  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.
