Galaxy-cluster-stacked Fermi-LAT III: substructure and radio-relic counterparts

Faint $\gamma$-ray signatures emerge in Fermi-LAT data stacked scaled to the characteristic $R_{500}$ radii of MCXC galaxy clusters. This third paper in a series shows a $4.3\sigma$ excess of discrete 4FGL-DR4 catalog $\gamma$-ray sources at the $r<1.5R_{500}$ radii of 205 clusters, coincident with an $r\sim R_{500}$ diffuse $2.6\sigma$ excess of 1-100 GeV emission from 75 high-latitude clusters. The source excess becomes highly ($>5\sigma$) significant when considering the substantial ($3.4\sigma$) and unexpectedly rapid quenching of $\gamma$-ray sources just inside the virial shock. The excess sources show radial, spectral, and luminosity distributions better matching radio-relic counterparts or substructure than present tentative classifications as blazar-candidates. Their spectral distribution is bimodal: flat-spectrum sources are consistent with enhanced hadronic emission behind weak, Mach $\sim2$ shocks, while softer sources may be phoenix counterparts.