Nonprecessional spin-orbit effects on gravitational waves from inspiraling compact binaries to second post-Newtonian order

Abstract

We derive all second post-Newtonian (2PN), non-precessional effects of spin-orbit coupling on the gravitational waveforms emitted by an inspiraling 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 δ-function description of the influence of the spins on the bodies’ energy-momentum tensor. This description was recently used by Mino, Shibata, and Tanaka (MST) in Teukolsky-formalism analyses of particles orbiting massive black holes, and is based on prior work by Dixon. We compute the 2PN contributions to the waveforms by combining the MST energy-momentum tensor with the formalism of Blanchet, Damour, and Iyer for evaluating the binary’s radiative multipoles, and with the well-known 1.5PN order equations of motion for the binary. Our results contribute at 2PN order only to the amplitudes of the waveforms. The secular evolution of the waveforms’ phase—the quantity most accurately measurable by LIGO—is not affected by our results until 2.5PN order, at which point other spin-orbit effects also come into play. We plan to evaluate the entire 2.5PN spin-orbit contribution to the secular phase evolution in a future paper, using the techniques of this paper.