  The equation of state of a dilute two-component asymmetric Fermi gas at
unitarity is subject to strong constraints, which affect the spatial density
profiles in atomic traps. These constraints require the existence of at least
one non-trivial partially polarized (asymmetric) phase. We determine the
relation between the structure of the spatial density profiles and the T=0
equation of state, based on the most accurate theoretical predictions
available. We also show how the equation of state can be determined from
experimental observations.
