Gas clumping in galaxy clusters
  The reconstruction of galaxy cluster's gas density profiles is usually
performed by assuming spherical symmetry and averaging the observed X-ray
emission in circular annuli. In the case of a very inhomogeneous and asymmetric
gas distribution, this method has been shown to return biased results in
numerical simulations because of the $n^2$ dependence of the X-ray emissivity.
We propose a method to recover the true density profiles in the presence of
inhomogeneities, based on the derivation of the azimuthal median of the surface
brightness in concentric annuli. We demonstrate the performance of this method
with numerical simulations, and apply it to a sample of 31 galaxy clusters in
the redshift range 0.04-0.2 observed with ROSAT/PSPC. The clumping factors
recovered by comparing the mean and the median are mild and show a slight trend
of increasing bias with radius. For $R<R_{500}$, we measure a clumping factor
$\sqrt{C}<1.1$, which indicates that the thermodynamic properties and
hydrostatic masses measured in this radial range are only mildly affected by
this effect. Comparing our results with three sets of hydrodynamical numerical
simulations, we found that non-radiative simulations significantly overestimate
the level of inhomogeneities in the ICM, while the runs including cooling, star
formation, and AGN feedback reproduce the observed trends closely. Our results
indicate that most of the accretion of X-ray emitting gas is taking place in
the diffuse, large-scale accretion patterns rather than in compact structures.
