0521855578 cambridge university press evolutionary processes in binary and multiple stars jul 2006

This page intentionally left blank Binary systems of stars are as common as single stars Stars evolve primarily by nuclear reactions in their interiors, but a star with a binary companion can also have its evolution influenced by the companion Multiple star systems can exist stably for millions of years, but can ultimately become unstable as one star grows in radius until it engulfs another This volume discusses the statistics of binary stars; the evolution of single stars; and several of the most important kinds of interaction between two (and even three or more) stars Some of the interactions discussed are Roche-lobe overflow, tidal friction, gravitational radiation, magnetic activity driven by rapid rotation, stellar winds, magnetic braking and the influence of a distant third body on a close binary orbit A series of mathematical appendices gives a concise but full account of the mathematics of these processes Peter Eggleton is a physicist at the Lawrence Livermore National Laboratory in California Following his education in Edinburgh, he obtained his Ph.D in Astrophysics from the University of Cambridge in 1965 He lectured for a short period at York University before returning to the University of Cambridge to conduct research from 1967 to 2000 as a Fellow of Corpus Christi College In 2000, he took up his current position at LLNL He is well known throughout the community as one of the most knowledgeable experts in binary star evolution Cambridge Astrophysics Series Series editors Andrew King, Douglas Lin, Stephen Maran, Jim Pringle and Martin Ward 10 17 18 19 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 Titles available in this series Quasar Astronomy by D W Weedman Molecular Collisions in the Interstellar Medium by D Flower Plasma Loops in the Solar Corona by R J Bray, L E Cram, C J Durrant and R E Loughhead Beams and Jets in Astrophysics edited by P A Hughes Gamma-ray Astronomy 2nd Edition by P V Ramana Murthy and A W Wolfendale The Solar Transition Region by J T Mariska Solar and Stellar Activity Cycles by Peter R Wilson 3K: The Cosmic Microwave Background Radiation by R B Partridge X-ray Binaries by Walter H G Lewin, Jan van Paradijs and Edward P J van den Heuvel RR Lyrae Stars by Horace A Smith Cataclysmic Variable Stars by Brian Warner The Magellanic Clouds by Bengt E Westerlund Globular Cluster Systems by Keith M Ashman and Stephen E Zepf Accretion Processes in Star Formation by Lee W Hartmann The Origin and Evolution of Planetary Nebulae by Sun Kwok Solar and Stellar Magnetic Activity by Carolus J Schrijver and Cornelis Zwaan The Galaxies of the Local Group by Sidney van den Bergh Stellar Rotation by Jean-Louis Tassoul Extreme Ultraviolet Astronomy by Martin A Barstow and Jay B Holberg Pulsar Astronomy 3rd Edition by Andrew G Lyne and Francis Graham-Smith Compact Stellar X-ray Sources by Walter Lewin and Michiel van der Klis E V O LUTIO NAR Y PR OCES S ES IN B I NARY AND M ULT IPLE S T AR S PETER EGGLETON Lawrence Livermore National Laboratory, California    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge  , UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521855570 © P Eggleton 2006 This publication is in copyright Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published in print format 2006 - - ---- eBook (EBL) --- eBook (EBL) - - ---- hardback --- hardback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Contents Preface page vii 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Introduction Background Determination of binary parameters