Measuring the Transverse Velocity of Strongly Lensed Gravitational Wave Sources with Ground Based Detectors

TL;DR

This paper proposes a method to measure the transverse velocity of strongly lensed gravitational wave sources using phase shifts in signals detected by next-generation ground-based detectors, enabling new insights into source environments and cosmological flows.

Contribution

It introduces a novel approach to determine the transverse velocity of lensed GW sources through differential Doppler shifts observable in GW phase signals.

Findings

Next-generation detectors can detect velocity-induced phase shifts in lensed GW signals.

The method enables probing the environment and motion of GW sources across redshift.

Hundreds of lensed GW mergers could be observed annually with this technique.

Abstract

Observations of strongly gravitationally lensed gravitational wave (GW) sources provide a unique opportunity for constraining their transverse motion, which otherwise is exceedingly hard for GW mergers in general. Strong lensing makes this possible when two or more images of the lensed GW source are observed, as each image essentially allows the observer to see the GW source from different directional lines-of-sight. If the GW source is moving relative to the lens and observer, the observed GW signal from one image will therefore generally appear blue- or redshifted compared to GW signal from the other image. This velocity induced differential Doppler shift gives rise to an observable GW phase shift between the GW signals from the different images, which provides a rare glimpse into the relative motion of GW sources and their host environment across redshift. We illustrate that detecting such GW phase shifts is within reach of next-generation ground-based detectors such as Einstein Telescope, that is expected to detect $\sim$hundreds of lensed GW mergers per year. This opens up completely new ways of inferring the environment of GW sources, as well as studying cosmological velocity flows across redshift.