Three‐dimensional Simulations of Jets from Keplerian Disks: Self‐regulatory Stability
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abstract
We present the extension of previous two-dimensional simulations of the
time-dependent evolution of non-relativistic outflows from the surface of
Keplerian accretion disks, to three dimensions. The accretion disk itself is
taken to provide a set of fixed boundary conditions for the problem. The 3-D
results are consistent with the theory of steady, axisymmetric, centrifugally
driven disk winds up to the Alfv\'en surface of the outflow. Beyond the
Alfv\'en surface however, the jet in 3-D becomes unstable to non-axisymmetric,
Kelvin-Helmholtz instabilities. We show that jets maintain their long-term
stability through a self-limiting process wherein the average Alfv\'enic Mach
number within the jet is maintained to order unity. This is accomplished in at
least two ways. First, poloidal magnetic field is concentrated along the
central axis of the jet forming a ``backbone'' in which the Alfv\'en speed is
sufficiently high to reduce the average jet Alfv\'enic Mach number to unity.
Second, the onset of higher order Kelvin-Helmholtz ``flute'' modes (m \ge 2)
reduce the efficiency with which the jet material is accelerated, and transfer
kinetic energy of the outflow into the stretched, poloidal field lines of the
distorted jet. This too has the effect of increasing the Alfv\'en speed, and
thus reducing the Alfv\'enic 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 upon them.
Finally, we suggest that jets go into alternating periods of low and high
activity as the disappearance of unstable modes in the sub-Alfv\'enic regime
enables another cycle of acceleration to super-Alfv\'enic speeds.