2025ApJ...980...68K

We investigate the relativistic, viscous, advective neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black holes, incorporating neutrino cooling. By adopting an effective potential to describe the spacetime geometry around the rotating black holes, we self-consistently solve the governing NDAF equations to obtain global transonic accretion solutions. Our findings indicate that, depending on the model parameters, namely, energy (ε), angular momentum (λ), accretion rate ($\dot{m}$), viscosity (α), and black hole spin (a_k), NDAFs may harbor standing shocks where the Rankine-Hugoniot shock conditions are satisfied. Utilizing these shock-induced NDAF solutions, we compute the neutrino luminosity (L_ν) and neutrino annihilation luminosity (${L}_{\nu \bar{\nu }}$) across a wide range of model parameters. We further calculate maximum neutrino luminosity (${L}_{\nu }^{{\rm{\max }}}$) and neutrino annihilation luminosity (${L}_{\nu \bar{\nu }}^{{\rm{\max }}}$), resulting in ${L}_{\nu }^{{\rm{\max }}}\sim 1{0}^{51-53}$ erg s^–1 (10^48–51 erg s^–1) and ${L}_{\nu \bar{\nu }}^{{\rm{\max }}}\sim 1{0}^{48-52}$ erg s^–1 (10^42–49 erg s^–1) for a_k = 0.99 (0.0). These findings suggest that shocked NDAF solutions are potentially promising to explain the energy output of gamma-ray bursts (GRBs). We employ our NDAF model formalism to elucidate ${L}_{\nu \bar{\nu }}^{{\rm{obs}}}$ for five GRBs with known redshifts and estimate their accretion rate ($\dot{m}$) based on the spin (a_k) of the central source of the GRBs studied here.