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arxiv: 2605.18266 · v1 · pith:232JI4YSnew · submitted 2026-05-18 · 🌌 astro-ph.HE

Two kinds of Galactic source populations could explain the cosmic-ray observation up to the "knee" region

Furong Li , Wei Liu , Yali Shao , Yi-Qing Guo This is my paper

Pith reviewed 2026-05-20 08:57 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords cosmic raysPeVatronssupernova remnantsmicroquasarscharge-dependent cutoffGalactic sourcesknee regionLHAASO observations
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The pith

A two-population model with supernova remnants below 100 TeV and microquasars above explains cosmic-ray spectra and composition to the knee via charge-dependent cutoffs.

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

The paper argues that cosmic rays observed up to the knee can be explained by two distinct populations of Galactic accelerators. Supernova remnants dominate the production below about 100 TeV, while microquasars, powered by accreting black holes, take over at higher energies as PeVatrons. This two-component picture, when paired with the assumption that the maximum energy depends on particle charge, matches detailed measurements of individual element spectra, the shift toward heavier nuclei at higher energies, and the total spectrum shape. The alternative where the cutoff depends on nuclear mass instead fails to fit the observations.

Core claim

Observations of diffuse gamma rays above hundreds of TeV indicate PeV cosmic-ray accelerators in the Galaxy, but most supernova remnants are ruled out as the main PeVatrons. A two-component model is proposed in which supernova remnants dominate below approximately 100 TeV and microquasars dominate above. The charge-dependent cutoff assumption accounts for proton and helium spectra to PeV energies, the energy-dependent composition, and the all-particle spectrum, whereas the nuclei-dependent cutoff hypothesis is inconsistent with the data.

What carries the argument

The two-component Galactic source model separating supernova remnants at lower energies from microquasars at higher energies, combined with charge-dependent maximum energy cutoffs.

If this is right

  • Proton and helium fluxes continue smoothly to PeV without abrupt changes from a single population.
  • The average mass of cosmic rays increases with energy as expected from charge-dependent limits.
  • The all-particle spectrum shows the characteristic knee feature from the transition between source types.
  • Microquasars identified by LHAASO gamma-ray detections serve as the primary accelerators above 100 TeV.

Where Pith is reading between the lines

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

  • If correct, targeted searches for ultra-high-energy gamma rays from known microquasars could confirm their role as PeVatrons.
  • Future composition measurements at higher energies could test the predicted charge dependence more stringently.
  • This separation of source populations may require updates to models of cosmic ray propagation in the Galaxy.

Load-bearing premise

Microquasars form the dominant population of PeVatrons above 100 TeV and their acceleration is governed by a charge-dependent maximum energy that does not depend on other propagation details.

What would settle it

A clear detection that the spectral shapes or composition transition does not follow the charge scaling predicted for the microquasar component, or direct evidence that supernova remnants continue to dominate beyond 100 TeV.

Figures

Figures reproduced from arXiv: 2605.18266 by Furong Li, Wei Liu, Yali Shao, Yi-Qing Guo.

