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Three-Dimensional MHD Simulations of Astrophysical Jet and Accretion Disk Hiromitsu Kigure, Kazunari Shibata (Kyoto U.) e-mail:[email protected] Motivation and Method Initial Conditions The 2.5-dimensional MHD simulations made the MHD jet acceleration and collimation mechanism clear (e.g., Shibata & Uchida 1986; Matsumoto et al. 1996; Kudoh et al. 1998). However, only a few 3-dimensional MHD simulations of jet formation with solving the accretion disk selfconsistently have been presented (e.g., Matsumoto & Shibata 1997; Matsumoto 1999). To investigate the stability of the MHD jet launched from the accretion disk, we performed 3-dimentional MHD simulations. The ideal MHD equations are solved by CIP-MOCCT method. 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). The cylindrical coordinate with (Nr, Nφ, Nz) = (173, 32, 197) is adopted. The size of computational domain is (rmax, zmax) = (7.5, 16.7). Axisymmetric Non-axisymmetric Perturbation in the Disk 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 0.1Vs 0 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 abovementioned v is replaced with random numbers between -1 and 1. The cases in which no perturbation is imposed are also calculated for a comparison. Sinusoidal Non-axisymmetric Structure in the Jets Random A typical (mainly displayed results Lobanov & Zensus (2001) found that the 3C273 jet has a double in this poster) helical structure and that it can be fitted by two surface modes and magnetic field three body modes of K-H instability. On the other hand, the jet strength is defined 2 2 launched from the disk in our simulation has a nonas Emg VA0 / VK 0 axisymmetric (m=2 like) structure in both perturbation cases. =5.0×10-4. 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, VAs34 14. In the random perturbation case, V12 0.87, VAs12 8.0, V34 0.39, VAs34 14. K-H body modes become unstable if 2 2 1/ 2 CsVA /(Cs 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. Dependences on the Magnetic Energy Jet velocity Mass outflow rate Mass accretion rate Connection of Non-axisymmetric Structure between Disk and Jet To investigate a connection of the non-axisymmetric structure in the jet and that in the disk, we calculate the Fourier spectra of the non-axisymmetric modes of the magnetic energy. The spectrum is calculated as , where . VF is the volume of the disk or the jet. EM is equal to B2/8π and m indicates the azimuthal wave number. The sinusoidal runs have the periodicity of , so that we calculate the spectra with even azimuthal wave number. The spectrum of the m=2 mode in the jet transiently increases in both perturbation cases around t=6.4. This is clearly seen in the EM distribution on z=2.0 plane. Before that, the spectrum of the m=2 mode in the disk also increases. This suggests that the non-axisymmetric structure produced in the disk propagates into the jet. It is also to be noted that the spectra in the jet decrease monotonously with time except the transient increase around t=6.4 although the spectra in the disk increase (with oscillation) with time. Sinusoidal perturbation case Random perturbation case 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. Summary We performed 3-dimensional MHD simulations of jet formation with solving the accretion disk self-consistently. The accretion disk is perturbed with a sinusoidal or random fluctuation of the rotational velocity to investigate the stability of the MHD jet ejected from the disk in 3-dimention. The jet has a non-axisymmetric (m=2 like) structure in the both perturbation cases. This structure is not caused by K-H instability. The corresponding m=2 like structure in the disk appears before that in the jet appears. This is confirmed by calculating the Fourier spectra of the magnetic energy. There is no remarkably dominant mode in the jet in the final stage of the both runs. The dependences of the jet velocity, mass outflow rate, and mass accretion rate on the magnetic field strength in the nonaxisymmetric cases are similar to those in the axisymmetric case. From these results, it can be said that the MHD jet in the nonaxisymmetric runs is launched from the accretion disk with axisymmetric-like properties at least about two orbital periods.