The thermal and non-thermal components within and between galaxy clusters Abell 399 and Abell 401

Abstract

We measure the local correlation between radio emission and Compton-$y$ signal across two galaxy clusters, Abell~399 and Abell~401, using maps from the Low-Frequency Array (LOFAR) and the Atacama Cosmology Telescope (ACT) + \Planck. These datasets allow us to make the first measurement of this kind at $\sim$arcminute resolution. We find that the radio brightness scales as $F_{\mathrm{radio}}\propto y^{1.5}$ for Abell~401 and $F_{\mathrm{radio}}\propto y^{2.8}$ for Abell~399. Furthermore, using \XMM data, we derive a sublinear correlation between radio and X-ray brightness for both the clusters ($F_{\mathrm{radio}}\propto F_{\mathrm{X}}^{0.7}$). Finally, we correlate the Compton-$y$ and X-ray data, finding that an isothermal model is consistent with the cluster profiles, $y\propto F_{\mathrm{X}}^{0.5}$. By adopting an isothermal--${\hat{I}}^2$ model, we are able, for the first time, to jointly use radio, X-ray, and Compton-$y$ data to estimate the scaling index for the magnetic field profile, $B(r)\propto n_{\mathrm{e}}(r{)}^{\hat{I}}\cdot$ in the injection and re-acceleration scenarios. Applying this model, we find that the combined radio and Compton-$y$ signal exhibits a significantly tighter correlation with the X-ray across the clusters than when the datasets are independently correlated. We find $\hat{I}\cdot \sim 0.6-0.8$. These results are consistent with the upper limit we derive for the scaling index of the magnetic field using rotation measure values for two radio galaxies in Abell~401. We also measure the radio, Compton-$y$, and X-ray correlations in the filament between the clusters but conclude that deeper data are required for a convincing determination of the correlations in the filament.

16 pages, 8 figures, Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal