Galaxy clusters, type Ia supernovae and the fine structure constant

Abstract

As is well known, measurements of the Sunyaev-Zeldovich effect can be combined with observations of the X-ray surface brightness of galaxy clusters to estimate the angular diameter distance to these structures. In this paper, we show that this technique depends on the fine structure constant, $α$. Therefore, if $α$ is a time-dependent quantity, e.g., $α=α_0 ϕ(z)$, where $ϕ$ is a function of redshift, we argue that current data do not provide the real angular diameter distance, $D_{\rm{A}}(z)$, to the cluster but instead $D_A^{data}(z) = ϕ(z)^2 D_{\rm{A}}(z)$. We use this result to derive constraints on a possible variation of $α$ for a class of dilaton runaway models considering a sample of 25 measurements of $D_A^{data}(z)$ in redshift range $0.023 < z < 0.784$ and estimates of $D_{\rm{A}}(z)$ from current type Ia supernovae observations. We find no significant indication of variation of $α$ with the present data.