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arxiv: 2605.24107 · v1 · pith:RI6N7ZYZnew · submitted 2026-05-22 · 🌌 astro-ph.HE

On the maximum neutrino flux of blazars in the one-zone leptohadronic model

Wei-Jian Li , Rui Xue , Ze-Rui Wang , Dingrong Xiong This is my paper

Pith reviewed 2026-06-30 14:47 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords blazarshigh-energy neutrinosleptohadronic modelone-zone emissionIceCubeX-ray constraints
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The pith

The one-zone leptohadronic model caps blazar neutrino fluxes below levels needed to explain IceCube associations.

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

The paper introduces an analytical method to calculate the highest neutrino flux possible in the one-zone leptohadronic jet model, expressed directly as a function of the observed X-ray flux and the physical parameters that can be realized in that framework. When this upper bound is applied to neutrino-candidate blazars, the predicted fluxes stay comparable to or below those from earlier one-zone calculations and fall short of the fluxes inferred from IceCube events. Numerical modeling of the same objects reproduces the analytical limits, reinforcing that a single emission zone cannot supply enough neutrinos to account for the observed associations.

Core claim

An analytical derivation yields the maximum neutrino flux as a function of observed X-ray flux within attainable one-zone leptohadronic parameters; application to candidate blazars and comparison with numerical models show that these fluxes do not significantly exceed prior one-zone results and remain below IceCube-inferred levels, indicating that the one-zone scenario alone is unlikely to explain high-energy neutrino-blazar associations.

What carries the argument

Analytical expression for the maximum neutrino flux in terms of the observed X-ray flux under one-zone leptohadronic constraints.

If this is right

  • One-zone leptohadronic models reach their neutrino ceiling at values already explored in earlier studies.
  • X-ray constraints set a firm upper limit on neutrino output that single-zone jets cannot surpass.
  • Alternative sites such as the jet base or hot corona must be considered to reach higher neutrino fluxes.

Where Pith is reading between the lines

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

  • If multi-zone models are required, the relative contribution of each zone to the total neutrino output becomes a testable quantity with future multi-messenger data.
  • The analytical bound offers a quick filter for ruling out one-zone explanations for new neutrino-blazar coincidences without full numerical fitting.

Load-bearing premise

The physical parameters that maximize neutrino output while respecting X-ray limits can actually be attained inside a single emission zone.

What would settle it

A measured neutrino flux from a blazar that exceeds the analytical maximum while its X-ray flux and other parameters remain within the range assumed for that maximum.

Figures

Figures reproduced from arXiv: 2605.24107 by Dingrong Xiong, Rui Xue, Wei-Jian Li, Ze-Rui Wang.

