A simple model of complete precessing black-hole-binary gravitational waveforms

TL;DR

This paper tackles the challenge of modeling gravitational waves from generic spinning black-hole binaries with precession across inspiral, merger, and ringdown. It introduces PhenomP, a frequency-domain IMR model built by twisting a non-precessing PhenomC waveform using PN precession angles, parameterized by three intrinsic parameters: $q$, $\chi_{\rm eff}$, and $\chi_p$. Fidelity tests against hybrid PN-NR waveforms show fitting factors exceeding $0.965$ for total masses $20$--$200\,M_\odot$, with particularly strong performance for precessing configurations. The approach offers an efficient, practical framework for GW searches and parameter estimation, and provides a roadmap for NR-calibrated refinements in the advanced-detector era.

Abstract

The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger and ringdown, is one of the most pressing theoretical problems in the build-up to the era of GW astronomy. We present the first such model in the frequency domain, "PhenomP", which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binary's mass ratio and an effective total spin parallel to the orbital angular momentum, which determines the inspiral rate) define an underlying non-precessing-binary model. The non-precessing-binary waveforms are then "twisted up" with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin, $χ_p$. All other parameters (total mass, sky location, orientation and polarisation, and initial phase) can be specified trivially. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the model's fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations --although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and as a simple conceptual framework to form the basis of generic-binary waveform modelling in the advanced-detector era.

Figures (2)

• Figure 1: Fitting factors between PhenomP (solid lines) and PhenomC (dashed lines), averaged over binary orientations, as described in the text. Each color is one case: $q=3$, $\chi_p = 0.75$ (black); $q=2$ double spin (red); $q=3$, $\chi_{\rm eff} = -0.5$ (green); $q=3$, $\chi_{\rm eff} = -0.125$ (blue). We see that in all cases PhenomP meets the 0.965 threshold for detection accuracy. Above 100 $M_\odot$ all of the curves are above 0.965.
• Figure 2: Fitting factors (FF) between a $q=3$ highly-precessing binary, and the non-precessing PhenomC and precessing PhenomP models, as a function of binary orientation angles $(\theta, \phi)$; at $\theta = 0$ an observer is oriented with the binary's total angular momentum. FF $<0.965$ for many orientations with PhenomC, while for PhenomP it is well above 0.965 for all orientations. See text for further details.