Secular stability limits for rotating polytropic stars

The Lagrangian variational principle is used to numerically locate the secular stability limits of rotating polytropes to nonaxisymmetric perturbations. It has been suggested that nonaxisymmetric modes, with exp(imφ) azimuthal dependence, set upper bounds on the rotation rate of compact stars when driven by gravitational radiation reaction. The results of this paper show that, in contrast to the m = 2 bar mode, the secular stability limits for modes with m > 2 are quite sensitive to the compressibility and angular momentum distribution of the polytrope.