GLANCE -- Gravitational Lensing Authenticator using Non-Modelled Cross-Correlation Exploration of Gravitational Wave Signals

Abstract

Gravitational lensing is the phenomenon where the presence of matter (called a lens) bends the path of light-like trajectories travelling nearby. Similar to the geometric optics limit of electromagnetic waves, gravitational lensing of gravitational waves (GWs) can occur in geometric optics condition when GW wavelength is much smaller than the Schwarzschild radius of the lens i.e. $λ_{GW} \ll$ R$^{\rm s}_{\rm lens}$. This is known as the strong-lensing regime for which a multiple-image system with different magnifications and phase-shifts is formed. We developed $\texttt{GLANCE}$, Gravitational Lensing Authenticator using Non-modelled Cross-correlation Exploration, a novel technique to detect strongly lensed GW signals. We demonstrate that cross-correlation between two noisy reconstruction of polarized GW signals shows a non-zero value when the signals are lensed counterparts. The relative strength between the signal cross-correlation and noise cross-correlation can quantify the significance of the event(s) being lensed. Since lensing biases the inference of source parameters, primarily the luminosity distance, a joint parameter estimation of the source and lens-induced parameters is incorporated using a Bayesian framework. We applied $\texttt{GLANCE}$ to synthetic strong lensing data and showed that it can detect lensed GW signals and correctly constrain the injected source and lens parameters, even when one of the signals is below match-filtered threshold signal-to-noise ratio. This demonstrates $\texttt{GLANCE}'$s capability as a robust detection technique for strongly lensed GW signals and can distinguish between lensed and unlensed events.