Measurements and simulation of Faraday rotation across the Coma radio relic

The aim of this work is to probe the magnetic field properties in relics and infall regions of galaxy clusters using Faraday Rotation Measures. We present Very Large Array multi-frequency observations of seven sources in the region South-West of the Coma cluster, where the infalling group NGC4839 and the relic 1253+275 are located. The Faraday Rotation Measure maps for the observed sources are derived and analysed to study the magnetic field in the South-West region of Coma. We discuss how to interpret the data by comparing observed and mock rotation measures maps that are produced simulating different 3-dimensional magnetic field models. The magnetic field model that gives the best fit to the Coma central region underestimates the rotation measure in the South-West region by a factor ~6, and no significant jump in the rotation measure data is found at the position of the relic. We explore different possibilities to reconcile observed and mock rotation measure trends, and conclude that an amplification of the magnetic field along the South-West sector is the most plausible solution. Our data together with recent X-ray estimates of the gas density obtained with Suzaku suggest that a magnetic field amplification by a factor ~3 is required throughout the entire South-West region in order to reconcile real and mock rotation measures trends. The magnetic field in the relic region is inferred to be ~2 microG, consistent with Inverse Compton limits.