Constraining Proper Motion of Strongly Lensed Eccentric Binary Mergers using Doppler Triangulation

TL;DR

This paper proposes a method called Doppler Triangulation to measure the proper motion of strongly lensed eccentric binary mergers using phase differences in gravitational wave signals, aiding in understanding source velocities.

Contribution

It introduces a novel approach to constrain the proper motion of lensed eccentric GW sources by analyzing phase shifts across multiple images, applicable to next-generation GW observatories.

Findings

Doppler Triangulation can effectively measure source proper motion.

Eccentric GW sources produce distinctive phase shift signatures.

Next-generation detectors will observe hundreds of such lensed events annually.

Abstract

Strong lensing of gravitational wave (GW) sources allows the observer to see the GW source from different lines-of-sight (LOS) through the corresponding images, which provides a way for constraining the relative proper motion of the GW source. This is possible as the GW signals received from each image will have slightly different projected velocity components, from which one can `Doppler-Triangulate' for the GW source velocity vector. The difference in projected velocity between the different images can be observationally inferred through pairwise GW phase measurements that accumulate over the time-of-observation. In this paper we study lensed eccentric GW sources and explore how the observable GW phase shift between images evolve as a function of time, eccentricity, lens- and binary parameters. Next generation GW observatories, including the Einstein Telescope and Cosmic Explorer, will see $\sim $hundreds/year of lensed GW sources, where a significant fraction of these are expected to be eccentric. We discuss the expected unique observables for such eccentric lensed GW sources, and the relation to their observable relative linear motion, which otherwise is exceedingly difficult to constrain in general.