Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Deciphering the spectral bumps of Galactic cosmic rays through gamma-ray observations of nearby molecular clouds

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A single nearby cosmic-ray source can be confirmed or ruled out by the energy-dependent gamma-ray spectra of nearby molecular clouds: close clouds should harden early, distant clouds late, while a Galaxy-wide bump would make all clouds…

desk verdict A clean, genuinely predictive gamma-ray test of the nearby-source explanation of the TeV CR bump, with caveats about background uniformity and detectability that a good referee can push on. read the letter →

arxiv 2501.14267 v1 pith:PEXCPUWX submitted 2025-01-24 astro-ph.HE hep-ph

Xing-Jian Lv , Xiao-Jun Bi , Kun Fang , Peng-Fei Yin , Meng-Jie Zhao This is my paper · ORCID
classification astro-ph.HEhep-ph
keywords cosmic-rayspectralbumpnearbysourcegiantmolecularcloudsgamma-rayindexdipoleanisotropydiffusionLHAASOTeV
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

This paper argues that the observed "TeV bump" in cosmic-ray proton and helium spectra, together with the amplitude and phase evolution of the cosmic-ray dipole anisotropy, can be explained by a single nearby cosmic-ray source, and that nearby giant molecular clouds (GMCs) can serve as natural detectors for that source through their gamma-ray emission. The central claim is that the energy dependence of each cloud's gamma-ray spectral index depends on the cloud's distance from the source: the closest clouds, Perseus and Taurus, should show an early hardening with a minimum index below 100 GeV, while more distant clouds should not reach their minimum until above 1 TeV. If the bump is instead a Galaxy-wide phenomenon, all clouds should show the same index-versus-energy behavior. A sympathetic reader would care because this converts an indirect, local measurement into a spatially resolved prediction that LHAASO and upcoming gamma-ray observatories can test.

What carries the argument

The central object is the energy-dependent gamma-ray spectral index, $\Gamma(E_\gamma) = -d\log F_\gamma / d\log E_\gamma$, computed from the predicted gamma-ray flux of each cloud. The flux is built from the proton intensity at the cloud location, which is the sum of a universal background sea and the contribution of a point-like burst source propagated with the spherically symmetric diffusion solution, then convolved with the proton-proton gamma-ray production cross section. The index curve does the argument's work because it is independent of the cloud mass-to-distance factor $A$ that sets the absolute flux level, while still carrying the distance-to-source information through the diffusion suppression factor $\exp(-r_s^2/(4Dt))$: closer clouds feel the source's contribution at lower energies, and that shift is what should appear as an earlier minimum in the index.

What would settle it

Measure the gamma-ray spectral index as a function of energy for the ten selected clouds, especially Taurus and Orion A, with LHAASO or CTA. If Taurus and Orion A both reach their hardest index at nearly the same energy, or both only above 1 TeV, the predicted distance ordering fails; if all ten clouds show indistinguishable index-versus-energy curves, the nearby-source explanation for the TeV bump and dipole anisotropy is contradicted.

Watch

Extended reading notes

Core claim

In the paper's own framing, the discovery is a predicted observable signature. A burst-like nearby source with a cutoff near tens of TeV, fitted to the AMS-02, DAMPE, and GRAPES-3 proton and helium spectra and to the dipole anisotropy amplitude and phase, produces gamma-ray spectra from ten GMCs within 1 kpc whose spectral-index curves are ordered by the clouds' distances to the source. For a source distance around 250 pc, Perseus and Taurus receive enough flux from the source to develop a pronounced bump and an early hardening, reaching their hardest spectral index below 100 GeV, whereas clouds such as Orion A, Cepheus, and Mon R2, being farther from the source, keep their index minimum above 1 TeV. Because the absolute gamma-ray flux of each cloud depends on the uncertain factor $A = M/d^2$, the paper identifies the energy dependence of the spectral index, not the flux normalization, as the feature that carries the information about the nearby source. The same calculation shows that for a source at 100 pc only Taurus is strongly affected, while for 400 pc the pattern is similar to 250 pc, so which clouds deviate can also help determine the source distance.

