Can full convection explain the observed short-period limit of the W UMa-type binaries?

Abstract

Stars become fully convective at low effective temperatures. The unique mass-radius relation for fully convective stars (at a given effective temperature) cannot be reconciled with such a relation for Roche geometry except for a unique combination of the orbital periods and effective temperatures : the Hayashi line for contact binaries. The dynamically stable contact systems cannot exist with effective temperatures lower than the full-convection point. It is shown that the more massive component has relatively thicker convective envelope and at low temperatures becomes fully convective first. Because of the energy transfer to the secondary, the full-convection point of the primary component is shifted to somewhat larger masses than for single stars (depending on the mass-ratio which determines how much radiating area provides the secondary)