High frequency JVLA observations of the radio mini-halo in the galaxy cluster RBS 797

In this Thesis, we studied the radio mini-halo hosted in the galaxy cluster RBS797. The cluster is known to host a powerful central Active Galactic Nucleus (AGN), X-ray cavities, and multiple shock fronts produced by the AGN feedback. The analysis presented in this work is based on multi-frequency radio observations, combining archival LOFAR data at 144 MHz and JVLA observations at 1.4 GHz, with new high-frequency JVLA data at 5.5 GHz. The central AGN emission was subtracted in the uv-plane in order to isolate the diffuse emission of the mini-halo. The goal of this work is to investigate the spectral properties of the mini-halo and to constrain the possible mechanisms responsible for the acceleration of relativistic electrons. In particular, the analysis focuses on the possible role of shock fronts generated by AGN activity in re-accelerating particles in the cluster core. The compact central sources were successfully subtracted, and combining new observations with archival data the integrated spectrum was computed, resulting in a single power law with no significant curvature. The spatially resolved spectral analysis revealed contrasting radial trends: at low frequencies the spectrum flattens with radius, while at higher frequencies it steepens toward the outskirts. This behaviour is not related to residual AGN emission and suggests the presence of an additional electron population. The surface-brightness profile is well reproduced by a two-component model consisting of a central AGN and an exponential mini-halo. Radiative age estimates of the electrons are comparable to the ages of nearby shocks, indicating that while the AGN likely did not originate the mini-halo, it may influence its spectral properties. The combination of spectral flattening at low frequencies and steepening at high frequencies appears unique to RBS 797 and suggests a complex interplay between AGN-driven shocks and turbulent re-acceleration in the cluster core.