High-energy neutrino signatures of embedded GRB jets in AGN disks: a dynamic jet-propagation framework
Relativistic jets embedded in active galactic nucleus (AGN) accretion disks are promising high-energy neutrino sources, but their emission is often estimated from a single representative jet state. We develop a time-dependent framework that follows jet-head propagation, evolving reverse-shock conditions, and particle cooling until the jet chokes or breaks out, and apply it to the SG and TQM disk models. For the representative choked cases, neutrino emission is dominated by the high-dissipation phase near jet stalling, allowing a stalling-state approximation to reproduce the trajectory-integrated, detector-weighted event yield within approximately $14\%$. In breakout cases, however, rapid jet-head acceleration across steep disk-density gradients suppresses reverse-shock dissipation and can cause single-state estimates to overpredict the fluence, even after accounting for the available energy budget. Full trajectory integration also reshapes the high-energy spectral tail and produces distinct detectability patterns across SMBH mass and disk radius for the two disk models. Some lower-density outer-disk cases develop harder tails extending into the 10--100 PeV range, motivating future ultra-high-energy neutrino searches. Resolving jet propagation dynamics is therefore indispensable for evaluating embedded transients across AGN disk environments and avoiding systematic biases in multi-messenger modeling.