Self-Consistent Modelling of Neutrino Production in Turbulent Black Hole Coronae

Abstract

Stochastic particle acceleration in magnetized turbulent plasmas has emerged as a key mechanism to explain multi-messenger signals from compact astrophysical environments. Self-consistent modelling remains challenging because it requires to treat simultaneously several non-linear kinetic processes, especially turbulence-driven acceleration and its feedback on the turbulent cascade, as well as the radiative and hadronic losses, including the reprocessing of electromagnetic radiation in radiatively dense environments. The present paper introduces the hybrid numerical code Turb-AM3 designed to this effect. This hybrid numerical code couples the state-of-the-art time-dependent lepto-hadronic radiative solver AM3 with a stochastic acceleration module that incorporates recent theoretical advances in turbulent acceleration and accounts for the dynamical damping of turbulence by accelerated particles. In a second part, we use this code to provide self-consistent time-dependent models of proton acceleration in the turbulent black hole corona of NGC~1068. We find that the IceCube neutrino signal is well reproduced for a standard set of physical parameters describing the black hole corona. The same template model accounts in a satisfactory way for IceCube observations of other active galactic nuclei. Furthermore, our exploration of parameter space allows us to predict detailed template spectral shapes for the TeV neutrino spectrum, which in turn help understand how future neutrino observations can constrain the properties of turbulent AGN coronae and the underlying acceleration mechanism. This Turb-AM3 framework provides a powerful tool to model multi-messenger emission in a broad variety of compact astrophysical environments.

Figures (9)

• Figure 1: Timescales of the different processes occurring in the AGN corona, including the escape of charged and neutral particles, the acceleration of protons, radiative and hadronic losses of protons and electrons/positrons, $\gamma\gamma$ annihilation of photons and the advection timescale of the coronal plasma.
• Figure 2: Photon (blue) and neutrino (red) spectra from NGC 1068 computed with Turb-AM3 for a fiducial set of parameters: $L_d = 5.0 \times 10^{44} \, \mathrm{erg \, s^{-1}}$, $R_\mathrm{cor} = 15 \, r_g$, $\xi_p = 0.1$, $\ell_c = 4.0 \, r_g$, $v_\mathrm{adv} = 0.03 \, c$, and $v_\mathrm{A} = 0.25 \, c$. The contributions from the different radiative and interaction processes are shown separately. BH denotes Bethe–Heitler pair production, $\gamma\gamma$ indicates photon–photon self-absorption, and IC refers to inverse Compton scattering. All spectra are shown as fluxes observed at Earth, assuming a luminosity distance of $10\,\mathrm{Mpc}$. Neutrino data from IceCube abbasiEvidenceNeutrinoEmission2025 and electromagnetic observations changOpenUniverseVOUBlazars2019thefermicollaborationFermiLargeArea2020magiccollaborationConstraintsGammarayNeutrino2019 are included for comparison. The stationary proton spectrum obtained with Turb-AM3 is displayed in grey in the inset, where the energy distribution is normalized to the background plasma pressure $P_\mathrm{th}$.
• Figure 3: Top panel: Time evolution of the integrated proton spectral energy distribution (SED) over the advection time $t_\mathrm{adv}$ (purple to blue), i.e. the plasma crossing time of the corona; the spectrum is expressed in units of the background plasma pressure. The stationary proton SED in the corona is shown in black. The green–orange curves display the proton SED evolution beyond $t_\mathrm{adv}$. The red curve corresponds to the proton SED obtained by integrating up to times well in excess of $t_\mathrm{adv}$, for illustration. These spectra correspond to the steady state solutions of Eq. (\ref{['eq:transport']}). Middle panel: same as the top panel, for the neutrino flux. Bottom panel: Time evolution of the magnetic turbulent cascade during the advection time. The gray region highlights the part of the inertial range that dominates particle acceleration of protons up to $100\,$TeV.
• Figure 4: Integrated proton (top panel), as well as photon and neutrino stationary (bottom panel) energy spectra. The initial energy fraction in non-thermal protons and the Alfvénic velocity are indicated for each model. The other parameters are $L_d = 5.0 \times 10^{44} \, \mathrm{erg \, s^{-1}}$, $R_\mathrm{cor} = 15 \, r_g$, $\ell_c = 4.0 \, r_g$, $v_\mathrm{adv} = 0.03 \, c$.
• Figure 5: Proton, photon, and neutrino stationary spectra for different coronal microphysics parameters, characterized by varying dimensionless time ratios $t_{\rm esc}/t_{\rm acc}$. The parameters $v_\mathrm{A}$ and $\ell_c$ are varied, while the others are fixed to $L_d = 5.0 \times 10^{44} \, \mathrm{erg\,s^{-1}}$, $R_\mathrm{cor} = 15 \, r_g$, $\xi_p = 0.1$, and $v_\mathrm{adv} = 0.03 \, c$. The same color in both panels corresponds to the same parameter set.