Cosmogenic neutrinos from FRII galaxies as potential origin of the ultra-high-energy KM3-230213A event

Abstract: Aim : We investigate whether the ultra-high-energy neutrino KM3-230213A can be interpreted as a cosmogenic neutrino produced by ultra-high-energy cosmic rays (UHECRs) accelerated in the lobes of FRII radio galaxies. Method : We model the UHECR, cosmogenic neutrino and photon fluxes expected at Earth using a recent luminosity-dependent density evolution of radio galaxies, empirical relations between radio luminosity and jet kinetic power, and standard assumptions for the UHECR output of FRII lobes. The FRII contribution to the UHECR population is derived self-consistently from the observed luminosity function, rather than imposed as a fixed normalization. The propagation of UHECRs and the production of secondary particles are computed with well-established numerical tools. Results : The predicted cosmogenic neutrino flux is compatible with that inferred from the detection of KM3-230213A, while remaining consistent with current UHECR and gamma-ray constraints. According to our models, the full GRAND observatory ($200\,000~\rm km<sup>2$) should detect between $\sim50$ and $\sim135$ neutrinos above $10<sup>{17}$~eV in ten years, allowing the diffuse UHE neutrino spectrum to be characterized. In contrast, the detection of individual FRII sources or statistically significant correlations with FRII catalogs is likely to remain challenging. At the highest energies, UHECR composition and anisotropy measurements, in particular those related to the nearby radio galaxy Cygnus~A, should provide complementary tests of this scenario. More generally, progress will likely rely on the combination of multimessenger observations with improved astrophysical constraints on particle acceleration and jet composition in FRII radio galaxies.

• The paper shows that FRII radio galaxies with reference maximum energies of at least 10²⁰ eV can reproduce the KM3-230213A neutrino flux while satisfying Auger and Fermi-LAT constraints.
• The self-consistent population model predicts FRIIs contribute no more than about 12% of the UHECR flux, while GRAND200k could detect roughly 50–135 events above 10¹⁷ eV over ten years.
• The analysis identifies Cygnus A as a major uncertainty for UHECR composition and anisotropy, but finds individual FRII–neutrino correlations will likely remain difficult to detect.

Motivation and context

The detection of the ultra-high-energy neutrino event KM3-230213A by KM3NeT (2608.16540) has renewed interest in cosmogenic neutrino production, i.e., neutrinos generated during the intergalactic propagation of ultra-high-energy cosmic rays (UHECRs) through photon backgrounds. The standard difficulty is well known: Auger composition measurements indicate a gradual shift toward heavier nuclei above the ankle, implying that the dominant UHECR sources have maximum rigidities below the threshold for pion production on CMB photons, which suppresses the expected cosmogenic flux. However, as pointed out by Decerprit & Allard (2011), a subdominant population of proton accelerators reaching $E_{\max} > 10^{20}$ eV with strong cosmological evolution could produce a large cosmogenic neutrino flux without conflicting with composition data. Globus et al. (2017) showed such a component (5% of the UHECR flux at $10^{19}$ eV) also evades Fermi-LAT constraints on the diffuse extragalactic $\gamma$-ray background (EGRB).

The paper under discussion asks whether FRII radio galaxies provide a physically motivated realization of this scenario. Its methodological advance over previous work is that the FRII contribution to the UHECR flux is not imposed as a normalization but derived self-consistently from the observed luminosity function, empirical radio–kinetic power relations, and a physically motivated cosmic-ray efficiency.

Model construction

The source population is described by the luminosity-dependent density evolution (LDDE) model of Šlaus et al. (2024), fitted to more than 5400 radio galaxies in the 1.4 GHz band, combined with the luminosity-dependent FRII fraction from de Jong et al. (2024). The transition between FRI- and FRII-dominated regimes occurs around $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$, and the FRII fraction is assumed not to evolve with redshift — an assumption the authors acknowledge as untested.

The jet kinetic luminosity $L_{\rm kin}$ is related to $L_{1.4}$ via the power-law fit to the Machalski et al. (2021) atlas of 361 FRII galaxies, $\log(L_{\rm kin}) = 21.22 + 0.895\,\log(L_{1.4})$, close to the Willott (1999) relation with $f=4$. The scatter around this relation is significant — roughly half a decade on either side — and this uncertainty propagates directly into all predictions.

