A consistent test of the distance-duality relation with galaxy clusters and Type Ia Supernovae

We propose a new consistent method to test the distance-duality relation which related the angular diameter distances (D-A) to the luminosity distances (D-L) in a cosmology-independent way. In order to avoid any bias brought by redshift incoincidence between galaxy clusters and Type Ia Supernovae (SNe Ia), as well as to ensure the integrity of the galaxy clusters samples, we obtain the luminosity distance of a certain SN Ia point at the same redshift of the corresponding galaxy cluster by interpolating from the nearby SNe Ia. With the observational data pairs at the same redshifts of the angular diameter distances from the complete 38 galaxy clusters for the spherical model and the corresponding luminosity distances interpolated from the Union 2 set, we find that eta equivalent to D-L(1 + z)(-2)/D-A = 1 is satisfied within 2 Sigma confidence level for parametrizations of eta(z), which are more stringent than previous results without considering redshift bias.