Neutrino Production in Active Galactic Nuclei

• Neutrino production in AGN is characterized by high-energy proton interactions with dense photon and matter fields in regions like disk coronae, jets, and transient events.
• Key mechanisms include photo-meson (pγ) and hadronuclear (pp) processes, with empirical scaling linking X-ray luminosity to neutrino emission.
• Observations from IceCube and X-ray studies support AGN as significant sources in the TeV–PeV neutrino background, guiding future cross-correlation analyses.

Active Galactic Nuclei (AGN) are the most luminous persistent sources in the Universe, powered by accretion onto supermassive black holes (SMBHs). These systems host physical environments where particle acceleration to extreme energies is inevitable. The production of high-energy (TeV–PeV) neutrinos in AGN is of particular interest after the detection of a diffuse astrophysical neutrino flux by the IceCube Observatory. Accumulating evidence—including neutrino associations with both blazars and radio-quiet Seyfert galaxies—suggests that AGN play a dominant role in the extragalactic neutrino background. The key mechanisms, physical environments, and empirical constraints on neutrino production in AGN are detailed below, focusing on the interplay of cosmic-ray acceleration, photon and matter targets, and the scaling relations that link neutrino emission to AGN observables.

1. Physical Environments and Neutrino Production Channels

Neutrino production in AGN is governed by the interaction of relativistic protons (cosmic rays) with dense photon or matter fields. The main environments are the inner jets (blazars), accretion disk coronae, and, for transient events, embedded stellar explosions in AGN accretion disks.

(a) Coronae and Disk-Corona Systems:

AGN coronae are hot, magnetized plasma layers located just above the optically thick, geometrically thin accretion disks. These regions, with typical radii $R_{\mathrm{corona}}\sim10^{13-14}$ cm and magnetic fields $B\sim10^2$–$10^4$ G, host intense soft X-ray radiation fields, with photon densities $n_{\mathrm{ph}}\sim10^{11-16}\,\mathrm{cm}^{-3}$ for $L_X\sim10^{42-44}$ erg/s (Chen et al., 22 Dec 2025, Abbasi et al., 2021, Fiorillo et al., 8 Apr 2025). Protons are accelerated via turbulence, magnetic reconnection, or shocks up to $E_p\gtrsim100$ TeV.

(b) Inner and Extended Jets:

In jet-dominated (radio-loud) AGN, such as blazars, neutrino production occurs in the inner parsec-scale jet regions through photo-meson production (pγ) with synchrotron and external (BLR/torus) photon fields (Murase et al., 2014, Boettcher, 2023). The relevant target photon fields and geometries determine the characteristic energy and beaming patterns of the neutrino signal.

(c) Transient Environments:

Explosive events embedded in AGN disks—for example, supernovae or mergers—inject shocks into dense disk gas, leading to efficient hadronuclear (pp) neutrino production after the breakout (Zhu et al., 2021, Zhou et al., 2022).

(d) Neutron–Disk Interactions:

An additional channel involves the injection of relativistic neutrons—liberated by photodisintegration of nuclei in the jets—which then interact and cascade in the accretion disk, efficiently producing neutrinos (Bednarek, 2016).

2. Microphysics of Neutrino Production

High-energy neutrinos originate from hadronic interactions of cosmic-ray protons via two dominant processes:

Photo-meson ($p\gamma$) Channel:

Relativistic protons interact with UV/X-ray photons:

$$p + \gamma \rightarrow \Delta^+ \rightarrow \left\{ \begin{array}{l} n + \pi^+ \rightarrow \mu^+ + \nu_\mu \rightarrow e^+ + \nu_e + \bar{\nu}_\mu + \nu_\mu\ p + \pi^0 \rightarrow 2\gamma \end{array} \right.$$

The $p\gamma$ energy threshold for interaction in the AGN frame is $E_p\varepsilon_\gamma\sim0.3\,\mathrm{GeV}^2$; for X-ray photons ($\varepsilon_\gamma\sim10\,\mathrm{keV}$), $E_p\sim10^5$ GeV is required (Kun et al., 2024, Chen et al., 22 Dec 2025).