Three ingredients fix the UHECR output:

• Cosmic-ray efficiency: under minimum-energy conditions, $\epsilon_{\rm cr} = \frac{4}{7}\frac{k}{1+k}$, approaching $4/7$ in the proton-dominated limit ($10^{19}$0). The authors are explicit that this fiducial value is an optimistic asymptotic normalization rather than a prediction; all fluxes scale linearly with $10^{19}$1.
• Maximum energy: $10^{19}$2, with three models corresponding to $10^{19}$3, $10^{19}$4, and $10^{19}$5 eV.
• Injection spectrum: an $10^{19}$6 power law with exponential cutoff, appropriate to non-relativistic diffusive shock acceleration in lobes.

The calculations use 1000 Monte Carlo realizations of the FRII distribution up to $10^{19}$7, anchored by cataloged nearby sources (notably Cygnus A, assigned $10^{19}$8), with propagation computed including photomeson interactions (SOPHIA) and EBL evolution (Gilmore et al. 2012). No extragalactic magnetic field (EGMF) is included in the baseline propagation.

Diffuse multimessenger signatures

UHECRs: the FRII contribution remains subdominant for all models, never exceeding ~12% around $10^{19}$9 eV (Model 3). Above $\gamma$0 eV, Model 3 contributes ~7%, consistent with current Auger composition constraints. Cygnus A alone contributes ~3% above $\gamma$1 eV and ~6% above $\gamma$2 eV in Model 3, so its assumed properties strongly shape the highest-energy spectrum and anisotropy expectations.

Cosmogenic neutrinos: Models 2 and 3 fall within the $\gamma$3 confidence interval of the flux inferred from KM3-230213A, while Model 1 falls slightly below the lower bound of the 90% interval. This is the central result: models with $\gamma$4 eV reconcile the KM3NeT event with the non-detections by Auger and IceCube. The flux is dominated by FRIIs with $\gamma$5; near the KM3-230213A energy, roughly half comes from $\gamma$6–3, and sources beyond $\gamma$7 — where the LDDE is least constrained — still contribute ~25%. For the completed KM3NeT, only ~2.5 events above $\gamma$8 eV are expected in ten years (Model 3), meaning the actual detection already corresponds to a positive fluctuation. In contrast, GRAND200k should detect ~50–135 events above $\gamma$9 eV in ten years for Models 2–3, sufficient to characterize the diffuse spectrum's shape.

Cosmogenic photons: unlike the neutrino flux, the photon flux varies by less than a factor of two across models because it is dominated by Bethe–Heitler pair production by protons around $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$0 eV, insensitive to $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$1. Adding the Model 3 contribution to the EGRB budget (point sources, star-forming galaxies, misaligned AGNs, and the dominant UHECR component) leaves the total below the measured EGRB except in the lowest band (1.04–1.99 GeV), where it exceeds it by only ~3% — within uncertainties. The gamma-ray constraints therefore remain satisfied.

Individual sources: Cygnus A

Cygnus A dominates the individual-source signal owing to its high radio luminosity ($L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$2) and proximity ($L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$3 Mpc). Two findings stand out:

First, magnetic effects do not erase its signal. Even for a 3 nG turbulent EGMF, the UHECR spectrum above a few $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$4 eV is essentially unchanged despite time delays, and most protons above 32 EeV arrive within $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$5–$L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$6 of the source direction once Galactic fields are included; several Galactic magnetic-field models even predict magnification by a factor of 2–5 toward Cygnus A through lensing.

Second, the kinetic luminosity of Cygnus A is the dominant uncertainty, spanning about one order of magnitude across literature estimates. The consequences are stark: adopting $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$7 raises the Cygnus A contribution to ~60% of the total flux around $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$8 eV — a proton fraction difficult to reconcile with Auger composition measurements — whereas $L_{1.4}\simeq10^{26}\,\mathrm{W\,Hz^{-1}}$9 reduces it to ~0.8%. Critically, changing this value leaves the diffuse neutrino flux almost unchanged while shifting the predicted proton abundance above $L_{\rm kin}$0 eV from 0.8% to ~60%. This decoupling differs fundamentally from continuous-source treatments such as Decerprit & Allard (2011), where the neutrino flux was directly proportional to the proton contribution: explicitly modeling rare discrete sources allows the nearest object to reshape the UHECR spectrum without affecting the neutrino background.

