The secular instability of slightly viscous magnetic Maclaurin spheroids

Abstract

The properties of rotating bodies close to their stability limits are investigated analytically. A homogeneous self-gravitating mass rotating about the 3-axis and having both a small amount of viscosity and a general axisymmetric magnetic field which vanishes at the surface is considered, and the ability of the field to limit the viscosity-induced instability in the Maclaurin sequence beyond the Maclaurin-Jacobi bifurcation point is evaluated. It is shown that even the slightest viscosity still produces the instability at the bifurcation point, which, however, is shifted by the field to a higher eccentricity level (greater than 0.8127). These findings are of interest to studies of rapidly rotating astronomical objects such as millisecond pulsars.