D. F., Weinberg, M. D.: Astrophys. J. 351 (1990) 121. 90Dl Demers, S., Kunkel, W. E., Grondin, L.: Publ. Astron. Sot. Pac. 102 (1990) 632. Land&-Bdmstein New Series VV3b

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6.2 Star clusters and associations 93C3 93Dl 93D2 93Fl 93F2 93Hl 93H2 93Kl 93K2 93L 93M1 93M2 93M3 93M4 930 93P1 93P2 93P3 93P4 93R 93Sl 9332 9383 9384 9385 9386 9387 93T 93W 93Y 932 94C 94Dl 94D2 94F 94G 94Hl 94H2 94K 94L 94Ml 94M2 94M3 94M4 94Pl 94P2 94R 94V

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324 95A 95B 95D 95H 95M 95P 95R 95s 95T

6.2 Star clusters and associations Ahumada, J., Lapasset, E.: Astron. Astrophys. Suppl. 109 (1995) 373. Blacker, T.: Astron. Astrophys. 299 (1995) 755. De Marchi, G., Paresce,F.: SpaceTel. Sci. Inst. Repr. Ser. 931 (1995). Hesser,J.E., in: [ml, p. 51. Minniti, D.: Astron. J. 109 (1995) 1663. Phinney, E.S., Kulkarni, S.R.: Nature (1995) in press. Richtler, T.: Rev. Mod. Astron. 8 (1995) 163. Sigurdsson, S., Phinney, E.S.: Astrophys. J. Suppl. 99 (1995) 609. Trager, S.C., King, I.R., Djorgovski, S.: Astron. J. 109 (1995) 218.

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