2019MNRAS.486.2496R

Quantitative modelling of the spectrospatial distributions of energetic electrons and protons in galactic haloes is needed in order to determine their interactions with the local plasma and radiation fields, and also to estimate their residual spectral densities in intracluster and intergalactic environments. We develop a semi-analytic approach for calculating the particle distributions in the halo based on a detailed diffusion model for particle propagation from acceleration sites and interactions in the galactic disc. Important overall normalization of our models is based on results from detailed modelling in the Galactic disc with the GALPROP code. This provides the essential input for determining particle distributions in the outer disc, which are used as source terms for calculating the distributions in the extensive halo for a range of values of key parameters affecting energy losses and propagation mode. Our modelling approach is applied to the two edge-on star-forming galaxies NGC 4631 and NGC 4666, for which recent mapping of radio emission in the inner halo provides the required overall normalization. We predict the levels and spatial profiles of radio, X-ray, and γ-ray emission in the haloes of these galaxies. Our quantitative modelling enables us to estimate the total calorimetric efficiencies of electrons and protons in star-forming galaxies, and to predict their residual spectral distributions in the outer halo and intergalactic space.