Galaxy clusters and a possible variation of the fine structure constant

Galaxy clusters have been used as a cosmic laboratory to verify a possible time variation of fundamental constants. Particularly, it has been shown that the ratio YSZDA2/CXZSYX, which is expected to be constant with redshift, can be used to probe a variation of the fine structure constant, α. In this ratio, YSZDA2 is the integrated comptonization parameter of a galaxy cluster obtained via Sunyaev-Zel'dovich (SZ) effect observations multiplied by its angular diameter distance, DA, YX is the X-ray counterpart and CXSZ is an arbitrary constant. Using a combination of SZ and X-ray data, a recent analysis found YSZDA2/CXZSYX=Cα(z)3.5, where C is a constant. In this paper, following previous results that suggest that a variation of α necessarily leads to a violation of the cosmic distance duality relation, DL/DA(1+z)2=1, where DL is the luminosity distance of a given source, we derive a new expression, YSZDA2/CXSZYX=Cα3.5η−1(z), where η(z)=DL/DA(1+z)2. In particular, considering the direct relation η(z)∝α(z)1/2, derived from a class of dilaton runaway models, and 61 measurements of the ratio YSZDA2/CXSZYX provided by the Planck collaboration, we discuss bounds on a possible variation of α. We also estimate the value of the constant C, which is compatible with the unity at 2σ level, indicating that the assumption of isothermality for the temperature profile of the galaxy clusters used in the analysis holds.