The interaction rate is: $$t_{p\gamma}^{-1}(E_p) = c \int d\varepsilon\, n_{\mathrm{ph}}(\varepsilon)\, \sigma_{p\gamma}(\varepsilon_r)\, \kappa_{p\gamma}$$ where $\sigma_{p\gamma}\sim5\times10^{-28}$ cm² near the $\Delta$-resonance, $\kappa_{p\gamma}\sim0.2$ is the inelasticity.

Hadronuclear ($pp$) Channel:

Relativistic protons collide with ambient nucleons: $$p + p \rightarrow \pi^\pm + X; \quad \pi^\pm \rightarrow \mu^\pm + \nu_\mu (\bar{\nu}_\mu) \rightarrow e^\pm + \nu_e (\bar{\nu}_e) + \nu_\mu (\bar{\nu}_\mu)$$ The $pp$ cross-section at TeV–PeV is $\sigma_{pp}\sim5\times10^{-26}$ cm².

Efficiency and Scaling:

The efficiency for $p\gamma$ or $pp$ interactions is given by the respective optical depths, $f_{p\gamma}=\tau_{p\gamma}$ and $f_{pp}$, and the fraction of proton energy converted into neutrinos is $η_ν\sim\min[1,τ_{p\gamma}]$ (for $p\gamma$) (Kun et al., 2024, Chen et al., 22 Dec 2025).

3. Scaling Relations and Population Synthesis

Empirical and theoretical work consistently supports a direct scaling between AGN X-ray luminosity and neutrino luminosity: $L_\nu \propto L_X^\alpha$ with $\alpha\sim1$ for coronal and mixed populations (Abbasi et al., 2021, Chen et al., 22 Dec 2025, Kun et al., 2024). The linear scaling arises because both proton magnetization and X-ray photon energy density are set by accretion physics and magnetic dissipation in the corona (Fiorillo et al., 8 Apr 2025, Karavola et al., 4 Jan 2026).

The observed correlation between all-flavor neutrino flux and hard X-ray (15–55 keV) flux is remarkably tight across both radio-loud and radio-quiet AGN, with $F_\nu\approx F_X$ within measurement uncertainties for confirmed neutrino emitters (Kun et al., 2024). This proportionality is attributed to efficient γ-ray attenuation in the coronal region, causing all pionic electromagnetic output to emerge as reprocessed X-ray flux.

Diffuse background calculations use AGN X-ray luminosity functions $\phi(L_X, z)$ (e.g., Ueda et al. 2014) integrated over the AGN population and redshift: $$\Phi_\nu(E_\nu) = \int dz \int dL_X\, \phi(L_X, z) \frac{dN_\nu}{dE_\nu}(L_X, z) \frac{1}{4\pi D_L^2(z)} \frac{dV_c}{dz}$$ (Chen et al., 22 Dec 2025, Fiorillo et al., 8 Apr 2025).

4. Observational Results and Empirical Constraints

Stacking analyses of IceCube data at the position of thousands of IR- and X-ray-selected AGN have yielded the following principal results:

• A $2.60\sigma$ post-trial excess of high-energy neutrino events coincident with IR-selected, X-ray-bright AGN, with best-fit spectral index $\gamma=1.94$ (IR sample), consistent with $E^{-2}$ Fermi acceleration (Abbasi et al., 2021).
• The observed neutrino spectrum matches the predicted one for stochastic/turbulent proton acceleration in magnetized AGN coronae with characteristic parameters $B\sim10^4$ G, $R\sim10$–$100\,r_g$, yielding $\langle E_\nu\rangle\sim10$ TeV and a sub-linear $L_\nu\propto L_X^{0.8}$ relation (Fiorillo et al., 8 Apr 2025).
• After completeness corrections, 27–100% of the observed astrophysical neutrino flux at $E\sim100$ TeV can be accounted for by AGN core populations under the linear X-ray–neutrino scaling (Abbasi et al., 2021).

A key discriminant of the coronal model is the absence or strong attenuation of GeV–TeV γ-rays emanating from the core; this ensures consistency with Fermi-LAT bounds and the observed lack of accompanying γ-ray signals in neutrino-bright Seyferts (Chen et al., 22 Dec 2025, Kun et al., 2024).

