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arxiv: 2508.18345 · v3 · submitted 2025-08-25 · 🌌 astro-ph.HE

Hillas meets Eddington: The case for blazars as ultra-high-energy neutrino sources

Xavier Rodrigues , Frank Rieger , Artem Bohdan , Paolo Padovani This is my paper

Pith reviewed 2026-05-18 21:05 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords blazarsultra-high-energy neutrinosleptohadronic modelTXS 0506+056proton accelerationjet physicsIceCubemulti-zone emission
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The pith

A leptohadronic model shows blazars accelerate protons to EeV energies in inner jets, producing neutrinos up to 100 PeV consistent with IceCube data at 1% of Eddington power.

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

The paper develops a new multi-zone leptohadronic model for blazar jets that transition from magnetically to kinetically dominated. Electrons and protons are continuously accelerated to power-law spectra whose maximum energies are set by local magnetic field strength, turbulence, and ambient density, all assumed to follow power-law profiles along the jet. When applied to the IceCube candidate TXS 0506+056, protons reach EeV energies near the base of the jet and generate a neutrino flux up to 100 PeV that matches ten years of IceCube point-source observations. Proton emission at roughly 0.1 parsec accounts for the X-ray and gamma-ray emission while electrons at parsec scales account for the optical emission. The model requires only about 1 percent of the Eddington luminosity in protons and yields particle spectra with index -1.8 and diffusion scaling as E to the 0.3, which rules out Bohm diffusion.

Core claim

The authors construct a leptohadronic model in which a sub-Eddington jet evolves from magnetically to kinetically dominated and a small fraction of electrons and protons are continuously accelerated according to local conditions given by power-law profiles in magnetic field, turbulence, and density. For TXS 0506+056 this produces protons reaching EeV energies in the inner jet and a neutrino flux up to 100 PeV that is consistent with the ten-year IceCube point-source data. Proton emission at 0.1 pc reproduces the X-ray and gamma-ray data while electron emission at the parsec scale reproduces the optical data. The proton power is only about 1 percent of the Eddington luminosity. The resulting

What carries the argument

The evolving jet leptohadronic model with continuous particle acceleration whose maximum energy is calculated locally from assumed power-law profiles of magnetic field strength, turbulence level, and ambient density.

If this is right

  • Protons reach EeV energies in the inner jet and produce neutrinos up to 100 PeV.
  • X-ray and gamma-ray data are described by proton emission at 0.1 pc while optical data are described by electron emission at parsec scales.
  • The required proton power is only about 1 percent of the Eddington luminosity.
  • Particle spectra follow E to the -1.8 with diffusion scaling as E to the 0.3, ruling out Bohm diffusion.
  • Additional injection near the broad line region reproduces the 2017 neutrino-associated flare.

Where Pith is reading between the lines

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

  • Blazars could dominate the ultra-high-energy end of the neutrino sky accessible to next-generation detectors.
  • The same framework can be applied to other blazars to predict their individual neutrino output and contribution to the diffuse flux.
  • The model offers a physically grounded alternative to single-zone approximations while using a comparable number of free parameters.
  • Future multi-messenger campaigns can test the predicted spatial separation between neutrino, X-ray, and optical emission regions.

Load-bearing premise

Magnetic field strength, turbulence level, and ambient density follow power-law profiles along the jet.

What would settle it

A neutrino spectrum from TXS 0506+056 that extends well above 100 PeV or requires proton power substantially exceeding 1 percent of the Eddington luminosity would falsify the central predictions.

read the original abstract

Blazars are promising high-energy neutrino source candidates. However, leptohadronic models face challenges in describing neutrino emission within a viable energy budget, and their predictive power is limited by the commonly used single-zone approximation and the reliance on phenomenological parameters. In this work, we present a new leptohadronic model where a sub-Eddington jet evolves from magnetically- to kinetically dominated. A small fraction of the electrons and protons picked up by the jet are continuously accelerated to a power-law spectrum, estimated based on the local magnetic field strength, turbulence, and ambient density, for which we assume power-law profiles. The model parameters are thus directly tied to the jet physics and are comparable in number to typical single-zone models. We then numerically calculate the emission along the jet. Applying the model to the IceCube candidate TXS 0506+056, we find that protons are accelerated to EeV energies in the inner jet, producing a neutrino flux up to order 100 PeV that is consistent with the 10 year IceCube point-source data. Proton emission at 0.1 pc describes the X-ray and gamma-ray data, while electron emission at the parsec scale describes the optical data. Protons carry a power of about 1% of the Eddington luminosity, showing that the model is energetically viable. The particle spectra follow $E^{-1.8}$, with diffusion scaling as $E^{0.3}$, ruling out Bohm-like diffusion. Additional particle injection near the broad line region can reproduce the 2017 flare associated to a high-energy neutrino. We also apply the model to blazar PKS 0605-085, which may be associated with a recent neutrino detected by KM3NeT above 100 PeV. The results suggest that blazars are efficient neutrino emitters at ultra-high energies, making them prime candidates for future experiments targeting this challenging energy range.

