Testing the gas mass density profile of galaxy clusters with distance   duality relation
  In this paper, assuming the validity of distance duality relation, $\eta=D_L(z)(1+z)^{-2}/D_A(z)=1$, where $D_A(z)$ and $D_L(z)$ are the angular and the luminosity distance respectively, we explore two kinds of gas mass density profiles of clusters: the isothermal $\beta$ model and the non-isothermal double-$\beta$ model. In our analysis, performed on 38 massive galaxy clusters observed by \textit{Chandra} (within the redshift range of $0.14<z<0.89$), we use two types of cluster gas mass fraction data corresponding to different mass density profiles fitted to the X-ray data. Using two general parameterizations of $\eta(z)$ (phenomenologically allowing for distance duality violation), we find that the non-isothermal double-$\beta$ model agrees better with the distance duality relation, while the isothermal $\beta$ model tends to be marginally incompatible with the Etherington theorem at 68.3% CL. However, current accuracy of the data does not allow to distinguish between the two models for the gas-density distribution at a significant level. 
Shuo Cao, Marek Biesiada, Xiaogang Zheng, Zong-Hong Zhu
astro-ph.CO