The distance duality relation and the temperature profile of Galaxy Clusters

The validity of distance duality relation, $\eta=D_L(z)(1+z)^{-2}/D_A(z)=1$, an exact result required by the Etherington reciprocity theorem, where $D_A(z)$ and $D_L(z)$ are the angular and luminosity distances, plays an essential part in cosmological observations and model constraints. In this paper, we investigate some consequences of such a relation by assuming $\eta$ a constant or a function of the redshift. In order to constrain the parameters concerning $\eta$, we consider two groups of cluster gas mass fraction data including 52 X-ray luminous galaxy clusters observed by Chandra in the redshift range $0.3\sim 1.273$ and temperature range $T_{\rm gas}> 4$ keV, under the assumptions of two different temperature profiles [1]. We find that the constant temperature profile is in relatively good agreement with no violation of the distance duality relation for both parameterizations of $\eta$, while the one with temperature gradient (the Vikhlinin et al. temperature profile) seems to be incompatible even at 99% CL.