Load-bearing premise

The load-bearing premise is that each giant molecular cloud is a passive target: cosmic rays penetrate freely, with no magnetic shielding or internal gradients, and the proton flux at a cloud is exactly the universal background plus the diffusion-delayed contribution of the single nearby source, with no other local sources interfering.

Editorial extensions

If this is right

  • LHAASO should detect a measurable difference between Taurus and Orion A: Taurus's gamma-ray spectrum should show a pronounced bump and an early hardening, while Orion A's spectrum should track the background until much higher energies.
  • CTA's energy resolution and full-sky coverage should allow the minimum-index energy to be measured for several clouds; a clean split between close clouds hardening below 100 GeV and distant clouds hardening above 1 TeV would support the nearby-source scenario.
  • If all selected clouds show the same index-versus-energy behavior, the TeV bump would be a Galaxy-wide feature and the nearby-source explanation of the local cosmic-ray data would be ruled out.
  • The pattern of which clouds deviate, with only Taurus affected for a 100 pc source and Perseus and Taurus affected for 250 or 400 pc, can break degeneracies in determining the source distance.
  • The predicted fluxes place many of the ten GMCs within reach of current and planned instruments, so the test can be carried out within realistic exposure times.

Reading between the lines

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

  • The same spectral-index technique could be applied to gamma rays from the diffuse interstellar medium around the source direction, giving a continuous two-dimensional map of the source's diffusion footprint instead of a handful of cloud samples.
  • If future observations find no distance ordering, the near-source hypothesis would not immediately die: magnetic shielding inside clouds or a non-uniform background cosmic-ray sea within 1 kpc could dilute the predicted signal, so cloud transport physics would need to be checked before concluding the source is absent.
  • The offset between close and distant clouds' minimum-index energies depends on the diffusion coefficient and source age, so precise measurements could yield an independent local measurement of the diffusion coefficient.
  • Applying the same framework to electrons and positrons from the same source would predict cloud-dependent gamma-ray or synchrotron emission that could be cross-checked with multi-wavelength observations.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes using gamma-ray observations of nearby giant molecular clouds (GMCs) as a spatial probe of a hypothesized nearby cosmic-ray (CR) source. The authors first fit a burst-like, point-source diffusion model to the local proton/helium spectra and dipole anisotropy data (Section II), obtaining best-fit parameters for fixed source distances rs = 100, 250, and 400 pc (Table I). They then calculate the CR flux at ten GMCs within ~1 kpc as the sum of a universal background sea and the source contribution (Section III, Eq. 5), and use a pion-decay model to predict each GMC's gamma-ray spectrum (Section IV). The central claim is that the energy dependence of the gamma-ray spectral index distinguishes GMCs close to the source (Perseus, Taurus), whose index minimum falls below 100 GeV, from distant GMCs, whose minimum lies above 1 TeV (Fig. 4); if the TeV bump is a widespread Galactic phenomenon, all GMCs should show a uniform index evolution. The authors argue this provides a direct, falsifiable test of the nearby-source scenario with LHAASO, CTA, SWGO, and future space detectors.

Significance. If the proposed test is robust, it would convert the indirect, local evidence for a nearby CR source into a spatially resolved and falsifiable prediction, a genuinely valuable step. The paper's specific new element is the use of the energy dependence of the gamma-ray spectral index, which is insensitive to the uncertain A-factor normalization of each GMC and therefore isolates the CR spectral shape at each cloud. The model reproduces the local CR and anisotropy data with chi2/dof = 259/270, and the qualitative separation between nearby and distant GMCs is clearly illustrated. The prediction is concrete and testable with forthcoming instruments. However, the test's validity rests on assumptions that are not fully quantified, in particular the uniformity of the background CR sea over the ~1 kpc volume and the treatment of extended-source sensitivities; these are the main weaknesses. The paper is clearly written and the derivation follows standard diffusion and gamma-ray production formalism, which makes the presented predictions easy to scrutinize and reproduce.

