Context : Interpretation of light curves of many types of binary stars requires the inclusion of the ( cor ) relation between surface brightness and local effective gravity .
Until recently , this correlation has always been modeled by a power law relating the flux or the effective temperature and the effective gravity , namely T _ { \mathrm { eff } } \propto g _ { \mathrm { eff } } ^ { \beta } .

Aims : We look for a simple model that can describe the variations of the flux at the surface of stars belonging to a binary system .

Methods : This model assumes that the energy flux is a divergence-free vector anti-parallel to the effective gravity .
The effective gravity is computed from the Roche model .

Results : After explaining in a simple manner the old result of Lucy ( 1967 , Zeit .
für Astrophys .
65,89 ) , which says that \beta \sim 0.08 for solar type stars , we first argue that one-dimensional models should no longer be used to evaluate gravity darkening laws .
We compute the correlation between \log T _ { \mathrm { eff } } and \log g _ { \mathrm { eff } } using a new approach that is valid for synchronous , weakly magnetized , weakly irradiated binaries .
We show that this correlation is approximately linear , validating the use of a power law relation between effective temperature and effective gravity as a first approximation .
We further show that the exponent \beta of this power law is a slowly varying function , which we tabulate , of the mass ratio of the binary star and the Roche lobe filling factor of the stars of the system .
The exponent \beta remains mostly in the interval [ 0.20 , 0.25 ] if extreme mass ratios are eliminated .

Conclusions : For binary stars that are synchronous , weakly magnetized and weakly irradiated , the gravity darkening exponent is well constrained and may be removed from the free parameters of the models .