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 $\eta(z)=D_L(z)(1+z)^{-2}/D_A(z)$, 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., $\eta(z)=1+\eta_0z$ and $\eta(z)=1+\eta_0z/(1+z)$, 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: $\eta(z)=\eta_0+\eta_1z$ and
$\eta(z)=\eta_0+\eta_1z/(1+z)$, 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.
