Abstract
A toy model of gamma-ray burst supernovae (GRB SNe) is discussed by considering the effects of the screw instability of the magnetic field in the black hole (BH) magnetosphere. The screw instability in the Blandford-Znajek (BZ) process (henceforth the SIBZ) can coexist with the screw instability in the magnetic coupling (MC) process (henceforth the SIMC). It turns out that both the SIBZ and SIMC occur inevitably, provided that the following parameters are greater than some critical values: (1) the BH spin, (2) the power-law index describing the magnetic field at the disk, and (3) the vertical height of the astrophysical load above the equatorial plane of the rotating BH. The features of several GRBs are well fitted. In our model the durations of the long GRBs depend on the evolution time of the half-opening angle. A small fraction of energy is extracted from the BH via the BZ process to power a GRB, while a large fraction of energy is extracted from the BH via the MC process to power an associated supernova. In addition, the variability timescales of tens of milliseconds in the light curves of the GRBs are fitted by two successive flares due to the SIBZ.
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