Anguilar momentum transport by tidal acoustic wave

Abstract

We give an analytic expression of the braking torque on a Jacobian ellipsoid rotating steadily in an environmental gas, based on the assumption that the ellipsoid rotates around its shortest principal axis with an angular momentum slightly larger than that at the bifurcation point of the Maclaurin spheroid. This braking torque is effected by the gravitational interaction between the ellipsoid matter and a spiral density configuration in the environmental gas. This spiral configuration, which we call a tidal acoustic wave, is caused by the zone of silence effect in a supersonic flow. With respect to a coordinates system rotating with the ellipsoid, a supersonic region appears outside a certain radius. In this supersonic region, the effect of the non-axisymmetric fluctuation in the ellipsoid potential propagates only along the downstream branches of the Mach waves. This one-sided response of the supersonic part causes the tidal acoustic wave. We restrict ourselves to the equatorial plane, and use an acoustic approximation of the basic equations under the assumption that the self-gravity effect of the environmental gas is negligible in comparison to the main gravity of the ellipsoid. The results are applied to the pre- and post-Main Sequence phases of a rotating star, and relating astrophysical problems are discussed.