The Three Hundred project: Radio luminosity evolution from merger-induced shock fronts in simulated galaxy clusters

Galaxy cluster mergers are believed to generate large-scale shock waves that are ideal sites for electron acceleration. We compute radio emission light curves for galaxy group and cluster mergers simulated in a cosmological context to study the dependence of radio luminosity on cluster mass, redshift, and impact parameter. We used model galaxy clusters from The Three Hundred project to identify cluster mergers characterised by the two main merging structures and follow their evolution throughout the simulated cosmic history. We found that the median non-thermal radio relic luminosity light curve produced in galaxy cluster mergers can be described by a skewed Gaussian function abruptly rising after core-passage of the secondary cluster that peaks after $\sim0.1-0.8\,$Gyr as a function of $M_{200,1}$, the mass of the primary, displaying a mass-dependent luminosity output increase of $\lesssim10$ to about $\gtrsim10-50$ times relative to the radio emission measured at core-passage for galaxy groups and clusters, respectively. In general, most merger orbits are fairly radial with a median opening angle of $\sim20^{\circ}$ before the collision. We also found that, independent of the cluster mass, less radial mergers tend to last longer, although the trend is weak. Finally, we found that the peak radio luminosity shows a significant correlation with mass, $P_{1.4}\propto M_{200,1}^{2.05}$, demonstrating that this relation holds all the way up from galaxy group scales to the most massive galaxy clusters. We conclude that cluster mass is the primary driver for radio `gischt' median luminosity, although there are significant variations for a given cluster mass. Our simulations suggest that the shock-driven, non-thermal radio emission observed on cluster outskirts are the result of massive galaxy cluster mergers at $z\lesssim1$, peaking at $z\sim0-0.5$.