  We have created a spatially homogeneous polariton condensate in thermal
equilibrium, up to very high condensate fraction. Under these conditions, we
have measured the coherence as a function of momentum, and determined the total
coherent fraction of this boson system from very low density up to density well
above the condensation transition. These measurements reveal a consistent power
law for the coherent fraction as a function of the total density over nearly
three orders of its magnitude. The same power law is seen in numerical
simulations solving the two-dimensional Gross-Pitaevskii equation for the
equilibrium coherence. This power law has not been predicted by prior
analytical theories.
