Neutrino-dominated relativistic viscous accretion flows around rotating black holes with shocks

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 ($\varepsilon$), angular momentum ($\lambda$), accretion rate ($\dot{m}$), viscosity ($\alpha$) and black hole spin ($a_{\rm k}$), NDAFs may harbor standing shocks where the Rankine-Hugoniot shock conditions (RHCs) are satisfied. Utilizing these shock-induced NDAF solutions, we compute the neutrino luminosity ($L_{\nu}$) 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 $L_{\nu}^{\rm max} \sim 10^{51-53}$ erg s$^{-1}$ ($10^{48-51}$ erg s$^{-1}$) and $L_{\nu \bar{\nu}}^{\rm max} \sim 10^{48-52}$ erg s$^{-1}$ ($10^{42-49}$ erg s$^{-1}$) for $a_{\rm k}=0.99$ (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 $L^{\rm obs}_{\nu \bar{\nu}}$ for five GRBs with known redshifts and estimate their accretion rate (${\dot m}$) based on the spin ($a_{\rm k}$) of the central source of GRBs under consideration.