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REVIEW 3 major objections 5 minor 52 references

The paper claims that the local cosmic-ray normalization is set by the random recent history of nearby sources, and this normalization uncertainty propagates into hadronic diffuse gamma-ray predictions, rising from roughly 30% at 100 GeV to

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Temporal stochasticity of cosmic-ray sources causes a normalization uncertainty in the local proton flux that propagates into a hadronic gamma-ray uncertainty of 30-100%, comparable to or exceeding experimental errors at very high energies.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection Hadronic normalization stochasticity is a real and underappreciated source of diffuse gamma-ray uncertainty, but the headline 30–100% band rests on hand-picked parameters and a 99% quantile rather than a standard error. the 3 major comments →

arxiv 2509.07481 v1 pith:LFARUWZM submitted 2025-09-09 astro-ph.HE hep-ph

Uncertainty in Hadronic Diffuse γ-Ray Emission from the Temporal Stochasticity of Cosmic-Ray Sources

Xing-Jian Lv , Xiao-Jun Bi , Kun Fang , Han-Xiang Hu , Peng-Fei Yin , Meng-Jie Zhao This is my paper
classification astro-ph.HE hep-ph
keywords hadronic diffuse gamma-ray emissioncosmic-ray source stochasticitytime-dependent cosmic-ray propagationlocal source historyvery high energy gamma raysGalactic cosmic rayssource normalization uncertaintytemporal variability
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper argues that diffuse gamma-ray models have overlooked a large theoretical uncertainty: the normalization of the Galactic cosmic-ray flux is measured at one place and time, so it inherits the random local history of nearby accelerators. That normalization feeds directly into the hadronic gamma-ray prediction, so the uncertainty survives line-of-sight averaging. Using time-dependent three-dimensional propagation simulations with discrete sources, the authors find the hadronic contribution is uncertain by about 30% near 100 GeV, growing to about 100% near 1 PeV in both the inner and outer Galactic plane. If right, very-high-energy diffuse gamma-ray data cannot be interpreted against a sharp steady-state hadronic model without folding in this stochastic normalization band.

Core claim

The paper claims that variability in the high-energy hadron flux, not just lepton flux, is a significant source of uncertainty in diffuse gamma-ray estimates. The dominant mechanism is normalization: the cosmic-ray flux observed at Earth today sets the overall CR normalization, and that value is highly sensitive to the local source history over the past few million years. A recent nearby source pushes the inferred normalization above the Galactic average; the absence of such sources pushes it below. This normalization variance propagates directly into the predicted hadronic gamma-ray intensity, yielding a theoretical uncertainty that grows from roughly 30% at 100 GeV to roughly 100% at 1 PeV

What carries the argument

The central mechanism is a fully three-dimensional, time-dependent simulation of cosmic-ray proton propagation in which sources appear at random positions at a chosen birth rate, stay active for a fixed lifetime, and inject a common broken power-law spectrum. The distinguishing step is separating two sources of variance: the small variance in the number of sources along a given line of sight (which largely averages out) and the larger variance in the overall normalization of the local CR flux, which is calibrated at one place and time. The latter is mapped into a gamma-ray uncertainty band by pinning the steady-state benchmark flux to the 99% quantile of the time-dependent local distribution

Load-bearing premise

The quantitative result rests on assuming a Galactic source birth rate of one per 500 years and a 10,000-year active lifetime, which yields only about 20 active sources; a larger true rate or longer active lifetime would shrink the fluctuations and could push the uncertainty below current experimental errors.

