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

¹ European Southern Observatory Karl-Schwarzschild-Straße 2 85748 Garching bei München, Germany
² Excellence Cluster ORIGINS Boltzmannstr. 2 D-85748 Garching bei München, Germany
³ Max-Planck-Institut für Plasmaphysik Boltzmannstr. 2 DE-85748 Garching, Germany
⁴ Institute for Theoretical Physics, Heidelberg University Philosophenweg 12 69120 Heidelberg, Germany

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 25 August 2025
Accepted: 17 December 2025

Abstract

Context. Jetted active galactic nuclei aligned with our line of sight known as 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 are limited by the commonly used single-zone approximation and reliance on phenomenological parameters.

Aims. We tested the scenario where energetic protons are continuously accelerated up to ultra-high energies in inner blazar jets, while accounting for the source energetics and jet dynamics.

Methods. We present a new leptohadronic model, where a sub-Eddington jet evolves from being magnetically to kinetically dominated. A constant fraction of 10⁻⁶–10⁻⁸ of the electrons and protons picked up by the jet are continuously accelerated to a power-law spectrum. We can estimate their normalization and maximum energies based on the local magnetic field strength, turbulence, and medium density, for which we assumed power-law profiles. The model parameters are thus directly tied to the jet physics and are comparable in number to a single-zone model. We then calculate the emission along the jet, including neutrinos and electromagnetic cascades.

Results. Applying the model to IceCube candidate TXS 0506+056, we find that protons accelerated in the inner jet produce a neutrino flux up to ∼100 PeV that is consistent with the public IceCube ten-year point-source data. Proton emission at 0.1 pc describes the X-ray and γ-ray data, while electron emission at the parsec scale describes the optical data. Protons carry a power of about 1% of the Eddington luminosity. 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 applied the model to the blazar PKS 0605-085, which could be associated with a recent neutrino detected by KM3NeT above 100 PeV.

Conclusions. Magnetic acceleration in blazar jets can describe multimessenger observations with viable energetics. Our model constrains jet properties such as the energy-dependent particle diffusion and predicts the spatial distribution of the multiwavelength and neutrino emission along the jet. 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.