Recent observations and theoretical work on gamma-ray bursts (GRBs) favor the central engine model of a Kerr black hole (BH) surrounded by a magnetized neutrino-dominated accretion flow (NDAF). The magnetic coupling between the BH and disk through a large-scale closed magnetic field exerts a torque on the disk, and transports the rotational energy from the BH to the disk. We investigate the properties of the NDAF with this magnetic torque. For a rapid spinning BH, the magnetic torque transfers enormous rotational energy from BH into the inner disk. There are two consequences: (i) the luminosity of neutrino annihilation is greatly augmented; (ii) the disk becomes thermally and viscously unstable in the inner region, and behaves S-Shape of the surface density versus accretion rate. It turns out that magnetically torqued NDAF can be invoked to interpret the variability of gamma-ray luminosity. In addition, we discuss the possibility of restarting the central engine to produce the X-ray flares with required energy.
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