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

TL;DR

This work evaluates how neglecting orbital eccentricity biases parameter estimation for future space-based GW detectors, focusing on B-DECIGO and LISA. It combines eccentric-harmonic waveform modeling (EccentricFD) with a time-domain detector response mapped into the frequency domain, and compares Fisher-Cutler-Vallisneri predictions to full Bayesian inferences across mock catalogs. The study identifies critical eccentricities where biases become statistically significant and demonstrates that waveform alignment extends the validity of linear-signal approximations, underscoring the necessity of including eccentricity in space-based GW templates. Overall, incorporating eccentricity into waveform models improves the reliability of intrinsic parameter recovery (e.g., $\mathcal{M}_c$, $\eta$, $d_L$) and enhances the scientific returns of future milli- to deci-Hz GW missions.

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.

Figures (9)

• Figure 1: Example eccentric time-frequency relations for different values of $\mathcal{M}_c$ and $e_0$, with $e_0$ defined at $f_0 = 0.1$ Hz
• Figure 2: Normalized FCV systematic biases $|\Delta \vec{\lambda}^{\text{sys}} / \sigma|$ for $\mathcal{M}_c$, $\eta$ and $d_L$ as functions of initial eccentricity $e_{0.1}$ for the six typical GW events. The vertical dotted line indicates the location of the critical eccentricity $e_{0}^{\text{cr}}$ on the axes.
• Figure 3: Waveform mismatches as a function of initial eccentricity $e_{0.1}$ for the selected events.
• Figure 4: Normalized FCV systematic biases $|\Delta \vec{\lambda}^{\text{sys}} / \sigma|$ for $\mathcal{M}_c$, $\eta$ and $d_L$ as functions of initial eccentricity $e_{0.0001}$ for the six typical GW events. The vertical dotted line indicates the location of the critical eccentricity $e_{0}^{\text{cr}}$ on the axes.
• Figure 5: Waveform mismatches as a function of initial eccentricity $e_{0.0001}$ for LISA events.