Quasi-normal modes of rotating relativistic stars - neutral modes for realistic equations of state

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 − 1.2M⊙, depending on the EOS. For 1.4M⊙ 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 1.4M⊙ 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/W )2 = 0.115− 0.048 M/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 post-merger angular momentum exceeds the maximum allowed to form a Kerr black hole. Subject headings: instabilities — relativity — stars: neutron — stars: oscillations — stars: rotation Department of Physics, University of Wisconsin-Milwaukee, PO Box 413, Milwaukee, WI 53201, USA [email protected]; [email protected] Max Planck Institute for Gravitational Physics (Albert-Einstein-Insitute) D-14473 Potsdam, Germany [email protected]