major comments (3)
  1. [Section III, Eq. (5) and Section IV, Fig. 4] The paper's central discriminator is the energy of the gamma-ray spectral-index minimum for different GMCs (below 100 GeV for Perseus/Taurus, above 1 TeV for the others). This mapping assumes that the background CR sea is identical at all GMC locations, as stated near Eq. (5): "the background CR flux remains consistent across all GMCs." The paper provides no quantitative estimate of how much the background CR spectrum can vary over the 100-800 pc scales spanned by the selected clouds. Spatial fluctuations in the ambient CR sea (e.g., gradients across the Local Bubble, older local sources, or spiral-arm structure) could produce a low-energy index minimum in a distant cloud or mask the minimum in a nearby cloud, breaking the claimed one-to-one correspondence between the observed index pattern and the single nearby-source hypothesis. Please provide an estimate or an upper limit on background spectral fluctuations on these scales, or incorporate a spatially varying background model, before the test can be considered decisive.
  2. [Section IV, top panel of Fig. 4] The detectability statements compare the predicted GMC flux with point-source sensitivity curves from Ref. [41], but the text itself notes that nearby GMCs have significant extensions (~1 degree) and that the sensitivity is reduced by a factor sqrt(1 + (theta/sigma_PSF(E))^2). This correction is not applied to any of the sensitivity curves or to the claim that "many of these chosen GMCs are likely to be detectable." For clouds such as Taurus and Orion A, which are emphasized as the best LHAASO targets, please quantify the expected reduction in sensitivity at the relevant energies and state whether the proposed spectral-index measurement remains feasible after this correction.
  3. [Section IV, Fig. 4 and Table I] The predicted gamma-ray fluxes and spectral-index curves in Fig. 4 are shown as single lines without any uncertainty bands. The best-fit model parameters in Table I have statistical uncertainties (e.g., D0 of 2.73 +/- 0.20 x 10^26 cm^2 s^-1, ts of 7.2 +/- 0.5 x 10^5 yr), and the text mentions that the GMC A factors have ~30% uncertainties. The key claim that Perseus and Taurus show an earlier hardening with a minimum below 100 GeV, while all other GMCs reach their minimum above 1 TeV, should be accompanied by a propagation of these uncertainties. Without such bands, it is unclear whether the predicted separation between the two groups is statistically significant, or whether the index-minimum energies could overlap within 1 sigma.
minor comments (5)
  1. [Section I] In the sentence about LHAASO, "future high-energy high-energy gamma-ray detectors" contains a duplicated "high-energy". The same paragraph also ends with "leading to diverse observed gamma-ray.", which is missing a noun such as "spectra".
  2. [Section II C] The sentence "We maintain rs fixed and and explore three cases" contains a duplicated "and".
  3. [Section IV] The phrase "This distinct is evident" should read "This distinction is evident".
  4. [Section II A and Appendix A] The manual rescaling of DAMPE helium and p+He energies (delta = 1.037 and 1.029) and the inflation of anisotropy error bars to 35% and 25 degrees are ad hoc and are not tested for their influence on the best-fit parameters. Since the fitted source parameters directly determine the GMC predictions, a short robustness check (e.g., varying delta or the error rescaling factors within reasonable ranges) would strengthen confidence in the results.
  5. [General] Reference [21] is listed as "arxiv eprint (2023)"; please provide the journal or arXiv identifier in the standard format used by other references.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gamma-ray spectral-index predictions are forward-model outputs from parameters fitted to independent local CR data.

