An analytic family of post-merger template waveforms

TL;DR

This paper introduces an analytical, closed-form model for the post-merger gravitational wave signal from binary black hole mergers, fitted to numerical relativity data, enabling improved analysis of gravitational wave observations.

Contribution

It presents a novel analytic, time-domain waveform template for the post-merger phase, fitted to numerical simulations and applicable to real gravitational wave data analysis.

Findings

Accurately reproduces post-merger waveform phasing within 0.01 radians.

Fits well to numerical relativity simulations across different parameters.

Potentially useful for extracting black hole properties from GW data.

Abstract

Building on the analytical description of the post-merger (ringdown) waveform of coalescing, non-precessing, spinning, (BBHs) introduced in Phys. Rev. D 90, 024054 (2014), we propose an analytic, closed form, time-domain, representation of the $\ell=m=2$ gravitational radiation mode emitted after merger. This expression is given as a function of the component masses and dimensionless spins $(m_{1,2},\chi_{1,2})$ of the two inspiralling objects, as well as of the mass $M_{\rm BH}$ and (complex) frequency $\sigma_{1}$ of the fundamental quasi-normal mode of the remnant black hole. Our proposed template is obtained by fitting the post-merger waveform part of several publicly available numerical relativity simulations from the Simulating eXtreme Spacetimes (SXS) catalog and then suitably interpolating over (symmetric) mass ratio and spins. We show that this analytic expression accurately reproduces ($\sim$~0.01 rad) the phasing of the post-merger data of other datasets not used in its construction. This is notably the case of the spin-aligned run SXS:BBH:0305, whose intrinsic parameters are consistent with the 90\% credible intervals reported by the parameter-estimation followup of GW150914 in Phys. Rev. Lett. 116 (2016) no.24, 241102. Using SXS waveforms as "experimental" data, we further show that our template could be used on the actual GW150914 data to perform a new measure the complex frequency of the fundamental quasi-normal mode so to exploit the complete (high signal-to-noise-ratio) post-merger waveform.