Testing X-ray measurements of galaxy cluster gas mass fraction using the cosmic distance-duality relation

We propose a consistency test for some recent X-ray gas mass fraction (f(gas)) measurements in galaxy clusters, using the cosmic distance-duality relation, eta(theory) = D-L (1 + z)(-2)/D-A, with luminosity distance (D-L) data from the Union2 compilation of type Ia supernovae. We set eta(theory) equivalent to 1, instead of assigning any red-shift parameterizations to it, and constrain the cosmological information preferred by f(gas) data along with supernova observations. We adopt a new binning method in the reduction of the Union2 data, in order to minimize the statistical errors. Four data sets of X-ray gas mass fraction, which are reported by Allen et al. (two samples), LaRoque et al. and Ettori et al., are analyzed in detail in the context of two theoretical models of f(gas). The results from the analysis of Allen et al.'s samples demonstrate the feasibility of our method. It is found that the preferred cosmology by LaRoque et al.'s sample is consistent with its reference cosmology within the 1 sigma confidence level. However, for Ettori et al.'s f(gas) sample, the inconsistency can reach more than a 3 sigma confidence level and this dataset shows special preference to an Omega(Delta) = 0 cosmology.