The cosmic ray ionisation and $\gamma$-ray budgets of star-forming galaxies

Cosmic rays in star-forming galaxies are a dominant source of both diffuse $\gamma$-ray emission and ionisation in gas too deeply shielded for photons to penetrate. Though the cosmic rays responsible for $\gamma$-rays and ionisation are of different energies, they are produced by the same star formation-driven sources, and thus galaxies' star formation rates, $\gamma$-ray luminosities, and ionisation rates should all be linked. In this paper we use up-to-date cross-section data to determine this relationship, finding that cosmic rays in a galaxy of star formation rate $\dot{M}_*$ and gas depletion time $t_\mathrm{dep}$ produce a maximum primary ionisation rate $\zeta \approx 1\times 10^{-16} (t_\mathrm{dep}/\mbox{Gyr})^{-1}$ s$^{-1}$ and a maximum $\gamma$-ray luminosity $L_\gamma\approx 4\times 10^{39} (\dot{M}_*/\mathrm{M}_\odot\mbox{ yr}^{-1})$ erg s$^{-1}$ in the 0.1 - 100 GeV band. These budgets imply either that the ionisation rates measured in Milky Way molecular clouds include a significant contribution from local sources that elevate them above the Galactic mean, or that CR-driven ionisation in the Milky Way is enhanced by sources not linked directly to star formation. Our results also imply that ionisation rates in starburst systems are only moderately enhanced compared to those in the Milky Way. Finally, we point out that measurements of $\gamma$-ray luminosities can be used to place constraints on galactic ionisation budgets in starburst galaxies that are nearly free of systematic uncertainties on the details of cosmic ray acceleration.