Is the non-isothermal double $β$-model incompatible with no time evolution of galaxy cluster gas mass fraction ?

Abstract

In this paper, we propose a new method to obtain the depletion factor $γ(z)$, the ratio by which the measured baryon fraction in galaxy clusters is depleted with respect to the universal mean. We use exclusively galaxy cluster data, namely, X-ray gas mass fraction ($f_{gas}$) and angular diameter distance measurements from Sunyaev-Zel'dovich effect plus X-ray observations. The galaxy clusters are the same in both data set and the non-isothermal spherical double $β$-model was used to describe their electron density and temperature profiles. In order to compare our results with those from recent cosmological hydrodynamical simulations, we suppose a possible time evolution for $γ(z)$, such as, $γ(z) = γ_0(1 + γ_1z)$. As main conclusions we found that: the $γ_0$ value is in full agreement with the simulations. { On the other hand, although the $γ_1$ value found in our analysis is compatible with $γ_1=0$ within 2$σ$ c.l., our results show a non-negligible time evolution for the depletion factor, unlike the results of the simulations. However, we also put constraints on $γ(z)$ by using the $f_{gas}$ measurements and angular diameter distances obtained from the flat $Λ$CDM model (Planck results) and from a sample of galaxy clusters described by a elliptical profile. For these cases no significant time evolution for $γ(z)$ was found. Then, if a constant depletion factor is an inherent characteristic of these structures, our results show that the spherical double $β$-model used to describe the galaxy clusters considered does not affect the quality of their $f_{gas}$ measurements.