Morphology of Galaxy Clusters: A Cosmological Model-Independent Test of   the Cosmic Distance-Duality Relation
  Aiming at comparing different morphological models of galaxy clusters, we use two new methods to make a cosmological model-independent test of the distance-duality (DD) relation. The luminosity distances come from Union2 compilation of Supernovae Type Ia. The angular diameter distances are given by two cluster models (De Filippis et al. and Bonamente et al.). The advantage of our methods is that it can reduce statistical errors. Concerning the morphological hypotheses for cluster models, it is mainly focused on the comparison between elliptical $\beta$-model and spherical $\beta$-model. The spherical $\beta$-model is divided into two groups in terms of different reduction methods of angular diameter distances, i.e. conservative spherical $\beta$-model and corrected spherical $\beta$-model. Our results show that the DD relation is consistent with the elliptical $\beta$-model at $1\sigma$ confidence level (CL) for both methods, whereas for almost all spherical $\beta$-model parameterizations, the DD relation can only be accommodated at $3\sigma$ CL, particularly for the conservative spherical $\beta$-model. In order to minimize systematic uncertainties, we also apply the test to the overlap sample, i.e. the same set of clusters modeled by both De Filippis et al. and Bonamente et al.. It is found that the DD relation is compatible with the elliptically modeled overlap sample at $1\sigma$ CL, however for most of the parameterizations, the DD relation can not be accommodated even at $3\sigma$ CL for any of the two spherical $\beta$-models. Therefore it is reasonable that the marked triaxial ellipsoidal model is a better geometrical hypothesis describing the structure of the galaxy cluster compared with the spherical $\beta$-model if the DD relation is valid in cosmological observations. 
Xiao-Lei Meng, Tong-Jie Zhang, Hu Zhan and Xin Wang
astro-ph.CO