What would settle it

Locate and count the Galactic supernova remnants or OB associations now actively accelerating nuclei above 100 TeV and measure their active acceleration timescales; if the implied number of active sources is much larger than about 20, the predicted 30-100% uncertainty band collapses. Alternatively, measure the diffuse gamma-ray flux with a next-generation very-high-energy telescope across many independent sky windows: if the observed scatter about the steady-state model is clearly smaller than the theoretical band, the normalization-stochasticity effect is overestimated.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Diffuse gamma-ray fits in the 100 GeV to 1 PeV range need to include a hadronic normalization uncertainty of tens to roughly 100 percent, not just lepton variability.
  • Very-high-energy data from LHAASO and Fermi-LAT cannot be used to rule out hadronic models unless this stochastic normalization band is folded into the model predictions.
  • The locally measured cosmic-ray spectrum at Earth is not necessarily the Galactic average, and the size of the bias grows with energy.
  • Multiple source populations with energy-dependent rates and lifetimes, or spatially varying diffusion, would tend to widen the uncertainty rather than shrink it.
  • If the true source birth rate is lower than assumed, as in proposed 'local knee' scenarios, the uncertainty in the hadronic gamma-ray flux becomes even larger.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same normalization-stochasticity argument should apply to diffuse neutrino emission from hadronic collisions, so predictions of the Galactic diffuse neutrino flux carry a comparable model uncertainty.
  • Because the effect grows with energy, local source history could masquerade as a spectral hardening or knee in the diffuse gamma-ray sky; separating it from genuine propagation physics requires comparing many independent sky directions.
  • A testable cross-check: measure the scatter of the diffuse gamma-ray flux across many independent sky windows above 10 TeV; a scatter much smaller than the predicted ~30-100% band would argue for a larger active-source population than assumed here.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper argues that temporal stochasticity of Galactic cosmic-ray (CR) proton sources produces a previously neglected theoretical uncertainty in hadronic diffuse gamma-ray emission, through the normalization of the locally measured CR flux. Using fully three-dimensional, time-dependent GALPROP simulations with discrete sources (R = 1/500 yr^-1, tau = 10^4 yr), it finds that the local proton flux fluctuates with an amplitude that grows with energy. Defining 'upper edge' and 'lower edge' scenarios at the 99% quantiles of the local-flux distribution and mapping them to gamma-ray intensities, it obtains a 30-100% uncertainty in both the inner and outer Galactic plane from 100 GeV to 1 PeV, which is claimed to be comparable to or larger than current Fermi-LAT and LHAASO uncertainties. The line-of-sight source-number variability is found to be much smaller, so the normalization effect is the dominant new contribution.

Significance. If correct, the paper would establish an important and previously underappreciated systematic in hadronic diffuse gamma-ray modeling: the local CR normalization inferred from measurements at the Solar System carries a stochastic offset that does not average out in line-of-sight integrations. The qualitative mechanism is physically well motivated and the use of full 3D time-dependent GALPROP is a clear strength. However, the quantitative headline is conditional on two non-standard choices—the use of a 99% central interval and a hand-picked, low source rate—both of which are acknowledged in the text as uncertain. The paper is therefore significant as a proof-of-concept and a cautionary result, but the specific 30-100% numbers are not yet presented in a form that supports direct comparison with 1-sigma experimental uncertainties.