Stellar multiplicity Nomenclature Statistics of binary parameters A Monte Carlo model Conclusion 1 13 16 17 27 29 2.1 2.2 2.3 2.4 2.5 2.6 Evolution of single stars Background Main sequence evolution Beyond the main sequence Stellar winds and mass loss Helium stars Unsolved problems 31 31 35 69 97 104 106 3.1 3.2 3.3 3.4 3.5 Binary interaction: conservative processes The Roche potential Modifications to structure and orbit Conservative Roche-lobe overflow Evolution in contact Evolutionary routes 109 109 117 128 144 147 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Slow non-conservative processes Gravitational radiation: mode GR Tidal friction: mode TF Wind processes: modes NW, MB, EW, PA, BP Magnetic braking and tidal friction: mode MB Stellar dynamos Binary-enhanced stellar winds: modes EW, MB Effects of a third body: mode TB Old Uncle Tom Cobley and all 158 158 159 168 178 183 192 200 207 v vi Contents Rapid non-conservative processes 5.1 Tidal friction and the Darwin instability: mode DI 5.2 Common envelopes and ejection: modes CE, EJ 5.3 Supernova explosion: mode SN 5.4 Dynamical encounters in clusters: mode DE 209 209 210 221 225 Accretion by the companion 6.1 Critical radii 6.2 Accretion discs 6.3 Partial accretion of stellar wind: mode PA 6.4 Accretion: modes BP, IR 6.5 Accretion in eccentric orbits 6.6 Conclusions 231 231 235 239 241 250 253 Appendix A The equations of stellar structure Appendix B Distortion and circulation in a non-spherical star Appendix C Perturbations to Keplerian orbits Appendix D Steady, axisymmetric magnetic winds Appendix E Stellar dynamos Appendix F Steady, axisymmetric, cool accretion discs References Subject index Stellar objects index 257 266 276 289 295 299 304 315 320 Preface This book is intended for those people, perhaps final-year undergraduates and research students, who are already familiar with the terminology of stellar astrophysics (spectral types, magnitudes, etc.) and would like to explore the fascinating world of binary stars I hope it will also be useful to those whose main astrophysical interests are in planets, galaxies or cosmology, but who wish to inform themselves about some of the basic blocks on which much astronomical knowledge is built I have endeavoured to put into one book a number of concepts and derivations that are to be found scattered widely in the literature; I have also included a chapter on the internal evolution of single stars In the interest of keeping this volume short, I have been brief, some might say cursory, in surveying the enormous literature on observed binary stars It is almost a truism that theoretical ideas stand or fall by comparison with observation My intention is to produce a second volume, with my colleagues Dr Ludmila Kiseleva-Eggleton and Dr Zhanwen Han, in which individual binary and triple stars that rate less than a line in this volume will be discussed in the paragraph or two each, at least, which they deserve In addition, the synthesis of large theoretical populations of binary stars will be discussed Some individual binaries can be seen as flying entirely in the face of the theoretical ideas outlined here – see OW Gem, Section 2.3.5 If I took at face value the notion that one well-measured counter-example is all that is needed to demolish a theory, then I would have given up long ago Rather, I think, it is necessary to persevere: not be paralysed by disagreement with observation, but also not to sweep disagreement under the carpet A number of problems that have to be considered may well be capable of being answered only by detailed numerical modelling, constructing three-dimensional