  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.
