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, $\alpha$. Therefore, if $\alpha$ is a time-dependent quantity, e.g., $\alpha ={\alpha }_0\varphi (z)$, where $\varphi$ is a function of redshift, we argue that current data do not provide the real angular diameter distance, $D_{\mathrm{A}}(z)$, to the cluster but instead $D_A^{data}(z)=\varphi (z{)}^2{D}_{\mathrm{A}}(z)$. We use this result to derive constraints on a possible variation of $\alpha$ 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 $D_{\mathrm{A}}(z)$ from current type Ia supernovae observations. We find no significant indication of variation of $\alpha$ with the present data.

8 pages, 4 figures, To appear in JCAP

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