models of a whole star, or of a pair of stars in a binary Massive computer resources will be needed for such investigations; for that reason I moved from Cambridge University to the Lawrence Livermore National Laboratory, California, where such resources are being developed This Laboratory has started the ‘Djehuty Project’ – named after the Egyptian god of astronomy – to pursue this long-term goal We hope that this project will supplement, though it cannot entirely replace, the simple ideas which this book discusses I am very grateful to many colleagues who have been generous of their time in discussing the issues of binary-star evolution Drs Zhanwen Han, Onno Pols, Klaus-Peter Schrăoder, Chris Tout and Ludmila Kiseleva-Eggleton have kindly supplied some figures, as well as much insight I particularly wish to thank Prof Piet Hut for his careful and critical reading of the manuscript, and suggestions for improvement, and Drs Kem Cook and Dave Dearborn for their patience in allowing me to pursue this topic vii viii Preface This work was performed under the auspices of the US Department of Energy, National Nuclear Security Administration by the University of 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critical radii for, 231–235 in eccentric orbits, 250–253 and orbit perturbation, 126 partial, 239–241 accretion discs bipolar output, 254 modelling, 235–237, 299–303 rotation, 238–239 size of, 238, 255 accretion-induced collapse, 247, 248 accretion ring, 142–143 in protostars, 61 AD sub-case, 149, 151, 153, 154 adaptive optics, adiabatic gradient 43 AE sub-case, 149, 150, 151, 153 AG sub-case, 149, 150, 151, 153 AI Vel variables, 56 AL sub-case, 149, 150, 151, 176 Alf´en radius, 178, 186, 187, 208, 232–233, 234, 235 Algol stars, 153, 154, 199–200, 227, 238 AM sub-case, 199 AN sub-case, 149, 151, 153, 156, 176, 225 angular momentum loss, 59–60, 135, 148, 154, 170 angular semi-major axis, 3, anisotropic supernova explosions, 222–223 Ap stars, 56 aperture synthesis, apsidal motion, 11–13, 121, 126, 127–128 AR sub-case, 149, 151, 153, 154, 156, 176 AS sub-case, 176 AS sub-case, 149, 150, 151, 153 astrometric binaries, astrometric observations, 2–4 AT Peg, 152 atmospheric blurring, AU sub-case, 175, 176 AUN sub-case, 175, 176 AUR sub-case, 175, 176 AUS sub-case, 175,176 AW sub-case, 175, 176 B case, 218 B-peculiar stars, 55–56 barium stars, 240–241 barytropes, 263–265 BB sub-case, 150, 156 BD sub-case, 150 Be stars, 55, 64 beginning giant branch (BGB), 32, 114 binaries, statistics, 65–69, 114 binary-binary encounters, 228–229 bipolar outflow, 254 bipolar re-emission (BP mode), 148, 168, 169, 173, 177, 242 BL sub-case, 150, 176 black holes evolutionary state notation, 147 formation of, 89, 90, 225, 254 mass of, 225 Schwarzchild radius, 232 and X-ray binaries, 248 blue loop, 85, 93 blue stragglers, 56, 227, 228 BN sub-case, 150, 156, 175, 176 bolometric vs visual luminosity, 36–37 Bondi–Hoyle accretion radius, 233, 234 BP mode, 148 see also bipolar re-emission BR sub-case, 150 breakup times, 15, 66, 67 breathing, 80 brown dwarfs, 13, 42, 57–59 BU sub-case, 156, 175, 176 BUN sub-case, 175, 176, 218 BUR sub-case, 175 BW sub-case, 175, 176 BY Dra stars, 57, 191 carbon flash, 87 carbon-oxygen core, 87–88 case A evolution, 137, 149–154, 253, 254 case B evolution, 137, 150, 153, 154–157 case C evolution, 137, 150, 153, 194–195, 218 case D evolution, 176 cataclysmic binaries, 242–243 cataclysmic variables, 242–243 CD sub-case, 150 CE mode, 148, 215–218, 240, 248 see also common envelope processes central condensation, 70–73 Centre des Donn´ees astronomiques de Strasbourg, visual orbit data, 