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Diffuse gamma-ray and neutrino emission from the Milky Way and the local knee in the cosmic ray spectrum

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Gamma-ray data reveal a local PeV cosmic-ray bubble around the Solar System.

desk verdict The universal-CR-spectrum excess above 100 TeV is robust and worth citing; the inferred bubble radii are illustrative, not measured. read the letter →

arxiv 2507.10823 v1 pith:V6GKQCVO submitted 2025-07-14 astro-ph.HE

C.Prevotat , Zh.Zhu , S.Koldobskiy , A.Neronov , D.Semikoz , M.Ahlers This is my paper
classification astro-ph.HE
keywords cosmic-raykneediffusegamma-rayemissionPeVbubbleLHAASOgalacticcosmicraysneutrinofromtheMilkyWayPeterscycles
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to show that the cosmic-ray spectrum measured locally with LHAASO, if assumed to be the same everywhere in the Milky Way, predicts more diffuse gamma-ray emission from the Galactic plane above 30 to 100 TeV than LHAASO actually observes. It argues that the cleanest explanation is that the highest-energy part of the local cosmic-ray spectrum is not universal: the Solar System sits inside a recent 'PeV bubble' of freshly injected cosmic rays, about 1.5 kpc in extent toward the inner Galaxy and 0.7 kpc toward the outer Galaxy. If this is right, the cosmic-ray knee is not a permanent, Galaxy-wide feature but a transient local event, and the spatial pattern of very-high-energy gamma-ray emission becomes a map of recent cosmic-ray injections.

What carries the argument

The central object is the local cosmic-ray spectrum decomposed into three 'Peters cycles', rigidity-scaled source populations whose spectral shape is identical for all nuclear groups, with the third, highest-energy cycle accounting for the knee region seen by LHAASO. The argument works by computing diffuse gamma-ray and neutrino yields from these spectra through pion-production calculations and gamma-ray absorption corrections, comparing the results with Fermi-LAT and LHAASO diffuse measurements, and then re-fitting the third cycle as emission from a finite spherical bubble around the Solar System. The bubble radius is the parameter that reconciles the model with the observed deficit.

What would settle it

Measure the >100 TeV diffuse gamma-ray flux in a grid of longitude bins along the inner Galactic plane and compare it with the gas-column-weighted universal-cosmic-ray prediction. If any distant, gas-rich direction shows the full universal-prediction flux, the Solar System cannot be inside a small local bubble; if the flux drops below the prediction everywhere above about 100 TeV, the local-bubble interpretation is supported.

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Extended reading notes

Core claim

The paper establishes that the pion-decay component of diffuse gamma-ray emission computed from a cosmic-ray spectrum fitted to LHAASO's precise knee-region measurements exceeds the measured LHAASO diffuse flux in the inner Galaxy above about 30 TeV and in the outer Galaxy above about 100 TeV. Removing the highest-energy rigidity component of the fitted cosmic-ray spectrum from the emission calculation removes the excess, which the authors interpret as evidence that these particles occupy a limited volume around the Solar System rather than the whole Galactic disk. Attributing that highest-energy component to a local PeV cosmic-ray bubble and fitting its size to the LHAASO data gives an extension of 1.5 ± 0.3 kpc toward the inner Galaxy and 0.7 ± 0.3 kpc toward the outer Galaxy.

Load-bearing premise

The whole excess calculation leans on a model of how much hydrogen gas lies along each line of sight, and the uncertainties in that gas model are not propagated; if the gas is overestimated, the predicted glow is too bright and the inferred bubble could be an artifact.

