On the secular instability of axisymmetric rotating stars to gravitational radiation reaction

The stability limits of inhomogeneous axisymmetric fluid configurations (represented as rotating polytropes with indices n = 0.5-3.0) for nonaxisymmetric modes with m = 2, 3, or 4 and the growth time scales of these modes are investigated analytically, generalizing the Eulerian variational principle of Ipser and Managan (1985). Numerical results are presented in tables and compared with those obtained by a Lagrangian method (Imamura et al., 1985); errors in the Lagrangian results are attributed to inadequacies in the trial function of Bardeen et al. (1977). The stability limits for m greater than 2 are found to be functions of the equation of state and rotation law, in contrast to the case with m = 2, and it is shown that these limits are always attained by uniformly rotating polytropes with n less than or equal to 3. The astrophysical implications of these findings for objects such as neutron stars and fast pulsars are briefly indicated.