2016ApJ...821...87E

We present a systematic study of non-thermal electron-proton plasma and its emission processes in starburst galaxies in order to explain the correlation between the luminosity in the radio band and the recently observed gamma luminosity. In doing so, a steady state description of the cosmic-ray (CR) electrons and protons within the spatially homogeneous starburst is considered where continuous momentum losses are included as well as catastrophic losses due to diffusion and advection. The primary source of the relativistic CRs, e.g., supernova remnants, provides a quasi-neutral plasma with a power-law spectrum in momentum where we account for rigidity-dependent differences between the electron and proton spectrum. We examine the resulting leptonic and hadronic radiation processes by synchrotron radiation, inverse Compton scattering, Bremsstrahlung, and hadronic pion production. Finally, the observations of NGC 253, M82, NGC 4945, and NGC 1068 in the radio and gamma-ray bands as well as the observed supernova rate are used to constrain a best-fit model. In the case of NGC 253, M82, and NGC 4945 our model is able to accurately describe the data, showing that: (i) supernovae are the dominant particle accelerators for NGC 253, M82, and NGC 4945, but not for NGC 1068; (ii) all considered starburst galaxies are poor proton calorimeters in which for NGC 253 the escape is predominantly driven by the galactic wind, whereas the diffusive escape dominates in NGC 4945 and M82 (at energies >1 TeV); and (iii) secondary electrons from hadronic pion production are important to model the radio flux, but the associated neutrino flux is below the current observation limit.