315 316 Subject index Cepheid variables, 147, 253 CF mode, 146 Chandrasekhar limit, 58 Chandrasekhar mass, 40, 75 circulation patterns, intrastellar material, 123–124 ‘close’ binaries, 18 CN case, 176 CNO cycle, 48–49 coeval stars, 97, 229 common envelope ejection, 148 common envelope processes, 61–62, 148, 150, 210–221, 253, 254 see also CE mode common proper motion pairs, conservative model, 111 contact binaries, 110–111 case A examples, 152 evolution, 144–147, 198 geometric notation, 148 modes of evolution, 148 stability, 198 convection, 33, 42–46, 107 convective entrainment, 48, 50 convective envelope turnover time, 46 convective mixing, 35, 47–51 convective overshooting, 34, 51, 107 convective stars, modelling, 42 core, definition of, 212–214 Coriolis force, 109, 110, 189 corotation radius, 232, 234 CR1 mode, 146 CU case, 176, 194, 218 CUD sub-case, 195, 218 cumulative distribution function, 20 CUN sub-case, 194, 218 CW case, 176, 195 D case, 217 Darwin instability, 122, 148, 162, 163, 209–210 DE mode, 225–230 detached binaries, 110, 148, 152 DI mode, 209–210, 218 differential rotation, 145 diffusion, 107, 226 Djehuty project, 256 Doppler tomography, 9, 10 dredge-up phase, 77 dwarf novae, 242–243 dynamical encounters in clusters, 148, 153, 225–230, 256 within triple systems, 255, 256 dynamical timescale, 148 dynamo activity, 183–192, 254, 295–298 eccentricity of orbits, 3, 24, 26, 27, 250–253 eclipse mapping, eclipsing binaries, 7–13 Eddington limit, 91, 219 Eddington luminosity, 234 Eddington mass, 38–39, 75 e-instability, 162, 163 EJ mode, 156, 220–221, 254 ellipsoid variation, 7, 8–9 enhanced wind, 96, 195 entrainment see convective entrainment envelope, expansion of, 70–73 episodic accretion, 250–251 equation of state, 33–34, 261 evolutionary states and modes, notation for, 147 EW mode, 169, 171, 195, 199, 200, 218, 246, 247 see also stellar wind Feige 24, 216, 217, 218 FGKM subdwarfs, 57 frequency, of binaries, 13–14, 28 galactic clusters, 78, 79 Galaxy, area and stellar population, 27 geometric states, notation for, 148 giant molecular clouds, 59 globular clusters binaries in, 18, 29 contraction of, 226 distribution of stars, 226 dynamical encounters in, 226 helium core-burning stars, 78–79 H-R diagram for, 79 life-time, 62, 63 and neutron stars, 250 stellar metallicity, 33 GR mode, 158–159, 207, 208, 243, 244–246 gravitational microlensing, 10 gravitational radiation, 148, 158–159, 188 gravothermal catastrophe, 226 GW Vir variables, 82 Hayashi limit, 74, 75 Hayashi track, 46, 73–74 helioseismology, 52–54 helium-burning stars, evolutionary state, 147 helium core, 49, 69–70 helium flash, 78 helium initial composition parameter (Y), 33 helium shell flash instability, 81, 85 helium stars, 104–106, 156 Herbig Ae/Be stars, 59 Herbig emission-line, 147 Herbig-Haro objects, 62, 63 Hertzsprung gap, 32, 67–68 stars, 147 Hertzsprung-Russell diagram, 31, 32 47 Tuc globular cluster, 79 giant branch, 32, 73 Hyades galactic cluster, 79 neighbouring stars, 80 see also main squence Hg/Mn stars, 56 hierarchical systems, 15 nomenclature, 16–17 high-mass stars, post-main sequence evolution, 87–95 Hipparcos satellite, 2, hot core stars, 147 hot remnant stars, 147 Hubble time, 31 Humphreys–Davidson limit, 90–91, 93, 102, 219 hydrodynamic timescale, 135 hydrogen-deficient (HdC) carbon stars, 104 hydrostatic equilibrium, 31, 266–268 inclination, of binary orbits, 3, 5–6 inner Lagrangian point, 110 interaction of binaries, 17–19, 29–30 intermediate-mass stars, post-main sequence evolution, 85–87 Subject index initial stellar composition, 32–33 ionisation, 262–263 IR mode, 148, 242, 248 isotropic