We apply a von Zeipel gravity darkening model to corotating binaries to
obtain a simple, analytical expression for the emergent radiative flux from a
tidally distorted primary orbiting a point-mass secondary. We adopt a simple
Roche model to determine the envelope structure of the primary, assumed massive
and centrally condensed, and use the results to calculate the flux. As for
single rotating stars, gravity darkening reduces the flux along the stellar
equator of the primary, but, unlike for rotating stars, we find that gravity
brightening enhances the flux in a region around the stellar poles. We identify
a critical limiting separation beyond which hydrostatic equilibrium no longer
is possible, whereby the flux vanishes at the point on the stellar equator of
the primary facing the companion. For equal-mass binaries, the total luminosity
is reduced by about 13 % when this limiting separation is reached.Comment: 7 pages, 5 figures, matches version published in Astrophysical
Journa
