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 η(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 cluster samples compiled by De Filippis et al. and Bonamente et al. Two parameterizations for η(z), i.e., η(z) = 1 + η₀ z and η(z) = 1 + η₀ z/(1 + z), are used. We find that the DD relation can be accommodated at 1σ confidence level (CL) for the De Filippis et al. sample and at 3σ CL for the Bonamente et al. sample. We also examine the DD relation by postulating two more general parameterizations: η(z) = η₀ + η₁ z and η(z) = η₀ + η₁ z/(1 + z), and find that the DD relation is compatible with the results from the De Filippis et al. and the Bonamente et al. samples at 1σ and 2σ CLs, respectively. Thus, we conclude that the DD relation is compatible with present observations.