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 _ { \odot } , depending on the EOS .
For 1.4 M _ { \odot } 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 \sim 0.07 - 0.09 for 1.4 M _ { \odot } stars and T / W \sim 0.06 for maximum mass stars .
This is to be contrasted with the Newtonian value of T / W \sim 0.14 .
We construct the following empirical formula for the critical value of T / W for the bar mode , ( T / W ) _ { 2 } = 0.115 - 0.048 M / M _ { max } ^ { sph } , 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 _ { max } ^ { sph } , 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 post-merger angular momentum exceeds the maximum allowed to form a Kerr black hole .