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The gas depletion factor $\gamma(z)$, i.e., the average ratio of the gas massfraction to the cosmic mean baryon fraction of galaxy clusters, plays a veryimportant role in the cosmological application of the gas mass fractionmeasurements. In this paper, using the newest catalog of 182 galaxy clustersdetected by the Atacama Cosmology Telescope (ACT) Polarization experiment, weinvestigate the possible redshift evolution of $\gamma(z)$ through a newcosmology-independent method. The method is based on non-parametricreconstruction using the measurements of Hubble parameters from cosmicchronometers. Unlike hydrodynamical simulations suggesting constant depletionfactor, our results reveal the trend of $\gamma(z)$ decreasing with redshift.This result is supported by a parametric model fit as well as by calculationson the reduced ACTPol sample and on the alternative sample of 91 SZ clustersreported earlier in ACT compilation. Discussion of possible systematic effectsleaves an open question about validity of the empirical relation$M_{tot}$-$f_{gas}$ obtained on very close clusters. These results might pavethe way to explore the hot gas fraction within large radii of galaxy clustersas well as its possible evolution with redshift, which should be studiedfurther on larger galaxy cluster samples in the upcoming X-ray/SZ clustersurveys.

The gas depletion factor in galaxy clusters: implication from Atacama Cosmology Telescope Polarization experiment measurements