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

Magnetic fields remain an elusive 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 the stacking of clusters to study average magnetic field properties. We recently presented a Karl G. Jansky Very Large Array survey of the 124 most massive Planck clusters at low redshift (z < 0.35), finding a clear depolarisation trend with the cluster impact parameter, with sources at smaller projected distances to the cluster centre showing more depolarisation. In this study, we combine the depolarisation information with the observed rotation measure (RM) and present an investigation of 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 RRM, closer to the cluster centres. Averaging all 124 clusters, we find a scatter within R-500 of sigma RRM = 209 +/- 37 rad m(-2), with background sources and cluster members showing similar values (200 +/- 33 and 219 +/- 66 rad m(-2), respectively). In the simple assumption of a uniform amplitude magnetic field with a single fluctuation scale Lambda c, this translates to an average magnetic field strength of 2 (Lambda(c)/10 kpc)(-0.5) mu G. The profile of sigma(RRM) as a function of the projected radius is inconsistent with a model that has a simple scaling B proportional to 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. Combining depolarisation and RM in a full forward model, we find that the magnetic field power spectrum roughly 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.