The evolution of low-mass close binary systems. V. Transport processes in the envelopes of contact components.
Starting from an adiabatic, isopotential, irrotational approximation to the hydrodynamic equations, we discuss the nature of mass flow in the envelopes of contact components of semidetached and contact systems. The local pressure reduction (or excess, in the case of the mass-gaining component of a contact binary) near L1 results in mass outflow from the interior (or inflow into the interior), as well as surface flow. The most heavily mass4aden streamlines are those originating deepest within the interior. This welling up of the interior allows a component with a deep convective envelope to be coupled through the inner Lagrangian point well before its photo sphere reaches its nominal Roche lobe. The horizontal pressure gradients characterizing the flow have scale heights typically only a fraction of the geometrical depth of contact. Consequently, Coriolis forces are less effective at impeding flow than previously thought. Eddy formation by Coriolis forces is inhibited by the turbulent viscosity of a convective medium, but the net effect of convection is further to impede net mass flow. Among observed contact systems the thermal diffusion time scale of the common envelope is found to be typically of the order of the sound travel time between components. Therefore flow between components can significantly perturb the vertical thermal structure of the common envelope only in the region near the inner Lagrangian point. A model of luminosity transfer in contact binaries is proposed in which large-scale heat transport is accomplished by the coupling of Eddington-Sweet-type circulation with the dynamical flow near L1. The large-scale circulation between components absorbs or releases energy in the envelope of each star according to whether or not it is in the same sense as the static vertical entropy gradient in that envelope. The stability of this configuration requires that the secondary components of contact systems with common convective envelopes develop higher envelope entropies (as observed in the W-type W Ursae Majoris systems) in order to drive the circulation in the proper sense. An approximate criterion is obtained for good thermal contact in a common envelope, and shown to accord well with observed depths of contact. The division of W Ursae Majoris systems into W-type and A-type systems reflects the convective or radiative nature of the common envelope at the inner critical surface. Subject headings: stars: binaries - stars: mass loss - stars: W Ursae Majoris