Determining the Spectrum of Cosmic Rays in Interstellar Space from the Diffuse Galactic Gamma-Ray Emissivity

More than 90% of the Galactic gas-related gamma-ray emissivity above 1 GeV is attributed to the decay of neutral pions formed in collisions between cosmic rays and interstellar matter, with lepton-induced processes becoming increasingly important below 1 GeV. Given the high-quality measurements of the gamma-ray emissivity of local interstellar gas between ~50 MeV and ~4 GeV obtained with the Large Area Telescope on board the Fermi space observatory, it is timely to re-investigate this topic in detail, including the hadronic production mechanisms. The emissivity spectrum will allow the interstellar cosmic-ray spectrum to be determined reliably, providing a reference for origin and propagation studies as well as input to solar modulation models. A method for such an analysis and illustrative results are presented.