It was suggested that the relativistic jets in gamma-ray bursts ( GRBs ) are powered via the Blandford-Znajek ( BZ ) mechanism or the annihilation of neutrinos and anti-neutrinos from a neutrino cooling-dominated accretion flow ( NDAF ) .
The advection and diffusion of the large-scale magnetic field of a NDAF is calculated , and the external magnetic field is found to be dragged inward efficiently by the accretion flow for a typical magnetic Prandtl number \mathscr { P } _ { m } = \eta / \nu \sim 1 .
The maximal BZ jet power can be \sim 10 ^ { 53 } -10 ^ { 54 }  erg s ^ { -1 } for an extreme Kerr black hole , if an external magnetic field with 10 ^ { 14 }  Gauss is advected by the NDAF .
This is roughly consistent with the field strength of the disk formed after a tidal disrupted magnetar .
The accretion flow near the black hole horizon is arrested by the magnetic field if the accretion rate is below than a critical value for a given external field .
The arrested accretion flow fails to drag the field inward and the field strength decays , and then the accretion re-starts , which leads to oscillating accretion .
The typical timescale of such episodic accretion is in an order of one second .
This can qualitatively explain the observed oscillation in the soft extend emission of short-type GRBs .