Three-dimensional Simulations of Jets from Keplerian Disks: Self-regulatory Stability

We present the extension of previous two-dimensional simulations of the time-dependent evolution of nonrelativistic outflows from the surface of Keplerian accretion disks to three dimensions. As in the previous work, we investigate the outflow that arises from a magnetized accretion disk that is initially in hydrostatic balance with its surrounding cold corona. The accretion disk itself is taken to provide a set of fixed boundary conditions for the problem. We find that the mechanism of jet acceleration is identical to what was established from the previous two-dimensional simulations. The three-dimensional results are consistent with the theory of steady, axisymmetric, centrifugally driven disk winds up to the Alfvén surface of the outflow. Beyond the Alfvén surface, however, the jet in three dimensions becomes unstable to nonaxisymmetric, Kelvin-Helmholtz instabilities. The most important result of our work is that while the jet is unstable at super-Alfvénic speeds, it survives the onset of unstable modes that appear in this physical regime. We show that jets maintain their long-term stability through a self-limiting process wherein the average Alfvénic Mach number within the jet is maintained to the order of unity. This is accomplished in at least two ways. First, the poloidal magnetic field is concentrated along the central axis of the jet forming a "backbone" in which the Alfvén speed is sufficiently high to reduce the average jet Alfvénic Mach number to unity. Second, the onset of higher order Kelvin-Helmholtz "flute" modes (m ≥ 2) reduces the efficiency with which the jet material is accelerated and transfers kinetic energy of the outflow into the stretched, poloidal field lines of the distorted jet. This too has the effect of increasing the Alfvén speed and thereby reducing the Alfvénic Mach number. The jet is able to survive the onset of the more destructive m = 1 mode in this way. Our simulations also show that jets can acquire corkscrew or wobbling types of geometries in this relatively stable end state depending on the nature of the perturbations on them. Finally, we suggest that jets go into alternating periods of low and high activity since the disappearance of unstable modes in the sub-Alfvénic regime enables another cycle of acceleration to super-Alfvénic speeds.