1999ApJ...510..854M

We compute zero-frequency (neutral) quasi-normal f-modes of fully relativistic and rapidly rotating neutron stars using several realistic equations of state (EOSs) for neutron star matter. The zero-frequency modes signal the onset of the gravitational radiation-driven instability. We find that the l=m=2 (bar) f-mode is unstable for stars with gravitational mass as low as 1.0-1.2 M_☉, depending on the EOS. For 1.4 M_☉ neutron stars, the bar mode becomes unstable at 83%-93% of the maximum allowed rotation rate. For a wide range of EOSs, the bar mode becomes unstable at a ratio of rotational to gravitational energies T/W∼0.07-0.09 for 1.4 M_☉ stars, and T/W∼0.06 for maximum mass stars. This is to be contrasted with the Newtonian value of T/W∼0.14. We construct the following empirical formula for the critical value of T/W for the bar mode, T/W₂=0.115-0.048M/M^sph_max, which is insensitive to the EOS to within 4%-6%. This formula yields an estimate for the neutral mode sequence of the bar mode as a function only of the star's mass M, given the maximum allowed mass M^sph_max, of a nonrotating neutron star. The recent discovery of the fast millisecond pulsar in the supernova remnant N157B supports the suggestion that a fraction of proto-neutron stars are born in a supernova collapse with very large initial angular momentum. If some neutron stars are born in an accretion-induced collapse of a white dwarf, then they will also have very large angular momentum at birth. Thus in a fraction of newly born neutron stars the instability is a promising source of continuous gravitational waves. It could also play a major role in the rotational evolution (through the emission of angular momentum) of merged binary neutron stars if their postmerger angular momentum exceeds the maximum allowed to form a Kerr black hole.