High-energy neutrino signatures of embedded GRB jets in AGN disks: a dynamic jet-propagation framework

The paper develops a time-dependent framework for calculating high-energy neutrino emission from relativistic jets embedded in active galactic nucleus (AGN) accretion disks, following the full jet propagation history rather than relying on single-state approximations.

The framework tracks jet-head propagation, evolving reverse-shock conditions, and particle cooling until the jet either chokes within the disk or breaks out. It is applied to two disk models: the SG (Sirko-Goodman) and TQM (Thompson-Quataert-Murray) prescriptions. The jet-head velocity is determined by the dimensionless jet-head luminosity, and the reverse shock becomes collisionless only when the Thomson optical depth of the unshocked jet satisfies a specific condition. Neutrino production is included only during collisionless reverse-shock phases.

Six representative trajectories are analyzed, spanning three dynamical regimes: breakout cases (SG-1, TQM-1, with engine-clock ratio Rdur ≤ 1), moderately choked cases (SG-2, TQM-2, Rdur 10–50), and deeply choked cases (SG-3, TQM-3, Rdur ≫ 103). The engine-clock ratio Rdur ≡ treq/tdur determines whether breakout occurs.

Key results:

1. Time-resolved emission: Breakout trajectories show a distinct signature where instantaneous flux increases during head deceleration and turns over as the head accelerates toward the disk surface. Choked trajectories show light curves that rise continuously or flatten toward the end, terminating abruptly upon engine exhaustion. The instantaneous spectra evolve in both normalization and high-energy cutoff.

2. Proton cooling hierarchy: Across all cases, pγ photomeson interactions dominate at the highest proton energies, Bethe-Heitler pair production occupies an intermediate band, and either pp interactions or adiabatic expansion dominates at lower energies. The ratio of photon-to-proton target densities scales as n′γ/n′p ∝ Γ̄h z h 1/2, continuously boosting pγ and BH pair production over pp collisions as the jet head advances during deceleration.

3. Single-state approximation validity: For all four choked trajectories, stalling-state approximations reproduce the full time-integrated detector event counts within ≈14%. This works because the reverse-shock dissipation power scales as 1 − βh, which peaks when the jet head decelerates to minimum velocity near the stalling radius, dominating the integrated yield.

4. Breakout cases: For breakout trajectories, jet propagation extends into outer disk layers where the head accelerates. In TQM disks with gentle density gradients, pre-breakout approximations with energy normalization Eiso Rdur agree within ≈9%. However, in SG disks with steep density gradients, late-stage acceleration drives 1 − βh → 0, and even the pre-breakout approximation overpredicts the true time-integrated yield by a factor of 2.6. Energy truncation cannot correct errors driven by dynamic dissipation evolution.

5. Detector yields: At DL = 100 Mpc, the representative cases yield expected IC86 muon-track counts ranging from order 0.1 to 1.4, with detection probabilities P = 1 − exp(−Ndet) up to ≈82% (Ndet ≈ 1.7). The SG model shows a high-probability region that broadens and shifts outward toward higher SMBH masses, while the TQM model generates an extended high-probability plateau with weaker mass dependence.

6. Spectral hardening: The low-density, deeply choked TQM-3 trajectory experiences reduced meson and muon cooling, producing a harder neutrino spectrum with a high-energy tail reaching 102 PeV. This tail overlaps the ultra-high-energy range targeted by IceCube-Gen2 Radio Array and approaches the low-energy edge of GRAND. However, this spectral hardening shifts part of the neutrino output away from the energy range contributing most efficiently to IC86 muon-track yields.

7. Flavor composition: After oscillation-averaged PMNS mixing, the Earth-side muon-flavor fraction is confined to a narrow 0.34–0.41 range across the energy spectrum. The time-dependent results show a prominent discrepancy with single-state approximations for SG-1, while choked trajectories and TQM-1 exhibit more similar flavor profiles.

The paper concludes that resolving jet propagation dynamics is indispensable for evaluating embedded transients across AGN disk environments, as single-state approximations can introduce systematic biases in multi-messenger modeling. The framework provides the physical foundation for future population-level multi-messenger synthesis incorporating distributions of engine duration, disk structure, and compact-object merger or collapse rates.

Improvements to AI Systems:

1. Time-Dependent Multi-Messenger Event Generators: Replace static single-state approximations with dynamic jet-propagation simulators that track jet-head velocity, reverse-shock luminosity, and particle cooling over time. The improved system can generate realistic neutrino light curves and spectra for AGN-embedded transients, correctly capturing the turnover in flux during breakout and the abrupt termination upon engine exhaustion.

2. Adaptive Physics-Integrated Inference Engines: Incorporate the derived scaling law n′γ/n′p ∝ Γ̄h z h 1/2 and the 1 − βh dissipation weighting into AI models. This enables the system to automatically prioritize pγ and Bethe-Heitler processes over pp interactions during deceleration phases, improving predictions of proton cooling hierarchies without manual recalibration.

3. Uncertainty-Aware Surrogate Models for Choked Jets: Train AI surrogates to exploit the finding that stalling-state approximations match time-integrated yields within ≈14% for choked jets. The improved system can rapidly estimate detector event counts (e.g., IC86 muon tracks) for large parameter sweeps of engine duration and disk density profiles, with built-in error bounds, enabling fast population-level scans.

4. Breakout-Aware Correction Modules: For breakout jets, implement a dynamic correction factor that accounts for late-stage head acceleration. In steep-density-gradient disks (e.g., SG), the system flags when pre-breakout approximations overpredict yields by >2× and applies a dissipation-evolution correction, rather than relying on energy truncation. This prevents systematic overestimation in multi-messenger follow-up predictions.

5. Spectral Hardening Detector and Optimizer: Use the finding that deeply choked, low-density trajectories produce harder spectra with tails reaching 102 PeV. The improved AI can identify which disk and engine parameters yield such ultra-high-energy neutrino tails, then optimize observational strategies for IceCube-Gen2 Radio Array and GRAND by shifting detection thresholds or exposure times to capture these events.

6. Flavor-Composition-Aware Classification: Integrate the narrow Earth-side muon-flavor fraction (0.34–0.41) and its energy dependence into AI-based event classifiers. The system can distinguish between breakout and choked jet scenarios by comparing observed flavor ratios to time-dependent predictions, reducing misclassification in neutrino telescopes.

7. Population-Level Multi-Messenger Synthesizer: Build a generative model that combines distributions of engine duration (Rdur), disk structure (SG vs. TQM), and merger/collapse rates. The improved system can produce synthetic catalogs of neutrino sources with realistic time-dependent emission, enabling joint likelihood analyses with gravitational-wave and electromagnetic surveys to constrain jet-choking fractions and AGN disk properties.