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Hard spectrum of cosmic rays in the Disks of Milky Way and Large Magellanic Cloud

The slope of the locally measured spectrum of cosmic rays varies from 2.8 for protons with energies below 200 GeV down to 2.5 for heavy nuclei with energies in the TeV-PeV range. It is not clear if the locally measured slope values are representative for those of the overall population of Galactic cosmic rays and if the slope of the cosmic ray spectrum varies across the Galaxy. We use the data of Fermi Space gamma-ray Telescope to derive a measurement of the slope of the cosmic ray spectrum across the Galactic Disk and to compare it with that of the Large Magellanic Cloud cosmic rays. A special choice of the background estimation regions allows us to single out the neutral pion decay component of the gamma-ray flux in the energy range above 10 GeV and to separate it from (a) emission from the local interstellar medium around the Solar system and (b) from the inverse Compton emission produced by cosmic ray electrons. Results. The spectrum of the pion decay gamma-ray emission from the Galactic disk in the energy band 10 GeV - 1 TeV has the slope 2.4. There is no evidence for the variation of the slope with Galactic longitude / distance from the Galactic Centre. The slope of the spectrum of cosmic rays derived from the gamma-ray data, 2.45, is harder than the slope of the locally observed cosmic ray proton spectrum. Pion decay emission from a powerlaw distribution of cosmic rays with the same hard slope also provides a fit to the gamma-ray spectrum of the Large Magellanic Cloud. Identical and hard slopes of the spectra of cosmic rays in the Milky Way and in the Large Magellanic Cloud are consistent with a straightforward theoretical model in which cosmic rays are injected by shock acceleration with the spectrum with the slope 2...2.1 which is subsequently modified by 1/3...1/2 by the energy-dependent escape of cosmic rays through the turbulent Galactic magnetic field.