Cosmic rays interacting with interstellar gas produce a diffuse flux of Galactic neutrinos and gamma rays. Carceller and Masip (JCAP 2017) showed that the prediction of this flux is dominated by two poorly known inputs: the cosmic-ray primary spectrum and mass composition above the knee (the steepening of the all-particle spectrum at a few PeV), which leaves the predicted Galactic neutrino flux at PeV energies uncertain by more than an order of magnitude (a factor of about 100 between a pure-proton and an iron-dominated composition at 5 PeV), and the low-energy cosmic-ray spectrum outside the heliosphere, which gives roughly 30% uncertainty in the gamma-ray flux near 1 GeV. Their calculation also neglected leptonic gamma-ray production and discrete local sources, and adopted a simplified correlation between cosmic-ray density and magnetic field strength that was never calibrated against detailed propagation codes. The problem is to determine the cosmic-ray spectrum and composition above the knee, together with the interstellar low-energy spectrum — the two dominant uncertainties identified by the source — well enough that the diffuse Galactic neutrino and gamma-ray fluxes are predicted with controlled, testable uncertainty. Substantial progress has since been made — LHAASO has measured the all-particle spectrum and mean logarithmic mass from 0.3 to 30 PeV and the proton spectrum up to 12 PeV, Tibet ASgamma and LHAASO have detected the diffuse gamma-ray flux up to about 1 PeV, and IceCube has observed Galactic-plane neutrino emission at 4.5 sigma — but the composition above the knee remains known only as a hadronic-model-dependent mean mass, not element by element, and the PeV Galactic neutrino flux prediction and detection remain open.

Background

Cosmic rays (CRs) are atomic nuclei, mostly protons and helium, accelerated in sources such as supernova remnants and confined by Galactic magnetic fields. Their all-particle spectrum steepens at around 3-5 PeV (about 106.5 GeV10^{6.5}\,\mathrm{GeV}), a feature called the knee, and returns to a harder index at the ankle near 109.5 GeV10^{9.5}\,\mathrm{GeV}. Direct satellite measurements reach only to a few hundred TeV per nucleus, so above the knee the composition must be inferred indirectly from air-shower observables such as the muon content and the shower-maximum depth, which are interpreted through hadronic interaction models like EPOS-LHC, SIBYLL and GHEISHA — event generators whose extrapolations differ enough to blur the inferred mass.

While traversing the interstellar (IS) gas, CRs undergo proton-proton and nucleus-gas collisions that produce neutral and charged pions; the neutral pions decay into diffuse gamma rays and the charged pions into neutrinos. This makes the diffuse Galactic gamma-ray and neutrino fluxes a direct probe of the CR density distribution in the Galaxy. Carceller and Masip (JCAP 03 (2017) 013) computed these fluxes using neutrino and photon yields from EPOS-LHC, SIBYLL and GHEISHA simulations of p, He and Fe collisions, assuming a CR density in the disk and halo correlated with the mean magnetic field strength (a generalization of the leaky-box model, the classic approximation in which CRs reside in a uniform box and escape with an energy-dependent residence time; dedicated numerical propagation codes such as GALPROP solve the transport equation on realistic gas and magnetic-field maps). Their central findings frame the open problem: at PeV energies the predicted fluxes depend very strongly on the assumed CR composition beyond the knee — the Galactic neutrino flux at 5 PeV is about 6 times larger if protons rather than helium dominate beyond the knee, and a factor of 0.06 (about 17 times) smaller if iron dominates, an overall proton-to-iron suppression of 1/100 — an uncertainty exceeding an order of magnitude and larger than the uncertainty in the atmospheric neutrino background. At 1-5 GeV, instead, the dominant uncertainty (about 30%, relevant to the gamma-ray excess from the Galactic center observed by the Fermi-LAT space telescope) is the CR spectrum outside the heliosphere: the solar wind carves a magnetic cavity that modulates the low-energy CR flux measured at Earth, and the underlying local interstellar spectrum (LIS) must be reconstructed, e.g. by combining Voyager data taken beyond the heliopause with AMS-02 measurements at Earth. The calculation excluded leptonic gamma rays (produced when CR electrons upscatter radiation fields via inverse Compton scattering, rather than by hadronic pion production) and the contribution of discrete nearby CR sources, and its CR-density–magnetic-field correlation was motivated physically — it agrees with complete GALPROP simulations only at the level of about 25% — and was never calibrated quantitatively against such full propagation codes.

