Is the non-isothermal double $\beta$-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 $\gamma (z)$, 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 $\beta$-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 $\gamma (z)$, such as, $\gamma (z)={\gamma }_0(1+{\gamma }_{1}z)$. As main conclusions we found that: the ${\gamma }_0$ value is in full agreement with the simulations. { On the other hand, although the ${\gamma }_1$ value found in our analysis is compatible with ${\gamma }_1=0$ within 2$\sigma$ 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 $\gamma (z)$ by using the $f_{gas}$ measurements and angular diameter distances obtained from the flat $\Lambda$CDM model (Planck results) and from a sample of galaxy clusters described by a elliptical profile. For these cases no significant time evolution for $\gamma (z)$ was found. Then, if a constant depletion factor is an inherent characteristic of these structures, our results show that the spherical double $\beta$-model used to describe the galaxy clusters considered does not affect the quality of their $f_{gas}$ measurements.

10 pages, 4 figures, I table, Accepted for publication in the Astroparticle Physics

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• A model-independent test of the evolution of gas depletion factor for SPT-SZ and Planck ESZ clusters
• Comparison of $\Lambda$CDM and $R_h=ct$ with updated galaxy cluster $f_{gas}$ measurements using Bayesian inference