Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phrvd..49.6274a&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 49, Issue 12, 15 June 1994, pp.6274-6297
Astronomy and Astrophysics
Astronomy
176
Gravitational Wave Detectors And Experiments, Wave Generation And Sources, Neutron Stars, Astrometric And Interferometric Binaries
Scientific paper
Merging compact binaries are currently regarded as the most promising source of gravitational waves for the planned Earth-based LIGO/VIRGO laser-interferometer detector system, and will be an important source also for similar, lower-frequency 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 spin-orbit and spin-spin 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 post2-Newtonian equations to describe the precession of the orbital plane, but only the leading-order (Newtonian, quadrupole-moment 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 spin-modulated gravitational waveform (within the post-Newtonian 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 transitional-precession 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 special-case, simple-precession, and transitional-precession solutions. An Appendix develops several diagrammatic aids for understanding intuitively the relation between the precessing orbit and the modulated waveform.
Apostolatos Theocharis A.
Cutler C. C.
Sussman Gerald J.
Thorne Kip S.
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