Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order

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, 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 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-onebody 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.

Self-Force Calculations with a Spinning Secondary

“…Although the conservative linear in spin self-force only contributes to the waveform at post-2-adiabatic order (and is thus not required for 1PA waveform modelling), the complete leading order self-force including the leading spin effects is interesting in its own right. Conservative self-force dynamics can be used to inform the effectiveone-body formalism [11] or 'EOB' for short (see [12][13][14][15][16][17][18]), especially with the discovery of the 'First Law of Binary Black Hole Mechanics' [19] and the development of powerful scattering techniques. As detector sensitivity improves, it will become increasingly critical to make use of this SF information to improve EOB models of spin effects, eccentricity, and small mass ratios.…”

Self-force calculations with a spinning secondary

“…Although the conservative linear in spin self-force only contributes to the waveform at post-2-adiabatic order (and is thus not required for 1PA waveform modelling), the complete leading order self-force including the leading spin effects is interesting in its own right. Conservative self-force dynamics can be used to inform the effectiveone-body formalism [11] or 'EOB' for short (see [12][13][14][15][16][17][18]), especially with the discovery of the 'First Law of Binary Black Hole Mechanics' [19] and the development of powerful scattering techniques [20]. As detector sensitivity improves, it will become increasingly critical to make use of this SF information to improve EOB models of spin effects, eccentricity, and small mass ratios.…”