  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_eff {\alpha} g_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),
which says that {\beta}=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_eff and log g_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.