Problem Statement

Following Carceller and Masip (JCAP 03 (2017) 013, arXiv:1610.02552), whose conclusions identify the dominant unknown inputs of the diffuse Galactic neutrino and gamma-ray calculation, the problem is to determine these inputs so that the fluxes are predicted with controlled uncertainty, at the level where they can be tested against observations from IceCube (the South Pole neutrino observatory), the LHAASO and Tibet ASgamma air-shower gamma-ray observatories, and the Fermi-LAT space telescope. Concretely: (1) measure the primary cosmic-ray spectrum and, critically, the mass composition above the knee (the band 106.7 GeV≲E≲109.5 GeV10^{6.7}\,\mathrm{GeV} \lesssim E \lesssim 10^{9.5}\,\mathrm{GeV} between knee and ankle), where the present unknown composition makes the predicted Galactic neutrino flux at PeV energies uncertain by more than an order of magnitude (approximately a factor of 100 between proton- and iron-dominated assumptions at 5 PeV, an uncertainty larger than that of the atmospheric neutrino background); and (2) determine the low-energy cosmic-ray spectrum outside the heliosphere (the local interstellar spectrum) well enough to reduce the approximately 30% uncertainty it induces in the diffuse gamma-ray flux near 1 GeV. These two items are the dominant uncertainties named by the source, and they serve one common objective — bringing the predicted diffuse Galactic neutrino and gamma-ray fluxes from GeV to PeV energies under quantified, testable uncertainty, small enough that the predictions can be meaningfully compared with, or constrained by, observations. Beyond them, the source's own calculation excluded leptonic gamma-ray production and discrete local sources and assumed a correlation between cosmic-ray density and magnetic field strength that agrees with complete GALPROP simulations only at the ~25% level. The binding constraint, and the part that remains fully open despite the LHAASO and IceCube progress recorded above, is the element-resolved cosmic-ray composition and spectrum above the knee.

References

  1. J. M. Carceller and M. Masip, "Diffuse flux of galactic neutrinos and gamma rays", JCAP 03 (2017) 013, DOI 10.1088/1475-7516/2017/03/013, arXiv:1610.02552, https://arxiv.org/abs/1610.02552
  2. Z. Cao et al. (LHAASO Collaboration), "Measurements of All-Particle Energy Spectrum and Mean Logarithmic Mass of Cosmic Rays from 0.3 to 30 PeV with LHAASO-KM2A", Phys. Rev. Lett. 132 (2024) 131002, DOI 10.1103/PhysRevLett.132.131002, arXiv:2403.10010, https://arxiv.org/abs/2403.10010
  3. Z. Cao et al. (LHAASO Collaboration), "Precise measurements of the cosmic ray proton energy spectrum in the "knee" region", Science Bulletin 70 (2025) 4173, DOI 10.1016/j.scib.2025.10.048, arXiv:2505.14447, https://arxiv.org/abs/2505.14447
  4. M. Amenomori et al. (Tibet ASgamma Collaboration), "First Detection of sub-PeV Diffuse Gamma Rays from the Galactic Disk: Evidence for Ubiquitous Galactic Cosmic Rays beyond PeV Energies", Phys. Rev. Lett. 126 (2021) 141101, DOI 10.1103/PhysRevLett.126.141101, arXiv:2104.05181, https://arxiv.org/abs/2104.05181
  5. Z. Cao et al. (LHAASO Collaboration), "Measurement of Ultra-High-Energy Diffuse Gamma-Ray Emission of the Galactic Plane from 10 TeV to 1 PeV with LHAASO-KM2A", Phys. Rev. Lett. 131 (2023) 151001, DOI 10.1103/PhysRevLett.131.151001, arXiv:2305.05372, https://arxiv.org/abs/2305.05372
  6. Z. Cao et al. (LHAASO Collaboration), "Measurement of Very-High-Energy Diffuse Gamma-Ray Emissions from the Galactic Plane with LHAASO-WCDA", Phys. Rev. Lett. 134 (2025) 081002, DOI 10.1103/PhysRevLett.134.081002, arXiv:2411.16021, https://arxiv.org/abs/2411.16021
  7. R. Abbasi et al. (IceCube Collaboration), "Observation of high-energy neutrinos from the Galactic plane", Science 380 (2023) adc9818, DOI 10.1126/science.adc9818, arXiv:2307.04427, https://arxiv.org/abs/2307.04427
  8. J. M. Carceller, J. I. Illana, M. Masip and D. Meloni, "Origin of the high energy neutrino flux at IceCube", Astrophys. J. 852 (2018) 59, DOI 10.3847/1538-4357/aa9d94, arXiv:1703.10786, https://arxiv.org/abs/1703.10786
  9. C. Bérat, C. Bleve, O. Deligny, F. Montanet, P. Savina and Z. Torrès, "Diffuse Flux of Ultra-high-energy Photons from Cosmic-Ray Interactions in the Disk of the Galaxy and Implications for the Search for Decaying Super-heavy Dark Matter", Astrophys. J. 929 (2022) 55, DOI 10.3847/1538-4357/ac5cbe, arXiv:2203.08751, https://arxiv.org/abs/2203.08751
  10. M. J. Boschini et al., "Inference of the Local Interstellar Spectra of Cosmic-Ray Nuclei Z <= 28 with the GalProp-HelMod Framework", Astrophys. J. Suppl. 250 (2020) 27, DOI 10.3847/1538-4365/aba901, arXiv:2006.01337, https://arxiv.org/abs/2006.01337