Probing cluster magnetism with embedded and background radio sources in Planck clusters

Magnetic fields remain an enigmatic part of the content of galaxy clusters. Faraday rotation and depolarisation of extragalactic radio sources are useful probes, but the limited availability of polarised radio sources necessitates stacking clusters to study average magnetic field profiles and correlation scales. We recently presented a VLA survey of the 124 most massive Planck clusters at low redshift ($z<0.35$), where a clear depolarisation trend with the cluster impact parameter was found. In this study, we combine the depolarisation information with the observed rotation measure (RM) and present an investigation into the average magnetic field properties of the sample, using both background sources and sources embedded in clusters. We observe a significant increase in the RM scatter, $\sigma_\mathrm{RRM}$, closer to the cluster centres. Averaging all 124 clusters, we find a scatter within $R_\mathrm{500}$ of $\sigma_\mathrm{RRM}=209\pm37$ rad m$^{-2}$, with background sources and cluster members showing similar values ($200\pm33$ and $219\pm66$ rad m$^{-2}$, respectively). In the simple assumption of a uniform magnetic field with a single fluctuation scale $\Lambda_c$, this translates to an average magnetic field strength of $2\,(\Lambda_c/10\mathrm{kpc})^{-0.5}\, \mu$G. The profile of $\sigma_\mathrm{RRM}$ as a function of projected radius is inconsistent with a model that has a simple scaling $B \propto n_e^\eta$, with an observed deficit near the centre of clusters possibly caused by the fact that the highest RM sources near the centre of clusters are depolarised. In a full forward model, we find that the magnetic field power spectrum agrees with the Kolmogorov value, but that none of the Gaussian random field models can fully explain the observed relatively flat profiles. This implies that more sophisticated models of cluster magnetic fields in a cosmological context are needed.
Comment: Submitted to A\&A on 2024-08-13