Importance of eccentricities in parameter estimation of compact binary inspirals with decihertz gravitational-wave detectors

Abstract: During its inspiral stage, a binary black hole (BBH) produces characteristic gravitational wave (GW) signals. The waveform of the GW signals can be described by the physical parameters of BBH, such as the masses of the black holes and the orbital eccentricity. Precise and accurate estimation of these parameters is crucial for GW astrophysics. In the aspect of precision, decihertz GW detectors are promising proposals, as they are anticipated to allow us to obtain highly precise parameter estimations for stellar-mass BBHs. However, the high-precision parameter estimation requires accurate GW waveform modeling. Otherwise, systematic errors can arise in estimated parameters. We emphasize the importance of considering the orbital eccentricity in constructing an accurate GW waveform model. B-DECIGO and MAGIS are used as benchmarks for decihertz GW detectors. We examine the significance of systematic error for a population of stellar-mass BBH inspirals. We found that the quasicircular GW waveform model exhibits significant systematic errors for BBH with a very small eccentricity $\sim 10^{-4}$ at GW frequency $0.1\, \text{Hz}$. The modeling accuracy can be substantially enhanced by incorporating the leading-order correction to GW phase evolution associated with eccentricity smaller than 0.01. The higher-order post-Newtonian corrections induced by eccentricity should be important only for eccentricity larger than 0.01.