Probing the cosmic distance-duality relation with the Sunyaev-Zel'dovich effect, X-ray observations and supernovae Ia

Context. The angular diameter distances toward galaxy clusters can be determined with measurements of Sunyaev-Zel'dovich effect and X-ray surface brightness combined with the validity of the distance-duality relation, D-L(z)(1 + z)(2)/D-A(z) = 1, where D-L(z) and D-A(z) are, respectively, the luminosity and angular diameter distances. This combination enables us to probe galaxy cluster physics or even to test the validity of the distance-duality relation itself. Aims. We explore these possibilities based on two different, but complementary approaches. Firstly, in order to constrain the possible galaxy cluster morphologies, the validity of the distance-duality relation (DD relation) is assumed in the Lambda CDM framework (WMAP7). Secondly, by adopting a cosmological-model-independent test, we directly confront the angular diameters from galaxy clusters with two supernovae Ia (SNe Ia) subsamples (carefully chosen to coincide with the cluster positions). The influence of the different SNe Ia light-curve fitters in the previous analysis are also discussed. Methods. We assumed that eta is a function of the redshift parametrized by two different relations: eta(z) = 1 +eta(0)z, and eta(z) = 1 + eta(0)z/(1 + z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we considered the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical and spherical isothermal beta models and spherical non-isothermal beta model. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. For both approaches we find that the elliptical beta model agrees with the distance-duality relation, whereas the non-isothermal spherical description is, in the best scenario, only marginally compatible. We find that the two-light curve fitters (SALT2 and MLCS2K2) present a statistically significant conflict, and a joint analysis involving the different approaches suggests that clusters are endowed with an elliptical geometry as previously assumed. Conclusions. The statistical analysis presented here provides new evidence that the true geometry of clusters is elliptical. In principle, it is remarkable that a local property such as the geometry of galaxy clusters might be constrained by a global argument like the one provided by the cosmological distance-duality relation.