A geometric approach to the precession of compact binaries

TL;DR

This paper introduces a geometrical method to define a stable, invariant reference frame for precessing binary systems, improving the analysis and modeling of gravitational waveforms by reducing extraneous rotational features.

Contribution

The paper presents a minimal-rotation frame aligned with the angular momentum, providing a more invariant and smoothly varying basis for gravitational waveform analysis in precessing binaries.

Findings

The minimal-rotation frame reduces fluctuations in gravitational wave phase.

Waveforms in this frame are more invariant under inertial frame rotations.

The approach simplifies the description of precessing systems using post-Newtonian approximations.

Abstract

We discuss a geometrical method to define a preferred reference frame for precessing binary systems and the gravitational waves they emit. This minimal-rotation frame is aligned with the angular-momentum axis and fixes the rotation about that axis up to a constant angle, resulting in an essentially invariant frame. Gravitational waveforms decomposed in this frame are similarly invariant under rotations of the inertial frame and exhibit relatively smoothly varying phase. By contrast, earlier prescriptions for radiation-aligned frames induce extraneous features in the gravitational-wave phase which depend on the orientation of the inertial frame, leading to fluctuations in the frequency that may compound to many gravitational-wave cycles. We explore a simplified description of post-Newtonian approximations for precessing systems using the minimal-rotation frame, and describe the construction of analytical/numerical hybrid waveforms for such systems.