Bayesian Analysis of Wave-Optics Gravitationally Lensed Massive Black Hole Binaries with Space-Based Gravitational Wave Detector

Abstract

Within a Bayesian statistical framework, we jointly estimate the source and lens parameters and evaluate the relative evidence between the lensed and unlensed models. This work focuses on the wave optics effects induced by a point mass (PM) lens on gravitational waves (GW) from equal-mass massive binary black holes (MBHB), and assesses the capability of the space-based GW detector Taiji to detect such effects. Specifically, we investigate the impact of the redshifted lens mass MLz in the range [3e5, 3e7] solar masses, impact parameter y in [10, 50], source redshift zs in [4, 6], and total source mass Ms in [1e5, 1e7] solar masses on parameter estimation and model selection. Our results show that, for the cases we studied, larger MLz increases the waveform mismatch MM, which directly enhances the waveform difference and the corresponding signal-to-noise ratio (SNR), thereby improving the ability to discriminate between the lensed and unlensed models. In contrast, for y > 50, both MM and SNR are too small to allow effective model discrimination in these cases. Parameter estimation further indicates that for y < 50, the degeneracy between the luminosity distance and MLz can be effectively broken. Although the Bayes factor decreases as zs increases, lensing signatures remain identifiable up to zs = 6. The role of Ms depends on the overlap of the GW signal with the detector sensitive band. Overall, effective model discrimination requires MM greater than or equal to 1e-7 (corresponding to SNR greater than 5).