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The evolution of the X-ray emitting gas mass fraction ($f_{gas}$) in massivegalaxy clusters can be used as an independent cosmological tool to probe theexpansion history of the Universe. Its use, however, depends upon a crucialquantity, i.e., the depletion factor $\gamma$, which corresponds to the ratioby which $f_{gas}$ is depleted with respect to the universal baryonic mean.This quantity is not directly observed and hydrodynamical simulations performedin a specific cosmological model (e.g., a flat $\Lambda$CDM cosmology) havebeen used to calibrate it. In this work, we obtain for the first timeself-consistent observational constraints on the gas depletion factor combining40 X-ray emitting gas mass fraction measurements and luminosity distancemeasurements from type Ia supernovae. Using Gaussian Processes to reconstruct apossible redshift evolution of $\gamma$, we find no evidence for suchevolution, which confirms the current results from hydrodynamical simulations.Moreover, our constraints on $\gamma$ can be seen as a data prior forcosmological analyses on different cosmological models. The currentmeasurements are systematic limited, so future improvements will depend heavilyon a better mass calibration of galaxy clusters and their measured densityprofiles.

Cosmological constraints on the gas depletion factor in galaxy clusters