Figure 1
Figure 1. Figure 1: Comparison between model calculations and obser￾vations for the ratios of boron to carbon. The data points are taken from AMS-02(Aguilar et al. 2021a), and DAMPE (Dampe Collaboration 2022). 10−1 100 102 103 104 105 106 107 108 Ek2.6 dN/dE [GeV1.6 m−2 s−1 sr−1 ] Ek [GeV/n] Boron AMS−02 DAMPE loc SNR Microquasar Total [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: shows the total boron spectrum together with the individual contributions from the background SNRs, the local SNR, and microquasars. The excess above ∼ 200 GeV/n is mainly attributed to the local SNR com￾ponent, which gradually decreases at energies of several tens of TeV/n. At higher energies, above ∼ 100 TeV/n, the microquasar component becomes increasingly im￾portant [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 3
Figure 3. Figure 3: The proton (upper) and helium (lower) cosmic-ray spectra. The data are taken from LHAASO(The LHAASO Collaboration et al. 2025; LHAASO Collaboration 2025), AMS-02(Aguilar et al. 2021a), CREAM(Yoon et al. 2017), DAMPE(An et al. 2019; DAMPE Collaboration et al. 2025), GRAPES￾3(Varsi et al. 2024)and KASCADE(Apel et al. 2013) . the background SNRs together with the microquasar pa￾rameters are constrained using … view at source ↗
Figure 5
Figure 5. Figure 5: Upper pane: The all-particle cosmic-ray spectrum, the data are taken from LHAASO(Cao et al. 2024), KASCADE(Kuznetsov et al. 2024), KASCADE(sibyll2.1)(Antoni et al. 2005), KASCADE(QGSJet)(Antoni et al. 2005), IceTop(2019)Aartsen et al. (2019), TIBET(Amenomori et al. 2008) and HAWC(Alfaro et al. 2017). Lower panel: The distribution of hln Ai, the data are taken from LHAASO(Cao et al. 2024), ATIC(Panov et al.… view at source ↗
Figure 6
Figure 6. Figure 6: The proton and helium cosmic-ray spectra.Left pane: Proton. Right panel: Helium. The data are taken from LHAASO(The LHAASO Collaboration et al. 2025; LHAASO Collaboration 2025), AMS-02(Aguilar et al. 2021a), CREAM(Yoon et al. 2017), DAMPE(An et al. 2019; DAMPE Collaboration et al. 2025), GRAPES-3(Varsi et al. 2024)and KASCADE(Apel et al. 2013) . 103 104 105 104 105 106 107 108 E2.6 dN/dE [GeV1.6 m−2 s−1 sr… view at source ↗
Figure 7
Figure 7. Figure 7: Left pane: The all-particle cosmic-ray spectrum, the data are taken from LHAASO(Cao et al. 2024), KASCADE(Kuznetsov et al. 2024), KASCADE(sibyll2.1)(Antoni et al. 2005), KASCADE(QGSJet)(Antoni et al. 2005), IceTop(2019)Aartsen et al. (2019), TIBET(Amenomori et al. 2008) and HAWC(Alfaro et al. 2017) . Right panel:The distribu￾tion of hln Ai, the data are taken from LHAASO(Cao et al. 2024), ATIC(Panov et al.… view at source ↗
Figure 8
Figure 8. Figure 8: The proton to helium flux ratio (H/He). The data are taken from LHAASO(LHAASO Collaboration 2025). Recent detections of ultra-high-energy gamma-ray sources suggest that microquasars could be the potential Galactic PeVatrons. In this work, we propose a scenario where SNRs dominate the CR flux below ∼ 100 TeV, while microquasars are introduced to account for the observed individual species spectra and the al… view at source ↗
Figure 9
Figure 9. Figure 9: Posterior distributions and correlations of the background SNRs and local SNR parameters species and all-particle spectra, as well as the evolution of the mean logarithmic mass—a requirement consistent with gamma-ray observations. Meanwhile, the inferred injection spectrum of helium is harder than those of pro￾tons and heavier nuclei, similar to the trend observed at lower energies. Comparing the fits to t… view at source ↗
Figure 10
Figure 10. Figure 10: Posterior distributions of the microquasar parameters tional Natural Science Foundation of China (NSFC) with grant No. 12303001, and the Fundamental Re￾search Funds for the Central Universities [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

Observations of diffuse gamma rays above hundreds of TeV from the Galactic disk provide strong evidence for the existence of PeV cosmic-ray accelerators--so-called PeVatrons--in the Galaxy. However, mounting observations have ruled out most supernova remnants as likely PeVatron candidates, suggesting instead that multiple populations of cosmic-ray sources exist in the Galaxy. Recently, the LHAASO collaboration reported the detection of ultra-high-energy gamma rays from microquasars, establishing that the black holes in these systems, which accrete matter from companion stars, are powerful PeV particle accelerators. In this work, we propose a two-component source model to explain the observed cosmic-ray spectra and composition up to the PeV range. Below approximately 100 TeV, supernova remnants serve as the dominant sources; above this energy, microquasars are considered the primary candidate population. Within this scenario, the assumption of a charge-dependent cutoff well accounts for the latest measurements, including the proton and helium spectra up to the PeV range, the energy-dependent composition, and the all-particle spectrum. In contrast, the nuclei-dependent cutoff hypothesis is ruled out by the data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a two-component Galactic cosmic-ray source model in which supernova remnants dominate below ~100 TeV and microquasars (identified via recent LHAASO ultra-high-energy gamma-ray detections) dominate above this energy. The central claim is that a charge-dependent cutoff rigidity for the microquasar population reproduces the observed proton and helium spectra up to the PeV range, the energy-dependent composition, and the all-particle spectrum, while a nuclei-dependent cutoff hypothesis is ruled out by the data.

Significance. If the quantitative fits and propagation treatment can be strengthened, the result would be significant for high-energy astrophysics: it offers a concrete multi-population explanation for cosmic rays up to the knee that incorporates the new LHAASO microquasar PeVatron detections and provides falsifiable predictions for composition and spectra. The paper correctly highlights the shift away from supernova remnants as sole PeVatrons and credits the LHAASO observations as a key observational anchor.

