Phenomenological template family for black-hole coalescence waveforms

TL;DR

This work introduces a phenomenological waveform family that unifies inspiral, merger, and ring-down by calibrating a Fourier-domain model to hybrids constructed from post-Newtonian and numerical-relativity waveforms. The authors build a two-parameter template bank in (M, η) with amplitude and phase structures that reproduce NR-PN hybrids with >99% fitting factors, enabling efficient searches for high-mass BBH coalescences in ground-based detectors. The approach promises extended reach beyond ~80 M⊙ and potentially improved sensitivity over existing inspiral- or ring-down-only searches, while acknowledging practical challenges such as real-data noise and the need for pipeline development. Future work includes refining the physical-to-phenomenological parameter mapping, robustness tests, and implementing a full search pipeline incorporating NR waveforms.

Abstract

Recent progress in numerical relativity has enabled us to model the non-perturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger, and ring-down stages of black hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to higher-mass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.

Figures (7)

• Figure 1: NR waveform (black) from an equal-mass simulation, along with the 'best-matched' 3.5PN waveform (red). The Hybrid waveform constructed from the above is also shown (dashed line).
• Figure 2: Fourier domain magnitude (left) and phase (right) of the hybrid waveforms. Symmetric mass-ratio $\eta$ of each waveform is shown in the legends.
• Figure 3: Fitting factors of the hybrid waveforms with the phenomenological waveform family. Horizontal axis shows the symmetric mass ratio of the binary, while different colours/markers correspond to different total masses.
• Figure 4: Hybrid waveform $h(t)$ and the best-matched phenomenological waveform $u(t)$ in the time domain for a $M= 40\, M_\odot, \eta = 0.25$ binary system. $u(t)$ is computed by taking the inverse Fourier transform of the phenomenological waveform $u(f)$. Both waveforms are normalised with respect to the Initial LIGO noise spectrum.
• Figure 5: Best-matched amplitude parameters $\bm{\alpha}_{\rm max}$ in terms of the physical parameters of the binary. The horizontal axis shows the symmetric mass-ratio of the binary and different colors/markers correspond to different total masses. Linear polynomial fits to the data points are also shown.