Cosmic-ray diffusion and the multi-phase interstellar medium in a dwarf galaxy. I. Large-scale properties and $\gamma$-ray luminosities

Dynamically, cosmic rays with energies above about one GeV/nucleon may be important agents of galaxy evolution. Their pressures compare with the thermal and magnetic ones impacting galactic gas accretion, fountains and galactic outflows, and alter the mass cycling between the gas phases, its efficiency depends on the properties of CR transport in the different media. We aim to study the dynamical role of CRs in shaping the interstellar medium of a galaxy when changing their propagation mode. We perform MHD simulations with the AMR code RAMSES of the evolution of the same isolated galaxy (dwarf galaxy of $10^{11}$ M$_{\odot}$ down to 9-pc resolution) and compare the impact of the simplest cosmic-ray transport assumption of uniform diffusion. We have also updated the observational relation seen between the $\gamma$-ray luminosities and SFR of galaxies using the latest detection of Fermi LAT sources. We find that the radial and vertical distributions, and mass fractions of the gas in the different phases are marginally altered when changing CR transport. We observe positive feedback of CR on the amplification of the magnetic field in the inner half of the galaxy, except for fast isotropic diffusion. The increase in CR pressure for slow or anisotropic diffusion can suppress star formation by up to 50\%, but the dual effect of cosmic-ray pressure and magnetic amplification can reduce star formation by a factor 2.5. The $\gamma$-ray luminosities and SFR of the simulated galaxies are fully consistent with the trend seen in the observations in the case of anisotropic $10^{27.5-29}$ cm$^2$ s$^{-1}$ diffusion and for isotropic diffusion slower or equal to $3 \times 10^{28}$cm$^2$ s$^{-1}$. These results, therefore, do not confirm claims of very fast $10^{29-31}$ cm$^2$ s$^{-1}$ diffusion to match the Fermi LAT observations.