Source Confusion of Massive Black Hole Binaries for the Taiji Mission

TL;DR

This work addresses source confusion for massive black hole binaries (MBHBs) in the Taiji mission. It combines three MBHB population models with Fisher information analyses using IMRPhenomD and IMRPhenomHM waveforms, plus full Bayesian MCMC validation, to quantify how overlapping time-frequency tracks degrade parameter estimation and how higher-order modes mitigate these effects. The results show genuine overlaps are relatively rare (around $0.31$–$4.2$ per year across models with ~100 detections/year), and higher-order modes substantially reduce parameter uncertainties and break degeneracies, even in overlap scenarios. The findings underscore the necessity of HM-inclusive waveform modeling for accurate inference and multi-messenger follow-up, with Bayesian analyses corroborating the Fisher forecasts and illustrating improved sky localization and distance-inclination disentanglement.

Abstract

We systematically investigate the source confusion of massive black hole binaries (MBHBs) for the Taiji space-based gravitational wave mission. Source confusion, arising from the overlap of signals in both time and frequency domains, can degrade parameter recovery accuracy. To assess this effect, we simulate three representative models MBHB populations to estimate event overlap events. Assuming 100 detections per year, only 0.31-4.2 overlaps are expected annually. Based on Fisher information matrix with the $\texttt{IMRPhenomD}$ and $\texttt{IMRPhenomHM}$ waveform models, we find that overlap significantly enlarges parameter uncertainties, while the inclusion of higher-order modes (HMs) effectively mitigates this effect. Severe confusion ($Δ\mathcal{M}_z / \mathcal{M}_z<$ 0.2%) occurs in fewer than 0.14% across the three population models. The full Bayesian analysis further corroborates the Fisher predictions, and also reveals that HMs help break key parameter degeneracies, with or without signal overlap. These findings underscore the importance of incorporating HMs for accurate inference in future space-based observations.

Figures (6)

• Figure 1: Time-frequency map of a representative PopIII simulation. The non-target signals shown in the figure are limited to those with cumulative SNR exceeding 10. The black vertical dashed line marks the observation window, which covers a duration of 15 days and extends up to 0.5 days after the merger of the target signal. Yellow traces denote all signals within the observation window that coincide with the target signal (black) in the time domain, while blue traces indicate those that coincide with it simultaneously in both the time and frequency domains. Only the time–frequency trajectories of the dominant $(2,2)$ mode are shown, and overlap is evaluated based solely on their crossings.
• Figure 2: Parameter uncertainty ratio $\gamma^i - 1$ as a function of chirp mass scale for the case $\Delta\mathcal{M}_z = 0$. Solid lines represent waveforms including HMs; dashed lines show results for the dominant $(2,2)$ mode only. The phase difference at the point of overlap is fixed ($\Delta\Phi (f_{\mathrm{ov}}) = 0$), and $f_{\mathrm{ov}}$ is chosen to scale inversely with the $\mathcal{M}_z$.
• Figure 3: Parameter uncertainty ratio $\gamma^i - 1$ as a function of $\Delta\mathcal{M}_z$ for the baseline parameter sets with $\mathcal{M}_z = 10^5~M_\odot$ (top) and $\mathcal{M}_z = 10^6~M_\odot$ (bottom). Left panels show results using only the dominant $(2,2)$ mode, while right panels include HMs. The variation range of $\Delta\mathcal{M}_z$ corresponds to about 1% of each magnitude of chirp mass. All cases assume $\Delta\Phi (f_{\mathrm{ov}})= 0$
• Figure 4: Parameter uncertainty ratio $\gamma^i - 1$ as a function of phase difference $\Delta\Phi=\Phi_1 - \Phi_2$ for the baseline parameter sets with $\mathcal{M}_z = 10^5\,M_\odot$. Dashed lines represent waveforms with the $(2,2)$ mode only. $\Phi_1$ and $\Phi_2$ are the signal phases in the TDI-$X_2$ channel. The $f_{\mathrm{ov}}$ is fixed and $\Delta \mathcal{M}_z = 0$.
• Figure 5: Corner plot of the posterior distribution for a single MBHB signal using MCMC sampling. Red contours indicate results with HMs; blue contours correspond to the dominant $(2,2)$ mode only. The shaded regions represent the 1$\sigma$ and 2$\sigma$ credible intervals.