[Paper Review] Eccentricity Estimate for Black Hole Mergers with Numerical Relativity Simulations

V. Gayathri, J. Healy+8 more|arXiv (Cornell University)|Sep 11, 2020

Pulsars and Gravitational Waves Research46 citations

TL;DR

The paper performs 611 eccentric and 920 non-eccentric numerical relativity simulations to assess GW190521, finding it most consistent with a highly eccentric merger (e ≈ 0.69) and quantifying support via Bayes factors.

ABSTRACT

The origin of black hole mergers discovered by the LIGO and Virgo gravitational-wave observatories is currently unknown. GW190521 is the heaviest black hole merger detected so far. Its observed high mass and possible spin-induced orbital precession could arise from the binary having formed following a close encounter. An observational signature of close encounters is eccentric binary orbit; however, this feature is currently difficult to identify due to the lack of suitable gravitational waveforms. No eccentric merger has been previously found. Here we report 611 numerical relativity simulations covering the full eccentricity range and an estimation approach to probe the eccentricity of mergers. Our set of simulations corresponds to $\sim 10^5$ waveforms, comparable to the number used in gravitational wave searches, albeit with coarser mass-ratio and spin resolution. We applied our approach to GW190521 and found that it is the most consistent with a highly eccentric ($e=0.69^{+0.17}_{-0.22}$; 90% credible level) merger within our set of waveforms. This interpretation is supported over a non-eccentric merger with $>10$ Odds ratio if $\gtrsim10\%$ of GW190521-like mergers are highly eccentric. Detectable orbital eccentricity would be evidence against an isolated binary origin, which is otherwise difficult to rule out based on observed mass and spin.

Motivation & Objective

• Motivate how eccentricity affects gravitational waveforms and merger origins.
• Develop a large NR waveform set spanning eccentricities and spins for robust GW data comparison.
• Evaluate GW190521 against eccentric NR waveforms using Bayesian parameter estimation and consistency checks.
• Assess how eccentricity impacts source properties and detection volume.

Proposed method

• Directly compare numerical relativity waveforms to LIGO-Virgo data using the RIFT framework.
• Marginalize over extrinsic parameters (distance, sky location, orientation) and redshifted mass in a Gaussian likelihood.
• Group waveforms by spin and orientation to analyze eccentricity dependence.
• Use a waveform consistency test (cWB) to guard against non-Gaussian detector noise.
• Compute Bayes factors comparing high-eccentricity versus low-eccentricity matches.

Experimental results

Research questions

• RQ1 Can GW190521 be better described by highly eccentric NR waveforms than by non-eccentric models?
• RQ2 What are the reconstructed binary parameters (masses, distance, eccentricity, spins) under an eccentric NR waveform framework?
• RQ3 How robust is the eccentricity inference to waveform sampling and prior choices?
• RQ4 What is the impact of eccentricity on the detectable volume compared with non-eccentric scenarios?

Key findings

• A Bayes factor of approximately 76 favors high eccentricity (e>0.5) over low eccentricity for GW190521.
• Zero eccentricity can be excluded at 90% confidence given the analysis setup.
• Reconstructed total mass and distance differ meaningfully when fitting with eccentric NR waveforms versus non-eccentric models.
• The sensitive volume is roughly twice as large for the reconstructed eccentric model compared with the non-eccentric case.
• The analysis identifies the GW190521 signal as most consistent with a highly eccentric merger within the NR waveform set.
• Injection studies show the method can distinguish high versus zero eccentricity waveforms.