major comments (3)
  1. [§III B, Fig. 4] The cyan band labeled 'Modeling Uncertainty' is a 99% central interval of the time-dependent local CR flux (Sec. III A, Figs. 2-3), while the Fermi-LAT and LHAASO error bars overlaid in Fig. 4 are conventional 1σ experimental uncertainties. The paper's central claim—'comparable to, or even exceed, current experimental uncertainties'—is therefore a comparison of a very wide quantile-based range with 1σ error bars. Because the distributions in Fig. 2 are strongly non-Gaussian with long tails, a 68% interval would be substantially narrower. The sentence in Sec. III A rejecting the 95% quantile as underestimating 'realistic fluctuations' does not resolve this: a statement about tail risk is not a definition of a standard uncertainty. The manuscript should either quote a 68% band, or explicitly compare like with like (e.g., a 99% experimental confidence band), and re-evaluate whether the head
  2. [§II, Time Dependent Calculations; §III B] The amplitude of the predicted uncertainty is set almost entirely by n = R*tau. The adopted R = 1/500 yr^-1 is the lowest of the rates cited in Sec. II (26Al: 1/35-125 yr^-1; OB stars: 1/200-250 yr^-1), and tau = 10^4 yr is an order of magnitude longer than the 10^2-10^3 yr acceleration durations quoted for the multi-TeV to PeV range. The paper itself states that 'a lower creation rate or shorter active time would increase the uncertainty, while higher values would reduce it.' Thus the 30-100% numbers are not a central estimate but an example from the high-fluctuation side of the plausible parameter space. The authors label the choice 'conservative' for the highest energies, but they do not quantify how much of the 30-100% band is due to this choice. A sensitivity scan over (R, tau), or over n, is needed to establish whether the headline claim holds for the rate ranges cited in Section I
  3. [§III A-B, Fig. 3] The construction of the 'Upper Edge'/'Lower Edge' gamma-ray band is under-specified. The text says the benchmark steady-state flux 'is required to lie within the 99% quantile of the time-dependent distribution,' and later that these scenarios 'directly map' onto the gamma-ray range. It is not stated which time steps are selected, how the local-flux quantile is translated into a global CR-density renormalization, or whether the benchmark is fit in each case. The Fig. 3 caption is also internally inconsistent: the colors/terms 'Upper Edge' and 'Lower Edge' appear to be crossed with 'enhanced'/'suppressed' relative to the Galactic average. Because the numerical size of the cyan band depends exactly on this mapping, the procedure needs to be defined precisely enough to reproduce.
minor comments (5)
  1. [Fig. 3 caption] The assignment of green/orange to 'Upper Edge'/'Lower Edge' and to 'enhanced'/'suppressed' is confusing as written; please clarify which color corresponds to which edge and to which physical scenario.
  2. [Fig. 4] Typo: 'Modeling Uncertaintiy' should be 'Modeling Uncertainty'.
  3. [References] References [37] and [41] are incomplete (missing journal/year/volume for Mertsch and for the LHAASO arXiv listing); please complete them.
  4. [Sec. IV] The summary repeats the adopted parameters 'one every 500 yr and active time of 10^4 yr' without the caveat that these are uncertain and that higher rates would reduce the quoted uncertainty; adding one sentence would prevent over-interpretation.
  5. [Sec. III B, Fig. 4] The orange band showing the factor-2.0 scaling for heavier nuclei is clearly labeled illustrative, but consider moving it to an appendix or separating it more visually from the main cyan uncertainty band so it cannot be mistaken for part of the central model prediction.

Circularity Check

0 steps flagged

No circularity: the gamma-ray uncertainty band is a forward-model output from assumed source parameters, not a fit to the target data.

full rationale

The paper's central claim—that temporal stochasticity of CR sources produces a hadronic diffuse gamma-ray uncertainty comparable to experimental errors at VHE—is obtained by a forward simulation chain. The transport equation (Eq. 1) is solved with GALPROP using the SA100 setup whose propagation parameters were calibrated against CR data (AMS-02, ACE/CRIS, Voyager 1), not against the gamma-ray data. The source rate R=1/500 yr^-1 and lifetime tau=10^4 yr are stated assumptions, explicitly described as poorly constrained and as a 'conservative choice'; they are not fit to the gamma-ray uncertainty that is the paper's target. The gamma-ray band in Fig. 4 is built by mapping the 99% quantiles of the simulated local CR flux distribution onto the gamma-ray intensity, with the steady-state benchmark anchored to CR measurements. The paper explicitly states that the Fermi-LAT and LHAASO data 'are not employed to calibrate or constrain the model.' Thus the prediction is not statistically forced by the target data. The self-citations (Refs. [46] and [51]) support ancillary discussion of multi-source classes and slow diffusion, but are not load-bearing for the main derivation. The use of 99% quantiles rather than 1-sigma intervals is a statistical presentation choice and a potential overstatement, but it is not circularity. No step reduces to its own input by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central result is driven by two hand-chosen parameters (R and tau) and a non-standard quantile definition. No new physical entities are introduced. The propagation model and source distribution are pulled from prior literature (SA100, GALPROP v57 docs). The linear mapping from local flux variation to global normalization is an assumed calibration procedure, not derived from first principles.

