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, alpha. 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, D-A, Y-X is the X-ray counterpart and C-XSZ is an arbitrary constant. Using a combination of SZ and X-ray data, a recent analysis found YSZDA2 /CXZSYX = C alpha(z)(3.5), where C is a constant. In this paper, following previous results that suggest that a variation of alpha necessarily leads to a violation of the cosmic distance duality relation, D-L/D-A(1 + z)(2) = 1, where D-L is the luminosity distance of a given source, we derive a new expression, YSZDA2/CXSZYX = C alpha(3.5)eta(-1)(z), where eta(z) = D-L/D-A(1 + z)(2). In particular, considering the direct relation eta(z) proportional to alpha(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 alpha. We also estimate the value of the constant C, which is compatible with the unity at 2 sigma level, indicating that the assumption of isothermality for the temperature profile of the galaxy clusters used in the analysis holds.