A possible energy mechanism for cosmological γ-ray bursts

Abstract

We suggest that an extreme Kerr black hole with a mass ∼106M⊙, a dimensionless angular momentum A ∼ 1 and a marginally stable orbital radius rms ∼ 3rs ∼ 1012M6 cm located in a normal galaxy may produce a γ-ray burst (GRB) by capturing and disrupting a star. During the capture period, a transient accretion disc is formed and a strong transient magnetic field ∼2.4 × 109M-1/2 6 G, lasting for rms/c ∼ 30M6 s, may be produced at the inner boundary of the accretion disc. A large amount of rotational energy of the black hole is extracted and released in an ultrarelativistic jet with a bulk Lorentz factor Γ larger than 103 via the Blandford-Znajek process. The relativistic jet energy can be converted into γ-radiation via an internal shock mechanism. The GRB duration should be the same as the lifetime of the strong transient magnetic field. The maximum number of sub-bursts is estimated to be rms/h ∼ (10-102) because the disc material is likely to break into pieces with a size about the thickness of the disc h at the cusp (2rs ≤ r ≤ 3rs). The shortest risetime of the burst estimated from this model is ∼h/Γc ∼ 3 × 10-4Γ-1 3(h/r)-2M6S. The model GRB density rate is also estimated.