5. Alternative and Supplementary Neutrino Production Mechanisms

(a) Inner Jet Production:

Jet-based scenarios, prominent in blazars, operate at lower ambient photon densities and yield distinct beaming patterns, with external photon fields producing neutrinos beamed as sharply as $\propto[1+\Gamma^2\theta^2]^{-(3+p)}$ (typical $p\sim2$–2.5) (Boettcher, 2023). The overall contribution to the isotropic neutrino background from FSRQs and BL Lacs is limited by IceCube upper bounds (FSRQs $\ll$ full observed signal, BL Lacs marginally allowed at PeV energies) (Murase et al., 2014, Jacobsen et al., 2015).

(b) Stellar Explosions in AGN Disks:

Supernovae and other transients embedded in AGN disks can produce significant neutrino bursts via $pp$ interactions post-breakout, but the cosmic rate and density structure of disks limit their diffuse contribution to $\sim10$% of IceCube’s background, even under optimistically dense circumdisk conditions (Zhu et al., 2021, Zhou et al., 2022).

(c) Neutron-Driven Cascade Models:

Photo-disintegration of nuclei in AGN jets injects relativistic neutrons toward the disk. Hadronic cascades ensue in high-density regions, yielding neutrino spectra matching IceCube observations if 5% of galaxies are AGN and a few percent of the neutrons are captured by the disk (Bednarek, 2016).

6. Key Constraints, Uncertainties, and Empirical Markers

• X-ray Luminosity and Variability: Strong, persistent hard X-ray flux and high mid-infrared (MIR) variability (δf) are reliable markers of AGN neutrino activity, discriminating confirmed neutrino emitters from the general AGN population (Zhou et al., 21 Nov 2025).
• Gamma-ray Opacity: Gamma-ray absorption by pair production ($\tau_{\gamma\gamma}\gg1$) in the corona is essential to hide accompanying γ-rays and remain compatible with Fermi-LAT constraints. The ratio $\tau_{\gamma\gamma}\simeq10^3\tau_{p\gamma}\gg1$ holds in the coronal models (Kun et al., 2024).
• Energy Partition and Magnetization: The level of coronal magnetization ($\sigma_p\sim10^5$) and fraction of magnetic energy converted to nonthermal protons ($η_p$) set the normalization of the neutrino flux (Karavola et al., 4 Jan 2026). Only $\sim10$% of AGN coronae need reach high $\sigma_p$ to fit the IceCube spectrum below PeV energies; above $E_\nu\sim1$ PeV, an additional contribution from BL Lac jets is required due to synchrotron cooling in strong magnetic fields.

7. Outlook and Theoretical Developments

Current and next-generation neutrino telescopes—IceCube-Gen2, KM3NeT, HUNT—combined with wide-field X-ray and MIR monitoring, will enable high-significance spatial and temporal cross-correlation studies to decisively test the AGN population origin of the TeV–PeV neutrino background (Chen et al., 22 Dec 2025). Essential measurement strategies include:

• Time-dependent stacking that prioritizes AGN with persistent high X-ray luminosity and large MIR amplitude over multi-year baselines.
• Energy-resolved spatial cross-correlation of neutrinos >100 TeV with high-completeness X-ray AGN catalogs; with angular resolution $\sim0.2^\circ$ and 5-year exposures, the AGN–neutrino connection can be probed at $2.4\sigma$ (IceCube-Gen2) to $8.6\sigma$ (HUNT) (Chen et al., 22 Dec 2025).

Critical theoretical uncertainties remain in the energy partition between magnetic, proton, and X-ray components of the corona; precise geometry and microphysics of the acceleration regions; completeness and bias of AGN X-ray catalogs; and scaling laws' possible dependence on AGN subclass (blazar, Seyfert, LLAGN, etc.) (Fiorillo et al., 8 Apr 2025, Jacobsen et al., 2015). Nevertheless, multiple lines of evidence now support AGN accretion-disk/coronae as the dominant source class for the observed diffuse extragalactic neutrino background in the TeV–PeV regime.