Angular Momentum Transport, Rotational Instabilities, Magnetic Fields and Mixing

Abstract

The energetics of mixing material through a chemical composition gradient is considered. In regions where nuclear reactions are significant the rate of energy input required to maintain mixing against the growing composition gradient is of the order of the internal energy per nuclear time scale, this is greater than the rate of energy available from most sources except nuclear reactions themselves. Thus angular momentum transport by material motion is only likely to be effective in convective zones (and any associated overshoot regions), and possibly by instabilities themselves driven by nuclear reactions. Even though the angular velocity gradient may be unstable, transport of angular momentum by rotationally driven instabilities will be inhibited. Transport by magnetic fields does not require material motion through a composition gradient and is likely to be very effective in establishing almost uniform rotation. If the rotation is not constant then the differential rotation produces a toroidal field which reacts back on the differential rotation leading to torsional oscillations with a period of the local Alfven travel time. Neighbouring field lines rapidly get out of phase with each other creating a large gradient in magnetic field and substantial dissipation. This is likely to establish almost uniform rotation as this is the lowest energy state for a given angular momentum.