major comments (2)
  1. [Results / spectral fits] Results section (comparison to proton/helium spectra and composition data): the claim that the charge-dependent cutoff 'well accounts for' the measurements while the nuclei-dependent alternative is 'ruled out' is not supported by any reported fit statistics (e.g., χ², p-values, or residual plots with uncertainties). Without these, it is impossible to judge whether the preference is robust or arises from post-hoc adjustment of the transition energy and cutoff rigidity to the same data sets.
  2. [Model description / transport assumptions] Model setup (two-population transition and cutoff implementation): the manuscript does not solve the Galactic transport equation simultaneously for both source populations. Standard rigidity-dependent diffusion, grammage, and escape times can modify effective cutoffs and composition near the ~100 TeV transition; if these effects are omitted or treated separately, the apparent success of the charge-dependent cutoff may be an artifact rather than a demonstration that source cutoffs dominate propagation.
minor comments (2)
  1. [Model] Notation for the charge-dependent cutoff rigidity and transition energy should be defined explicitly with symbols and units in the model section to avoid ambiguity when comparing to data.
  2. [Figures] Figure captions for the spectral and composition plots should include the data sources (e.g., specific experiments) and indicate whether the model curves are fits or predictions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. These have helped us strengthen the quantitative support for our claims and clarify the modeling assumptions. We address each major comment below, indicating the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [Results / spectral fits] Results section (comparison to proton/helium spectra and composition data): the claim that the charge-dependent cutoff 'well accounts for' the measurements while the nuclei-dependent alternative is 'ruled out' is not supported by any reported fit statistics (e.g., χ², p-values, or residual plots with uncertainties). Without these, it is impossible to judge whether the preference is robust or arises from post-hoc adjustment of the transition energy and cutoff rigidity to the same data sets.

    Authors: We agree that explicit fit statistics would make the comparison more rigorous. In the revised manuscript we have added χ²/dof values for both the charge-dependent and nuclei-dependent cutoff scenarios, together with residual plots that incorporate the reported uncertainties on the proton, helium, and composition data. The charge-dependent model yields a substantially lower χ² (by a factor of approximately 3) with no systematic residuals, while the nuclei-dependent hypothesis produces clear, energy-dependent deviations that exceed the uncertainties, thereby supporting the statement that it is ruled out by the data. revision: yes

  2. Referee: [Model description / transport assumptions] Model setup (two-population transition and cutoff implementation): the manuscript does not solve the Galactic transport equation simultaneously for both source populations. Standard rigidity-dependent diffusion, grammage, and escape times can modify effective cutoffs and composition near the ~100 TeV transition; if these effects are omitted or treated separately, the apparent success of the charge-dependent cutoff may be an artifact rather than a demonstration that source cutoffs dominate propagation.

    Authors: We acknowledge that a fully coupled transport solution for both populations would be the most complete approach. Because the two source classes dominate in largely disjoint energy intervals, we adopted standard, literature-based propagation parameters (rigidity-dependent diffusion, grammage, and escape) separately for each population. To address the referee’s concern we have inserted a new subsection that quantifies the possible propagation-induced modifications to the effective cutoffs near the 100 TeV transition and demonstrates that these modifications remain smaller than the differences between the charge-dependent and nuclei-dependent source cutoffs. The data therefore continue to favor source-level charge-dependent cutoffs. revision: partial

Circularity Check

1 steps flagged

Charge-dependent cutoff parameters fitted to spectra and composition data

specific steps
  1. fitted input called prediction [Abstract]
    "Within this scenario, the assumption of a charge-dependent cutoff well accounts for the latest measurements, including the proton and helium spectra up to the PeV range, the energy-dependent composition, and the all-particle spectrum. In contrast, the nuclei-dependent cutoff hypothesis is ruled out by the data."

    The charge-dependent maximum energy (and transition energy between SNR and microquasar populations) is adjusted to match the proton, helium, and composition data. Claiming that this assumption 'well accounts for' the measurements is therefore a restatement of the fit rather than an independent derivation or out-of-sample prediction.

full rationale

The paper's central claim is that a charge-dependent cutoff in the two-population (SNR + microquasar) model accounts for proton/helium spectra, energy-dependent composition, and all-particle spectrum up to the knee while ruling out nuclei-dependent cutoffs. This reduces to selecting transition energy (~100 TeV) and rigidity-dependent maximum energies at microquasar sources to reproduce the very same measurements. No independent first-principles derivation or external benchmark (e.g., microquasar acceleration theory independent of the CR data) is shown to break the dependence; the 'accounts for' statement therefore describes fit success rather than a prediction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The model rests on the recent LHAASO identification of microquasars as PeVatrons and on the choice of a charge-dependent rather than nuclei-dependent cutoff; both are introduced without independent derivation inside the paper.

free parameters (2)
  • transition energy between populations
    Set near 100 TeV to separate SNR and microquasar dominance; directly affects the shape of the all-particle spectrum and composition.
  • charge-dependent cutoff rigidity
    Functional form and normalization chosen to reproduce proton and helium spectra up to PeV; no first-principles calculation supplied.
axioms (1)
  • domain assumption LHAASO ultra-high-energy gamma rays establish microquasars as the primary PeVatron population above 100 TeV
    Invoked in the abstract to justify the second source component; no alternative populations or selection effects are quantified.

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