Three-dimensional MHD Simulations of Jets from Accretion Disks

We report the results of 3-dimensional magnetohydrodynamic (MHD) simulations of a jet formation by the interaction between an accretion disk and a large scale magnetic field. The disk is not treated as a boundary condition but is solved self-consistently. To investigate the stability of MHD jet, the accretion disk is perturbed with a non-axisymmetric sinusoidal or random fluctuation of the rotational velocity. The dependences of the jet velocity $(v_z)$, mass outflow rate $(\dot{M}_w)$, and mass accretion rate $(\dot{M}_a)$ on the initial magnetic field strength in both non-axisymmetric cases are similar to those in the axisymmetric case. That is, $v_z \propto B_0^{1/3}$, $\dot{M}_w \propto B_0$ and $\dot{M}_a \propto B_0^{1.4}$ where $B_0$ is the initial magnetic field strength. The former two relations are consistent with the Michel's steady solution, $v_z \propto (B_0^2/\dot{M}_w)^{1/3}$, although the jet and accretion do not reach the steady state. In both perturbation cases, a non-axisymmetric structure with $m=2$ appears in the jet, where $m$ means the azimuthal wave number. This structure can not be explained by Kelvin-Helmholtz instability and seems to originate in the accretion disk. Non-axisymmetric modes in the jet reach almost constant levels after about 1.5 orbital periods of the accretion disk, while all modes in the accretion disk grow with oscillation. As for the angular momentum transport by Maxwell stress, the vertical component, $<B_\phi B_z/4\pi>$, is comparable to the radial component, $<B_\phi B_r/4\pi>$, in the wide range of initial magnetic field strength.