Comparing gravitational waves from nonprecessing and precessing black hole binaries in the corotating frame

TL;DR

This study quantitatively compares gravitational waveforms from precessing and nonprecessing black hole binaries in a corotating frame, demonstrating that precessing signals can often be approximated by nonprecessing models with high accuracy.

Contribution

It provides a detailed analysis of the correspondence between precessing and nonprecessing binary waveforms, highlighting the conditions and limitations of this approximation.

Findings

Corotating-frame waveforms resemble nonprecessing analogs over relevant frequency bands.

Precessing simulations can be fitted by nonprecessing models with over 95% accuracy.

Missing degrees of freedom in nonprecessing models limit their effectiveness for certain parameter estimations.

Abstract

Previous analytic and numerical calculations suggest that, at each instant, the emission from a precessing black hole binary closely resembles the emission from a nonprecessing analog. In this paper we quantitatively explore the validity and limitations of that correspondence, extracting the radiation from a large collection of roughly two hundred generic black hole binary merger simulations both in the simulation frame and in a corotating frame that tracks precession. To a first approximation, the corotating-frame waveforms resemble nonprecessing analogs, based on similarity over a band-limited frequency interval defined using a fiducial detector (here, advanced LIGO) and the source's total mass $M$. By restricting attention to masses $M\in 100, 1000 M_\odot$, we insure our comparisons are sensitive only to our simulated late-time inspiral, merger, and ringdown signals. In this mass region, every one of our precessing simulations can be fit by some physically similar member of the \texttt{IMRPhenomB} phenomenological waveform family to better than 95%; most fit significantly better. The best-fit parameters at low and high mass correspond to natural physical limits: the pre-merger orbit and post-merger perturbed black hole. Our results suggest that physically-motivated synthetic signals can be derived by viewing radiation from suitable nonprecessing binaries in a suitable nonintertial reference frame. While a good first approximation, precessing systems have degrees of freedom (i.e., the transverse spins) which a nonprecessing simulation cannot reproduce. We quantify the extent to which these missing degrees of freedom limit the utility of synthetic precessing signals for detection and parameter estimation.