Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins

TL;DR

The study tackles the challenge of generating accurate inspiral-merger-ringdown waveforms for binary black holes with non-precessing spins by marrying post-Newtonian inspiral models with numerical-relativity merger data to produce a compact, three-parameter (mass $M$, symmetric mass ratio $η$, and a single spin parameter $χ$) Fourier-domain IMR template. The waveform family uses a phenomenological amplitude and phase with coefficients $ψ_k$ and $μ_k = igl"){f1, f2, σ, f3}$ that are fitted to equal-spin NR hybrids and constrained by the test-mass limit, ensuring smooth behavior through merger and ringdown. The templates demonstrate faithful and efficient approximations to NR hybrids, with high fitting factors for both equal- and unequal-spin configurations and reasonable capture of precessing systems, enabling more effective searches and parameter estimation. This approach accelerates the integration of NR results into GW data analysis, improves detection rates for spinning binaries, and can be extended to additional harmonics and broader parameter ranges for current and future detectors.

Abstract

We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime, thus significantly improving the expected detection rates.

Figures (3)

• Figure 1: Top and right plots: Match and FF of our IMR templates with equal-spin hybrid waveforms constructed from simulation sets (1)--(3). Bottom left: FF of non-spinning IMR templates proposed in Ajith:2007kxAjith:2007xh with the same hybrids.
• Figure 2: Top panel: Match and FF of our templates with unequal-spin hybrid waveforms constructed from simulation sets (iv) and (v), and the Caltech-Cornell non-spinning simulation. Bottom left: FF with precessing hybrids constructed from sets (vi) and (vii), and the RIT simulation. Bottom right: Fraction of precessing PN waveforms ($M=10 M_\odot$) producing fitting factor FF with the IMR templates --- 85% (62%) 37% of the binaries with $q = 1\, (4) \,9$ produce FF $> 0.965$.
• Figure 3: Distance to optimally oriented equal-mass binaries with spin $\chi$ producing SNR 8 in Initial LIGO.