Simulating cosmic ray electron spectra and radio emission from an active galactic nucleus jet outburst in a cool-core cluster

Active galactic nucleus (AGN) powered jets can accelerate cosmic ray electrons, leading to the observed radio synchrotron emission. To simulate this emission, jet dynamics in galaxy clusters must be coupled to electron spectral modelling. We ran magneto-hydrodynamic (MHD) simulations of a single AGN jet outburst in a Perseus-like galaxy cluster and adopted a sub-grid model for the acceleration of cosmic ray protons and electrons at unresolved internal shocks in the jet. We evolved cosmic ray electron spectra along Lagrangian trajectories using the Fokker-Planck solver C REST and computed the non-thermal emission using C RAYON +. The resulting total electron spectrum reaches a steady-state slope at high momenta, with a gradually decreasing normalisation over time, while the lower-momentum portion continues to resemble a freely cooling spectrum. The interaction of the jets with the turbulent cluster environment inflates lobes which rise buoyantly, induce amplification of the magnetic fields, and uplift old cosmic ray populations in the wake of the bubbles. We connected radio spectral indices to electron injection ages: at a given radio frequency, weaker magnetic fields are illuminated by higher momenta electrons, whose age is determined by the last injection event. On the other hand, stronger magnetic fields are illuminated by lower momenta electrons, whose age is determined by the maximum energy injection event in the past. This powerful cosmic ray electron modelling approach allows us to relate the underlying MHD properties to electron spectra and the resulting radio synchrotron emission, thereby enabling us to infer the underlying physics from synthetic radio observations in future studies.