TY - JOUR

T1 - Constraining the orbital eccentricity of inspiralling compact binary systems with Advanced LIGO

AU - Favata, Marc

AU - Kim, Chunglee

AU - Arun, K. G.

AU - Kim, Jeongcho

AU - Lee, Hyung Won

N1 - Funding Information:
We thank Shaon Ghosh for helpful feedback on the manuscript and Edwin Son for plotting assistance. M. F. was supported by NSF (National Science Foundation) Grants No. PHY-1308527 and No. PHY-1653374, and a grant from the Simons Foundation (554674, M. F.). C. K. was supported by National Research Foundation (NRF) Grants (No. 2018R1D1A1B07047677, No. 2021R1F1A1062969). K. G. A. is partially supported by the Swarnajayanti Fellowship Grants No. DST/SJF/PSA-01/2017-18, No. EMR/2016/005594, MATRICS grant (Mathematical Research Impact Centric Support) MTR/2020/000177 of the Science and Engineering Research Board (SERB), and a grant from the Infosys Foundation. H. W. L. and J. K. were supported by National Research Foundation (NRF) Grant (No. 2018R1D1A1B0549338). The authors are also grateful to KISTI (Korea Institute of Science and Technology Information) for providing computing resources through the GSDC (Global Science experimental Data hub Center). This manuscript is assigned LIGO DCC number P2100284.
Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/1/15

Y1 - 2022/1/15

N2 - The detection of ∼50 coalescing compact binaries with the Advanced LIGO and Virgo detectors has allowed us to test general relativity, constrain merger rates, and look for evidence of tidal effects, compact object spins, higher waveform modes, and black hole ringdowns. An effect that has not yet been confidently detected is binary eccentricity, which might be present in a small fraction of binaries formed dynamically. Here we discuss general limits on eccentricity that can, in-principle, be placed on all types of compact object binaries by a detector operating at the design sensitivity of Advanced LIGO. Using a post-Newtonian model for gravitational-wave phasing valid in the small eccentricity regime, we assess the relative measurement error for eccentricity for a variety of spinning and nonspinning binaries. Errors and correlations involving the mass and spin parameters are also investigated. We find that decreasing the low frequency limit of a detector's observational frequency band is one of the key design factors for increasing the odds of measuring binary eccentricity. We also introduce and analytically explore the eccentric chirp mass parameter, which replaces the chirp mass as the key measurable parameter combination in eccentric gravitational waveform models. The eccentric chirp mass parameter explains a degeneracy between the chirp mass and the eccentricity. This degeneracy leads to a bias in the standard chirp mass parameter. We also investigate the systematic parameter bias that arises when eccentric systems are recovered using circular waveform templates. We use both Fisher matrix and Bayesian-inference-based Markov Chain Monte Carlo (MCMC) methods to investigate these parameter estimation issues, and we find good agreement between the two approaches (for both statistical and systematic errors) in the appropriate signal-to-noise ratio regime. This study helps to quantify how effectively one can use eccentricity measurements as a probe of binary formation channels.

AB - The detection of ∼50 coalescing compact binaries with the Advanced LIGO and Virgo detectors has allowed us to test general relativity, constrain merger rates, and look for evidence of tidal effects, compact object spins, higher waveform modes, and black hole ringdowns. An effect that has not yet been confidently detected is binary eccentricity, which might be present in a small fraction of binaries formed dynamically. Here we discuss general limits on eccentricity that can, in-principle, be placed on all types of compact object binaries by a detector operating at the design sensitivity of Advanced LIGO. Using a post-Newtonian model for gravitational-wave phasing valid in the small eccentricity regime, we assess the relative measurement error for eccentricity for a variety of spinning and nonspinning binaries. Errors and correlations involving the mass and spin parameters are also investigated. We find that decreasing the low frequency limit of a detector's observational frequency band is one of the key design factors for increasing the odds of measuring binary eccentricity. We also introduce and analytically explore the eccentric chirp mass parameter, which replaces the chirp mass as the key measurable parameter combination in eccentric gravitational waveform models. The eccentric chirp mass parameter explains a degeneracy between the chirp mass and the eccentricity. This degeneracy leads to a bias in the standard chirp mass parameter. We also investigate the systematic parameter bias that arises when eccentric systems are recovered using circular waveform templates. We use both Fisher matrix and Bayesian-inference-based Markov Chain Monte Carlo (MCMC) methods to investigate these parameter estimation issues, and we find good agreement between the two approaches (for both statistical and systematic errors) in the appropriate signal-to-noise ratio regime. This study helps to quantify how effectively one can use eccentricity measurements as a probe of binary formation channels.

UR - http://www.scopus.com/inward/record.url?scp=85122574936&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.105.023003

DO - 10.1103/PhysRevD.105.023003

M3 - Article

AN - SCOPUS:85122574936

SN - 2470-0010

VL - 105

JO - Physical Review D

JF - Physical Review D

IS - 2

M1 - A96

ER -