full rationale

The nearby-source parameters in Table I are fitted exclusively to local CR proton/helium spectra and CR dipole anisotropy data (Section II). The gamma-ray fluxes and the energy-dependent spectral indices in Fig. 4 are then computed by taking the resulting CR spectra at each GMC and convolving them with the proton-proton cross-section via Eq. (5); no gamma-ray observation or GMC A-factor enters the fit. The distance-dependent ordering of spectral-index minima is therefore a genuine forward-model prediction, not a quantity forced by construction. The only self-citations (Refs. [17,23]) concern the nearby-source hypothesis, energy-scale rescaling, and an assumed 1:1 proton/helium injection ratio; none of these is load-bearing in the sense of assuming the gamma-ray result, because the present paper performs its own fits to independent data. The stated assumptions that CRs freely penetrate the clouds and that the background CR sea is uniform across all GMCs are physical modeling simplifications that could be questioned, but they are not circular reductions of the paper's central claim; any concern about them is a correctness or robustness risk, not a circularity finding.

Assumptions & free parameters 13 free parameters · 8 assumptions · 0 invented entities

The central claim rests on a chain of standard astrophysical assumptions: a burst-like point-source diffusion solution, a universal CR background, free penetration of GMCs, and hadronic gamma-ray production. The main free parameters are the nearby-source properties and the background shape, all fixed using local CR and anisotropy data rather than gamma-ray data. The most ad hoc choices are the manual rescalings of DAMPE energies and dipole anisotropy errors in Section II.A and Appendix A. No new particles, forces, or conserved quantities are introduced.

free parameters (13)
  • Diffusion coefficient D0 = 1.09e26, 2.73e26, and 4.37e26 cm2/s for rs=100, 250, and 400 pc
    Fitted to CR spectra and anisotropy; sets the propagation scale for the nearby source contribution.
  • Source age ts = 2.86e5, 7.2e5, and 11.5e5 yr for rs=100, 250, and 400 pc
    Fitted from the bump structure of dipole amplitude; controls how far source CRs have traveled.
  • Cutoff energy Ec = 38.7 TeV
    Fitted; produces the TeV softening and scales with charge in the injection spectrum.
  • Injected CR energy Ecr = 0.21, 3.31, and 13.56 x 10^50 erg for the three rs cases
    Fitted normalization; determines the absolute size of the source contribution at each cloud.
  • Source right ascension RA = 37 degrees
    Fitted to dipole phase; selects which GMCs lie close to the source.
  • Source distance rs = Fixed at 100, 250, and 400 pc
    Not fitted; scanned to bracket the allowed range from injection-energy considerations.
  • Background spectrum parameters = alpha_p=2.83, alpha_He=2.78, Eb=4 TeV, dalpha=0.23, s=5.0, Eknee=5 PeV
    Fixed from fits to CR data below and above the TeV bump; used as the universal CR sea.
  • Background anisotropy normalization and slope = c1=0.6, c2=0.45
    Fixed to match diffusion-coefficient energy dependence from B/C; used to combine background and source anisotropy.
  • Dipole anisotropy error bar inflation = 35% for amplitude, 25 degrees for phase
    Chosen in Appendix A to make chi2 per data point less than one; inflates experimental uncertainties.
  • DAMPE energy rescaling delta = 1.037 for helium, 1.029 for p+He
    Manual correction for inter-experiment energy-scale offset between AMS-02 and DAMPE.
  • Injection spectral index gamma = 2.15
    Fixed to typical Fermi acceleration value rather than fitted.
  • Proton-to-helium injection ratio = 1:1
    Assumed, following the earlier nearby-source model of Ref. [23].
  • Nuclear enhancement factor xi_N = 1.8
    Fixed from previous GMC gamma-ray studies; scales the absolute gamma-ray flux.
assumptions (8)
  • domain assumption Point-source, burst-like injection in an infinite homogeneous diffusive medium solves the CR propagation problem (Eq. 1).
    Invoked in Section II.B.1; valid only if spatial scales are much smaller than the diffusion halo height.
  • domain assumption The nearby source lies in the Galactic plane and the background anisotropy points toward the Galactic center.
    Section II.B.2; used to fix geometry and to fit the source right ascension.
  • domain assumption CRs freely penetrate GMCs and gamma rays arise from hadronic pp interactions with a constant nuclear enhancement factor.
    Section III, Eq. (5) and text 'Assuming that CRs can freely penetrate the cloud'; ignores magnetic shielding or internal gradients.
  • ad hoc to paper AMS-02 and DAMPE helium/p+He spectra can be reconciled by multiplicative energy rescaling.
    Section II.A; delta=1.037 and 1.029 chosen manually rather than derived from a calibration.
  • ad hoc to paper Dipole anisotropy systematic discrepancies can be absorbed by uniformly inflating all amplitude and phase errors.
    Appendix A; rescaling is chosen to drive chi2 per point below one, which can hide genuine model tension.
  • domain assumption The diffusion coefficient in the solar neighborhood may differ from the Galactic average and is therefore a free parameter.
    Section II.C; follows Ref. [17] and justifies fitting D0 rather than using B/C-derived values.
  • domain assumption The injection cutoff energy scales with charge Z.
    Section II.B.1, Eq. (2); expected for acceleration/propagation cutoffs but not independently tested here.
  • domain assumption Only protons and helium contribute significantly to the CR flux and anisotropy in the energy range of interest.
    Section II.B.2; neglects heavier nuclei and leptons.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Deciphering the spectral bumps of Galactic cosmic rays through gamma-ray observations of nearby molecular clouds." pith.science (2026). https://pith.science/paper/PEXCPUWX

