The f-mode instability in relativistic neutron stars

TL;DR

This paper presents the first relativistic calculations of the f-mode instability in rapidly rotating neutron stars, showing it can grow quickly and may be detectable by gravitational wave observatories.

Contribution

It provides the first relativistic analysis of the f-mode instability in rotating neutron stars using the Cowling approximation, improving upon previous Newtonian models.

Findings

Minimum gravitational growth timescale of 10^3-10^4 seconds near Kepler frequency.

Instability active above 0.92 times the Kepler frequency.

Instability window exists for temperatures between 10^9 and 2×10^{10} K.

Abstract

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.