Spininduced orbital precession and its modulation of the gravitational waveforms from merging binaries
Abstract
Merging compact binaries are currently regarded as the most promising source of gravitational waves for the planned Earthbased LIGO/VIRGO laserinterferometer detector system, and will be an important source also for similar, lowerfrequency detectors that might be flown in space (e.g., the proposed LISA mission). During the orbital inspiral, if one or both bodies are rapidly rotating, the general relativistic spinorbit and spinspin coupling (i.e., the ``dragging of inertial frames'' by the bodies' spins) cause the binary's orbital plane to process. In this paper we analyze the resulting modulation of the inspiral gravitational waveform, using post^{2}Newtonian equations to describe the precession of the orbital plane, but only the leadingorder (Newtonian, quadrupolemoment approximation) equations to describe the orbit, the radiation reaction, the inspiral, and the wave generation. We derive all the formulas one needs to readily compute the spinmodulated gravitational waveform (within the postNewtonian approximation and the approximation that the precession frequency is much smaller than the orbital frequency). We also develop intuition into what the modulated signals ``look like,'' by a variety of means. We provide approximate, analytical solutions for the precessional motion and the modulated waveforms for two important special cases: the case where the bodies have nearly equal masses and the case where one of the bodies has negligible spin. For these cases, for almost all choices of binary parameters, the motion is a simple precession of the orbital angular momentum around the nearly fixed direction of the total angular momentum, with a few tens of precession periods as the waves sweep through the LIGO/VIRGO observational band. However, when the spin and orbital angular momenta are approximately antialigned, there is a transitionalprecession epoch during which their near cancellation causes the binary to ``lose its gyroscopic bearings'' and tumble in space, with a corresponding peculiar sweep of the waveform modulation. We also explore numerically the precessional behaviors that occur for general masses and spins; these typically appear quite similar to our specialcase, simpleprecession, and transitionalprecession solutions. An Appendix develops several diagrammatic aids for understanding intuitively the relation between the precessing orbit and the modulated waveform.
 Publication:

Physical Review D
 Pub Date:
 June 1994
 DOI:
 10.1103/PhysRevD.49.6274
 Bibcode:
 1994PhRvD..49.6274A
 Keywords:

 04.80.Nn;
 04.30.Db;
 97.60.Jd;
 97.80.Af;
 Gravitational wave detectors and experiments;
 Wave generation and sources;
 Neutron stars;
 Astrometric and interferometric binaries