An interference-based method for the detection of strongly lensed gravitational waves

Abstract

The strongly lensed gravitational wave (SLGW) is a promising transient phenomenon. However, the long-wave nature of gravitational waves poses a significant challenge in identification of its host galaxy. To tackle this challenge, we propose a method triggered by the wave optics effect of microlensing. The microlensing interference introduce frequency-dependent fluctuations in the waveform. Our method consists of three steps. First, we reconstruct the waveforms by using the template-independent and template-dependent methods. The mismatch of two reconstructions serves as an indicator of SLGWs. This step can identify approximately $10\%$ SLGWs. Second, we pair the SLGWs' multiple-images by employing the sky localization overlapping. Because we have pre-identified at least one image through microlensing, the false alarm probability for pairing SLGWs is significantly reduced. Third, we search the host galaxy by requiring the consistency of time-delays between galaxy-galaxy lensing and SLGW. By combing the stage-IV galaxy survey and the third-generation gravitational wave detectors, we expect to find, on average, 1 quadruple-image system per 3 years. The merit of this method can significantly facilitate the pursuit of time-delay cosmography, discovery of compact objects and multi-messenger astronomy.