A new analytic representation of the ringdown waveform of coalescing spinning black hole binaries

TL;DR

This paper introduces a novel multiplicative method to analyze and represent the ringdown phase of gravitational wave signals from coalescing spinning black hole binaries, improving accuracy and efficiency.

Contribution

It presents a new multiplicative decomposition approach for the ringdown waveform, differing from traditional linear quasi-normal mode analysis, and demonstrates its effectiveness on numerical waveforms.

Findings

Accurately fits the ringdown waveform with the new method.

Provides a more efficient representation of the ringdown signal.

Enhances the analytical modeling of gravitational wave signals.

Abstract

We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\it linear} decomposition of the multipolar complex waveform $h(t)$ in a sum of quasi-normal modes, our procedure relies on a {\it multiplicative} decomposition of $h(t)$ as the product of the fundamental quasi-normal mode with a remaining time-dependent complex factor whose amplitude and phase are separately fitted. As an illustrative example, we apply our analysis and fitting procedure to the ringdown part of a sample of sixteen $\ell=m=2$ equal-mass, spinning, nonprecessing, numerical waveforms computed with the SP$_{\rm E}$C code,now publicly available in the SXS catalogue. Our approach yields an efficient and accurate way to represent the ringdown waveform, thereby offering a new way to complete the analytical effective-one-body inspiral-plus-plunge waveform.