NONPRECESSIONAL SPIN-ORBIT EFFECTS ON GRAVITATIONAL-WAVES FROM INSPIRALING COMPACT BINARIES TO 2ND POST-NEWTONIAN ORDER

We derive all second post-Newtonian (2PN), non-precessional effects of spin-orbit coupling on the gravitational waveforms emitted by an insp iraling binary composed of spinning, compact bodies in a quasicircular orbit. Previous post-Newtonian calculations of spin-orbit effects (at 1.5PN order) relied on a fluid description of the spinning bodies. We simplify the calculations by introducing into post-Newtonian theory a delta-function description of the influence of the spins on the bodie s' energy-momentum tenser. This description was recently used by Mine, Shibata, and Tanaka (MST) in Teukolsky-formalism analyses of particle s orbiting massive black holes, and is based on prior work by Dixon. W e compute the 2PN contributions to the waveforms by combining the MST energy-momentum tensor with the formalism of Blanchet, Damour, and Iye r for evaluating the binary's radiative multipoles, and with the well- known 1.5PN order equations of motion for the binary. Our results cont ribute at 2PN order only to the amplitudes of the waveforms. The secul ar evolution of the waveforms' phase-the quantity most accurately meas urable by LIGO-is not affected by our results until 2.5PN order, at wh ich point other spin-orbit effects also come into play. We plan to eva luate the entire 2.5PN spin-orbit contribution to the secular phase ev olution in a future paper, using the techniques of this paper.