Cosmological-model-independent tests for the distance-duality relation from Galaxy Clusters and Type Ia Supernova

We perform a cosmological-model-independent test for the distance-duality (DD) relation $\eta (z)=D_L(z)(1+z{)}^{-2}\mathrm{/}{D}_A(z)$, where $D_L$ and $D_A$ are the luminosity distance and angular diameter distance respectively, with a combination of observational data for $D_L$ taken from the latest Union2 SNe Ia and that for $D_A$ provided by two galaxy clusters samples compiled by De Filippis {\it et al.} and Bonamente {\it et al.}. Two parameterizations for $\eta (z)$, i.e., $\eta (z)=1+{\eta }_{0}z$ and $\eta (z)=1+{\eta }_{0}z\mathrm{/}(1+z)$, are used. We find that the DD relation can be accommodated at $1\sigma$ confidence level (CL) for the De Filippis {\it et al.} sample and at $3\sigma$ CL for the Bonamente {\it et al.} sample. We also examine the DD relation by postulating two more general parameterizations: $\eta (z)={\eta }_0+{\eta }_{1}z$ and $\eta (z)={\eta }_0+{\eta }_{1}z\mathrm{/}(1+z)$, and find that the DD relation is compatible with the results from the De Filippis {\it et al.} and the Bonamente {\it et al.} samples at $1\sigma$ and $2\sigma$ CLs, respectively. Thus, we conclude that the DD relation is compatible with present observations.