The distance duality relation and the temperature profile of galaxy clusters

The validity of distance duality relation, η = DL(z)(1 + z)−2/DA(z) = 1, an exact result required by the Etherington reciprocity theorem, where DA(z) and DL(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 η a constant or a function of the redshift. In order to constrain the parameters concerning η, we consider two groups of cluster gas mass fraction data including 52 X-ray luminous galaxy clusters observed by Chandra in the redshift range from 0.3 to 1.273 and temperature range Tgas > 4 keV, under the assumptions of two different temperature profiles. We find that the constant temperature profile is in relatively good agreement with no violation of the distance duality relation for both parameterizations of η, while the one with temperature gradient (the Vikhlinin et al. temperature profile) seems to be incompatible even at 99% CL.