Publications of the Astronomical Society of the Pacific
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PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC Vol. 83 October 1971 No. 495 EVOLUTION IN CLOSE BINARY SYSTEMS* ZDENEK KOPAL Department of Astronomy, University of Manchester, England Received 25 June 1971 A comparison of the consequences of current theories of stellar evolution with known observational aspects of close binary systems leads to the following conclusions. 1. Systems with both components on the main sequence conform satisfactorily to our present expectations in most observational aspects. In particular, components which are equal (or comparable) in mass appear to be also comparable in their spectra and absolute dimensions. They also rotate without exception in the direction of their orbital revolution, and about axes which are nearly perpendicular to the orbital plane. 2. Their post-main-sequence evolution towards the giant branch results in a widespread "evolutionary paradox," in which the component leading in evolution (having expanded to fill its Roche limit) proves to be the less massive of the two. The existence of contact com- ponents in systems of total mass less than 1-2 O casts some doubt, however, on the possibility that such systems became semidetached as a consequence of thermonuclear hydrogen deple- tion within the lifetime of our Galaxy. 3. A hypothesis that this situation is the result of a changeover in the role caused by transfer of mass between them can be made compatible with the observed absence of a transient phase in which the more massive star has reached the Roche limit first only if a mass transfer at a rate of 10-5 to 10~4 O /yr is limited to 1(^-105 years, and occurs with velocities generally less than 102 km/sec. This would, however, require the density of such temporary gas streams to be of the order of 10^-1021 particles per cm3 (i.e., 10-6 to 10-3 g/cm3 for hydrogen), and optically completely thick. 4. The gas streams actually observed by spectroscopic means in many semidetached systems fall short of these requirements by several orders of magnitude; and any mass transfer by these would become noticeable only on a long (nuclear) time scale. 5. The existence of binary systems like Sirius or Procyon (consisting of a main-sequence star attended by a white dwarf) — in which very wide separation of both components largely precludes mass transfer — suggests that a loss of mass of their white dwarfs must have occurred with velocities sufficient to remove it altogether from the system — as it happens in Wolf-Rayet stars or novae. 6. Another significant fact concerning close binaries in their post-main-sequence evolutionary stage is a virtually complete absence of such binaries with mass ratios close to one — in contrast with their relatively high frequency encountered on the main sequence, and in spite of an increased probability of discovery. The reason why these should become extinct in the post-main-sequence stage is unknown. 7. Close binaries of the W UMa type are much too numerous in space to be regarded as evolutionary descendants of detached main-sequence systems of comparable masses and dimensions. A hypothesis is, therefore, advanced that their origin was by contraction towards two preexisting mass centers in close proximity of each other — a contraction which became arrested (by the onset of hydrogen burning) at, or even beyond, their respective Roche limits — thus resulting in the formation of systems with properties as we see them today. 8. The observed excesses of photometric over dynamical ellipticities of W UMa-type systems point to the conspicuous gravity-darkening operative over their surfaces — not smaller than that to be expected for the case of radiative equilibrium in subsurface layers. *One in a series of review articles currently appearing in the Publications. 521 © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 522 ZDENEK KOPAL 9. The kinematic properties of W UMa-type binaries are different (and their concentra- tion towards the galactic plane more pronounced) than those of the subdwarf systems of U Gem type — facts which throw some doubt on the possibility of evolutionary connection between the two groups of stars. Key words: stellar evolution — binary stars individual evolutionary stages may become I. Introduction impossible to accomplish. 1 As is known only too well, the evolution of the A more favorable situation would obtain if we stars constitutes a process which (barring excep- could identify a group of stars of the same age tional phases bordering on instability) unrolls and initial composition, which may differ among on so slow a time scale that no changes arising themselves only in mass. Such groups are indeed from it can become perceptible within a cos- known to exist — to wit, stellar associations and mically fleeting span of time, such as the time star clusters of different types, whose HR interval human beings have been observing the diagrams reflect nothing else but evolutionary stars since the dawn of the astronomical science. dispersion of equally old stars of different mass However, atomic and nuclear physics has now after a certain lapse of time. However — except progressed to the stage at which the cosmic for relative luminosities — the individual proper- history of self-gravitating configurations of ties of such cluster stars are again not known to stellar mass and size can be broadly recon- us any better than if such stars were solitary structed on theoretical grounds — at least travelers through space. The situation becomes throughout most of their lives — from the cradle only a little better in the extreme case of associa- to the grave. In particular, it has been generally tions we call double or multiple stars — visual recognized that the evolution of the stars repre- binaries of known periods, for which the masses sents — in effect — an initial-value problem, the of the individual components are obtainable whole course of which is governed by the star's from a knowledge of their parallax and absolute initial mass and composition (to which we should orbits; but their radii are known to us no more add, perhaps, also the initial angular momen- than if these stars were single. tum) — the mass (and, to a lesser extent, momen- In order to learn more about the stars as tum) remaining essentially unaltered at least individuals, we must turn our attention to close throughout long evolutionary epochs; while the binary systems — and, in particular, to those composition changes irreversibly in the course of which by an accident of the orientation of their time as a result of gradual depletion of hydrogen orbital planes with respect to our line of sight and other types of nuclear fuel. happen to become eclipsing variables; for these No theories of this process are, however, as constitute so far our sole source of information yet sufficiently specific —let alone infallible — concerning the masses, densities, and absolute and they must continually be tested by con- dimensions of the individual stars other than our fronting their consequences with the actual sun. The significance of such systems for a properties of real stars at different phases of their documentation of the story of stellar evolution is evolution. The discriminating power of such manifest: namely, they provide a unique oppor- tests depends, in turn, on the range of informa- tunity for tracing the effects of differential evo- tion offered by the test objects. Single stars lution of stars of virtually the same age and which move alone through space are, unfortu- initial composition, which may differ in initial nately, not very revealing in this respect; for mass (or momentum). Moreover, a close binary their basic physical characteristics — such as the system represents a liaison of two stars which masses and absolute dimensions — are not indi- are bound to remain together through all vidually obtainable, and can be surmised only vicissitudes of their subsequent evolution no by statistical methods. Moreover, a sample of matter how long the latter may be. And the stars selected at random in any part of the longer it lasts, the more revealing a comparison galactic space would contain objects of very may become of the actual properties of two different ages as well as initial masses and com- partners of the same age constituting an indis- position. As a result, an identification of their soluble union. © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System EVOLUTION IN CLOSE BINARY SYSTEMS 523 It will be the aim of the present paper to cording to most recent estimates (cf. Dommanget examine, from this point of view, known physical 1970; or Jaschek and Gomez 1970) more than properties of close binary systems in order to one-half of all main-sequence stars are double inquire into the extent to which they conform or multiple, and have been so from the stage at to theoretical expectations based on the evolu- which a preexisting gas cloud collapsed into tion of the two components of such systems as individual stars. Whether the origin of multiple stellar individuals. This story, the commence- stars is to be sought in a "simultaneous condensa- ment of which goes back less than 20 years in the tion" or "capture" at a distance comparable with past, is still full of gaps — some very tantalizing their present separation in close pairs is largely ones —but it does not lack many points of a matter of semantics, for in dense star associa- interest. In fact, it plays a central role in docu- tions both processes amount to very much the menting the story of stellar evolution; and while same thing. being (at least, up to a point) broadly in agree- Be that as it may, however, both components ment with theoretical expectations, it discloses of ordinary close pairs evolved probably side by also many facts which have not been previously side in the course of the last stage of their con- anticipated.