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

Xavier Rodrigues, Frank Rieger, Artem Bohdan, Paolo Padovani

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.

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

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 , with diffusion scaling as , 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.

Paper Structure

This paper contains 13 sections, 15 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model description
  3. Jet dynamics
  4. How multimessengers constrain particle acceleration
  5. Nonthermal emission
  6. Application to IceCube candidate TXS 0506+056
  7. Application to KM3NeT candidate PKS 0605-085
  8. Discussion
  9. Conclusion
  10. Dissection of the neutrino emission
  11. High-energy neutrino events from blazar candidates
  12. Application to 3HSP J1528+2004, an IceCube candidate in the Northern Sky
  13. Further details on the extended jet model implementation

Figures (7)

  • Figure 1: Two scenarios of diffusion and acceleration. Upper panel: Diffusive shock acceleration with a diffusion coefficient $D^\prime_E\sim E^{\prime-1}$. Lower panel: Stochastic acceleration with $D^\prime_E\sim E^{\prime0.3}$. The timescales are given for the wide range of parameters $\eta$, $B^\prime$, and $R^\prime_\mathrm{j}$ expected at distances $10^{17}\,\mathrm{cm}\lesssim r\lesssim \mathrm{pc}$, as detailed in the main text. Black crosses show the maximum energy of electrons and protons predicted by the respective scenario. Green bands show the allowed range of $E^\prime_\mathrm{e}$ and $E^\prime_\mathrm{p}$ necessary to describe the multimessenger data.
  • Figure 2: Extended jet model applied to the IceCube candidate blazar TXS 0506+056, fitted to the average multiwavelength emission Rodrigues:2024fhu and during the 2017 flaring event 2018Sci...361.1378IKeivani:2018rnh. The top panels show the best-fit spectra. The color curves show the photon emission by primary electrons (blue), photon emission by protons (red), and muon neutrino emission (purple) from the successive zones along the jet. The dashed curves in panel b show the emission from the flare zone. The black curves show the total emission. The green band shows the 68% CL limits on the neutrino point source flux from the source Rodrigues:2024fhu, and the dark red curve the UHE sensitivity of IceCube-Gen2 2021JPhG...48f0501A. The pink curve shows the BLR and accretion disk continuum emission, and the bright green curve the host galaxy contribution Rodrigues:2024fhu. In panels c-g, we show the evolution along the extended jet of the jet energetics (c), dynamics (d), particle profile (e) and emission (f, g).
  • Figure 3: Extended jet model applied to KM3NeT candidate blazar PKS 0605-085. Data adopted from Rodrigues:2023vbv. The curves are color coded as in Fig. . The magenta band shows the muon energy of the event KM-230213.
  • Figure 4: Predicted muon neutrino energy flux (left) and number flux (right) for the two UHE neutrino source candidates discussed in the main text. The emission of neutrinos above 1 PeV is led by interactions with broad line photons (orange) and above 10 PeV by interactions with the thermal photons from the dust torus (purple). The dashed gray curves show the neutrino emission expected without external photons (corresponding to a true BL Lac). In the upper panel, we show in green the 68% CL limits on the ten-year point-source flux from the direction of TXS 0506+056 under the assumption of a hard signal spectrum Rodrigues:2024fhu and in red the latest IceCube ultra-high-energy flux limits IceCubeCollaborationSS:2025jbi. The pink band in the bottom panel is the energy range of the KM-230213A muon detected by KM3NeT KM3NeT:2025npi.
  • Figure 5: Extended jet model applied to IceCube candidate blazar 3HSP J1528+2004 Rodrigues:2024fhu. The curves are color-coded as in Fig. .
  • ...and 2 more figures