free parameters (4)
  • Source creation rate R = 1/500 yr^-1
    Chosen by hand, representing the low end of published SN/CR source rate estimates (26Al: 1/35-125 yr, OB stars: 1/200-250 yr, electron spectrum: 1/500 yr, all cited in Sec. II). Smaller R increases fluctuations; the paper calls this conservative for maximizing the claimed uncertainty.
  • Source active lifetime tau = 10^4 yr
    Chosen as the upper end of CR injection durations for sub-TeV particles, per Sec. II. Combined with R, it gives n=R*tau=20 active sources in the Milky Way, which the paper identifies as the key driver of fluctuation amplitude.
  • Quantile threshold for uncertainty band = 99%
    The paper defines the hadronic uncertainty using the 99% central quantile of the local flux distribution, instead of a standard 68% or 95% interval. Sec. III A justifies this by non-Gaussian tails, but it widens the band and directly contributes to the claim that uncertainties exceed experimental errors.
  • Heavier nuclei scaling factor = 2.0
    Applied to illustrate the potential contribution of heavier nuclei to the flux magnitude, described in Sec. III B as 'intended solely for illustration and not rigorous.' It does not affect the cyan uncertainty band, which is proton-only.
axioms (5)
  • standard math The transport equation (Eq. 1) with diffusion, convection, reacceleration, energy losses, and fragmentation correctly describes CR propagation.
    Invoked in Sec. II as the governing equation; standard in the field and implemented in GALPROP.
  • domain assumption The local CR flux is used to normalize the global source term, so a fluctuation in local flux translates linearly to a fluctuation in the inferred source normalization and hence in the hadronic gamma-ray emission.
    Central to the paper's logic in Sec. III B; the paper assumes this linear mapping without deriving it from the simulation, saying only that the scenarios 'directly map onto the range of gamma-ray intensities.'
  • domain assumption A single source population with a common injection spectrum contributes at all energies.
    Stated in Sec. II ('all sources share the same spectrum') and acknowledged in Sec. III B as a simplification; multiple source classes would enhance the uncertainty at high energies.
  • domain assumption Only protons are needed to capture the hadronic gamma-ray uncertainty; heavier nuclei contribute a constant multiplicative factor.
    Sec. II: 'only protons are injected in the simulations... uncertainties in the emission from heavier nuclei are expected to be comparable.' Sec. III B scales by 2.0 only for illustration.
  • ad hoc to paper The benchmark steady-state flux is required to lie within the 99% quantile of the time-dependent distribution, which defines the upper/lower edge scenarios.
    Sec. III A: 'in each case this benchmark... is required to lie within the 99% quantile of the time-dependent distribution.' This constraint is introduced to connect the steady-state model to the fluctuating simulation.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Uncertainty in Hadronic Diffuse $\gamma$-Ray Emission from the Temporal Stochasticity of Cosmic-Ray Sources." pith.science (2026). https://pith.science/paper/LFARUWZM

@misc{pith2026250907481,
  author       = {Pith},
  title        = {Pith review of: Uncertainty in Hadronic Diffuse $\gamma$-Ray Emission from the Temporal Stochasticity of Cosmic-Ray Sources},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LFARUWZM}},
  note         = {Machine review of arXiv:2509.07481}
}
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read the original abstract

Diffuse $\gamma$-ray emission is a key probe of cosmic rays (CRs) distribution within the Galaxy. However, the discrepancies between observations and theoretical model expectations highlight the need for refined uncertainty estimates. In the literature, spatial and temporal variability of lepton flux has been discussed as an uncertainty in diffuse $\gamma$-ray estimation. In the present work, we demonstrate that variability in the high energy CR hadron flux is an important, yet previously underappreciated, source of uncertainty in diffuse $\gamma$-ray estimates. To assess this effect, we perform fully three-dimensional, time-dependent GALPROP simulations of CR protons injected from discrete Galactic sources. Our results reveal that the uncertainty in the hadronic component of diffuse $\gamma$ rays is non-negligible and can be comparable to, or even exceed, current experimental uncertainties at very high energies. This finding challenges the conventional assumption that only leptonic fluctuations are relevant to diffuse $\gamma$-ray modeling.

Figures

Figures reproduced from arXiv: 2509.07481 by Han-Xiang Hu, Kun Fang, Meng-Jie Zhao, Peng-fei Yin, Xiao-Jun Bi, Xing-Jian Lv.

