HEAD Division Meeting 1999, April 1999
Session 19. Gravitational Wave Astronomy
Poster, Tuesday, April 13, 1999, 8:30am-6:02pm, Gold Room

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[19.01] Resonant Tidal Excitations of Rotating Neutron Stars in Coalescing Binaries

Wynn Ho, Dong Lai (Cornell University)

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 the f-mode resonance to occur before coalescence, the NS must have rapid rotation, with spin frequency \nus>710~Hz for (22,2)-resonance and \nus>570~Hz for (33,3)-resonance (M=1.4M\odot and R=10~km; however, for R=15km, these spin frequencies become 330~Hz and 250~Hz). Because of strong tidal coupling, f-mode resonances induce a large change in the number of orbital cycles, N\rm orb, with maximum N\rm orb~ 10-1000 for (22,2)-resonance and N\rm 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\rm orb<0.1. For the dominant g-mode (22,2)-resonance, even modest rotation (\nus<100~Hz) can enhance the resonant effect on the orbit by shifting resonance to a smaller orbital frequency. However, because of the weak coupling, N\rm 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\rm orb<10-2(R/10~{\rm km})10(M/ 1.4~M\odot)-20/3 is negligible for canonical NS parameters but can be appreciable if the NS radius is larger.

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