Gravity darkening and brightening in binaries

TL;DR

This paper models how gravity darkening and brightening affect the radiative flux in corotating binary stars, revealing flux variations and a critical separation where equilibrium fails, impacting the system's luminosity.

Contribution

It provides an analytical model for flux distribution in tidally distorted binaries, incorporating gravity brightening effects not previously detailed.

Findings

Gravity darkening reduces equatorial flux.

Gravity brightening enhances polar flux.

Total luminosity decreases by 13% at critical separation.

Abstract

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.