Figure 1
Figure 1. Figure 1: FIG. 1: Left: Temporal evolution of the CR proton flux at the solar location for selected energies (100 GeV, 1 TeV, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The impact of local source history on the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Steady-state CR proton spectrum (solid black [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: is calculated assuming a source creation rate of one every 500 yr and an active time of 104 yr per source. A lower creation rate or shorter active time would in￾crease the uncertainty, while higher values would reduce it. Our calculation further assumes that a single source population contributes to the Galactic CR flux. However, recent studies suggest that multiple classes of CR sources may exist, each do… view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

52 extracted references · 20 canonical work pages · 13 internal anchors

  1. [1]

    Gamma rays as probes of cosmic-ray propagation and interactions in galaxies

    L. Tibaldo, D. Gaggero, and P. Martin, Universe7, 141 (2021), arXiv:2103.16423 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  2. [2]

    Becker Tjus and L

    J. Becker Tjus and L. Merten, Phys. Rept.872, 1 (2020), arXiv:2002.00964 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  3. [3]

    Ackermannet al.(Fermi-LAT), Astrophys

    M. Ackermannet al.(Fermi-LAT), Astrophys. J.750, 3 (2012), arXiv:1202.4039 [astro-ph.HE]

    Pith/arXiv arXiv 2012

  4. [4]

    Abramowskiet al.(H.E.S.S.), Phys

    A. Abramowskiet al.(H.E.S.S.), Phys. Rev. D90, 122007 (2014), arXiv:1411.7568 [astro-ph.HE]

    Pith/arXiv arXiv 2014

  5. [5]

    Bartoliet al.(ARGO-YBJ), Astrophys

    B. Bartoliet al.(ARGO-YBJ), Astrophys. J.806, 20 (2015), arXiv:1507.06758 [astro-ph.IM]

    Pith/arXiv arXiv 2015

  6. [6]

    Caoet al.(LHAASO), Phys

    Z. Caoet al.(LHAASO), Phys. Rev. Lett.134, 081002 (2025), arXiv:2411.16021 [astro-ph.HE]

    arXiv 2025

  7. [7]

    Zhang, X

    R. Zhang, X. Huang, Z.-H. Xu, S. Zhao, and Q. Yuan, Astrophys. J.957, 43 (2023), arXiv:2305.06948 [astro- ph.HE]

    Pith/arXiv arXiv 2023

  8. [8]

    T. A. Porter, G. J´ ohannesson, and I. V. Moskalenko, The Astrophysical Journal887, 250 (2019), arXiv:1909.02223 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  9. [9]

    P. D. Marinos, T. A. Porter, G. P. Rowell, G. J´ ohannesson, and I. V. Moskalenko, Astrophys. J. 981, 93 (2025), arXiv:2411.03553 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  10. [10]

    P. D. Marinos,High-Energy Cosmic-Ray Propaga- tion in the Milky Way and the Associated Diffuse Gamma-Ray Emission, Ph.D. thesis, Adelaide U. (2023), arXiv:2504.18796 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  11. [11]

    I. V. Moskalenko and A. W. Strong, Astrophys. J.493, 694 (1998), arXiv:astro-ph/9710124

    Pith/arXiv arXiv 1998

  12. [12]

    A. W. Strong and I. V. Moskalenko, Astrophys. J.509, 212 (1998), arXiv:astro-ph/9807150

    Pith/arXiv arXiv 1998

  13. [13]

    A. W. Strong, I. V. Moskalenko, and V. S. Ptuskin, An- nual Review of Nuclear and Particle Science57, 285 (2007), arxiv:astro-ph/0701517

    Pith/arXiv arXiv 2007

  14. [14]

    E. S. Seo and V. S. Ptuskin, The Astrophysical Journal 431, 705 (1994)

    work page 1994

  15. [15]

    V. S. Berezinskii, S. V. Bulanov, V. A. Dogiel, and V. S. Ptuskin,Astrophysics of Cosmic Rays(1990)

    work page 1990

  16. [16]

    T. A. Porter, G. Johannesson, and I. V. Moskalenko, Astrophys. J. Supp.262, 30 (2022), arXiv:2112.12745 [astro-ph.HE]

    Pith/arXiv arXiv 2022

  17. [17]

    T. P. Robitaille, E. Churchwell, R. A. Benjamin, B. A. Whitney, K. Wood, B. L. Babler, and M. R. Meade, Astron. Astrophys.545, A39 (2012), arXiv:1208.4606 [astro-ph.GA]

    Pith/arXiv arXiv 2012

  18. [18]

    M. S. Pshirkov, P. G. Tinyakov, P. P. Kronberg, and K. J. Newton-McGee, Astrophys. J.738, 192 (2011), arXiv:1103.0814 [astro-ph.GA]

