The Proper Motion of Strongly Lensed Binary Neutron Star Mergers in LIGO/Virgo/Kagra can be Constrained by Measuring Doppler Induced Gravitational Wave Dephasing

TL;DR

This paper shows that gravitational wave phase differences from strongly lensed binary neutron star mergers can be used to measure the source's transverse velocity, providing insights into galaxy cluster dynamics within a few years.

Contribution

It introduces a method to constrain the transverse velocity of lensed neutron star mergers through GW dephasing, combining semi-analytical and numerical Bayesian techniques.

Findings

Detectable dephasing signatures for velocities around 1800 km/s at A+ sensitivity.

Most likely detectable dephasing for velocities above 2000 km/s at A# sensitivity.

Measurement of source transverse velocity via GW dephasing could be achieved within a few years.

Abstract

Strongly lensed binary neutron star (NS-NS) mergers are expected to be observed once LIGO/Virgo/Kagra reaches the planned A+ or proposed A\# sensitivity. We demonstrate that the relative transverse velocity of the source-lens system can be constrained by comparing the phase of the two associated gravitational wave (GW) images, using both semi-analytical and numerical Bayesian methods. For A+ sensitivity, a one-sigma NS-NS merger signal in magnification $(\mu=200)$ and redshift $(z_{\rm S}=1)$ will carry a marginally detectable dephasing signature for a source transverse velocity of $\sim 1800$ km/s. This is comparable to the velocity dispersion of large galaxy clusters. Assuming the same population distribution, the most likely source parameters of $\mu=100$ and $z_{\rm S}=1.4$ are always expected to showcase detectable dephasing imprints for A\# sensitivity, provided they are moving with transverse velocities larger than $\sim 2000$ km/s. We conclude that a first measurement of the relative transverse velocity of a source via GW dephasing methods is likely only a few years away.