A semi-analytical model for the formation and evolution of radio relics in galaxy clusters

Radio relics are Mpc-sized synchrotron sources located in the peripheral regions of galaxy clusters. Models based on diffuse shock acceleration (DSA) scenario have been widely accepted to explain formation radio relics. However, a critical challenge these models is that most observed shocks seem too weak generate detectable emission, unless fossil electrons, population mildly energetic electrons accelerated previously, included models. To address this issue, we present new semi-analytical model describe and evolution by incorporating relativistic into DSA theory, which constrained sample 14 relics, employ Press-Schechter formalism simulate $20^{\circ} \times 20^{\circ}$ sky field at 50, 158, 1400 MHz, respectively. Results show contribute significantly can radiation four orders magnitude brighter than solely produced thermal 158 power distribution our simulated relic catalog reconcile $P_{1400}-M_{\mathrm{vir}}$ relation. We predict $7.1\%$ clusters with $M_{\mathrm{vir}} > 1.2\times 10^{14}\,\mathrm{M}_{\odot}$ would host consistent result $10 \pm 6\%$ given LoTSS DR2. It also found expected cause severe foreground contamination future EoR experiments, similar halos. The possibility AGN providing seed evaluated calculating number radio-loud AGNs encounter during its propagation.