Figure 1
Figure 1. Figure 1: TXS 0506+056 associated with IC-170922A. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. In the upper left panel, the red line with arrows represents the parameter space under the severe KN effect corresponding to Eq. (4). The area within the black lines with arrows represents the peak frequency constra… view at source ↗
Figure 2
Figure 2. Figure 2: TXS 0506+056 associated with GVD-210418CA. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles in upper panels have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: TXS 0506+056 associated with IC-220918A. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles in upper panels have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: PKS 0735+178 associated with IC-211208A. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles in upper panels have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: GB6 J2113+1121 associated with IC-191001A. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles in upper panels have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: 5BZB J0630-2406 associated with IC J0630-2353. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles in upper panels have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: PKS 1502+106 associated with IC-190730A. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles in upper panels have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: PKS B1424-418 associated with Big Bird. Upper panels: the parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles in upper panels have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: GB6 J1040+0617 associated with IC-141209A. The parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: 3HSP J095507.1+355101 associated with IC-200107A. The parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. In the left panel, the red line with arrows represents the parameter space under the severe KN effect corresponding to Eq. (4). The area within the black lines with arrows represents the peak frequency constraint, corre… view at source ↗
Figure 11
Figure 11. Figure 11: TXS 0506+056 associated with IC-170922A. The parameter space (left panel) and the fitting result of the SED for different radii of blob (right panel) under the SSC-dominated case. The line styles have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: TXS 0506+056 associated with IC-170922A. Upper panels: the fitting results of the SED for R = 1 × 1015 cm (left panel) and R = 1×1016 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 2×1015 cm (left panel) and R = 2 × 1016 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 2 × 1015 cm (left panel) and R = 2 × 1016 cm … view at source ↗
Figure 13
Figure 13. Figure 13: TXS 0506+056 associated with GVD-210418CA. Upper panels: the fitting results of the SED for R = 1 × 1016 cm (left panel) and R = 1 × 1017 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 1 × 1016 cm (left panel) and R = 1 × 1018 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 1 × 1016 cm (left panel) and R = 1 × 10… view at source ↗
Figure 14
Figure 14. Figure 14: TXS 0506+056 associated with IC-220918A. Upper panels: the fitting results of the SED for R = 1 × 1016 cm (left panel) and R = 1×1017 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 1×1016 cm (left panel) and R = 1 × 1019 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 1 × 1016 cm (left panel) and R = 1 × 1019 cm … view at source ↗
Figure 15
Figure 15. Figure 15: PKS 0735+178 associated with IC-211208A. Upper panels: the fitting results of the SED for R = 1 × 1015 cm (left panel) and R = 1×1016 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 1×1015 cm (left panel) and R = 1 × 1019 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 1 × 1015 cm (left panel) and R = 1 × 1019 cm … view at source ↗
Figure 16
Figure 16. Figure 16: GB6 J2113+1121 associated with IC-191001A. Upper panels: the fitting results of the SED for R = 1×1017 cm (left panel) and R = 1×1018 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 4×1014 cm (left panel) and R = 1 × 1015 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 4 × 1014 cm (left panel) and R = 1 × 1015 cm … view at source ↗
Figure 17
Figure 17. Figure 17: 5BZB J0630-2406 associated with IC J0630-2353. Upper panels: the fitting results of the SED for R = 1 × 1016 cm (left panel) and R = 1 × 1017 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 3 × 1015 cm (left panel) and R = 6 × 1015 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 3 × 1015 cm (left panel) and R = 6 … view at source ↗
Figure 18
Figure 18. Figure 18: PKS 1502+106 associated with IC-190730A. Upper panels: the fitting results of the SED for R = 1 × 1018 cm (left panel) and R = 1×1019 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 1×1015 cm (left panel) and R = 1 × 1018 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 1 × 1015 cm (left panel) and R = 1 × 1018 cm … view at source ↗
Figure 19
Figure 19. Figure 19: PKS B1424-418 associated with Big Bird. Upper panels: the fitting results of the SED for R = 1 × 1019 cm (left panel) and R = 1×1020 cm (right panel) under the SSC-dominated case. Middle panels: the parameter space for R = 2×1016 cm (left panel) and R = 1 × 1017 cm (right panel) under the EC-dominated case. Lower panels: the fitting results of the SED for R = 2 × 1016 cm (left panel) and R = 1 × 1017 cm (… view at source ↗
Figure 20
Figure 20. Figure 20: GB6 J1040+0617 associated with IC-141209A. The fitting results of the SED for R = 1 × 1016 cm (left panel) and R = 1 × 1017 cm (right panel) under the SSC-dominated case. The colored dashed and solid lines respectively represent the secondary pair cascade emission and the neutrino spectrum for different parameter combinations, which correspond to the color bar. The quasi-simultaneous data, neutrino data a… view at source ↗
Figure 21
Figure 21. Figure 21: 3HSP J095507.1+355101 associated with IC-200107A. The fitting results of the SED for R = 1×1015 cm (left panel) and R = 1 × 1016 cm (right panel) under the SSC-dominated case. The colored dashed and solid lines respectively represent the secondary pair cascade emission and the neutrino spectrum for different parameter combinations, which correspond to the color bar. The quasi-simultaneous data, neutrino d… view at source ↗
read the original abstract

The origin of extragalactic high-energy neutrinos remains a major mystery in astrophysics, with blazars as leading candidate sources. The widely adopted one-zone leptohadronic jet model, however, faces severe challenges from stringent X-ray observational constraints. In this work, we present an analytical approach that derives the maximum neutrino flux as a function of the observed X-ray flux and the corresponding physical parameters attainable within the one-zone leptohadronic framework. Applying this approach to a sample of neutrino candidate blazars, we further perform numerical modeling and find agreement between analytical and numerical results. Both approaches consistently show that the model-predicted neutrino fluxes do not significantly exceed those obtained in previous one-zone studies and remain below the flux levels inferred from IceCube observations, suggesting that the one-zone scenario alone is unlikely to fully account for high-energy neutrino-blazar associations. This highlights the importance of considering multi-zone models or alternative production sites (e.g., jet base, hot corona) to better explain high-energy neutrino origins in blazars.

