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.