The f-mode instability in relativistic neutron stars

Rapidly spinning neutron stars are known to harbour pulsation modes that may become unstable and grow in amplitude by emitting gravitational radiation. Among the various stellar modes, the f-mode is the one typically considered as a promising source of gravitational radiation for ground-based detectors such as LIGO and VIRGO. Improving the existing work in Newtonian stellar models, we present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. Using a relativistic polytropic stellar model, we obtain a minimum gravitational growth timescale (for the dominant l=m=4 mode) of the order of 10^3-10^4 s near the Kepler spin frequency Omega_K, which is substantially shorter than the Newtonian value. By accounting for dissipation in neutron star matter, i.e. shear/bulk viscosity and superfluid mutual friction, we calculate the associated f-mode instability window. For our specific stellar model, the instability is active above 0.92 \times Omega_K and for temperatures \sim (10^9 - 2 \times 10^{10}) K, characteristic of newborn neutron stars.