Equilibrium states of nonsynchronous stars in detached binaries

Abstract

Effects of nonsynchronous spin on equilibrium states for the radiative envelopes of detached components of close binary systems are investigated. On the assumption that the nonsynchronous speeds are much less than the relative orbital velocity of the component stars, the full set of stellar structure equations, generalized to include the gasdynamical and heat-transport effects of spin, are analyzed to linear order in the ratio of nonsynchronous speed to relative orbital velocity. The most general form of the velocity field is derived, and a specific case that approaches rigid rotation is considered in the limit where a single-star configuration is approached. The pressure, density, and temperature departures from the Roche model are obtained, with particular emphasis on the case that approaches rigid rotation. The surface shape of a nonsynchronous equilibrium state is calculated, and von Zeipel's gravity-darkening law is generalized to slightly nonsynchronous equilibria.