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 derives an analytical upper bound on the neutrino flux from blazars in the one-zone leptohadronic model, expressed as a function of the observed X-ray flux and attainable physical parameters (magnetic field, Doppler factor, particle densities). It applies the bound to a sample of neutrino-candidate blazars, performs numerical modeling on those sources, and reports agreement between the two approaches. Both indicate that predicted neutrino fluxes remain consistent with prior one-zone studies and below IceCube-inferred levels, leading to the conclusion that the one-zone scenario alone is unlikely to explain high-energy neutrino-blazar associations.

Significance. If the bound is correctly derived and the attainable-parameter premise holds, the work supplies a practical, observationally grounded constraint that quantifies the tension between X-ray limits and neutrino production in single-zone leptohadronic jets. The explicit agreement between the analytical expression and numerical results on real sources is a methodological strength that increases the result's utility for future modeling.

major comments (2)
  1. [Analytical derivation and parameter selection (likely §3)] The central claim that the derived maximum is attainable within a single emission zone without violating other multi-wavelength constraints rests on the choice of parameter values; the manuscript should explicitly demonstrate, for at least one source, that the optimizing values (B, δ, n_p, etc.) simultaneously satisfy the observed SED shape outside the X-ray band.
  2. [Comparison of analytical and numerical results (likely §4)] The abstract and main text state that analytical and numerical results agree, yet no quantitative metric (fractional difference, χ², or propagated uncertainty on the neutrino flux) is provided; without this, the robustness of the bound against parameter variations cannot be assessed.
minor comments (2)
  1. [Throughout] Notation for the maximum neutrino flux (e.g., Φ_ν^max) should be introduced once and used consistently; currently the abstract and body appear to switch between descriptive phrases and symbols.
  2. [Application to candidate sources] A short table listing the adopted parameter ranges for the analytical bound (B, δ, etc.) and the corresponding X-ray flux values for the sample sources would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and the recommendation for minor revision. We address the points below.

read point-by-point responses

  1. Referee: [Analytical derivation and parameter selection (likely §3)] The central claim that the derived maximum is attainable within a single emission zone without violating other multi-wavelength constraints rests on the choice of parameter values; the manuscript should explicitly demonstrate, for at least one source, that the optimizing values (B, δ, n_p, etc.) simultaneously satisfy the observed SED shape outside the X-ray band.

    Authors: We agree that an explicit demonstration is valuable to support the attainability of the maximum neutrino flux. In the revised version of the manuscript, we will add a subsection or appendix showing, for one representative source such as TXS 0506+056, that the parameter set (including B, δ, and particle densities) used to achieve the maximum neutrino flux also reproduces the observed multi-wavelength SED outside the X-ray band, thereby satisfying the one-zone model constraints. revision: yes

  2. Referee: [Comparison of analytical and numerical results (likely §4)] The abstract and main text state that analytical and numerical results agree, yet no quantitative metric (fractional difference, χ², or propagated uncertainty on the neutrino flux) is provided; without this, the robustness of the bound against parameter variations cannot be assessed.

    Authors: We concur that providing a quantitative metric would enhance the assessment of agreement. We will revise the manuscript to include the fractional differences between the analytical upper bounds and the numerical neutrino flux predictions for the sources in our sample, as well as any relevant uncertainties from parameter variations. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The central derivation expresses the maximum neutrino flux as an analytical function of directly observed X-ray flux together with physical parameters attainable inside the one-zone leptohadronic framework. This supplies an external observational anchor rather than defining the neutrino quantity in terms of itself or fitting it to neutrino data. Numerical modeling on candidate sources is used only for confirmation and does not alter the bound. No self-citation chain is invoked to justify the uniqueness of the bound, and the conclusion that one-zone predictions remain below IceCube levels follows from the X-ray constraint without reduction to the target result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the one-zone leptohadronic framework and the attainability of parameters that maximize neutrino output while matching X-ray data; no explicit free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption The one-zone leptohadronic jet model provides a complete description of the relevant emission processes in blazars.
    The entire derivation and comparison to IceCube data assumes this modeling framework holds without additional zones or sites.

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Forward citations

Cited by 1 Pith paper

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

  1. Locating the Production Sites of High-Energy Neutrinos in Blazar Jets

    astro-ph.HE 2026-06 unverdicted novelty 5.0

    Efficient neutrino production requires an external radiation field stronger than the magnetic field near the broad-line region, but this conflicts with single-zone broadband emission, implying the neutrino site must b...

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