Testing the cosmic distance duality with X-ray gas mass fraction and
  supernovae data
  In this paper we discuss a new cosmological model-independent test for the
cosmic distance duality relation (CDDR), $\eta =
D_{L}(L)(1+z)^{-2}/D_{A}(z)=1$, where $D_{A}(z)$ and $D_{L}(z)$ are the angular
and luminosity distances, respectively. Using the general expression for X-ray
gas mass fraction ($f_{gas}$) of galaxy clusters, $f_{gas} \propto
D_L{D_A}^{1/2}$, we show that $f_{gas}$ observations jointly with type Ia
supernovae (SNe Ia) data furnish a validity test for the CDDR. To perform our
analysis we use 38 $f_{gas}$ measurements recently studied by two groups
considering different assumptions to describe the clusters (La Roque {\it{et
al.}} 2006 and Ettori {\it{et al.}} 2009) and two subsamples of SNe Ia distance
luminosity extracted from the Union2 compilation. In our test we consider the
$\eta$ parameter as a function of the redshift parameterized by two different
functional forms. It is found that the La Roque {\it{et al.}} (2006) sample is
in perfect agreement with the duality relation ($\eta = 1$) whereas the Ettori
{\it{et al.}} (2009) sample presents a significant conflict.
