SEARCH TEMPLATES FOR GRAVITATIONAL-WAVES FROM PRECESSING, INSPIRALINGBINARIES

Searches for gravitational waves with the LIGO-VIRGO-GEO detector netw ork will require families of ''search templates'' with which to cross correlate the noisy detectors' output. This paper introduces a fitting factor (FF), as a quantitative measure of how well the best template in a family ''fits''. hypothetical gravitational waveform, in the pres ence of a specific detector noise spectrum. An FF < 0.9 corresponds to a 27% reduction in the event rate of the relevant signals; therefore a family of templates that leads to FF's below 0.9 should be considere d inadequate. The FF is used to explore the adequateness of several fa milies as search templates for gravitational waves from compact inspir aling binaries. The binaries are taken to move in circular orbits, and the ''advanced LIGO noise spectrum'' is assumed for the detectors. We first study the acceptability of the simplest three-parameter templat e family, the so-called ''Newtonian family.'' From previous studies by Finn, Krolak, Kokotas, Schafer, Dhurandar, and Balasubramanian, we in fer that post-Newtonian effects in the true waveforms of binaries with vanishing spins cause the Newtonian family to have an unacceptable lo w FF (similar to 0.6 to 0.8). We then study the influence of waveform modulations caused by spin-induced orbital precession,, and we isolate the modulation effects from other post-Newtonian effects by pretendin g that the true signals are pure Newtonian with modulation. Many diffe rent parameters influence the precession and then the waveform modulat ion. A wide range of parameter values is explored, and intuition is de veloped into which parameters most strongly influence the FF. It is sh own that the unmodulated Newtonian template family works quite well (F F > 0.9 for almost all parameter values) in searches for the modulated Newtonian signal from two 1.4M. neutron stars (NS's) with one of them maximally spinning. By contrast, for a maximally spinning 10M. black hole (BH) with a nonrotating 1.4M. NS, the Newtonian template family p roduces FF < 0.9 for more than half of all the binaries' orientations, if the spin and orbital angular momenta are misaligned by 30 degrees. We introduce a new four-parameter template family, which has the form of the nonmodulated post(1)-Newtonian signal from a zero-spin-binary Although, there is a substantial improvement of the FF's for a spin-mo dulated Newtonian signal, the FF's for nonmodulated post(1.5)-Newtonia n waveforms are still very poor (similar to 0.5-0.8) Therefore we prop ose another foe-parameter template family that has the same form as a nonmodulated post(1.5)-Newtonian signal with all the spin-related para meters stripped off. This template family works post(1.5)-Newtonian mo dulated signals quite well. These results suggest that, in a few years , when waveforms have been computed up to post(3)-Newtonian order, a g ood template family will be the four-parameter post(3)-Newtonian wavef orms for zero-spin binaries, augmented by some appropriate modulations to deal with misaligned, rapidly spinning BH-NS systems. Finally, we extend our investigations to the space-based low-frequency LISA detect or.