Observability of point sources and correlations

Neutrino–source correlation is preserved because parent protons above $L_{\rm kin}$1 eV undergo photomeson interactions within ~30 Mpc of the source (essentially all $L_{\rm kin}$2 eV neutrinos above $L_{\rm kin}$3), before deflections become significant. Nevertheless, detectability is poor: all 361 FRIIs in the Machalski et al. atlas combined yield only ~3 GRAND events in ten years; Cygnus A yields ~0.24 events for the baseline $L_{\rm kin}$4, or ~3 events only under the high-$L_{\rm kin}$5 assumption that conflicts with composition data. Correlation studies with bright FRII catalogs ($L_{\rm kin}$6) fare little better: the ~11 such galaxies within $L_{\rm kin}$7 contribute on average only one of ~135 expected GRAND events. Identifying FRII galaxies as UHE neutrino sources through catalog correlations is thus likely to remain challenging.

Lobe versus jet acceleration

An exploratory extension to all radio galaxies (FRI included, acceleration in relativistic jets) shows that if FRI galaxies follow a less radiatively efficient relation (Willott $L_{\rm kin}$8), jets can account for a substantial fraction or the bulk of the observed UHECR flux, consistent with Rodrigues et al. (2021). Notably, however, the resulting cosmogenic neutrino flux is nearly identical to the lobe scenario, since the most luminous FRIIs dominate neutrino production regardless. Cosmogenic neutrinos alone therefore cannot discriminate between lobe- and jet-dominated acceleration; UHECR spectrum, composition, and anisotropy measurements retain far greater discriminating power. Jet-dominated scenarios additionally face tighter anisotropy constraints given the low local source density, though agreement with Auger data can be achieved for specific parameter combinations.

Limitations and open questions

Several caveats bear directly on the results. The adopted $L_{\rm kin}$9 is an optimistic upper limit; all fluxes scale linearly with it. The assumption of a purely protonic composition is justified by the weak dependence of the neutrino flux on mass for fixed rigidity, but the injected spectral index $L_{1.4}$0 matters: deviations of ±0.15 change the UHECR energy fraction by roughly a factor of three. A high-pass-filter escape model hardening the escaping spectrum to $L_{1.4}$1–1 modifies the neutrino flux only moderately near the KM3-230213A energy, but confined UHECRs interacting inside the source would add neutrinos not accounted for here, making the quoted fluxes potential lower limits. The LDDE is poorly constrained beyond $L_{1.4}$2, yet those redshifts contribute ~25% of the flux at the relevant energies. Whether Cygnus A can accelerate particles to the highest energies remains contested, with radio-based arguments (Araudo et al. 2018) favoring inefficient acceleration and particle-in-cell simulations (Cerutti & Giacenti 2023) a more favorable view. Finally, no quantitative assessment of catalog-correlation significance was performed, pending complete FRII catalogs and realistic angular-resolution modeling.

Conclusion

This work demonstrates that FRII radio galaxies, modeled self-consistently from their observed luminosity function and energetics, constitute a plausible origin for KM3-230213A: for $L_{1.4}$3 eV, the predicted cosmogenic neutrino flux matches the event-inferred flux within $L_{1.4}$4 while remaining compatible with Auger UHECR data and Fermi-LAT EGRB constraints, with FRIIs contributing at most ~10% of the UHECR flux between $L_{1.4}$5 and $L_{1.4}$6 eV. The scenario makes two distinct observational predictions: GRAND200k should record ~50–135 cosmogenic neutrinos above $L_{1.4}$7 eV in ten years, enabling spectral characterization, while individual-source identification will remain out of reach. The most incisive tests lie instead in UHECR observations — particularly improved composition measurements from the Auger upgrade constraining the proton output of Cygnus A — and in SKA-era multiwavelength studies of jet composition and particle acceleration. The paper leaves open whether the required high maximum rigidities are actually achieved in FRII hotspots, and whether the wide range of allowed Cygnus A contributions can be narrowed by independent constraints on its kinetic luminosity and the intervening magnetic fields.