Bayesian Analysis of Gravitational Wave Microlensing Effects from Galactic Double White Dwarfs

Gravitational waves (GWs) from the galactic double white dwarf (DWD) systems are one of the primary targets for upcoming space-based detectors. Due to their vast abundance and widespread distribution throughout the Galactic disk and bulge, these systems may provide a high-statistical population for probing GW microlensing effects induced by Galactic compact objects. To evaluate the detectability of such effects, in this work we simulate the four-year observation of DWD systems by Taiji, in the form of a second-generation Time Delay Interferometry (TDI) data stream. Within a Bayesian inference framework, we estimate parameters for lensed GWs from DWD systems for different values of the lens parameters, including the lens mass $M_\mathrm{L}\in [10, 10^6]$\,M$_\odot$, the effective velocity $v_\mathrm{eff}\in [50, 500]$\,km/s and the initial separation $L\in [R_\mathrm{E}, 3R_\mathrm{E}]$, and obtain the uncertainties of the corresponding parameters. These results characterize the capability of future Taiji observations to probe such systems. We further employ the Bayesian model selection framework to distinguish between lensed and unlensed scenarios, and investigate the impacts of three key physical parameters of the lens system: $M_\mathrm{L}$, $v_\mathrm{eff}$, and $L$ on distinguishing lensing events. Our results show that when $M_\mathrm{L}$ is below $10^5$\,M$_\odot$ or $L\geq3R_\mathrm{E}$, it is not possible to distinguish between lensed and unlensed models. For $v_\mathrm{eff}$, although the Bayes factor decreases as $v_\mathrm{eff}$ decreases, the lensed and unlensed models can still be distinguished within our parameter range.