    Pith/arXiv arXiv 2011

  19. [19]

    J´ ohannesson, T

    G. J´ ohannesson, T. A. Porter, and I. V. Moskalenko, Astrophys. J.856, 45 (2018), arXiv:1802.08646 [astro- ph.HE]

    Pith/arXiv arXiv 2018

  20. [20]

    Johannesson, T

    G. Johannesson, T. A. Porter, and I. V. Moskalenko, Astrophys. J.879, 91 (2019), arXiv:1903.05509 [astro- ph.HE]

    Pith/arXiv arXiv 2019

  21. [21]

    L. J. Gleeson and W. I. Axford, Astrophys. J. Lett.149, L115 (1967)

    work page 1967

  22. [22]

    L. J. Gleeson and W. I. Axford, The Astrophysical Jour- nal154, 1011 (1968)

    work page 1968

  23. [23]

    Potgieter, Living Rev

    M. Potgieter, Living Rev. Solar Phys.10, 3 (2013), arXiv:1306.4421 [physics.space-ph]

    Pith/arXiv arXiv 2013

  24. [24]

    Kachelrieß, I

    M. Kachelrieß, I. V. Moskalenko, and S. Ostapchenko, Comput. Phys. Commun.245, 106846 (2019), arXiv:1904.05129 [hep-ph]

    Pith/arXiv arXiv 2019

  25. [25]

    Kachelriess, S

    M. Kachelriess, S. Ostapchenko, and J. Tjems- land, Comput. Phys. Commun.287, 108698 (2023), arXiv:2206.00998 [hep-ph]

    Pith/arXiv arXiv 2023

  26. [26]

    K. M. G´ orski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelman, Astro- phys. J.622, 759 (2005), arXiv:astro-ph/0409513

    Pith/arXiv arXiv 2005

  27. [27]

    T. A. Porter, G. Johannesson, and I. V. Moskalenko, Astrophys. J.846, 67 (2017), arXiv:1708.00816 [astro- ph.HE]

    Pith/arXiv arXiv 2017

  28. [28]

    A. Bell, K. Schure, B. Reville, and G. Giacinti, Mon. Not. Roy. Astron. Soc.431, 415 (2013), arXiv:1301.7264 [astro-ph.HE]

    Pith/arXiv arXiv 2013

  29. [29]

    Gaggero, F

    D. Gaggero, F. Zandanel, P. Cristofari, and S. Gabici, Mon. Not. Roy. Astron. Soc.475, 5237 (2018), arXiv:1710.05038 [astro-ph.HE]

    Pith/arXiv arXiv 2018

  30. [30]

    Cristofari, Universe7, 324 (2021), arXiv:2110.07956 [astro-ph.HE]

    P. Cristofari, Universe7, 324 (2021), arXiv:2110.07956 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  31. [31]

    Time-Dependent Escape of Cosmic Rays from Supernova Remnants, and their Interaction with Dense Media

    I. Telezhinsky, V. V. Dwarkadas, and M. Pohl, Astron. Astrophys.541, A153 (2012), arXiv:1112.3194 [astro- ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  32. [32]

    K. M. Schure and A. R. Bell, Mon. Not. Roy. Astron. Soc.435, 1174 (2013), arXiv:1307.6575 [astro-ph.HE]

    Pith/arXiv arXiv 2013

  33. [33]

    C. D. Dermer and G. Powale, Astron. Astrophys.553, A34 (2013), arXiv:1210.8071 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  34. [34]

    Cosmic-ray acceleration and escape from post-adiabatic Supernova remnants

    R. Brose, M. Pohl, I. Sushch, O. Petruk, and T. Kuzyo, Astron. Astrophys.634, A59 (2020), arXiv:1909.08484 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  35. [35]

    Diehl, H

    R. Diehl, H. Halloin, K. Kretschmer,et al., Nature (Lon- don)439, 45 (2006), arXiv:astro-ph/0601015 [astro-ph]

    Pith/arXiv arXiv 2006

  36. [36]

    A. L. Quintana, N. J. Wright, and J. M. Garc ´ ıa, Monthly Notices of the Royal Astronomical Society538, 1367 (2025), https://academic.oup.com/mnras/article- pdf/538/3/1367/62429096/staf083.pdf

    work page 2025

  37. [37]

