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Local H~{\sc i} emissivity measured with the {\it Fermi}-LAT and implications for cosmic-ray spectra

Cosmic-ray (CR) electrons and nuclei interact with the Galactic interstellar gas and produce high-energy $γ$ rays. The $γ$-ray emission rate per hydrogen atom, called emissivity, provides a unique indirect probe of the CR flux. We present the measurement and the interpretation of the emissivity in the solar neighborhood for $γ$-ray energy from 50~MeV to 50~GeV. We analyzed a subset of 4 years of observations from the Large Area Telescope (LAT) aboard the {\it Fermi Gamma-ray Space Telescope} ({\it Fermi}) restricted to absolute latitudes $10^o<|b| <70^o$. From a fit to the LAT data including atomic, molecular and ionized hydrogen column density templates as well as a dust optical depth map we derived the emissivities, the molecular hydrogen to CO conversion factor $X_{CO}=(0.902\pm0.007) \times 10^{20}$ cm$^{-2}$ (K km s$^{-1}$)$^{-1}$ and the dust-to-gas ratio $X_{DUST}=(41.4\pm0.3) \times 10^{20}$ cm$^{-2}$ mag$^{-1}$. Moreover we detected for the first time $γ$-ray emission from ionized hydrogen. We compared the extracted emissivities to those calculated from $γ$-ray production cross-sections and to CR spectra measured in the heliosphere. We observed that the experimental emissivities are reproduced only if the solar modulation is accounted for. This provides a direct detection of solar modulation observed previously through the anticorrelation between CR fluxes and solar activity. Finally we fitted a parametrized spectral form to the heliospheric CR observations as well as to the {\it Fermi}-LAT emissivity and obtained compatible local interstellar spectra for proton and Helium kinetic energy per nucleon between between 1 and 100~GeV and for electron-positrons between 0.1 and 100~GeV.