supernova explosions, 221–222 Kelvin–Helmholtz timescale, 70 Keplerian orbits, perturbation of, 126–128 and apsidal motion, 127–128, 278–280 fundamental equations, 276–278, 285–287 and gravitational radiation, 284–285 and mass loss, 126, 285–287 and precession, 128, 279–280 and third body interaction, 287–288 and tidal friction, 126, 280–284 Kippenhahn–Weigert cases, 137 see also case A evolution; case B evolution; case C evolution Kozai cycles, 18–19, 62–63, 192, 200, 203, 205, 207 Kramers’ opacity law, 38, 43, 44 Lane–Emden equation, 37 Lagrangian points, 110 Ledoux criterion, 50 light curve analysis, low-mass binaries and case B evolution, 198 dynamos, 198 example statistics, 196–197 low-mass stars, post-main sequence evolution, 74–85 luminosity, 40 on Hertsprung track, 73–74 initial, 36 and mass loss, 131 magnetic braking and case A binaries, 153 and contact binaries, 198–199 massive stars, 192–193 modelling, 178–181, 182–183 and orbital periods, 169 for single stars, 180–181 and tidal friction, 181–189 timescale, 188 Tout–Pringle model, 190 see also MB mode magnetic fields, stellar, 64–65, 107 magnetic winds, 178–179, 289–294 magnetohydrodynamics, 60, 63, 289–294 magnetospheres, 231, 232 main sequence anomalous stars, 54–57 black dwarfs, 58 brown dwarfs, 13, 42, 57–59 evolution in: formulae for, 35–37; convection, 42–54; polytropic approximation 37–42 examples, 65–69 lifetime, 70 magnetic fields, 64–65 rotation, 64 star formation, 59–63 termination, 36, 42, 63–64 mass distribution, 19–21, 27–29 mass functions, 5–6, 19–21 mass loss in AGB evolution, 83–85 and case A evolution, 154 317 modelling, 107 OB stars, 97–98 and orbital perturbation, 126 and stellar winds, 97–103 types of, 103 mass ratio distribution, 23–26, 27–29 non-conservative models, 171 notation for, 16 observable, 3–4, 6–7 in wide binaries, 254 mass transfer forward, 146, 148 Kippenhahn–Weigert cases, 137 modes of, 135 onset of, 137–139 problems, 254 rate of, 146 reverse, 146, 148, 253–254 masses, statistics of, 19–21 massive binaries, 173–177 massive stars see high-mass stars; magnetic braking; very high mass stars maximum-entropy algorithms, MB mode, 148, 182 and Algols, 199, 200 and cataclysmic variables, 243, 244, 246, 247, 248 see also magnetic braking; stellar wind merged binaries, 18, 22, 146, 211, 230 meshpoints, in modelling, 34–35, 107, 256, 258, 260 metallicity parameter, 33 microlensing, 10 millisecond pulsars, 249, 250 Milne–Eddington atmosphere model, 107 Mira variables, 82, 253 mixing-length theory, 33, 45 modes of evolution, 135 modelling of stellar evolution, 34–35, 257–265 see also meshpoints modes of evolution, notation for, 148–149 Monte Carlo methods, 20, 21, 23, 27–29 multiplicity, of stars, 13–15 N-body gravitational dynamics, 226, 227 NE mode, 199, 243, 246, 247, 248, 249 neighbouring stars density of, 27 H-R diagram for, 80 neutral points, 110, 111 neutrinos, 34, 54 neutron stars and accretion, 249 dynamical encounters, 227 evolutionary states, 147 formation of, 89, 254 mass of, 90 rotation of, 93–94 and X-ray binaries, 248 nomenclature, 16–17, 147–148 non-conservative processes, definition, 158 non-hierarchical systems, definition, 15 non-radial pulsators, 55, 69 non-spherical stars, 117–126, 266–275 circulation velocity, 272 dissipation rate, 273–274 distortion, 268–271 hydrostatic-equilibrium model, 266–268 318 Subject index non-spherical stars (cont.) inter-stellar force, 272 quadrupole tensor, 272 Schwarzschild derivation, 271–272 tidal velocity, 272–273 normal winds, 148, 195 novae, 242–243, 255 nuclear evolution timescale, 135, 139, 148, 188, 198 nuclear reaction rates, 34, 38 NW mode, 