Angular velocity of gravitational radiation from precessing binaries and the corotating frame

TL;DR

This paper introduces an angular velocity concept for gravitational waveforms from precessing binaries, enabling a consistent corotating frame that simplifies waveform analysis and improves parameter inference.

Contribution

It defines a geometrically meaningful angular velocity for waveforms, facilitating the construction of a corotating frame applicable to both precessing and nonprecessing systems.

Findings

Provides a robust method for waveform comparison

Enables accurate hybrid waveform construction

Simplifies analysis of precessing binary signals

Abstract

This paper defines an angular velocity for time-dependent functions on the sphere, and applies it to gravitational waveforms from compact binaries. Because it is geometrically meaningful and has a clear physical motivation, the angular velocity is uniquely useful in helping to solve an important---and largely ignored---problem in models of compact binaries: the inverse problem of deducing the physical parameters of a system from the gravitational waves alone. It is also used to define the corotating frame of the waveform. When decomposed in this frame, the waveform has no rotational dynamics and is therefore as slowly evolving as possible. The resulting simplifications lead to straightforward methods for accurately comparing waveforms and constructing hybrids. As formulated in this paper, the methods can be applied robustly to both precessing and nonprecessing waveforms, providing a clear, comprehensive, and consistent framework for waveform analysis. Explicit implementations of all these methods are provided in accompanying computer code.