Mock Catalogs of Strongly Lensed Gravitational Waves via a Halo Model Approach with Spaceborne Detectors

Future spaceborne gravitational-wave (GW) detectors, such as LISA and DECIGO, are expected to detect a large number of GW events, a fraction of which may be strongly lensed by intervening galaxies or galaxy clusters. In this work, we develop a comprehensive framework to simulate strongly lensed GWs in the context of spaceborne detectors. Based on realistic astrophysical models for both the source population and the lens distribution, we construct mock catalogs of lensed GW events, referred to as GW–LMC–space. Our results show that, for a 4 yr LISA observation, the expected number of lensed events ranges from 0 to 131, depending on the adopted formation model of massive black hole binaries (MBHBs). The corresponding lensing probability for MBHBs can reach up to ∼0.3%. For DECIGO, we find that the number of lensed events in a 1 yr observation is expected to lie in the range of 0–44, with a lensing probability of ∼0.15% for stellar-mass binary black holes (BBHs), binary neutron stars (BNSs), and neutron star–black hole binaries (NSBHs). We further show that the overlap of lensed signals is a common feature in spaceborne detectors, which can significantly affect both the signal-to-noise ratio (SNR) estimation and event identification. These results highlight the importance of accounting for signal overlap in the analysis of strongly lensed GW events in future spaceborne GW observations.