The anomalous mass-luminosity relation for the components of a contact binary system is usually explained by postulating strong energy transfer from the primary to the secondary. It has been assumed that the transfer occurs in the common convective envelope surrounding the two stars, but so far the only attempt at a model for the energy transfer has been the sideways convection model of Hazlehurst and Meyer-Hofmeister (1973), which assumes a large-scale circulation of material between the two components.

Any detailed discussion of the dynamics in the common envelope must take account of the predominantly vertical motions associated with normal thermal convection, of Coriolis forces and of viscosity. We have constructed an approximate model for the horizontal transfer of energy between the two components, using a mixing-length approach and taking all three factors into account. The major factors are the vertical convection and the Coriolis forces, which together prevent a large-scale circulation of the type proposed by Hazlehurst and Meyer-Hofmeister. Instead, the flow breaks up into smallscale eddies whose horizontal scale is determined by the interaction of convection, Coriolis forces and viscosity. This has the important qualitative consequence that horizontal energy transfer will occur only if the mean horizontal pressure gradient between the two stars exceeds a certain minimum value. This condition can easily be satisfied in the adiabatic zone of the envelope, but may be an important restriction in the super-adiabatic zone.

Using our model, we were able to estimate the entropy difference between components which is required to transfer enough energy to explain the observed mass-luminosity relation. We found that equal entropy models are possible only if the contact is deep. Unequal entropy models are possible for any degree of contact, so long as the contact extends down as far as the adiabatic zone. If, as has been suggested, the depth of contact increases during evolution then zero-age models must have shallow contact and hence unequal entropies. Deep contact equal entropy models would then form as a result of evolution.

A difficulty is that in our model insufficient energy transfer can occur in the super-adiabatic zone to produce WUMa light curves for the unequal entropy models. This may mean that further work is needed on the exact surface conditions in these stars.

The energy transfer problem in contact binaries is briefly reviewed.

The evolution of contact binaries with common convective envelopes has been studied. Gravitational energy due to the mass exchange is taken into account in both stars, which turned out to be of crucial importance. Three qualitatively different evolutionary tracks have been found for an initial system 1.2M⊙ + 1.0M⊙. One of these corresponds to those found by Moss (1971), in which mass transfers, on a long time scale (≈5 × 108 yr), from the less massive component to the heavier. The second is similar to the solution found by Hazlehurst and Meyer-Hofmeister (1973), in which the evolution proceeds towards equal masses in a much shorter time scale (≈2 × 107 yr). The third possibility is similar to the first one, but its time scale is 10 times shorter (≈5 × 107 yr). The true evolutionary track may well oscillate randomly around the different solutions (rapid period changes).

Asymmetric light curves and period changes of contact binaries can be explained by large-scale prominence activity. From the mass outflow accompanying this activity the mean lifetime of a contact binary is estimated as 5 × 107 yr. From the lifetimes of contact binaries and normal solar type dwarfs on the one hand and the proportion of the former among the latter in equal volumes of space on the other hand, it is concluded that (almost) all solar type dwarfs were contact binaries at the beginning of their main sequence life.

Red colours: B–V=+1.23, U-B = + 1.03 and short period: P=0.2207 days place CC Com at the lower temperature end of the period-colour relation for the W UMa-type binaries. Contrary to the typical behaviour of (B–V) which shows reddening during both minima, the (U–B) index reveals rather large scatter, especially when different nights are intercompared. In addition (U–B) seems to decrease abnormally during some of primary minima when the colours change to B–V = + 1.29 and U–B = +0.99; it is unclear whether the ultraviolet excess δ(U–B) of about +0.11 is not related to these changes. Small night-to-night changes seem to be present in the V-light curve as well.

The large amplitudes of light variations (0.86 and 0.74 mag) and the presence of total eclipses with semi-duration of about 7 deg in phase permit to determine the geometrical elements with rather high accuracy in spite of larger than normal observational errors due to the faintness of the system (V= 11.3-12.2). CC Com belongs to the W-type systems with the relative temperature excess of secondary component X= +0.058 ± 0.002. Other elements are: i = 8806 ± 0.09, q = 0.511 ± 0.009, f = 0.78 ± 0.03 for the assumed Te0 = 4300 K. To obtain a perfect fit to the light curve, the gravity darkening exponent was also varied with the resulting value β = 0.09 ± 0.02.

There are indications that CC Com might belong to the Coma cluster.

Four-colour photometry of 24 W UMa-type systems is presented.

The ratio between rotational angular momentum, Jrot, and orbital angular momentum, Jorb, in close binary systems and its variation with mass ratio is studied. The tables and the graphs give this variation for detached systems, contact systems, semidetached systems and for systems containing a supernova-remnant component and a contact component. For this study some statistical relations of close binary stars were used.

The ratio Jrot/Jorb is sensitive to the variation of the mass ratio q. If q differs much from unity and if the concentration of the stellar matter is moderate (polytropic index n ~ 3), the neglect of rotational angular momentum, Jrot, is not justified.

Parameters are derived for two massive, unevolved, contact binaries.

We have examined the distribution of the semi-major axes of the binary systems in the Sixth Catalogue of the Orbital Elements of Spectroscopic Binary Systems (and its extensions) and the correlation of semi-major axis with other properties of the systems. The total distribution has a single peak near asini=107km. Evolved systems have wider separations and smaller mass ratios than unevolved systems. Among each type separately, the distribution of mass ratios is bimodal and small mass ratio is correlated with large separation. These data appear to show evidence of two mechanisms of binary system formation and of the process of mass transfer in close binaries.

We consider six possible origins for the RS CVn binaries based on the following possibilities. RS CVn binaries might now be either pre-main-sequence or post-main-sequence. A pre-main-sequence binary might not always have been a binary but might have resulted from fission of a rapidly rotating single pre-main-sequence star. The main-sequence counterparts might be either single stars or binaries.

To decide which of the six origins is possible, we consider the following observed data for the RS CVn binaries: total mass, total angular momentum, lack of observed connection with regions of star formation, large space density, kinematical age, and the visual companion of WW Dra. In addition we consider lifetimes and space densities of single stars and other types of binaries.

The only origin possible is that the RS CVn binaries are in a thermal phase following fission of a main-sequence single star. In this explanation the single star had a rapidly rotating core which became unstable due to the core contraction which made it begin to evolve off the main sequence. The present Be stars might be examples of such parent single stars.

This has been a very good meeting. If you cannot read some or all of the papers in full, read at least these remarks. It is an attempt to summarize the highlights, naturally an attempt too imperfect, biased, and highly subjective.

Only authors explicitly named in the text and figures are indexed; thus, co-authors are not necessarily included, nor are authors noted in tables.

The compilation includes texts, figures, tables and discussions following the presentations of papers; abstracts are normally excluded, unless the full paper does not appear in this volume. The page references are not necessarily complete.

Star Index