Resonant Tidal Excitations of Rotating Neutron Stars in Coalescing Binaries

In a coalescing neutron star-neutron star (NS-NS) or neutron star-black hole (NS-BH) binary, oscillation modes of the NS can be resonantly excited by the companion during the final minutes of the inspiral. The resonant energy transfer between the orbit and NS speeds up or slows down the inspiral and induces a phase change in the emitted gravitational waves from the binary. A tidal resonance, (jk,m), occurs when the mode frequency equals m times the orbital frequency. For f-mode resonance to occur before coalescence, the NS must have rapid rotation, with spin frequency nu_s>710Hz for (22,2)-resonance and nu_s>570Hz for (33,3)-resonance (M=1.4Mo and R=10km; however, for R=15km, these spin frequencies become 330Hz and 250Hz). Because of strong tidal coupling, f-mode resonances induce a large change in the number of orbital cycles, N_orb, with maximum N_orb~10-1000 for (22,2)-resonance and N_orb~1 for (33,3)- resonance. Such resonant effects, if present, must be included in constructing waveform templates used in searching for gravitational wave signals. Higher order f-mode resonances can occur at slower rotation rates, but N_orb<0.1. For the dominant g-mode (22,2)-resonance, even modest rotation (nu_s<100Hz) can enhance the resonant effect on the orbit by shifting resonance to a smaller orbital frequency. However, because of the weak coupling, N_orb lies in the range 10^-3-10^-2 (depending on the NS EOS) and is probably negligible for the purpose of detecting gravitational waves. R-mode resonances require misaligned spin-orbit inclinations, and the dominant resonances correspond to (22,3) and (22,1). Since tidal coupling depends strongly on rotation rate, N_orb<10^-2(R/10km)^(10)(M/1.4Mo)^(-20/3) is negligible for canonical NS parameters but can be appreciable if the NS radius is larger.