General Relativistic Magnetohydrodynamic Simulations of the Gravitational Collapse of a Rotating Star with Magnetic Field as a Model for Gamma-Ray Bursts

We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of the gravitational collapse of a magnetized rotating massive star as a model of gamma ray bursts (GRBs). Initially, a few M⊙ black hole is produced at the center of the stellar remnant with a weak shock standing at a radius of a few hundred km and the post-shock gas falling onto the central black hole. We show the formation of a disk-like structure and the generation of a jet-like outflow inside the shock wave launched at the core bounce. We have found the jet is accelerated by the magnetic pressure and the centrifugal force and is collimated by the pinching force of the toroidal magnetic field amplified by the rotation and the effect of geometry of the poloidal magnetic field. The maximum velocity of the jet is mildly relativistic (∼ 0.3 c). The velocity of jet becomes larger as the initial rotational velocity of stellar matter gets faster. On the other hand, the dependence on the initial magnetic field strength is a bit more complicated: the velocity of jet increases with the initial field strength in the weak field regime, then is saturated at some intermediate field strength, and decreases beyond the critical field strength. These results are related to the stored magnetic energy determined by the balance between the propagation time of Alfvén wave and the rotation time of the disk (or twisting time). Department of Astronomy, Kyoto University, Sakyo, Kyoto 606-8502, Japan; [email protected] Department of Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan; [email protected] Department of Engineering, Toyama University, Gofuku, Toyama 930-8555, Japan; [email protected] Kwasan and Hida Observatory, Kyoto University, Yamashina, Kyoto 607-8471, Japan; [email protected]