SPIN-INDUCED ORBITAL PRECESSION AND ITS MODULATION OF THE GRAVITATIONAL WAVE-FORMS FROM MERGING BINARIES

Merging compact binaries are currently regarded as the most promising source of gravitational waves for the planned Earth-based LIGO/VIRGO l aser-interferometer detector system, and will be an important source a lso for similar, lower-frequency detectors that might be flown in spac e (e.g., the proposed LISA mission). During the orbital inspiral, if o ne or both bodies are rapidly rotating, the general relativistic spin- orbit and spin-spin coupling (i.e., the ''dragging of inertial frames' ' by the bodies' spins) cause the binary's orbital plane to precess. I n this paper we analyze the resulting modulation of the inspiral gravi tational waveform, using post2-Newtonian equations to describe the pre cession of the orbital plane, but only the leading-order (Newtonian, q uadrupole-moment approximation) equations to describe the orbit, the r adiation reaction, the inspiral, and the wave generation. We derive al l the formulas one needs to readily compute the spin-modulated gravita tional waveform (within the post-Newtonian approximation and the appro ximation that the precession frequency is much smaller than the orbita l frequency). We also develop intuition into what the modulated signal s ''look like,'' by a variety of means. We provide approximate, analyt ical solutions for the precessional motion and the modulated waveforms for two important special cases: the case where the bodies have nearl y equal masses and the case where one of the bodies has negligible spi n. For these cases, for almost all choices of binary parameters, the m otion is a simple precession of the orbital angular momentum around th e nearly fixed direction of the total angular momentum, with a few ten s of precession periods as the waves sweep through the LIGO/VIRGO obse rvational band. However, when the spin and orbital angular momenta are approximately anti-aligned, there is a transitional-precession epoch during which their near cancellation causes the binary to ''lose its g yroscopic bearings'' and tumble in space, with a corresponding peculia r sweep of the waveform modulation. We also explore numerically the pr ecessional behaviors that occur for general masses and spins; these ty pically appear quite similar to our special-case, simple-precession, a nd transitional-precession solutions. An Appendix develops several dia grammatic aids for understanding intuitively the relation between the precessing orbit and the modulated waveform.