Phenomenological relationship between eccentric and quasicircular orbital binary black hole waveform

Abstract

Eccentricity has become an increasingly important parameter in gravitational wave studies as it can clearly reflect the dynamics of compact object mergers. Obtaining an accurate and fast gravitational waveform template is of paramount importance for accurately estimating gravitational wave parameters. This paper aims to conduct an extensive study of the phenomenological fitting model proposed by Setyawati and Ohme [Phys. Rev. D 103, 124011 (2021)] for adding eccentricity into quasicircular orbital waveforms. We expand the scope of this research by studying the waveform for a mass ratio range of [1, 7], an initial eccentricity range of [0, 0.4], and a continuous time period beyond the fixed time period of $[\ensuremath{-}1500M,\ensuremath{-}29M]$. We also investigate the model in higher-order harmonic modes, as well as spin-aligned and spin-precessing waveforms. After expanding some fitting parameters, we have discovered that the model can be applied to mass ratios $q\ensuremath{\in}[1,7]$. Additionally, it can be applied to almost the entire time period of numerical relativity, including up to $12000M$ prior to merger. It can accommodate higher eccentricities up to ${e}_{0}=0.4$, but its accuracy decreases with increasing initial eccentricity. For a specific initial eccentricity ${e}_{0}$ and time period such as $[\ensuremath{-}2000M,\ensuremath{-}300M]$, mismatches obtained are approximately less than ${10}^{\ensuremath{-}4}$ for ${e}_{0}\ensuremath{\in}[0,0.1]$, less than ${10}^{\ensuremath{-}3}$ for ${e}_{0}\ensuremath{\in}[0.1,0.2]$, less than ${10}^{\ensuremath{-}2}$ for ${e}_{0}\ensuremath{\in}[0.2,0.3]$, and less than ${10}^{\ensuremath{-}1}$ for ${e}_{0}\ensuremath{\in}[0.3,0.4]$ for mass ratio 1-3, and an order of magnitude worse for mass ratio 4-7. The dependence of the mismatch on eccentricity is due to the fact that as the initial eccentricity increases, the eccentricity estimator ${e}_{X}$ deviates further from the expected cosine function, leading to a larger deviation in the morphology of the eccentric waveform and a reduced accuracy in the model's fitting. It can be applied to higher-order modes and yields similar overlap results. Furthermore, by introducing a shift parameter $g$, it can be approximately applied to spin-aligned waveforms. After obtaining spin-precession effects for the special case of strong precession, our model can also be applied to the general spin-precessing case. In summary, this phenomenological model allows for the construction of eccentric gravitational wave templates for nonspinning, spin-aligned or spin-precessing binary systems. It provides an efficient method for generating templates and sheds light on the phenomenological and universal relationship between eccentric and quasicircular waveforms.

Topics & Concepts