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