Efficient multi-timescale dynamics of precessing black-hole binaries

TL;DR

This paper advances analytical and numerical methods for modeling black-hole binary spin precession at second post-Newtonian order, introducing a new parametrization that improves computational efficiency and captures complex precession phenomena relevant for gravitational-wave astronomy.

Contribution

It introduces a novel reparametrization using weighted spin difference, enabling closed-form solutions and faster evolution simulations for precessing black-hole binaries.

Findings

Implementation in PRECESSION v2 achieves 50x speedup.

Accurate modeling of spin precession phenomena.

Efficient evolution from large separations for astrophysical applications.

Abstract

We present analytical and numerical progress on black-hole binary spin precession at second post-Newtonian order using multi-timescale methods. In addition to the commonly used effective spin which acts as a constant of motion, we exploit the weighted spin difference and show that such reparametrization cures the coordinate singularity that affected the previous formulation for the case of equal-mass binaries. The dynamics on the precession timescale is written down in closed form in both coprecessing and inertial frames. Radiation reaction can then be introduced in a quasi-adiabatic fashion such that, at least for binaries on quasi-circular orbits, gravitational inspirals reduce to solving a single ordinary differential equation. We provide a broad review of the resulting phenomenology and rewrite the relevant physics in terms of the newly adopted parametrization. This includes the spin-orbit resonances, the up-down instability, spin propagation at past time infinity, and new precession estimators to be used in gravitational-wave astronomy. Our findings are implemented in version 2 of the public Python module PRECESSION. Performing a precession-averaged post-Newtonian evolution from/to arbitrarily large separation takes $\lesssim 0.1$ s on a single off-the-shelf processor - a 50x speedup compared to our previous implementation. This allows for a wide variety of applications including propagating gravitational-wave posterior samples as well as population-synthesis predictions of astrophysical nature.