@misc{pith2026250114267,
  author       = {Pith},
  title        = {Pith review of: Deciphering the spectral bumps of Galactic cosmic rays through gamma-ray observations of nearby molecular clouds},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PEXCPUWX}},
  note         = {Machine review of arXiv:2501.14267}
}
abstract

The observed spectral bump in cosmic-ray (CR) proton and helium spectra, along with the phase and amplitude evolution of CR dipole anisotropy, provide plausible yet indirect evidence for the presence of a nearby CR source. This study investigates the potential of giant molecular clouds (GMCs) located near the solar system to act as natural probes of CRs from the nearby source, with their gamma-ray emissions serving as indicators of spatial variations in CR flux within the solar neighborhood resulting from this source. We show that a nearby source, accounting for the CR data, could imprint distinct features on the $\gamma$-ray spectra of different GMCs. We expect that these features are detectable by LHAASO and upcoming high-energy $\gamma$-ray observatories, providing a powerful test for the hypothesized nearby source. Notably, we find that determining the energy dependence of the $\gamma$-ray spectral index offers a promising approach to investigate the nearby source and constrain its distance. Conversely, if the spectral bump is a widespread Galactic phenomenon, the energy dependence would exhibit uniformity across all GMCs, distinguishing the underlying mechanism accounting for the spectral bump from the scenario involving a nearby source.

Figures

Figures reproduced from arXiv: 2501.14267 by the authors.

Figure 1
Figure 1. FIG. 1: Cartoon illustrating the basic concept of our [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Left: The proton and helium spectra calculated using the best-fit parameters for the nearby source, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The positions of the selected GMCs in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Top: The expected [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The B-spline fitting results for the amplitude [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Top: The expected [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Implication of multiple source populations of Galactic cosmic rays from proton and helium spectra

    astro-ph.HE 2025-11 conditional novelty 5.0 of 10

    The proton and helium spectra from 1 GeV to 10 PeV can be reproduced only by adding two local sources or a second background population on top of the standard cosmic-ray background.

