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Cosmic-ray spatial distribution and diffuse gamma-ray and neutrino fluxes

Paolo Lipari1,2,3,* and Silvia Vernetto4,5,†

  • *Contact author: paolo.lipari@roma1.infn.it
  • †Contact author: vernetto@to.infn.it
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Phys. Rev. D 113, 103001 – Published 1 May, 2026

DOI: https://doi.org/10.1103/5kq1-gqhw

Abstract

Determining the spatial distribution of Galactic cosmic rays (CRs) is fundamental to understand how these particles propagate in interstellar space and to infer their source spectra. The most sensitive method of studying this problem is observing the gamma-ray and neutrino diffuse fluxes produced in the inelastic interactions of CR protons and nuclei with interstellar gas that encode the energy and spatial distributions of the interacting particles. Most theoretical models assume that the spatial and energy dependencies of the spectra of CR protons and nuclei are factorized, so that the CR energy spectra have the same shape at all points of the Milky Way. However, on the base of the Fermi-LAT observations, some authors have tentatively inferred that particles in the inner regions of the Milky Way have significantly harder spectra. Recently the ground-based telescopes Tibet-ASγ, LHAASO, and HAWC have extended the measurements of the diffuse gamma-ray flux to much higher energies, and the IceCube neutrino telescope has obtained evidence for a ν flux from the Galactic disk. These new measurements allow for new tests of the factorization hypothesis, and disfavor models in which the spectral shape of CR protons and nuclei is harder in the inner part of the Galaxy. In fact, the LHAASO data above 30 TeV are in better agreement with the opposite hypothesis, that cosmic rays is the inner Galaxy have softer spectra than those in the outer Galaxy. This result, that has currently only modest significance due to large statistical and systematic uncertainties, could be explained by assuming that the CR confinement volume increases with energy. An alternative explanation is that a significant fraction of cosmic rays in the multi-PeV energy range is of extragalactic origin.

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Phys. Rev. D 113, 103001– Published 1 May, 2026
  • Received 15 September 2025
  • Accepted 25 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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