  The evolution of the X-ray emitting gas mass fraction ($f_{gas}$) in massive
galaxy clusters can be used as an independent cosmological tool to probe the
expansion history of the Universe. Its use, however, depends upon a crucial
quantity, i.e., the depletion factor $\gamma$, which corresponds to the ratio
by which $f_{gas}$ is depleted with respect to the universal baryonic mean.
This quantity is not directly observed and hydrodynamical simulations performed
in a specific cosmological model (e.g., a flat $\Lambda$CDM cosmology) have
been used to calibrate it. In this work, we obtain for the first time
self-consistent observational constraints on the gas depletion factor combining
40 X-ray emitting gas mass fraction measurements and luminosity distance
measurements from type Ia supernovae. Using Gaussian Processes to reconstruct a
possible redshift evolution of $\gamma$, we find no evidence for such
evolution, which confirms the current results from hydrodynamical simulations.
Moreover, our constraints on $\gamma$ can be seen as a data prior for
cosmological analyses on different cosmological models. The current
measurements are systematic limited, so future improvements will depend heavily
on a better mass calibration of galaxy clusters and their measured density
profiles.
