Secular Instability of g-Modes in Rotating Neutron Stars

Gravitational radiation tends to drive gravity modes in rotating neutron stars unstable. For an inviscid star, the instability sets in when the rotation frequency is about 0.7 times the corresponding mode frequency of the nonrotating star. Neutron stars with spin frequencies $\go 100$ Hz are susceptible to this instability, with growth time of order years. However, it is likely that viscous dissipation suppresses the instability except for a narrow range of temperatures around $10^9$ K. We also show that the viscosity driven instability of g-modes is absent.