    Mertsch, JCAP11, 045, arXiv:1809.05104 [astro- ph.HE]

    P. Mertsch, JCAP11, 045, arXiv:1809.05104 [astro- ph.HE]

    Pith/arXiv arXiv

  38. [38]

    Aguilaret al.(AMS), Physics Reports The Al- pha Magnetic Spectrometer (AMS) on the International Space Station: Part II - Results from the First Seven Years,894, 1 (2021)

    M. Aguilaret al.(AMS), Physics Reports The Al- pha Magnetic Spectrometer (AMS) on the International Space Station: Part II - Results from the First Seven Years,894, 1 (2021)

    work page 2021

  39. [39]

    Anet al.(DAMPE), Sci

    Q. Anet al.(DAMPE), Sci. Adv.5, eaax3793 (2019), arXiv:1909.12860 [astro-ph.HE]

    Pith/arXiv arXiv 2019

  40. [40]

    Varsiet al.(GRAPES-3), Phys

    F. Varsiet al.(GRAPES-3), Phys. Rev. Lett.132, 051002 (2024)

    work page 2024

  41. [41]

    Caoet al.(LHAASO), arXiv eprint (2025), arXiv:2505.14447 [astro-ph.HE]

    Z. Caoet al.(LHAASO), arXiv eprint (2025), arXiv:2505.14447 [astro-ph.HE]

    arXiv 2025

  42. [42]

    Mori, Astropart

    M. Mori, Astropart. Phys.31, 341 (2009), arXiv:0903.3260 [astro-ph.HE]

    Pith/arXiv arXiv 2009

  43. [43]

    Probing the galactic cosmic-ray density with current and future $\gamma$-ray instruments

    G. Peron and F. Aharonian, Astron. Astrophys.659, A57 (2022), arXiv:2110.08778 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  44. [44]

    J. R. Hoerandel, Astropart. Phys.19, 193 (2003), arXiv:astro-ph/0210453

    Pith/arXiv arXiv 2003

  45. [45]

    T. K. Gaisser, T. Stanev, and S. Tilav, Front. Phys. (Bei- jing)8, 748 (2013), arXiv:1303.3565 [astro-ph.HE]

    Pith/arXiv arXiv 2013

  46. [46]

    Precise measurement of the cosmic-ray spectrum and $\left \langle \ln A \right \rangle$ by LHAASO -- connecting the Galactic to the extragalactic components

    X.-J. Lv, X.-J. Bi, K. Fang, Y.-Q. Guo, H.-H. He, L.-L. Ma, P.-F. Yin, Q. Yuan, and M.-J. Zhao, Astrophys. J. 979, 225 (2025), arXiv:2403.11832 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  47. [47]

    Energy dependence of the knee in the cosmic ray spectrum across the Milky Way

    C. Prevotat, M. Kachelriess, S. Koldobskiy, A. Neronov, and D. Semikoz, Phys. Rev. D110, 103035 (2024), arXiv:2407.11911 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  48. [48]

    Prevotat, Z

    C. Prevotat, Z. Zhu, S. Koldobskiy, A. Neronov, D. Semikoz, and M. Ahlers, arXiv eprint (2025), 7 arXiv:2507.10823 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  49. [49]

    Tomassetti, Astrophys

    N. Tomassetti, Astrophys. J. Lett.752, L13 (2012), arXiv:1204.4492 [astro-ph.HE]

    Pith/arXiv arXiv 2012

  50. [50]

    Understanding the spectral hardenings and radial distribution of Galactic cosmic rays and Fermi diffuse gamma-rays with spatially-dependent propagation

    Y.-Q. Guo and Q. Yuan, Phys. Rev. D97, 063008 (2018), arXiv:1801.05904 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  51. [51]

    M.-J. Zhao, K. Fang, and X.-J. Bi, Phys. Rev. D104, 123001 (2021), arXiv:2109.04112 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  52. [52]

    A common origin of multi-messenger spectral anomaly of galactic cosmic rays

    Y.-H. Yao, X.-L. Dong, Y.-Q. Guo, and Q. Yuan, Phys. Rev. D109, 063001 (2024), arXiv:2308.15866 [astro- ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.