Higher-order spin effects in the dynamics of compact binaries II. Radiation field
Luc Blanchet, Alessandra Buonanno, Guillaume Faye
TL;DR
The paper derives higher-order spin-orbit effects in the gravitational radiation field for compact binaries by computing spin contributions to the mass-type and current-type quadrupole moments at $2.5PN$ and $1.5PN$ respectively, including non-compact-source terms. Using the previously obtained spin-precession and energy results (Paper I) and the PN wave-generation formalism with finite-part regularization, the authors obtain the secular orbital-phase evolution and the GW energy flux for spinning binaries, with explicit expressions in the center-of-mass frame and for quasi-circular orbits. They also introduce constant-magnitude spin variables to simplify precession and phasing, derive the precession frequencies, and provide the carrier phase and accumulated cycles, highlighting that $2.5PN$ spin terms can rival or exceed spin-spin contributions in certain regimes. The results improve GW templates for spinning binaries relevant to LIGO/Virgo/GEO/TAMA and LISA, clarify discrepancies with earlier work, and underscore the need for including these higher-order spin effects in parameter estimation. Overall, the work delivers essential analytic expressions for spin-orbit couplings in the radiation field and demonstrates their practical impact on GW data analysis.
Abstract
Motivated by the search for gravitational waves emitted by binary black holes, we investigate the gravitational radiation field of point particles with spins within the framework of the multipolar-post-Newtonian wave generation formalism. We compute: (i) the spin-orbit (SO) coupling effects in the binary's mass and current quadrupole moments one post-Newtonian (1PN) order beyond the dominant effect, (ii) the SO contributions in the gravitational-wave energy flux and (iii) the secular evolution of the binary's orbital phase up to 2.5PN order. Crucial ingredients for obtaining the 2.5PN contribution in the orbital phase are the binary's energy and the spin precession equations, derived in paper I of this series. These results provide more accurate gravitational-wave templates to be used in the data analysis of rapidly rotating Kerr-type black-hole binaries with the ground-based detectors LIGO, Virgo, GEO 600 and TAMA300, and the space-based detector LISA.