Steady-State or Not? The Evolution of Cosmic Ray Electron Spectra in Galaxies

Abstract

Cosmic ray (CR) electrons are key tracers of non-thermal processes in galaxies, yet their spectra are often modelled under the untested assumption of steady state between injection and cooling. In this work, we present a time-dependent modelling of CR electron spectra in a galactic context using the CREST code, applied to magnetohydrodynamical simulations of an isolated Milky Way-mass galaxy performed with AREPO. CR electrons are injected at supernova sites and evolved with adiabatic changes and cooling processes on Lagrangian tracer particles, including losses from synchrotron, inverse Compton, bremsstrahlung, and Coulomb interactions. We compare these fully time-dependent spectra to local and global steady-state models computed with CRAYON+, as well as to one-zone analytic steady-state solutions. We find that the global CR electron spectrum in the simulated galactic disk closely resembles a steady-state solution up to energies of 500 GeV, with deviations only at higher energies where cooling times become shorter than injection timescales. High-energy electrons are dominated by recently injected populations that have not yet reached equilibrium, however, producing a steeper spectrum and lower normalisation than a steady-state model predicts. Spatially, the electrons modelled on-the-fly with CREST are more confined to the star-forming disk, in contrast to the more extended distributions from steady-state post-processing models. Our results demonstrate that while steady-state assumptions capture the bulk CR electron population in star-forming disks, a time-dependent treatment is essential to describe the high-energy and outflowing components.