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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 angularand the luminosity distance respectively, we explore two kinds of gas massdensity profiles of clusters: the isothermal $\beta$ model and thenon-isothermal double-$\beta$ model. In our analysis, performed on 38 massivegalaxy clusters observed by \textit{Chandra} (within the redshift range of$0.14<z<0.89$), we use two types of cluster gas mass fraction datacorresponding to different mass density profiles fitted to the X-ray data.Using two general parameterizations of $\eta(z)$ (phenomenologically allowingfor 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 theoremat 68.3% CL. However, current accuracy of the data does not allow todistinguish between the two models for the gas-density distribution at asignificant level.

Testing the gas mass density profile of galaxy clusters with distance duality relation