Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals

TL;DR

This paper presents an approximation method that simplifies modeling generic precessing binary gravitational waveforms by mapping them to a two-dimensional non-precessing parameter space, achieving high accuracy and facilitating waveform construction.

Contribution

The authors introduce a simple, accurate mapping from precessing to non-precessing waveforms, enabling easier modeling of complex binary inspiral signals for gravitational wave detection.

Findings

Mapping matches > 0.99 with parameter biases Δχ ≤ 0.04

Effective for transitional precession cases

Potential to extend to merger phase modeling

Abstract

One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a seven-dimensional space of intrinsic parameters) can be mapped to a two-dimensional space of non-precessing binaries, characterized by the mass ratio and a single effective total spin. The mapping consists of a time-dependent rotation of the waveforms into the quadrupole-aligned frame, and is extremely accurate (matches $> 0.99$ with parameter biases in the total spin of $\Delta \chi \leq 0.04$), even in the case of transitional precession. In addition, we demonstrate a simple method to construct hybrid post-Newtonian--numerical-relativity precessing-binary waveforms in the quadrupole-aligned frame, and provide evidence that our approximate mapping can be used all the way to the merger. Finally, based on these results, we outline a general proposal for the construction of generic waveform models, which will be the focus of future work.