148 see also stellar wind O – C diagrams, 10–12 oblique pulsators, 56 OBN stars, 55 Of stars, 54 opacity, 34, 38, 42, 43, 73 open clusters see galactic clusters orbital periods distribution, 19, 21–23 Monte Carlo model, 27–29 of spectroscopic binaries, of triple systems, 23 of visual binaries, overcontact configuration, 111 P Cyg stars, 91, 93, 103, 148 PA mode, 148, 246 see also partial accretion; stellar wind parallax, 2, partial accretion, 169–178, 239–241 see also PA mode PC mode, 148 periods, statistics, 114 perturbations, Keplerian orbits, 126–128 photometric binaries, 7–8 photometric observations, photospheres, modelling, 107 planetary nebulae, 147, 211, 215 polytropes, 37–42, 121–122 polytropic envelope, 42 polytropic index, 37–38, 39, 70, 71, 73 Population I/ II/ III stars, 33, 57 precession, 126, 128 pre-main sequence state, 147 primordial binaries, 227 primordial elements, 31 primordial triples, 227 proton-proton cycle, 48 protostars, 62 pseudosynchronism, 161 pulsars equation of state, 94–95 magnetic fields, 94–95 millisecond, 249, 250 radio, 7, 13 rotation, 94–95 X-ray, 7, 147 quadruple systems, examples, 206–207 quadrupoles, 126, 127, 207 R CrB variables, 104 radial pulsations, 55, 80 radiative region, of core, 43–45 radio pulsars, 7, 13 Rayleigh–Taylor instability, 87, 144, 254 red giants abbreviation for, 147 central condensation, 263–265 evolution, 76–78 examples, 95–97 lifetime, 75 luminosity, 75 and magnetic braking, 189 mass loss, 97, 99–100 mass transfer, 136 red supergiants, 147, 213, 255 reflection effect, 7, Reimer’s Law, 99, 100 relative orbits, reverse BU case, 225 roAp stars, 56 Roche lobes, 110, 111–112, 118, 250 Roche-lobe overflow, 62, 115–116, 126 effect of rotation, 119–120 and gainer, 140–144 from loser, 129–140 reverse (RLOF), 225, 246, 253, 254, 255 Roche potential, 109–117 Rossby number, 45, 184 rotation, of stars, 64–65 modelling, 107 non-uniform, 209–210 and Roche-lobe overflow, 119–120 and tidal distortion, 121 RR Lyr variables, 80 RS CVn binaries, 193 Salpeter initial mass function, 19–20 Scalo initial mass function, 20–21 Schwarzchild criterion, 50 Schwarzschild radius, 232, 234 Sco-Cen, 63 selective diffusion, 53 semiconvection, 47, 48–50, 107 semidetached binaries case A evolution, 152 configuration, 110 and contact binaries, 198 notation for, 148 Roche overflow, 146 SF mode, 146 SF1 mode, 146 SF2 mode, 146 single-star wind, 148, 195 size of stars, minimum, 13 Slowly Pulsating B stars, 55 SN mode, 148, 221–225 see also supernovae softness index, 39–40, 71–72 speckle interferometry, 3, spectroscopic binaries, 5–7 spectroscopic observations, s-process, 57, 82, 240 SR mode, 146 SR1 mode, 249 SR3 mode, 146 star formation, 33, 59–63 starbursts, 29 star-forming regions, 59, 63 Subject index statistics of binaries, 65–69, 114 stellar dynamos, 183–192, 254, 295–298 stellar wind, 168–177 and accretion, 232 companion-enhanced, 148 enhanced, 96, 195 and mass loss, 97–103 and massive binaries, 173–177 Mestel–Spruit model, 178 modelling, 35 normal, 148, 195 and partial accretion, 239–241 superwinds, 100, 148 see also EW mode; MB mode; PA mode Strong λ 4077 stars, 57 sub-clusters, 60, 62 supernovae formation of, 88–89, 221–223 types of, 87, 92, 93 and X-ray binaries, 223–225 see also SN mode supersoft X-ray sources, 245, 247 superwinds, 100, 148 SW mode, 148 see also stellar wind T Tau stars, 59, 147 Taurus-Auriga cloud, 59 TB mode, 148, 205 see also third bodies temperature gradients, 43 temperature, initial, 36 temperature, on Hayashi track, 74 terminal main sequence, 32, 63–64 TF mode, 148, 159–168, 195 see also tidal friction thermal relaxation