Lens Stochastic Diffraction: A Signature of Compact Objects in Gravitational-Wave Data

Abstract

Every signal propagating through the universe is diffracted by the gravitational field of intervening objects, known as gravitational lenses. Diffraction is most efficient when caused by compact objects, which form additional images of any source. Although secondary images are typically too weak to stand out in the noise, they can be detected collectively using gravitational waves (GWs) by leveraging 1) knowledge of the primary signal and 2) scaling of the signal's strength with the angular offset. The ensemble of secondary signals constitutes \textit{lens stochastic diffraction} (LSD): correlated Poisson-distributed fluctuations following a GW event due to intervening compact objects. The amplitude and temporal distribution of these signals encode the abundance of the lenses, their mass spectrum and their density profiles. By including all secondary signals over all resolved GW events, LSD offers an improvement of ${\sim}2.5$ orders of magnitude over the identification of individual lensed images, for objects with mass $M_l\gtrsim 10^3 M_\odot$ and size $\lesssim 1{\rm pc}(M_l/10^4M_\odot)^{1/2}$. The framework generalizes to wave optics, where halos too diffuse to form images imprint localized features on the waveform. Developing data-analysis techniques will allow LSD to probe compact dark-matter halos and allow next-generation instruments to detect supermassive black holes, given the abundance expected from quasar luminosity studies.