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Three-Dimensional MHD Simulation of Astrophysical Jet by CIP-MOCCT Method Hiromitsu Kigure (Kyoto U.), Kazunari Shibata (Kyoto U.), Seiichi Kato (Osaka U.) Abstract The acceleration and collimation mechanisms of astrophysical jets are still not made clear and various models have been proposed. One of the most promising models is magnetohydorodynamic (MHD) acceleration from accretion disks. We develop the CIP-MOCCT scheme to three-dimensional cylindrical code and solve the interaction between an accretion disk and a large-scale magnetic field. To investigate the stability of the jet, a non-axisymmetric perturbation is imposed on the rotational velocity of the disk. The jet launched from the disk has a non-axisymmetric structure but the dependences of the jet velocity, mass outflow rate, and mass accretion rate on the magnetic field strength are similar to those in axisymmetric case. Basic Equation and Numerical Method Introduction –Astrophysical Jets and MHD Model– Astrophysical Jet: Plasma flow with very high velocity from, e.g., AGNs, YSOs, XRBs, etc. One of the most promising model for jet launching and collimation is the MHD model. The magnetic field penetrating the accretion disk is twisted by the rotation of accretion disk. The toroidal magnetic field propagates as the torsional Alfven waves (TAWs), making naturally a helical field. The collimated shape of the jets is explained by the hoop-stress of the helical field. To investigate the stability of the disk and jet system, we perform the three-dimensional non-axisymmetric ideal MHD simulation with solving the disk self-consistently (e.g., Matsumoto & Shibata 1997, Steinacker & Henning 2001). We solve these ideal MHD equations by CIP-MOCCT method. The magnetic induction equation is solved by the MOC-CT (Evans & Hawley 1988, Stone & Norman 1992). The others are solved by the Constrained Interpolation Profile (CIP) method (Yabe & Aoki 1991; Yabe et al. 1991). The number of grid points is (Nr, Nφ, Nz) = (173, 32, 197). The size of computational domain is (rmax, zmax) = (7.5, 16.7). The ratio of specific heats (γ) is equal to 5/3. 2 2 The nondimensional parameter, Emg VA0 / VK 0 , decides the initial magnetic field strength. We use eight values of this parameter and investigate the dependences of the jet velocity, mass outflow rate, and mass accretion rate on the initial magnetic field strength. Non-axisymmetric Perturbation in the Disk Initial Conditions As an initial condition, we assume that an equilibrium disk rotates in a central point-mass gravitational potential (e.g., Matsumoto et al. 1996, Kudoh et al. 1998). It is also assumed that there exists a corona outside the disk with uniformly high temperature. The corona is in hydrostatic equilibrium without rotation. The initial magnetic field is assumed to be uniform and parallel to the rotation axis of the disk; (Br, Bφ, Bz) = (0, 0, B0). To investigate the stability of the disk and jet system, we add the nonaxisymmetric perturbation. Two types of perturbations are adopted: Either sinusoidal or random perturbation is imposed on the rotational velocity of the accretion disk. In sinusoidal perturbation cases, v 0.1Vs0 sin 2 , where Vs0 is the sound velocity at (r,z)=(r0,0) (see Matsumoto & Shibata 1997, Kato 2002). In random perturbation cases, the sinusoidal function in the above-mentioned v random numbers between -1 and 1. The cases in which no is replaced with perturbation is imposed are also calculated for a comparison. Axisymmetric Sinusoidal Non-axisymmetric Structure in the Jets Lobanov & Zensus (2001) found that the 3C273 jet has a double helical structure and it can be fitted by two surface modes and three body modes of K-H instability. On the other hand, the jet launched from the disk in our simulation has a nonaxisymmetric (m=2 like) structure in both perturbation cases. The stability condition for non-axisymmetric K-H surface modes is 1/ 2 , where V V1 V2 (Hardee & 1 2 2 2 V VAs ( B1 B2 ) 41 2 Rosen 200). Lobanov & Zensus 2001 Two figures below show the distribution of logarithmic density on the z=2.0 plane at t=7.0. We check the above-mentioned stability condition between the point 1 and 2, and between the point 3 and 4. In the sinusoidal perturbation case, V12 0.68, VAs12 7.1, V34 0.19, VAs12 14. In the random perturbation case, V12 0.87, Random Dependences on the Magnetic Energy Jet velocity Mass outflow rate Mass accretion rate VAs12 8.0, V34 0.39, VAs12 14. K-H body modes become unstable if 2 2 1/ 2 VsVA /(Vs VA ) V j VSM , or, VFM V j . The jets satisfy the former unstable condition for a little time but after that the jets become stable for that condition. Therefore, neither surface modes nor body modes of K-H instability can explain the production of this nonSinusoidal perturbation case Random perturbation case axisymmetric structure. The dependences of the maximum velocities, the maximum mass outflow rates, and the maximum mass accretion rates of jets on the magnetic energy. (A) Axisymmetric cases (no perturbation), (B) Sinusoidal perturbation cases, (C) Random perturbation cases. The broken line shows the Vz∝Emg1/6, dMw/dt∝ Emg0.5, or, dMa/dt∝ Emg0.7.