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.Subject headings: accretion, accretion disk-black hole physics -magnetic fieldsgamma rays: bursts -neutrinos Recently, the magnetic coupling (MC) between the central spinning BH and their surrounding accretion disk has been paid much attention (e.g. Blandford 1999;van Putten 1999;Li & Paczynski 2000;Li 2002;Wang et al. 2002). As a variant of the BZ process, the MC process exerts a torque on the disk, and transports the rotational energy from the BH to the disk. The effects of MC torque has been discussed in some disk models, for example, Lai (1998) and Lee (1999) in a neutron star with slim disk, Li (2002), Wang et al. (2002Wang et al. ( , 2003, Kluzniak and Rappaport (2007) in a compact object with thin disk, Ye et al. (2007) and Ma et al. (2007) in a BH with advection-dominated accretion flow (ADAF). It is found, the disk properties are greatly changed and its luminosity is augmented significantly due to the rotational energy of BH extracted in the MC process. Therefore, it is attractive for us to investigate the effects of MC torque on NDAF. To highlight the effects of MC torque, we ignore other MHD process, such as BZ and BP mechanism, and we refer to this model as
MCNDAF.This paper is organized as follows. In Sect. 2 we describe the MCNDAF model, which is a relativistic steady state thin disk. The effects of MHD stress are described by the dimensionless parameter α. The main equations are based on DPN02 and NPK01.Recently, GLL06, Chen & Beloborodov (2006) and Shibata et al. (2006Shibata et al. ( , 2007 argued that the general relativistic (GR) effects are important for NDAF, so we introduce GR correction factors to the equations. The MC torque appears in the angular momentum equation.
