Identifying Type-II Strongly-Lensed Gravitational-Wave Images in Third-Generation Gravitational-Wave Detectors

Strong gravitational lensing is a gravitational wave (GW) propagation effect that influences the inferred GW source parameters and the cosmological environment. Identifying strongly-lensed GW images is challenging as waveform amplitude magnification is degenerate with a shift in the source intrinsic mass and redshift. However, even in the geometric-optics limit, Type-II strongly-lensed images cannot be fully matched by Type-I (or unlensed) waveform templates, especially with large binary mass ratios and orbital inclination angles. We propose to use this mismatch to distinguish individual Type-II images. Using planned noise spectra of Cosmic Explorer, Einstein Telescope and LIGO Voyager, we show that a significant fraction of Type-II images can be distinguished from unlensed sources, given sufficient SNR ($\sim 30$). Incorporating models on GW source population and lens population, we predict that the yearly detection rate of lensed GW sources with detectable Type-II images is 172.2, 118.2 and 27.4 for CE, ET and LIGO Voyager, respectively. Among these detectable events, 33.1%, 7.3% and 0.22% will be distinguishable via their Type-II images with a log Bayes factor larger than 10. We conclude that such distinguishable events are likely to appear in the third-generation detector catalog; our strategy will significantly supplement existing strong lensing search strategies.