The Structure of Contact Binaries

According to an argument of Kuiper's, contact binaries with unequal components cannot exist at age zero This result comes from a comparison of the mass-radius relation for single, homogeneous stars with the condition to be fulfilled by the radii of the components if the surface of the binary is to be an equipotential There is good evidence, however, that W Ursae Majoris stars do occur at age zero with unequal components. To resolve this contradiction, the structure of common envelopes for contact binaries is investigated. It is found that when the common envelope is convective the adiabatic constants of the envelopes of the two companions must be equal. Then, since the radius of a star with a convective envelope is sensitive to the adiabatic constant, it follows that the mean radii of the components differ, in this case, from the radii of the corresponding single stars. Thus Kuiper's argument does not apply when the common envelope is convective It is then shown, using Kuiper's simple approach, that contact binaries with convective common en- velopes probably can exist at age zero with unequal components. This leads to a simple model for a zero- age W UMa star that predicts how the properties of these stars, including their mass ratios, depend on the mass of one component When these predictions are compared with observation, some qualitative agreement is found, but the detailed agreement, especially with Eggen's period-color relation, is not very good I. INTRODUCTIO