Parameter estimation of eccentric massive black hole binaries with LISA and its cosmological implications

Abstract

Future space-based gravitational wave (GW) observatories such as LISA will detect massive black hole binaries (MBHBs), which are expected to be accompanied by electromagnetic counterparts, thereby providing bright standard sirens for cosmology. The orbital eccentricity of MBHBs can significantly improve the parameter estimation of GWs because the multiple harmonics induced by eccentricity provide additional information and help break down the degeneracies among waveform parameters. In this paper, we use the EccentricFD waveform and construct 5-year GW event catalogs for LISA under three population models (popIII, Q3d and Q3nod). For the three models, we find that an initial eccentricity of $e_0=0.4$ at $10^{-4}$ Hz yields improvements in sky localization and distance inference by a factor of $\mathcal{O}(10)$ in the best cases. As a consequence, the average number of bright sirens increases substantially: from 8 to 11 (PopIII), 6 to 12 (Q3d) and 13 to 24 (Q3nod). This increase in event number, together with enhanced localization and distance inference, leads to tighter cosmological constraints. In the $Λ$CDM model, for instance, the relative uncertainty on $H_0$ is reduced from $8.17\%$ to $4.35\%$ for the Q3d model, corresponding to an improvement of approximately $47\%$. We also investigate the improvement in constraints on the dark energy equation of state and modified GW propagation when combining bright sirens with the latest cosmic microwave background data. These results demonstrate that eccentricity is a remarkably significant feature in GW detection and parameter estimation, enabling more accurate measurements of the Universe with future space-based observatories.

Figures (17)

• Figure 1: The SNR of the two typical binaries with LISA when $e_0=0$. "popIII" correponds to $(m_1,m_2)=(10^{2.7},10^{2.6})~M_{\odot}$ at $z=1$ and "Q3d" is $(m_1,m_2)=(10^{5.5},10^{5.3})~M_{\odot}$ at $z=4.3$.
• Figure 2: The error and improvement ratio $R$ for luminosity distance and sky localization for the typical Q3d MBHB observed by LISA.
• Figure 3: The error and improvement ratio $R$ for luminosity distance and sky localization for the typical popIII MBHB observed by LISA.
• Figure 4: Sky localization uncertainty $\Delta \Omega$ and relative luminosity distance uncertainty $\Delta d_L/d_L$ for events from the Q3nod model observed by LISA over 5 years, for different initial eccentricities. The top panels show the absolute values of $\Delta \Omega$ and $\Delta d_L/d_L$, while the bottom panels display the corresponding improvement factors $R$ relative to the circular case.
• Figure 5: Comparison of the Hubble diagrams (top row) and cosmological constraints (bottom row). The Hubble diagram of bright sirens observed by LISA over a 5-year mission for each population model with the $e_0=0$ and $e_0=0.4$. The constraints of Hubble constant $H_0$ and matter density parameter $\Omega_m$ with $\Lambda$CDM from bright sirens observed by LISA in 5-year for each population model with the $e_0=0$ and $e_0=0.4$. The contours correspond to the 68% and 95% credible regions.