Bayesian Analysis of Wave-optics Gravitationally Lensed Massive Black Hole Binaries with a 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. We investigate the wave-optics effects induced by a point-mass lens on gravitational waves (GWs) from massive binary black holes with comparable component masses ( q = 0.9) and assess the capability of the space-based GW detector Taiji to detect such effects. Specifically, we investigate the impact of the redshifted lens mass M Lz ∈ [3 × 10 5 , 3 × 10 7 ] M ⊙ , the dimensionless impact parameter y is scaled in terms of the Einstein radius of the lens with y ∈ [10, 50], the source redshift z s ∈ [4, 6], and the total source mass M s ∈ [10 5 , 10 7 ] M ⊙ on parameter estimation and model selection. Our results indicate that larger M Lz values reduce the fitting factor ( F F ), thereby amplifying the waveform residual and its associated residual signal-to-noise ratio ( SNR res ), which enhances the ability to distinguish between lensed and unlensed models. Conversely, for y ≥ 50, the F F approaches 1 and SNR res becomes too small to allow effective model discrimination. For y ≤ 30, the degeneracy between the luminosity distance d L and M Lz can be effectively broken. While the Bayes factor decreases with increasing source redshift z s , lensing signatures remain identifiable up to z s = 6. The influence of the total source mass M s depends on the overlap of the GW signal with the detector’s sensitive band. Overall, effective model discrimination generally requires an SNR res ≥ 5 (corresponding to F F ≤ 0.9999994 for the results presented in this work).