Quasi‐normal Modes of Rotating Relativistic Stars: Neutral Modes for Realistic Equations of State

We compute zero-frequency (neutral) quasi-normal f-modes of fullyrelativistic and rapidly rotating neutron stars, using several realisticequations of state (EOSs) for neutron star matter. The zero-frequency modessignal the onset of the gravitational radiation-driven instability. We findthat the l=m=2 (bar) f-mode is unstable for stars with gravitational mass aslow 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 rotationrate. For a wide range of EOSs, the bar mode becomes unstable at a ratio ofrotational to gravitational energies T/W \sim 0.07-0.09 for 1.4 M_\odot starsand T/W \sim 0.06 for maximum mass stars. This is to be contrasted with theNewtonian value of T/W \sim 0.14. We construct the following empirical formulafor 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 towithin 4 - 6 %. This formula yields an estimate for the neutral mode sequenceof the bar mode as a function only of the star's mass, M, given the maximumallowed mass, M_{max}^{sph}, of a nonrotating neutron star. The recentdiscovery of the fast millisecond pulsar in the supernova remnant N157B,supports the suggestion that a fraction of proto-neutron stars are born in asupernova collapse with very large initial angular momentum. Thus, in afraction of newly born neutron stars the instability is a promising source ofcontinuous gravitational waves. It could also play a major role in therotational evolution (through the emission of angular momentum) of mergedbinary neutron stars, if their post-merger angular momentum exceeds the maximumallowed to form a Kerr black hole.Comment: 12 pages, 5 figures, submitted to Ap