Reference graph

Works this paper leans on

52 extracted references · 23 canonical work pages · cited by 1 Pith paper

  1. [41]

    Blasi, Astron

    P. Blasi, Astron. Astrophys. Rev. 21, 70 (2013), arXiv:1311.7346 [astro-ph.HE]

    arXiv 2013

  2. [1]

    2: Left: The proton and helium spectra calculated using the best-fit parameters for the nearby source, compared with data from AMS-02 [22], DAMPE [8, 9, 11], and GRAPES-3 [12]

    CR spectrum The propagation of CR nuclei within our fitting range, E ≳ 50 GV, is dominated by the diffusion process, with 3 104 E2.7dN/dE[m−2s−1sr−1GeV1.7] 2×Proton Helium Total BKG Local Source 102 103 104 105 106 Total Energy [GeV] 104 E2.7dN/dE[m−2s−1sr−1GeV1.7] p+He total Proton Helium AMS-02 DAMPE GRAPES 3 10−4 10−3 Amplitude A1 Model ARGO Baksan EAS...

    work page

  3. [2]

    dipole anisotropy The CR anisotropy results from the combined contri- butions of the CR background and the nearby sources. In general, the total dipole anisotropy can be expressed as [34]: ∆ = P i ¯Ii∆ini · nmaxP i ¯Ii , (4) where i represents the i-th origin of CRs, including both the background and potential nearby sources, ¯I denotes the mean CR intens...

    work page

  4. [3]

    Increased flux with proximity: The closer a GMC 6 101 102 103 104 105 106 Total Energy [GeV] 10−9 10−8 10−7 E2.6dN/dE[m−2s−1GeV1.6] CTA(50h)VLAST LHAASO(5 year) SWGO(5 year) 10 % Crab 1 % Crab 0.1 % Crab Perseus Taurus Hercules R CrA Ophiuchi Lupus Chamaeleon OrionA Cepheus MonR2 102 103 104 105 106 Total Energy [GeV] 103 104 E2.7dN/dE[m−2s−1sr−1GeV1.7] C...

    work page

  5. [4]

    Consequently, GMCs in closer proxim- ity to the nearby source are influenced by its CR flux at lower energies, leading to an earlier harden- ing in their CR spectrum

    Earlier spectral hardening for closer GMCs: The energy dependence of the diffusion coefficient causes low-energy CRs to diffuse at a slower rate, requiring more time for them to transport longer distances. Consequently, GMCs in closer proxim- ity to the nearby source are influenced by its CR flux at lower energies, leading to an earlier harden- ing in the...

    work page

  6. [5]

    Gabici, C

    S. Gabici, C. Evoli, D. Gaggero, P. Lipari, P. Mertsch, E. Orlando, A. Strong, and A. Vittino, Int. J. Mod. Phys. D 28, 1930022 (2019), arXiv:1903.11584 [astro-ph.HE]

    arXiv 2019

  7. [6]

    A. D. Panov et al., Bull. Russ. Acad. Sci. Phys. 71, 494 (2007), arXiv:astro-ph/0612377. 8

    work page Pith review arXiv 2007

  8. [7]

    H. S. Ahn et al., The Astrophysical Journal 714, L89 (2010), arxiv:1004.1123 [astro-ph.HE]

    work page Pith review arXiv 2010

Show all 52 references
  1. [8]

    Y. S. Yoon et al., The Astrophysical Journal 839, 5 (2017), arxiv:1704.02512 [astro-ph.HE]

    2017 arXiv

  2. [9]

    Adriani et al

    O. Adriani et al. (PAMELA), Science 332, 69 (2011), arxiv:1103.4055 [astro-ph.HE]

    2011 arXiv

  3. [10]

    Aguilar, D

    M. Aguilar, D. Aisa, B. Alpat, et al. (AMS), Physical Review Letters 115, 211101 (2015)

    2015

  4. [11]

    Aguilar, D

    M. Aguilar, D. Aisa, B. Alpat, et al. (AMS), Physical Review Letters 114, 171103 (2015)

    2015

  5. [12]

    An et al

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

    2019 arXiv

  6. [13]

    Alemanno et al., Phys

    F. Alemanno et al., Phys. Rev. Lett. 126, 201102 (2021), arXiv:2105.09073 [astro-ph.HE]

    2021 arXiv

  7. [14]

