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

TL;DR

This work presents 3D MHD simulations of a single AGN jet outburst in a Perseus-like cool-core cluster, coupled to a sub-grid CR acceleration model and a Fokker-Planck treatment of CR electrons. By evolving CRes along Lagrangian trajectories with Crest and computing synchrotron emission with Crayon+, the authors reveal how high-momentum CRes reach a steady-state slope while lower-momentum CRes freely cool, and how jet-driven lobes amplify magnetic fields and uplift old CR populations. The study clarifies how radio spectral indices relate to electron injection ages through the ν_c/ν_sync relationships, showing that stronger fields probe younger, high-momentum electrons while weaker fields illuminate older, low-momentum populations. The results provide a framework to infer underlying MHD conditions from observed radio properties in cool-core clusters and set the stage for multi-jet, time-dependent studies of AGN feedback.

Abstract

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 run magneto-hydrodynamic (MHD) simulations of a single AGN jet outburst in a Perseus-like galaxy cluster and adopt a sub-grid model for the acceleration of cosmic ray protons and electrons at unresolved internal shocks in the jet. We evolve cosmic ray electron spectra along Lagrangian trajectories using the Fokker-Planck solver Crest and compute the non-thermal emission using Crayon+. The resulting total electron spectrum reaches a steady-state slope at high momenta, with a gradually decreasing normalization 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 connect 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 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 observed radio properties.

Figures (13)

• Figure 1: Projections of a single jet outburst in a Perseus-like cluster showing volume-weighted quantities from left to right: mass density, magnetic field, jet mass fraction, CRp energy density. All projections have a depth $\pm$ 60 kpc from the cluster centre. The low-density jet-inflated lobes drag up gas in their wake, amplifying the magnetic field. In contrast to the gas density, in which only the lobes are visible, the mixing of jet material and CRps with the ICM is visible in the central 100 kpc. A movie can be seen https://youtu.be/aMdoZijtoWU.
• Figure 2: Idealized non-thermal spectra for a single CRe population experiencing compression, dilution, and both simultaneously (in addition to Coulomb and synchrotron/inverse Compton cooling, which narrows the distribution at low and high momenta, respectively). The initial and final CRe distributions are shown as black dotted and dashed lines, respectively. In each case, the vector arrow is calculated based on the expected change in $f(p)$ and $p$ due to changes in the density $\rho_{\rm{gas}}$ and the jet tracer $X_{\rm{jet}}$. Left: adiabatic compression of the gas that raises the density by 1000, which leads to an increase in the normalization and a shift in momentum (Eq. \ref{['eq:adiabatic_change']}). Middle: dilution of the CRe population due to a decrease of $X_{\rm{jet}}$ by 1000, which causes a decrease in the normalization of the spectrum (Eq. \ref{['eq:dilution']}). Right: combination of compression and dilution. The density increases by a factor of 1000, and $X_{\rm{jet}}$ is chosen to decrease such that the normalization is left unchanged. In such a scenario, the CRe distribution still moves to the right due to compression.
• Figure 3: Idealized non-thermal spectra for a single CRe population showing different scenario throughout 100 Myr of evolution. All acceleration events correspond to a power-law CRe population with the same power-law index of $\alpha_{\mathrm{inj}} = 2.2$, shown in dashed lines. Left: freely cooling spectrum--a single acceleration event followed by cooling. The arrow shows the location of the transition momentum between the non-cooled and cooled parts of the spectrum, which shifts to lower momenta over time due to synchrotron losses. Middle: archetype steady-state spectrum characterized by acceleration with a constant source function and continuous cooling resulting in a steepening of the spectral index by one at high momenta. Right: acceleration with an exponentially decreasing source function and continuous cooling (fiducial model) results in a freely cooling spectrum except at high momenta where it exhibits a steady state slope (black dotted line) with decreasing normalization.
• Figure 4: Volume-weighted non-thermal electron spectra throughout 220 Myr of evolution of which the jet is active for the first 50 Myr. Left: adiabatic changes and mixing effects are switched off and the peak of the spectrum in the mid-momenta range changes relatively little after the jet injection, due to the long cooling times at these energies. Right: including adiabatic changes and mixing results in a similar normalization in comparison to the left panel, albeit with a shift of the peak in the first 100 Myr. This can be explained by compression and dilution counteracting each other. The upward and downward arrows show the spectral evolution during and after jet activity, respectively. The spectral index of the accelerated CRes is $\alpha_{\mathrm{inj}} = 2.2$. The sharp feature seen at $p = 10$ in the left panel is due to the limit for the minimum injection momentum $p_\mathrm{inj,min}$ of the power-law electron population. Although momenta $p < 10$ are hence initially thermal (shown by the greyed out region of the spectrum), they are quickly populated by Coulomb cooling. The steady-state slope (dotted black line) at high momenta is observed in both spectra.
• Figure 5: Top row: Time evolution of the jet, CRp and CRe energies. The latter is shown with two models: one with only adiabatic and mixing terms, and one with adiabatic and mixing effects, Coulomb and radiative losses. Bottom row: Time evolution of the energy fractions $\xi$ between jet, CRp and CRe energies. We recover the energy fractions in our simulation output that were chosen as parameters (see Eqs. \ref{['eq:fraction_jet_crp']} and \ref{['eq:fraction_crp_cre']}), confirming that our acceleration algorithms behave as expected, with minor deviations for the CRe energy due to discretization effects (see text and Appendix \ref{['sec:appendix_CRep_distributions']} for details).