High accuracy post-Newtonian and numerical relativity comparisons involving higher modes for eccentric binary black holes and a dominant mode eccentric inspiral-merger-ringdown model

TL;DR

This paper compares post-Newtonian and numerical relativity gravitational waveforms for eccentric binary black holes, constructing hybrid and analytical models that highlight the importance of including eccentricity and higher modes for accurate gravitational wave analysis.

Contribution

It introduces a new eccentric IMR waveform model combining PN and NR results, and demonstrates the significance of eccentricity and higher modes in gravitational wave data analysis.

Findings

Eccentricity impacts waveform overlaps significantly for lighter BBHs.

Higher modes and eccentricity reduce overlaps with circular models, especially at higher inclination angles.

Current quasi-circular models may be inadequate for signals with initial eccentricities above 0.1.

Abstract

Spherical harmonic modes of gravitational waveforms for inspiraling compact binaries in eccentric orbits from post-Newtonian (PN) theory accurate to third post-Newtonian order, and those extracted from numerical relativity (NR) simulations for binary black holes (BBHs) are compared. We combine results from the two approaches (PN and NR) to construct time-domain hybrid waveforms that describe the complete evolution of BBH mergers through inspiral-merger-ringdown (IMR) stages. These hybrids are then used in constructing a fully analytical dominant mode ($\ell$=2, $|m|$=2) eccentric IMR model. A simple extension to a multi-mode model based on this dominant mode model is also presented. Overlaps with quasi-circular IMR waveform models including the effect of higher modes, maximized over a time- and phase-shift, hint at the importance (mismatches $>1\%$) of including eccentricity in gravitational waveforms when analysing BBHs lighter than $\sim 80 M_{\odot}$, irrespective of the binary's eccentricity (as it enters the LIGO bands), or mass-ratio. Combined impact of eccentricity and higher modes seems to become more apparent through smaller overlaps with increasing inclination angles and mass ratios. Additionally, we show that the state-of-the-art quasi-circular models including the effect of higher modes will not be adequate in extracting source properties for signals with initial eccentricities $e_0$ $\gtrsim0.1$.