    Atkin et al

    E. Atkin et al. , JETP Lett. 108, 5 (2018), arXiv:1805.07119 [astro-ph.HE]

    2018 arXiv

  8. [15]

    Alemanno et al

    F. Alemanno et al. (DAMPE, (DAMPE Collab- oration)*), Phys. Rev. D 109, L121101 (2024), arXiv:2304.00137 [astro-ph.HE]

    2024

  9. [16]

    Varsi et al

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

    2024

  10. [17]

    Ahlers and P

    M. Ahlers and P. Mertsch, Prog. Part. Nucl. Phys. 94, 184 (2017), arXiv:1612.01873 [astro-ph.HE]

    2017 arXiv

  11. [18]

    A. W. Strong, I. V. Moskalenko, and V. S. Ptuskin, Ann. Rev. Nucl. Part. Sci. 57, 285 (2007), arXiv:astro- ph/0701517

    2007

  12. [19]

    Liu, Y.-Q

    W. Liu, Y.-Q. Guo, and Q. Yuan, JCAP 10, 010, arXiv:1812.09673 [astro-ph.HE]

    arXiv

  13. [20]

    Yue et al., Front

    C. Yue et al., Front. Phys. (Beijing) 15, 24601 (2020), arXiv:1909.12857 [astro-ph.HE]

    2020 arXiv

  14. [21]

    Fang, X.-J

    K. Fang, X.-J. Bi, and P.-F. Yin, Astrophys. J. 903, 69 (2020), arXiv:2003.13635 [astro-ph.HE]

    2020 arXiv

  15. [22]

    Neronov, D

    A. Neronov, D. Malyshev, and D. V. Semikoz, Astron. Astrophys. 606, A22 (2017), arXiv:1705.02200 [astro- ph.HE]

    2017 arXiv

  16. [23]

    Aharonian, G

    F. Aharonian, G. Peron, R. Yang, S. Casanova, and R. Zanin, Phys. Rev. D 101, 083018 (2020), arXiv:1811.12118 [astro-ph.HE]

    2020 arXiv

  17. [24]

    Albert et al

    A. Albert et al. , Astrophys. J. 914, 106 (2021), arXiv:2101.08748 [astro-ph.HE]

    2021 arXiv

  18. [25]

    J. Liu, B. Liu, and R. Yang, arxivEprint (2023), arXiv:2304.14107 [astro-ph.HE]

    2023 arXiv

  19. [26]

    Aguilar et al

    M. Aguilar et al. (AMS), Phys. Rept. 894, 1 (2021)

    2021

  20. [27]

    Lv, X.-J

    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, arxiv eprint (2024), arXiv:2403.11832 [astro-ph.HE]

    2024 arXiv

  21. [28]

    W. Gao, H. He, H. Lv, S. Cui, and W. Zhang (LHAASO), PoS ICRC2023, 478 (2023)

    2023

  22. [29]

    Yuan, S.-J

    Q. Yuan, S.-J. Lin, K. Fang, and X.-J. Bi, Phys. Rev. D 95, 083007 (2017), arXiv:1701.06149 [astro-ph.HE]

    2017 arXiv

  23. [30]

    J. R. H¨ orandel, Astroparticle Physics 19, 193 (2003), arxiv:astro-ph/0210453

    2003 arXiv

  24. [31]

    A. D. Erlykin and A. W. Wolfendale, J. Phys. G 27, 941 (2001)

    2001

  25. [32]

    Caprioli, JCAP 05, 026, arXiv:1103.2624 [astro- ph.HE]

    D. Caprioli, JCAP 05, 026, arXiv:1103.2624 [astro- ph.HE]

    arXiv

  26. [33]

    A. R. Bell, K. M. Schure, and B. Reville, Mon. Not. Roy. Astron. Soc. 418, 1208 (2011), arXiv:1108.0582 [astro- ph.HE]

    2011 arXiv

  27. [34]

