Imprints of cosmic rays in multifrequency observations of the interstellar emission

Ever since the discovery of cosmic rays (CRs), significant advancements have been made in modelling their propagation in the Galaxy and in the Heliosphere. However, propagation models suffer from degeneracy of many parameters. To complicate the picture, the precision of recent data have started challenging existing models. To tackle these issues, we use available multifrequency observations of the interstellar emission from radio to gamma rays, together with direct CR measurements, to study local interstellar spectra (LIS) and propagation models. As a result, the electron LIS is characterized without any assumption on solar modulation, and favourite propagation models are put forwards. More precisely, our analysis leads to the following main conclusions: (1) the electron injection spectrum needs at least a break below a few GeV; (2) even though consistent with direct CR measurements, propagation models producing a LIS with large all-electron density from a few hundreds of MeV to a few GeV are disfavoured by both radio and gamma-ray observations; (3) the usual assumption that direct CR measurements, after accounting for solar modulation, are representative of the proton LIS in our similar to 1 kpc region is challenged by the observed local gamma-ray HI emissivity. We provide the resulting proton LIS, all-electron LIS, and propagation parameters based on synchrotron, gamma-ray, and direct CR data. Aplain diffusion model and a tentative diffusive-reacceleration model are put forwards. The various models are investigated in the inner-Galaxy region in X-rays and gamma rays. Predictions of the interstellar emission for future gamma-ray instruments (e-ASTROGAM and AMEGO) are derived.