Forecasting Strongly Lensed Binary Black Hole Rates from the Stochastic Gravitational-Wave Background with TianQin

Abstract

The millihertz stochastic gravitational-wave background (SGWB) provides a population-level probe of stellar-mass binary black holes (BBHs) and their cosmic merger history. We develop a framework using TianQin alone to propagate SGWB-informed BBH population constraints into forecasts of strongly lensed BBH mergers detectable by ground-based gravitational-wave detectors. The framework distinguishes between lensed events with at least one detected image and lens systems in which both images are detected and successfully associated. Using a one-year mock observation, we infer the BBH population and propagate the resulting posterior through a galaxy-scale lensing model with image-level selection. For the adopted system-magnification threshold, \(μ_{\rm sys}\ge 2\), the median predicted rate of lensed events with at least one detected image is \(R_{\rm event}^{\rm det}=5.50\times10^{-4}\,\mathrm{yr}^{-1}\), while the median rate of associated two-image lens systems is \(R_{\rm sys}^{\rm det}=2.54\times10^{-4}\,\mathrm{yr}^{-1}\); the median detectable system fraction is \(\mathcal{F}_{\rm sys}^{\rm det}=3.35\times10^{-4}\). Compared with the prior-only propagation, the pooled 16th--84th percentile widths decrease by 6.5\% for the event rate, 6.4\% for the system rate, and 4.0\% for the system fraction. Our work establishes a quantitative link between millihertz SGWB inference and forecasts of strongly lensed BBH mergers for ground-based gravitational-wave observations.