    Tomassetti, Astrophys

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

    2012 arXiv

  28. [35]

    Y.-Q. Guo, Z. Tian, and C. Jin, Astrophys. J. 819, 54 (2016), arXiv:1509.08227 [astro-ph.HE]

    2016 arXiv

  29. [36]

    M.-J. Zhao, K. Fang, and X.-J. Bi, Phys. Rev. D 104, 123001 (2021), arXiv:2109.04112 [astro-ph.HE]

    2021 arXiv

  30. [37]

    Abu-Zayyad, D

    T. Abu-Zayyad, D. Ivanov, C. C. H. Jui, J. H. Kim, J. N. Matthews, J. D. Smith, S. B. Thomas, G. B. Thom- son, and Z. Zundel, The knee and the second knee of the cosmic-ray energy spectrum (2018), arXiv:1803.07052 [astro-ph.HE]

    2018 arXiv

  31. [38]

    C. S. Shen and C. Y. Mao, Astrophys.J.Lett. 9, 169 (1971)

    1971

  32. [39]

    H. P. Dembinski, R. Engel, A. Fedynitch, T. Gaisser, F. Riehn, and T. Stanev, PoS ICRC2017, 533 (2018), arXiv:1711.11432 [astro-ph.HE]

    2018 arXiv

  33. [40]

    G´ enolini et al., Phys

    Y. G´ enolini et al., Phys. Rev. D 99, 123028 (2019), arXiv:1904.08917 [astro-ph.HE]

    2019 arXiv

  34. [42]

    Zucker, J

    C. Zucker, J. S. Speagle, E. F. Schlafly, G. M. Green, D. P. Finkbeiner, A. A. Goodman, and J. Alves, The Astrophysical Journal 879, 125 (2019)

    2019

  35. [43]

    F. A. Aharonian, Space Sci. Rev. 99, 187 (2001), arXiv:astro-ph/0012290

    2001 arXiv

  36. [44]

    Kafexhiu, F

    E. Kafexhiu, F. Aharonian, A. M. Taylor, and G. S. Vila, Phys. Rev. D 90, 123014 (2014), arXiv:1406.7369 [astro- ph.HE]

    2014 arXiv

  37. [45]

    Peron and F

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

    2022 arXiv

  38. [46]

    Addazi et al

    A. Addazi et al. (LHAASO), Chin. Phys. C 46, 035001 (2022), arXiv:1905.02773 [astro-ph.HE]

    2022

  39. [47]

    Albert et al., Arxiv Eprint (2019), arXiv:1902.08429 [astro-ph.HE]

    A. Albert et al., Arxiv Eprint (2019), arXiv:1902.08429 [astro-ph.HE]

    2019 arXiv

  40. [48]

    B. S. Acharya et al. (CTA Consortium), Science with the Cherenkov Telescope Array (WSP, 2018) arXiv:1709.07997 [astro-ph.IM]

    2018 arXiv

  41. [49]

    Astrophys. J. Suppl. 199, 31 (2012), arXiv:1108.1435 [astro-ph.HE]

    2012 arXiv

  42. [50]

    X. Pan, W. Jiang, C. Yue, S.-J. Lei, Y.-X. Cui, and Q. Yuan, Nucl. Sci. Tech. 35, 149 (2024), arXiv:2407.16973 [astro-ph.IM]

    2024 arXiv

  43. [51]

    Cagnoli, D

    I. Cagnoli, D. Kyratzis, and D. Serini (HERD), Nucl. Instrum. Meth. A 1068, 169788 (2024)

    2024

  44. [52]

    C. T. A. Observatory and C. T. A. Consortium, 10.5281/zenodo.5499840 (2021). Appendix A: Rescaling of the error bars of CR data To ensure the consistent combination of data from dif- ferent experiments without excessively reducing the con- straining power, we adopt a strategy ...

    2021 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.