Testing X-ray Measurements of Galaxy Cluster Gas Mass Fraction Using the
  Cosmic Distance-Duality Relation
  We propose a consistency test of some recent X-ray gas mass fraction
($f_{\rm{gas}}$) measurements in galaxy clusters, using the cosmic
distance-duality relation, $\eta_{\rm{theory}}=\dl(1+z)^{-2}/\da$, with
luminosity distance ($\dl$) data from the Union2 compilation of type Ia
supernovae. We set $\eta_{\rm{theory}}\equiv1$, instead of assigning any
redshift parameterizations to it, and constrain the cosmological information
preferred by $f_{\rm{gas}}$ 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. (2 samples), LaRoque et al. and Ettori et al., are
detailedly analyzed against two theoretical modelings of $f_{\rm{gas}}$. The
results from the analysis of Allen et al.'s samples prove 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 1-$\sigma$ confidence level.
However, for Ettori et al.'s $f_{\rm{gas}}$ sample, the inconsistency can reach
more than 3-$\sigma$ confidence level and this dataset shows special preference
to an $\Ol=0$ cosmology.
