Development of General Relativistic Magnetohydrodynamic Code and its
  Application to Central Engine of Long Gamma-Ray Bursts
  In order to investigate formation of relativistic jets at the center of a
progenitor of a long gamma-ray burst (GRB), we develop a two-dimensional
general relativistic magnetohydrodynamic (GRMHD) code. We show the code passes
many, well-known test calculations, by which the reliability of the code is
confirmed. Then we perform a numerical simulation of a collapsar using a
realistic progenitor model. It is shown that a jet is launched from the center
of the progenitor. We also find that the mass accretion rate after the launch
of the jet shows rapid time variability that resembles to a typical time
profile of a GRB. The structure of the jet is similar to the previous study: a
poynting flux jet is surrounded by a funnel-wall jet. Even at the final stage
of the simulation, bulk Lorentz factor of the jet is still low, and total
energy of the jet is still as small as 10^48 erg. However, we find that the
energy flux per unit rest-mass flux is as high as 10^2 at the bottom of the
jet. Thus we conclude that the bulk Lorentz factor of the jet can be
potentially high when it propagates outward. It is shown that the outgoing
poynting flux exists at the horizon around the polar region, which proves that
the Blandford-Znajek mechanism is working. However, we conclude that the jet is
launched mainly by the magnetic field amplified by the gravitational collapse
and differential rotation around the black hole, rather than the
Blandford-Znajek mechanism.
