  Using many-body results available from diagrammatic and {\it ab initio} Monte
Carlo calculations we analyze the phase diagram
$\mu=(\mu_{\uparrow}+\mu_{\downarrow})/2$ versus
$h=(\mu_{\uparrow}-\mu_{\downarrow})/2$ of a unitary Fermi gas at zero
temperature with population imbalance and unequal masses. We identify different
regions where the gas is superfluid, partially polarized or fully polarized and
determine the corresponding coexistence conditions. The asymmetry in the phase
diagram, caused by the mass imbalance, and its effect on the
Chandrasekhar-Clogston limit for the critical polarization are explicitly
discussed. The equation of state of the superfluid and normal phases is
employed, within the local density approximation, to predict novel phase
separated configurations in the presence of harmonic trapping potentials.