oscillations, 146 thermal timescale, 70, 130, 135, 136, 139, 148, 188 thermal-equilibrium models, mass loss, 135 third bodies, 126, 153 and apsidal motion, 202–203, 206 and binary evolution, 18–19 and eccentricity of orbits, 202–204, 205 and inner binary orbits, 200–201 and periodicy, 11, 12–13 and perturbation of orbits, 204–205 and precession, 202, 203, 206 and tidal friction, 204–205 see also TB mode 319 Thomson scattering, 43, 44, 234 Thorne–ytkow objects, 147, 223, 225 tidal friction and angular monentum, 255 and Darwin instability, 209–210 and dynamo activity, 254 and massive binaries, 173–177 and magnetic braking, 178–183 and massive binaries, 173–177 orbit perturbation, 126, 229, 280–284 timescale, 188 see also TF mode tidal velocity, 121–122, 273–274 timescales, 188 timesteps, in models, 34, 35 triple systems examples, 206–207 third-body effects, 14, 200–207, 255 two-body gravitational relaxation, 63 Type I supernovae, 87, 92, 93 Type II supernovae, 87, 92, 93 very high mass stars, 88, 91, 93 ‘very wide’ binaries, 18 viscosity, 232, 235–237, 255 visual binaries, definition, 2–4 visual orbits, 3–4 white dwarfs, 75–76 mass transfer, 136–137, 247 notation for, 147 wide binaries, 18 winds see stellar wind Wolf–Rayet stars, 54–55 classification, 91–92 evolution of, 93 as helium stars, 104 mass loss, 98, 101–102 notation for, 147 stellar wind, 92 X-ray binaries, 90 high-mass, 223–225 low-mass, 226, 248–250 X-ray pulsars, 7, 147 X-ray sources, supersoft, 245, 247 zero-age main sequence (ZAMS), 32 Stellar objects index 0045-7319, 165–166, 223–225 0534-69, 174, 175 0957-666, 216, 217, 218 105 Her, 240 1101 + 364, 216, 217, 218 13471-1258, 216 1414-0848, 216 16 Cyg, 14 1704 + 481, 216, 217, 218 1704 + 481.2, 216 Pup, 155, 156 41 Dra, 204 −43◦ 14304, 240 47 Tuc cluster, 79 53 Per stars, 55 93 Leo, 95 AA Dor, 197, 216, 217–218 ADS 11061, 203–204 AE Aqr, 245 AE Aur, 229 AF Gem, 152, 153 AG Dra, 216, 217, 218, 240 AH Vir, 152, 154, 196, 199 α Aur, 193–194 α Aur, 95 α Cen, α CMa, 216, 217, 218 α CMi, 216, 217, 218 α Equ, 95 α Gem, 15 AM CVn, 244, 245 AM Her, 245 Ap stars, 56 AR Lac, 193 AR Mon, 197, 200 AS Cam, 12, 17 AS Eri, 152, 154, 196, 199, 200 AT Peg, 152 AY Cet, 197, 216, 217, 218 BD Cam, 240 Be stars, 55, 64 BE UMa, 216, 217, 218 β Cap, 207 β Lyr, 126 β Per (Algol), 10, 11, 196, 207 β Pic stars, 56, 61 BM Ori, 66, 67, 126 BP Cru, 224, 225 BT Mon, 245 320 BV Cen, 244, 245, 246 BY Dra stars, 57, 191 CC Cet, 216, 217, 218 CC Com, 196 Cepheid variables, 147, 253 CN And, 196, 198 CQ Cep, 174, 175 CQ Dra, 207 CV Ser, 174, 175 Cyg X-3, 159 δ Cap, 66, 67 δ Cep, 56 δ Del stars, 56 δ Lib, 152, 153 δ Ori A, 155, 156, 220–221 δ Sct pulsators, 56 δ Sge, 95, 97 DI Her, 66, 68 DL Vir, 197, 200, 207 DM Per, 152, 153, 194, 207 DN Ori, 196, 199 DQ Her, 245 DR Dra, 216, 240, 241 EG UMa, 216, 217, 218 EG52, 216, 217, 218 EK Cep, 66, 67 EM Cyg, 245 EN Lac, 66, 67, 249 ε CrA, 152, 154, 196, 198, 199 ε Vir, EQ Tau, 196 ER UMa, 245 EV Cnc, 227 η And, 95 η Car, 91 η Ori, 66, 69, 207 Feige 24, 216, 217, 218 FF Aqr, 197, 215, 216, 217, 218, 244 FT Lup, 196, 198 G1 229 AB, 13 G203-47, 216, 217, 218 G77-61, 216, 217, 218 γ Cas, 223, 225 γ Dor variables, 56 γ Per, 95, 97 Stellar objects index GG Lup, 66, 68 GK Per, 244, 245, 246 GK Vir, 216 GP Com, 245 GP Vel, 163, 224,225 GQ Mus, 245 HD 17817, 216 HD 20214, HD 31487, 240 HD 49798, 216, 217, 218 HD 51956, 155, 156 HD 77247, 240 HD 109648, 12, 13, 15, 16 HD 109648, 194 HD 121447, 216, 217, 218 HD 123949, 240 HD 137569, 216, 217, 218 HD 140913, 13 HR 3579, HR Cam, 216, 217, 218 Hyades cluster, 79 HR2030, 95, 96 HT Cas, 245 HU Tau, 152, 153 HW Vir, 216, 217, 218 HZ Her, 248, 249 I Ori, 63 IC 4651 cluster, 52 III Cen, 63 IK Peg, 216, 217, 218 IN Com, 216 ι Ori, 153, 229 IP Peg, 237 IQ Cam, 216, 217, 218 J0737 + 3039, 224 J0737-3039, 159 J1012 + 5307, 248 J1640 + 2224, 248 J1751-305, 248, 249, 250 J1857 + 0943, 248, 249 J1915 + 1606, 224, 225 J1915, 159 κ Peg, 206 KV Vel, 216, 217, 218, 246 λ And, 193 λ Boo stars, 57 λ Eri variables, 55 λ Tau, 152, 153, 194, 207 LM Com, 216, 217, 218 LY Aur, 152, 153, 229 LZ Cep, 152 M67 cluster, 52, 227-228 μ Col, 229 μ Ori, 207 MV Lyr, 245 NN Ser, 216, 217, 218 o Ceti, 17-18 Orion cloud, 59 Orion Nebula cluster, 66, 67 321 OW Gem, 193, 194 OW Gem, 95, 96, 97 OY Car, 237, 245 OY Car, accretion disc, 237 P Cyg stars, 91, 93, 148 p Vel, 206 φ Per, 155, 156, 223 QS Vul, 95, 97 QU Vul, 243, 245 QV Nor, 224 QZ Car, 207, 229 R CMa, 152, 154, 196, 199 RR Lyn, 66, 67 RR Lyr variables, 80 RS CVn binaries, 193 RS CVn, 95, 96, 193 RT And, 152, 196 RT Lac, 197, 200 RW Dor, 196 RW UMa, 193 RX Cas, 196 RX J0806, 159 RZ Cas, 196 RZ Cnc, 197, 200 RZ Eri, 95, 96, 193, 194, 195 RZ Oph, 155, 156 RZ Pyx, 152 RZ Sct, 155, 156, 238 S Cnc, 196, 199 S Dor, 91 S1082, 228 Sco-Cen, 63 SS Lac, 66, 69, 202 ST LMi, 245 SU Cyg, 207 Sun Alf´en radius, 178 differential rotation, 145 dynamo effect, 185 magnetic fields, 65 mass loss, 97 rotation, 64, 65, 125 SV Cen, 152 SX Cas, 197 SZ Cen, 66, 68 SZ Psc, 193 T CrB, 240 T Pyx, 245 T Tau, 65–66 τ Boo, 14 τ CMa, 207 τ Per, 95 θ Tuc, 197, 200 Trapezium cluster, 15, 66, 67 TT Aur, 152, 154 TT Hya, 196 TU Mus, 152 TV Cas, 152 TV Mus, TX UMa, 152, 153 TY CrA, 66–67, 69 TZ For, 95 322 Stellar objects index U Cep, 10, 11, 196 U CrB, 152, 153, 154 U Gem, 245 u Her, 152, 154 υ And, 14 υ Sgr, 155, 156, 220 U Sco, 244, 245, 246 UU Aqr, 245 UU Sge, 9, 216, 217, 218 UV Cet, 13, 246 UV Leo, 196 UX CVn, 216 UX UMa, 245 UY Vol, 248 V Pup, 152, 154 V Sge, 245, 247–248, 248 V1010 Oph, 196 V1033 Sco, 248 V1341 Cyg, 248, 249 V1343 Aql, 224 V1357 Cyg, 224, 225 V1379 Aql, 197, 200, 216 V1488 Cyg, 95, 97 V1521 Cyg, 159, 224, 225 V2012 Cyg, 240 V2174 Cyg, 155, 220 V2214 Cyg, 216 V2291 Oph, 95 V348 Car, 174, 175, 176 V356 Sgr, 155, 156 V361 Lyr, 152, 154, 196, 198, 199 V379 Cep, 155, 156–157, 216, 220, 221 V382 Cyg, 174, 175 V388 Cyg, 196 V398 Car, 174, 175 V404 Cyg, 248 V415 Car, 95 V429 Car, 174, 175 V444 Cyg, 174, 175 V448 Cyg, 174, 175 V471 Tau, 216, 217, 218 V477 Lyr, 216 V499 Sco, 152 V505 Mon, 155, 156, 220 V616 Mon, 248 V618 Mon, 248 V624 Her, 66, 67, 68 V635 Cas, 223, 224, 225 V640 Mon, 152, 154, 174, 175 V643 Ori, 193-194 V645 Cen (Proxima Centuri), V651 Mon, 197, 215, 216, 217, 218, 244 V652 Her, 216 V695 Cyg, 95 V725 Tau, 223, 224 V729 Cyg, 174, 175 V760 Sco, V779 Cen, 224, 225 V832 Ara, 240 V907 Sco, 207 Vela X-1, VV Ori, 152, 194, 207 VZ Psc, 196, 198 W Crv, 196, 199 W UMa, 152, 154, 196 WW Dra, 193 X Per, 223, 225 ξ Cet, 240 ξ Tau, 206 ξ1 Cet, XY UMa, 66, 67, 68 XZ Cep, 152 Y Cyg, 152 YY Gem, 196 Z Cha, 9, 245 Z Her, 193 Z Vul, 152, 154 ζ Aur, 95, 97 ζ Cap, 240 ζ Cyg, 240 ζ Oph stars, 55 ZZ Cyg, 196, 199 ... kept in mind that even single stars present many evolutionary problems, and so it is not surprising that many binary stars Introduction Questions about binary stars can be divided very loosely into... Determination of binary parameters If we are interested in determining the masses and radii of stars, then we have to turn almost right away to binary stars, since it is only by measuring orbital... Kiseleva-Eggleton and Dr Zhanwen Han, in which individual binary and triple stars that rate less than a line in this volume will be discussed in the paragraph or two each, at least, which they deserve In addition,