Abstract
Accurate waveform models are crucial for gravitational-wave data analysis, and since spin has a significant effect on the binary dynamics, it is important to improve the spin description in these models. In this paper, we derive the spin-orbit (SO) coupling at the fifth-and-a-half post-Newtonian (5.5PN) order. The method we use splits the conservative dynamics into local and nonlocal-in-time parts, and then relates the local-in-time part to gravitational self-force results by exploiting the simple mass-ratio dependence of the post-Minkowskian expansion of the scattering angle. We calculate the nonlocal contribution to the 5.5PN SO dynamics to eighth order in the small-eccentricity expansion for bound orbits, and to leading order in the large-eccentricity expansion for unbound orbits. For the local contribution, we obtain all of the 5.5PN SO coefficients from first-order self-force results for the redshift and spin-precession invariants, except for one unknown that could be fixed in the future by second-order self-force results. However, by incorporating our 5.5PN results in the effective-one-body formalism and comparing its binding energy to numerical relativity, we find that the remaining unknown has a small effect on the SO dynamics, demonstrating an improvement in accuracy at that order.
Highlights
Gravitational-wave (GW) observations [1–3] have improved our understanding of compact binary systems, their properties, and their formation channels [4,5]
A crucial component in searching for GW signals and inferring their parameters is accurate analytical waveform models, in which spin is an important ingredient given its significant effect on the orbital dynamics
Three main analytical approximation methods exist for describing the dynamics during the inspiral phase: the post-Newtonian (PN), the post-Minkowskian (PM), and the small-mass-ratio [gravitational self-force (GSF)] approximations
Summary
Gravitational-wave (GW) observations [1–3] have improved our understanding of compact binary systems, their properties, and their formation channels [4,5]. (1) In Sec. II, we calculate the nonlocal contribution to the 5.5PN SO Hamiltonian for bound orbits, in a small-eccentricity expansion up to eighth order in eccentricity. II, we calculate the nonlocal contribution to the 5.5PN SO Hamiltonian for bound orbits, in a small-eccentricity expansion up to eighth order in eccentricity We do this for a harmonic-coordinates Hamiltonian, and incorporate those results into the gyro-gravitomagnetic factors in an EOB Hamiltonian. We calculate the redshift and spin-precession invariants from the total Hamiltonian, and match their smallmass-ratio expansion to first-order self-force (1SF) results. This allows us to recover all of the coefficients of the local part except for one unknown. The main results of this paper are provided in the Supplemental Material as a Mathematica file [183]
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