Magnetic fields in the outskirts of PSZ2 G096.88+24.18 from a depolarization analysis of radio relics

Abstract

Radio relics are diffuse, non-thermal radio sources present in a number of merging galaxy clusters. They are characterized by elongated arc-like shapes and highly polarized emission (up to sim 60<!PCT!>) at gigahertz frequencies, and are expected to trace shock waves in the cluster outskirts induced by galaxy cluster mergers. Their polarized emission can be used to study the magnetic field properties of the host cluster. In this paper, we investigate the polarization properties of the double radio relics in PSZ2 G096.88+24.18 using the rotation measure (RM) synthesis, and try to constrain the characteristics of the magnetic field that reproduce the observed depolarization as a function of resolution (beam depolarization). Our aim is to understand the nature of the low polarization fraction that characterizes the southern relic with respect to the northern relic. We present new $1-2$ GHz Karl G. Jansky Very Large Array (VLA) observations in multiple configurations. We derived the RM and polarization of the two relics by applying the RM synthesis technique, and thus solved for bandwidth depolarization in the wide observing bandwidth. To study the effect of beam depolarization, we degraded the image resolution and studied the decreasing trend of polarization fraction with increasing beam size. Finally, we performed 3D magnetic field simulations using multiple models for the magnetic field power spectrum over a wide range of scales, in order to constrain the characteristics of the cluster magnetic field that can reproduce the observed beam depolarization trend. Using RM synthesis, we obtained a polarization fraction of ($18.6 0.3$)<!PCT!> for the northern relic and ($14.6 0.1$)<!PCT!> for the southern one. Having corrected for bandwidth depolarization, and after noticing the absence of relevant complex Faraday spectrum, we inferred that the nature of the depolarization for the southern relic is external, and possibly related to the turbulent gas distribution within the cluster, or to the complex spatial structure of the relic. The best-fit magnetic field power spectrum, which reproduces the observed depolarization trend for the southern relic, was obtained for a turbulent magnetic field model, described by a power spectrum derived from cosmological simulations, and defined within the scales of $ min kpc $ and $ max kpc $. This yields an average magnetic field of the cluster within 1$ Mpc ^3$ volume of $ G