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Current-day cosmic ray (CR) propagation studies use static Milky-Way modelsand fit parametrized source distributions to data. Instead, we usethree-dimensional magneto-hydrodynamical (MHD) simulations of isolated galaxieswith the moving-mesh code AREPO that self-consistently accounts forhydrodynamic effects of CR protons. In post-processing, we calculate theirsteady-state spectra, taking into account all relevant loss processes. We showthat this steady-state assumption is well justified in the disc and generallyfor regions that emit non-thermal radio and gamma rays. Additionally, we modelthe spectra of primary electrons, accelerated by supernova remnants, andsecondary electrons and positrons produced in hadronic CR proton interactionswith the gas. We find that proton spectra above 10 GeV only weakly depend ongalactic radius, while they acquire a radial dependence at lower energies dueto Coulomb interactions. Radiative losses steepen the spectra of primary CRelectrons in the central galactic regions while diffusive losses dominate inthe outskirts. Secondary electrons exhibit a steeper spectrum than primariesbecause they originate from the transported steeper CR proton spectra.Consistent with Voyager-1 and AMS-02 data, our models (i) show a turn-over ofproton spectra below GeV energies due to Coulomb interactions so that electronsstart to dominate the total particle spectra and (ii) match the shape of thepositron fraction up to 10 GeV. We conclude that our steady-state CR modelingin MHD-CR galaxy simulations is sufficiently realistic to capture the dominanttransport effects shaping their spectra, arguing for a full MHD treatment toaccurately model CR transport in the future.

Cosmic rays and non-thermal emission in simulated galaxies. I. Electron and proton spectra compared to Voyager-1 data