Radial distribution of the diffuse<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>γ</mml:mi></mml:mrow></mml:math>-ray emissivity in the Galactic disk

The Fermi-LAT data accumulated over 7 years of $\ensuremath{\gamma}$-ray observations, together with the high resolution gas (CO HI) and the dust opacity maps, are used to study the emissivity of $\ensuremath{\gamma}$-rays induced by interactions of cosmic rays (CRs) with the interstellar medium. Based on the dust opacity templates, the $\ensuremath{\gamma}$-ray emissivity was measured for 36 segments of the Galactic plane. Furthermore, the $\ensuremath{\gamma}$-ray emissivity was evaluated in six Galactocentric rings. Both the absolute emissivity and the energy spectra of $\ensuremath{\gamma}$-rays derived in the interval 0.2--100 GeV show significant variations along the galactic plane. The density of CRs, derived under the assumption that $\ensuremath{\gamma}$-rays are predominately produced in CR interactions with the interstellar gas, is characterized by a strong radial dependence. In the inner Galaxy the CR density substantially exceeds the density in the outer parts of the Galaxy: by a factor of a few at 10 GeV, and by more than an order of magnitude at 1 TeV. Remarkably, the energy distribution of CRs appears to be substantially harder than the energy spectrum obtained from direct measurements of local CRs. At the same time, the flux and the energy spectrum of multi-GeV protons derived from $\ensuremath{\gamma}$-ray data in the outskirts of the Galaxy is quite close to the measurements of local CRs.