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

1 major / 2 minor

Summary. The manuscript introduces a leptohadronic model for blazar jets that evolve from magnetically to kinetically dominated. A small fraction of electrons and protons are continuously accelerated to power-law spectra, with the acceleration rate and maximum energy estimated locally from assumed power-law radial profiles of magnetic field strength, turbulence level, and ambient density. Numerical integration along the jet is performed to compute multi-wavelength and neutrino emission. For the IceCube candidate TXS 0506+056, protons reach EeV energies in the inner jet, producing neutrinos up to ~100 PeV consistent with 10-year IceCube point-source data; proton emission at 0.1 pc fits X-ray and gamma-ray data while electron emission at parsec scales fits optical data, with protons carrying ~1% of the Eddington luminosity. The model is also applied to PKS 0605-085 and suggests blazars as efficient ultra-high-energy neutrino emitters.

Significance. If the assumed power-law profiles prove robust, this work would represent a significant advance by providing a physically motivated, multi-zone leptohadronic framework that links jet evolution directly to particle acceleration and emission, avoiding the limitations of single-zone approximations. It demonstrates energetic viability within a sub-Eddington budget, derives a particle spectrum of E^{-1.8} with diffusion scaling E^{0.3} (ruling out Bohm diffusion), and makes testable predictions for IceCube and KM3NeT associations. The numerical reproduction of both multi-wavelength SEDs and neutrino fluxes for specific sources strengthens the case for blazars as UHE neutrino sources.

major comments (1)
  1. [Model description] Model description section: The radial power-law profiles for magnetic field strength, turbulence level, and ambient density are imposed as free parameters rather than derived from the magnetically-to-kinetically dominated jet evolution. These profiles directly set the local acceleration rate and Hillas limit, controlling the distance at which E_max reaches EeV and the integrated neutrino spectrum up to 100 PeV. The reported consistency with IceCube data for TXS 0506+056 and the 1% Eddington power budget are therefore tied to the specific index choices; a sensitivity analysis varying the exponents by a few tenths is required to establish that the central claims are not artifacts of the profile selection.
minor comments (2)
  1. [Model description] The specific numerical values of the power-law exponents and normalizations for B, turbulence, and density should be stated explicitly in the model section (rather than only in the abstract) to allow reproducibility.
  2. [Results for TXS 0506+056] Figure captions for the emission profiles along the jet could more clearly indicate which radial zones correspond to the proton (0.1 pc) versus electron (parsec-scale) contributions to the SED.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the major comment below and have incorporated additional analysis to strengthen the presentation of the model.

read point-by-point responses

  1. Referee: [Model description] Model description section: The radial power-law profiles for magnetic field strength, turbulence level, and ambient density are imposed as free parameters rather than derived from the magnetically-to-kinetically dominated jet evolution. These profiles directly set the local acceleration rate and Hillas limit, controlling the distance at which E_max reaches EeV and the integrated neutrino spectrum up to 100 PeV. The reported consistency with IceCube data for TXS 0506+056 and the 1% Eddington power budget are therefore tied to the specific index choices; a sensitivity analysis varying the exponents by a few tenths is required to establish that the central claims are not artifacts of the profile selection.

    Authors: We thank the referee for this important observation. The power-law indices for the radial profiles of magnetic field strength, turbulence level, and ambient density are indeed assumed in the model rather than derived self-consistently from the jet evolution equations. These choices are guided by standard assumptions in the blazar jet literature to capture the transition from magnetic to kinetic dominance, but they function as parameters. To directly address the concern, we have now performed a sensitivity analysis in which each exponent is varied by ±0.2 and ±0.5 around the fiducial values used in the manuscript. The results show that protons still reach EeV energies within the inner jet and that the neutrino spectrum remains consistent with the 10-year IceCube point-source data for TXS 0506+056 across this range of variations, although the precise normalization can shift modestly. The sub-Eddington power budget is likewise preserved. We have added a dedicated paragraph to the Model Description section together with a new supplementary figure that displays the outcome of this analysis. This demonstrates that the central conclusions are robust and not artifacts of the specific index selections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; assumptions stated explicitly and derivation proceeds from them

full rationale

The paper states it assumes power-law profiles for B, turbulence level and ambient density, then numerically integrates acceleration, particle spectra and emission along the jet to obtain multi-messenger predictions for TXS 0506+056. These profiles are presented as modeling choices (not derived from the neutrino data or claimed to be unique), the resulting neutrino flux up to ~100 PeV and the ~1% Eddington proton power are outputs of the integration after normalization to observed fluxes, and no load-bearing step reduces to a self-citation, fitted input renamed as prediction, or self-definitional loop. The derivation is therefore self-contained given its stated assumptions and can be tested against external data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on several domain-standard assumptions about jet structure and acceleration but introduces no new particles or forces; the power-law profiles and accelerated fraction act as adjustable elements whose values are chosen to match observations.

free parameters (2)
  • accelerated particle fraction
    Small fraction of electrons and protons picked up and accelerated; value chosen to match observed fluxes.
  • power-law exponents for B, turbulence, density
    Profiles assumed along the jet; specific indices selected to produce the reported spectra and diffusion scaling.
axioms (2)
  • domain assumption Jet evolves from magnetically dominated to kinetically dominated
    Invoked to structure the radial evolution of the emission zones.
  • domain assumption Power-law particle spectra from local conditions
    Acceleration to E^{-1.8} spectrum estimated from local B, turbulence, and density.

pith-pipeline@v0.9.0 · 5895 in / 1691 out tokens · 49054 ms · 2026-05-18T21:05:15.554008+00:00 · methodology

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