Measuring the gas clumping in Abell 133
  This paper continues a series in which we developed a non-parametric method
to measure inhomogeneities in the gas distribution from X-ray observations of
galaxy clusters. In this work, we apply our method to Chandra X-ray
observations of Abell 133 and present the determination of the gas clumping
factor from X-ray cluster data. We find that the gas clumping factor in Abell
133 increases with radius and reaches $\sim 2-3$ at $0.9\,R_{200}$. This is in
good agreement with the predictions of hydrodynamical simulations and our
previous determination. We then observe a general trend of steepening in the
radial profiles of the clumping-corrected gas density beyond $0.3\, R_{200}$,
with a logarithmic slope of $\sim 2.6$ at $0.9\,R_{200}$. The observed density
profiles appear to be flatter compared to simulations, but in agreement with
previous observational findings. In addition, we observe that the measured
temperature decreases steadily with radius toward the outskirts of A133, while
the entropy increases monotonically with radius, gently flattening in the outer
volumes. With respect to theoretical predictions from pure gravitational
collapse, the results presented here point to an entropy excess in the central
regions, which extends out to large radii. These results suggest that gas
inhomogeneities should be treated properly when interpreting X-ray measurements
in the envelope of galaxy clusters. We finally discuss how the brightness
distribution keeps a record of the large-scale structures formation scenario,
providing a snapshot of the 'melting pot' in the virialization region.
