Systematic Biases in Gravitational-Wave Parameter Estimation from Neglecting Orbital Eccentricity in Space-Based Detectors

Abstract: Accurate modeling of gravitational-wave signals is essential for reliable inference of compact-binary source parameters, particularly for future space-based detectors operating in the milli- and deci-Hertz bands. In this work, we systematically investigate the parameter-estimation biases induced by neglecting orbital eccentricity when analyzing eccentric compact-binary coalescences with quasi-circular waveform templates. Focusing on the deci-Hertz detector B-DECIGO and the milli-Hertz detector LISA, we model eccentric inspiral signals using a frequency-domain waveform that incorporates eccentricity-induced higher harmonics and the time-dependent response of spaceborne detectors. We quantify systematic biases in the chirp mass, symmetric mass ratio, and luminosity distance using both Bayesian inference and the Fisher-Cutler-Vallisneri (FCV) formalism, and assess their significance relative to statistical uncertainties. By constructing mock gravitational-wave catalogs spanning stellar-mass and massive black-hole binaries, we identify critical initial eccentricities at which systematic errors become comparable to statistical errors. We find that for B-DECIGO, even very small eccentricities, $e_0\sim 10^{-4}-10^{-3}$ at 0.1 Hz, can lead to significant biases, whereas for LISA such effects typically arise at larger eccentricities, $e_0\sim 10^{-2}-10^{-1}$ at $10^{-4}$ Hz, due to the smaller number of in-band cycles. Comparisons between FCV predictions and full Bayesian analyses demonstrate good agreement within the regime where waveform mismatches remain small, especially when extrinsic parameters are pre-aligned to minimize mismatches. Our results highlight the necessity of incorporating eccentricity in waveform models for future space-based gravitational-wave observations.