Ringdown mode amplitudes of precessing binary black holes

TL;DR

This work targets the challenging problem of modeling ringdown amplitudes for precessing binary black holes, where multiple quasi-normal modes are excited by complex merger dynamics. It leverages the SXS NR catalog to extract mode amplitudes in a ringdown frame and trains Gaussian Process Regression surrogates in a 6D parameter space (and a 7D extension) to predict amplitudes for the dominant and subdominant modes, using an EMOP-based reference time for ringdown onset. The study reveals smooth phenomenology across the 6D space, with significant precession-induced mode competition and asymmetry; the resulting GPR fits outperform prior aligned-spin models, delivering mismatches typically below a few percent for important modes and enabling robust data-analysis applicability. The models are publicly released, offering a practical tool to improve waveform modeling, GR tests, and parameter estimation for current and next-generation gravitational-wave detectors, while outlining clear paths for future expansion to more NR data and additional modes.

Abstract

The ringdown phase of a binary black-hole merger encodes key information about the remnant properties and provides a direct probe of the strong-field regime of General Relativity. While quasi-normal mode frequencies and damping times are well understood within black-hole perturbation theory, their excitation amplitudes remain challenging to model, as they depend on the merger phase. The complexity increases for precessing black-hole binaries, where multiple emission modes can contribute comparably to the ringdown. In this paper, we investigate the phenomenology of precessing binary black hole ringdowns using the SXS numerical relativity simulations catalog. Precession significantly impacts the ringdown excitation amplitudes and the related mode hierarchy. Using Gaussian process regression, we construct the first fits for the ringdown amplitudes of the most relevant modes in precessing systems.

Figures (17)

• Figure 1: Distribution of SXS simulations in the ${(\delta, \chi_{\rm s}, \theta_{\rm f})}$ parameter space. Each panel refers to a different mass ratio intervals; numbers and colors indicate the number of simulations in each bin.
• Figure 2: Distribution of ringdown amplitudes for the dominant and first two subdominant modes. The nominal threshold $A_{lm} = 0.03$ helps identify modes expected to play a significant role.
• Figure 3: Distributions of fitted amplitude values $A_{lm}$ (left panel), fit errors $\varepsilon^{\rm NR}_{ lm}$ (middle panel), and fit errors related to simulations with $A_{lm}>10^{-2}$ (right panel). Solid lines correspond to median values, while dashed lines refer to $5^{\rm th}$ and $95^{\rm th}$ percentiles.
• Figure 4: Amplitudes of the $(2,2)$ and $(2,1)$ modes across some 2D sections of our 6D parameter space. Each circle indicates a NR simulation.
• Figure 5: Amplitude of the $(3,3)$ more across some 2D sections of our 6D parameter space. Each circle indicates a NR simulation.