Simulation Study of Binary Mergers of Galaxy Clusters I: Properties of Merger Shocks and Radio Emission

Abstract

We investigate binary mergers of galaxy clusters, the formation of shocks, and the resulting radio relics using three-dimensional simulations. The initial setup consists of two idealized spherical subclusters with a mass ratio below three, each permeated by turbulent magnetic fields, and we follow their merger with a high-order accurate magnetohydrodynamic (MHD) code. In parallel, we track the acceleration of cosmic-ray electrons (CRe) via diffusive shock acceleration (DSA) at merger-driven shocks, together with radiative cooling and Fermi-II (turbulent) acceleration in the postshock region, employing a newly developed Eulerian Fokker-Planck solver. Synchrotron emission is computed from the simulated CRe distribution and magnetic fields. In this paper, we detail these numerical approaches and present the first results obtained with them. Two prominent axial shocks emerge along the merger axis; the shock ahead of the heavier subcluster systematically attains a higher Mach number, although it is more compact, than that ahead of the lighter subcluster. Turbulent magnetic fields, which are both inherited from the initial conditions and amplified during the merger, produce patchy, fine-scale structures in the radio surface brightness. Because of the combined effects of turbulent acceleration, spatially nonuniform magnetic fields, and the curved geometry of merger shocks, the volume-integrated radio spectra show deviations from the canonical power-law steepening expected for a planar shock with a uniform field. Reacceleration of preexisting fossil CRe enhances the surface brightness. Our results highlight the coupled roles of merger dynamics, MHD turbulence, and CRe physics in shaping the observed properties of radio relics in cluster outskirts.