Clusters of galaxies and variation of the fine structure constant

Abstract

We propose a new method to probe for variations in the fine structure constant $\ensuremath{\alpha}$ using clusters of galaxies, opening up a window on a new redshift range for such constraints. Hot clusters shine in the x-ray mainly due to bremsstrahlung, while they leave an imprint on the cosmic microwave background (CMB) frequency spectrum through the Sunyaev-Zel'dovich effect. These two physical processes can be characterized by the integrated Comptonization parameter ${Y}_{\mathrm{SZ}}{D}_{A}^{2}$ and its x-ray counterpart, the ${Y}_{X}$ parameter. The ratio of these two quantities is expected to be constant from numerical simulations and current observations. We show that this fact can be exploited to constrain $\ensuremath{\alpha}$, as the ratio of the two parameters depends on the fine structure constant as $\ensuremath{\propto}{\ensuremath{\alpha}}^{3.5}$. We determine current constraints from a combination of Planck SZ and XMM-Newton data, testing different models of variation of $\ensuremath{\alpha}$. When fitting for a constant value of $\ensuremath{\alpha}$, we find that current constraints are at the 0.8% level, comparable with current CMB bounds. We discuss strategies for further improving these constraints by at least a factor $\ensuremath{\sim}3$.