Hyperaccreting Disks around Magnetars for Gamma-Ray Bursts: Effects of Strong Magnetic Fields

(Abridged) The hyperaccreting neutron star or magnetar disks cooled via neutrino emission can be a candidate of gamma-ray burst (GRB) central engines. The strong field $\geq10^{15}-10^{16}$ G of the magnetar can play a significant role in affecting the disk properties and even lead to the funnel accretion process. We investigate the effects of strong fields on the disks around magnetars, and discuss implications of such accreting magnetar systems for GRB and GRB-like events. We discuss quantum effects of the strong fields on the disk, and use the MHD conservation equations to describe the behavior of the disk flow coupled with a large scale field, which is generated by the star-disk interaction. In general, stronger fields give higher disk densities, pressures, temperatures and neutrino luminosity, and change the electron fraction and degeneracy state significantly. A magnetized disk is always viscously stable outside the Alfv\'{e}n radius, but will be thermally unstable near the Alfv\'{e}n radius where the magnetic field plays a more important role in transferring the angular momentum and heating the disk than the viscous stress. The funnel accretion process will be only important for an extremely strong field, which creates a magnetosphere inside the Alfv\'{e}n radius and truncates the plane disk. Because of higher temperature and more concentrated neutrino emission of the magnetar surface ring-like belt region covered by funnel accretion, the neutrino annihilation rate from the accreting magnetars can be much higher than that from accreting neutron stars without fields. Furthermore, the neutrino annihilation mechanism and the magnetically-driven pulsar wind from the magnetar surface can work together to generate and feed an ultra-relativistic jet along the stellar magnetic poles.