Numerical and Analytical Solutions of Neutrino-dominated Accretion Flows with a Non-zero Torque Boundary Condition and its Applications in Gamma-Ray Bursts

A stellar-mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of a “no torque” boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses and reexamine their properties. We find that an NDAF with such a boundary torque can be powerful enough to account for those bright short GRBs, energetic long GRBs, and ultra-long GRBs. The disk becomes viscously unstable, which makes it possible to interpret the variability of GRB prompt emission and the steep decay phase in the early X-ray afterglow. Finally, we study the gravitational waves radiated from a processing BH-NDAF. We find that the effects of the boundary torque on the strength of the gravitational waves can be ignored.