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 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 per cent confidence level (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.