Editorial extensions

If this is right

  • If the local-bubble scenario is right, the cosmic-ray knee is not the same feature everywhere in the Galaxy; other regions have their own knee features set by recent local injections.
  • LHAASO's deeper exposure should reveal strong variation of the >100 TeV diffuse gamma-ray flux from one line of sight to another, tracking where fresh PeV cosmic rays currently reside.
  • Because gamma-rays and neutrinos share the same pion-production parentage, the same excess should appear as a suppression of the predicted high-energy neutrino flux from the same sky regions, testable with future neutrino telescopes.
  • The fitted bubble sizes of 1.5 kpc inward and 0.7 kpc outward locate the Solar System asymmetrically inside this recent injection, pointing roughly toward the inner Galaxy and giving a target for identifying the source.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extension: the same decomposition could be applied to a longitude-resolved map of 100 TeV to 1 PeV gamma-ray emission, turning each high-energy spectral component that appears locally but not globally into a tracer of a recent cosmic-ray injection event.
  • Extension: the local-bubble interpretation predicts a small arrival-direction anisotropy in local cosmic rays at and above the knee, roughly aligned with the inferred bubble direction, which current and future observatories could search for.
  • Extension: the inner-Galaxy radius of 1.5 ± 0.3 kpc may be better interpreted as a lower bound if the injected particles have not had time to fill the whole bubble; combining the radius with a diffusion model could yield an age estimate for the recent injection event.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper constructs two independent models of the Galactic cosmic-ray (CR) spectrum up to the knee (a three-Peters-cycle fit, Model A, and a DRAGON-2 diffusion-break fit, Model B), both calibrated to AMS-02, DAMPE, CALET, LHAASO, IceTop and Auger data. Assuming the local CR spectrum is universal throughout the Milky Way, the authors compute diffuse gamma-ray and neutrino emission from the inner (15°<l<125°) and outer (125°<l<235°) Galactic plane, normalizing the gamma-ray prediction to Fermi-LAT at 10 GeV with a 0.85 pion-decay fraction. Comparing to LHAASO diffuse gamma-ray data, they find the predicted pion-decay flux exceeds the measured diffuse flux above ~30 TeV (inner) and ~100 TeV (outer). They interpret this excess as evidence for a "local PeV CR bubble" and fit its radius, obtaining 1.5±0.3 kpc toward the inner Galaxy and 0.7±0.3 kpc toward the outer Galaxy; they also compare neutrino predictions to rescaled IceCube template fluxes.

Significance. If the claimed discrepancy is real, it challenges the standard assumption of a universal CR spectrum in the Galaxy and suggests that the knee is produced by a local, recent CR injection. The use of two independent CR models (Peters cycles and DRAGON-2) to predict the diffuse emission is a strength, and the consistency of the two predictions supports the robustness of the spectral-shape mismatch. The predicted gamma-ray and neutrino fluxes are falsifiable and the comparison to IceCube is a useful cross-check. However, the inference of bubble radii is not on the same footing as the discrepancy itself: it relies on a one-zone toy model with no spatial test.

major comments (3)
  1. [Section V, Fig. 3] The bubble-radii claim (R = 1.5 ± 0.3 kpc inner, 0.7 ± 0.3 kpc outer) is based only on the region-averaged spectra of the inner and outer Galaxy. The model predicts a characteristic longitude profile of >100 TeV emission that is localized around the Sun, but the paper does not compare this prediction with LHAASO's spatial data. A position-dependent CR spectrum (e.g., a radial gradient of the knee energy or of the escape rate) could produce the same two region-averaged spectra with different "bubble" sizes. Without a longitude-profile test, the quoted radii are not uniquely determined; they should be presented as illustrative, not as measured extensions.
  2. [Section V] The uncertainties on the bubble radii (0.3 kpc) are not derived from a statistical fit or from propagation of the input uncertainties (CR fit parameters, gas models, 10 GeV normalization, gamma-ray absorption). The text states only that the bubble radius was "adjusted" until the model "fits" the LHAASO data. Please specify the fitting procedure, the chi-square or likelihood used, and how the 0.3 kpc uncertainty was obtained; alternatively, state explicitly that these are systematic ranges from varying model assumptions.
  3. [Sections III and IV] The decomposition of the local CR spectrum into a steady-state component (Peters cycles 1 and 2) and a local knee component (Peters cycle 3) is an assumption of the toy model, not a result. The same LHAASO proton spectrum that defines the third cycle is then used as the spectrum inside the bubble, and the bubble radius is fit to the gamma-ray data. This leaves a degeneracy between the amplitude of the local component and its spatial extent. A minimal test would be to fix the bubble spectrum from an independent CR propagation model (e.g., a recent source injection) and fit only the geometry, or to include an alternative spatially varying CR model and compare fits.
minor comments (6)
  1. [Section III, Fig. 3 caption] The caption reads "155◦ < l <125◦", which appears to be a typo; it should be "15◦ < l <125◦" consistent with the text in Section III.
  2. [Section V] There is a typo "tot he" in the sentence "the CRs with the spectrum corresponding tot he 3rd Peters cycle"; it should be "to the".
  3. [Section III] The word "intergrals" in "line-of-sight intergrals" should be "integrals".
  4. [Section III] The 0.85 pion-decay fraction at 10 GeV and its quoted 10% uncertainty are not propagated to the predicted fluxes above 100 TeV; please add a systematic band or state explicitly that the excess is insensitive to this normalization.
  5. [Appendix A] The 10% upward shift of Auger energies is described, but its effect on the fitted CR spectra (and hence on the predicted gamma-ray flux) is not quantified; a short discussion would help.
  6. [Figures 3 and 4] The figure captions and legends are dense; consider adding a clear legend directly in the figure distinguishing the diffuse (masked) LHAASO data, total flux, Model A1/A2/A3, Model B, and IceCube templates.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gamma-ray excess is a genuine model prediction checked against independent LHAASO data, and the bubble radii are admitted fits, not predictions.

