S9-3 Numerical Simulations of Plasmas in Black Hole Magnetosphere
Shinji Koide
Faculty of Engineering, Toyama University , 3190 Gofuku, Toyama 930-8555, Japan930-8555
Relativistic jets from several kinds of objects in the universe have been found. It is believed that they are
all formed by violent phenomena near the black holes. However, the distinct mechanism of the jetformation has not yet been shown. Here we show the possibility of the relativistic jet formation by theinteraction between the plasma and the magnetic field near the rapidly rotating black hole numerically.

1. Introduction
In the universe, relativistic jets are observed in
active galactic nuclei (including quasars and BL
Lactae objects), microquasars in our galaxy, andcentral objects of gamma-ray bursts [1]. In spite ofthe drastic difference of the scale and the Lorentz
factor of these kinds of jets, it is believed that these
relativistic jets are formed by the extreme
phenomena around the black hole at the center ofthe objects. The definite mechanism of the jet has
not yet been shown. There are two problems withrespect to the jet formation, i.e. the acceleration andcollimation of the gas/plasma. The magnetic
mechanism is becoming most promising because it
can explain both of the problems at once. To
investigate the magnetic mechanism, we have
performed numerical simulations of generalrelativistic magnetohydrodynamics (GRMHD). We
showed that jet is ejected from the rotating disk
around the black hole with the global, verticalmagnetic field [2]. However, the maximum speed of
the jet is (0.3-0.5)c, where c is light speed, which is
sub-relativistic. Recently, we reported therelativistic outflow formation by the radial
magnetic field from the ergosphere around the very
rapidly rotating black hole [3]. In the ergosphereany material, information, or energy must rotate in
the same direction as the black hole due to theframe-dragging effect of the rotating black hole.
The relativistic outflow is powered by the framedragging effect through the magnetic field.
However, the relativistic outflow is not collimatedso we haven’t found any relativistic jet yet. There
are two important, various elements in thesimulation setting. One is the initial conditions of
the plasma and the other is the magnetic field
configuration around the black hole. According to
the previous calculations, we think the magnetic
field configuration is more important for the
relativistic jet formation around the black hole. We

have already used the uniform and radial magnetic
field configurations around the black hole. The next
simple configuration is dipole magnetic field.
However, the black hole can not have dipole
magnetic field because of the causality at the blackhole horizon, i.e. the electric current inside of theblack hole horizon never influence to the magnetic
field outside of the horizon. Therefore, we use themagnetic field caused by the electric current loop
located on the equatorial plane around the rotating
black hole for this study.
2. Numerical Methods
We have performed GRMHD simulations ofplasmas around black holes [2-6]. The calculations
are based on the general relativistic conservation
laws of particle number, momentum, and energy ofplasma and magnetic field and Maxwell equations.
We assume the electric resistivity is zero. We also
assume Kerr space-time around black hole. Here weuse the rotation parameter of the black hole,a =0.99995, that means the black hole rotatesalmost maximally. We solve the equations with the3+1 formalism numerically by simplified TVD
scheme which was developed by S. F. Davis [7]. We
set the quasi-equilibrium state of the plasma
initially, where the plasma is in hydrostatic
equilibrium far from the black hole horizon, and theplasma falls into the black hole smoothly near thehorizon. The initial magnetic field is calculated by
the vector potential of the current loop as shown inFigure 1 (solid lines: magnetic field lines). The
current loop locates at r=3rS, where rS is
Schwarzschid radius. The black region at the origin
shows the inside of the black hole horizon(r £ 0.505rS). The broken- line shows the surface ofthe ergosphere. The mass density near the current
loop center is larger than the uniform density of thesurrounding plasma (Fig. 1, gray-scale). Initially,
the plasma near the current loop center rotates with

Fig. 1. The initial condition of the mass density (grayscale) and the magnetic field (solid lines) of the GRMHD
simulation around Kerr black hole ( a =0.99995). The
center of the electric current loop locates at R=3rS, z=0.

the Kepler velocity (circular orbit rotation velocity)and the momentum of the plasma is zero except for
the region. It is noted that the system has axisymmetry and the symmetry with respect toequatorial plane.
3. A Test Result
We show a test result of the GRMHD
simulations of the plasma of the black holemagnetosphere with the magnetic field by theelectric current loop here. Figure 2 shows the stateof the plasma and magnetic field at t=32tS, where tS=rS/c. The plasma falls into the black hole except
for the region of the closed magnetic tube aroundthe current loop. In the closed magnetic tube, theplasma almost stops against the strong gravity ofthe black hole. The gray-scale which indicates
Bf2 / rc 2 ( Bf and r is the azimuthal component of
the magnetic field and the mass density of theplasma, respectively) of Fig. 2 shows that theazimuthal component of the magnetic field lines
across the ergosphere are twisted due to the framedragging effect of the rapidly rotating black hole.
The twist of the magnetic field lines propagatesalong the magnetic field lines against the plasma
falling. If we can perform longer term simulation
than present one, the twist of the field lines may
spread and become very strong. It is expected thatthe magnetic pressure of the strongly twisted
magnetic flux tube blows off the plasma and therelativistic jet is formed. The explosion of theclosed magnetic flux tube will produce the antiparallel magnetic field configuration. Then theFig. 2. The state of the plasma and the magnetic field at
t=32tS. The solid lines show the magnetic field lines andthe arrows show the plasma velocity. The gray-scale
2

2shows the value of Bf / rc .

magnetic reconnection will happen and theadditional fast jet may be formed. This mechanismof the jet formation is already proposed using the
non-relativistic numerical simulation with respect
to the fast (but non-relativistic) jets from theprotosteller objects [8]. The essence of thesemodels are very similar to the unified model ofsolar flare [9].

Acknowledgments
We thank Kazunari Shibata, Takahiro Kudoh,and David L. Meier for their important, essential
contributions to this study.
References[1] D. L. Meier, S. Koide, and Y. Uchida: Science 291(2001) 84.
[2] S. Koide, D. L. Meier, K. Shibata, and T. Kudoh:
Astrophys. J. 563 (2000) 668.
[3] S. Koide: Astrophys. J. Letters 606 (2004) L45.
[4] S. Koide, K. Shibata, T. Kudoh, and D. L. Meier:
Science 295 (2002) 1688.
[5] S. Koide: Phys. Rev. D 67 (2003) 104010.
[6] S. Koide, K. Shibata, and T. Kudoh: Butsuri 58(2003) 743 [in Japanese].
[7] S. Koide, K. Shibata, and T. Kudoh: Astrophys. J.
522 (1999) 727.
[8] M. R. Hayashi, K. Shibata, and R. Matsumoto:
Astrophys. J. 468 (1996) L37.
[9] K. Shibata: Astrophys. Sp. Sci. 264 (1999) 129.