  We study experimentally and numerically the equilibrium density profiles of a
trapped two-dimensional $^{87}$Rb Bose gas, and investigate the equation of
state of the homogeneous system using the local density approximation. We find
a clear discrepancy between in-situ measurements and Quantum Monte Carlo
simulations, which we attribute to a non-linear variation of the optical
density of the atomic cloud with its spatial density. However, good agreement
between experiment and theory is recovered for the density profiles measured
after time-of-flight, taking advantage of their self-similarity in a
two-dimensional expansion.