full rationale

The derivation chain is non-circular. In Section II, Models A and B are fitted only to direct cosmic-ray measurements (AMS-02, DAMPE, CALET, LHAASO proton/all-particle spectra, IceTop, and Auger). In Section III, these fitted spectra are used to compute pion-decay gamma-ray and neutrino yields with the external AAfrag code and external gas models; the predicted gamma-ray spectra are then normalized at 10 GeV using Fermi-LAT diffuse modeling. Only in Section IV are the resulting predictions compared with LHAASO and Fermi-LAT gamma-ray data and IceCube neutrino estimates. No LHAASO gamma-ray measurement enters the CR fits or the yield calculation, so the reported excess above 30/100 TeV is a spectral-shape prediction rather than a restatement of an input. The local PeV bubble radii are not predictions: the paper states, 'We have adjusted the bubble radius in such a way that the sum of the steady-state diffuse emission ... fits LHAASO data,' making the radii explicitly fitted to the data they describe. The main self-citation, Ref. [32], is used for methodology ('Following the approach of Ref. [32]') and to note that the excess 'has already been noticed in Ref. [32]'; this is corroborative and non-load-bearing, since the present work independently repeats the derivation with new LHAASO proton data and Fermi-LAT/LHAASO gamma-ray data. Hence no circular step is exhibited; the central comparison is self-contained against external benchmarks, and the score is 0.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

The central predictions depend on numerous fitted CR spectral parameters, gas distribution models, and the assumed universal CR spectrum. The most consequential free parameters for the final inference are the two bubble radii, which are fit to the LHAASO gamma-ray data. The local bubble itself is an invented entity introduced to explain the excess, with no independent observational handle.

free parameters (5)
  • Bubble radius, inner Galaxy = 1.5 +/- 0.3 kpc
    Adjusted so the sum of steady-state and bubble emission fits LHAASO diffuse gamma-ray flux in Section V; not independently predicted.
  • Bubble radius, outer Galaxy = 0.7 +/- 0.3 kpc
    Adjusted so the Model A prediction matches LHAASO data in the outer Galaxy region in Section V.
  • Model A third Peters cycle parameters (R30, R31, alpha3, alpha4, delta, N3 per element) = R30=4.15e5 GV, R31=7.78e7 GV, alpha3=0.12, alpha4=3.79, delta=0.78; N3 values in Table I
    Fitted to LHAASO all-particle spectrum, mean logarithmic mass, and proton spectrum in the knee region (Section II.A).
  • Model B upper diffusion break parameters (R45, R56, delta4, delta5, delta6, s45, s56) = R45=1e5 GV, R56=4e6 GV, delta4=0.453, delta5=0.15, delta6=1.5, s45=0.022, s56=0.31
    Adopted to fit LHAASO proton data in Appendix B, Table III.
  • Auger energy scale shift = +10% on energy
    Applied in Appendix A to align Auger data with LHAASO and IceTop; a hand-chosen calibration adjustment.
assumptions (5)
  • domain assumption The cosmic-ray spectrum measured locally is representative of the entire Milky Way (universal spectrum assumption) in the baseline models.
    Stated in the abstract and Section II; this is the core assumption being tested by comparing predicted and observed diffuse emission.
  • domain assumption The atomic (HI) and molecular (H2) gas distributions from Ref. [47] accurately trace the target gas for pion production.
    Used in Section III to compute line-of-sight integrals; uncertainties in gas column density directly scale the predicted gamma-ray flux.
  • domain assumption The pion-decay component constitutes 0.85 of the total Fermi-LAT diffuse flux at 10 GeV for |b| < 10 deg, and this fraction is a lower bound for |b| < 5 deg.
    Invoked in Section III to normalize the predicted pion-decay flux; the paper assigns only a 10% uncertainty to this normalization.
  • domain assumption The gamma-ray absorption model for CMB, starlight, and infrared radiation fields from Refs. [52,53] is correct.
    Used in Section III and Appendix C to compute the survival probability of photons above 30 TeV.
  • ad hoc to paper The third Peters cycle in Model A represents a local, spatially limited PeV CR bubble that is not present elsewhere in the Galaxy.
    Introduced in Section V to reconcile the model excess with LHAASO data; it is an interpretation rather than a derivation from independent evidence.
invented entities (1)
  • Local PeV CR bubble
    purpose: To explain the excess of predicted over observed diffuse gamma-ray flux above 100 TeV and to account for the local knee in the cosmic-ray spectrum.
    The bubble is inferred from the same LHAASO gamma-ray data used to fit its radius. The paper notes consistency with observed variations of the 100 TeV flux along the Galactic plane, but this is not a unique falsifiable prediction independent of the fit.

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Cite this review

Pith. "Pith review of Diffuse gamma-ray and neutrino emission from the Milky Way and the local knee in the cosmic ray spectrum." pith.science (2026). https://pith.science/paper/V6GKQCVO

@misc{pith2026250710823,
  author       = {Pith},
  title        = {Pith review of: Diffuse gamma-ray and neutrino emission from the Milky Way and the local knee in the cosmic ray spectrum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6GKQCVO}},
  note         = {Machine review of arXiv:2507.10823}
}
read the original abstract

The LHAASO observatory has recently measured details of the cosmic-ray (CR) spectrum in the knee region (1 -- 10 PeV) with unprecedented precision, including its average CR mass composition and the spectrum of the proton component. We use these precision measurements, combined with direct measurements of CRs by space-based detectors, to derive predictions for the spectrum of diffuse gamma-ray and neutrino emission from the interstellar medium under the assumption that the CR spectrum is universal throughout the Milky Way. We compare these predictions with the Fermi-LAT and LHAASO measurements of the diffuse gamma-ray flux from inner and outer Galactic Plane regions and with estimates of the neutrino flux based on the IceCube data for the same Galactic Plane regions. We notice that the model predictions exceed LHAASO gamma-ray measurements at energies above 100 TeV. This excess can be interpreted within a CR knee model assuming a "local PeV CR bubble''. Within this model, we infer the extension of the local PeV CR bubble of 1.5 +/- 0.3 kpc in the direction of the inner Galaxy and of 0.7+/-0.3 kpc toward the outer Galaxy.

Figures

Figures reproduced from arXiv: 2507.10823 by the authors.

Figure 1
Figure 1. FIG. 1: Cosmic ray spectra obtained for p, He, CNO and heavy elemental groups with Model A, composed of three [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Result of the fit for the all-particles spectrum, and mean logarithmic mass of the CR spectrum with model [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: All flavor neutrino flux for Inner and Outer Galaxy regions as measured by LHAASO (without the source [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Absorption of the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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Forward citations

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