The Proper Motion of Strongly Lensed Binary Neutron Star Mergers in LIGO/Virgo/Kagra Can Be Constrained by Measuring Doppler-induced Gravitational-wave Dephasing

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 semianalytical and numerical Bayesian methods. For A+ sensitivity, a 1 σ NS–NS merger signal in magnification ( μ = 200) and redshift ( z _S = 1) will carry a marginally detectable dephasing signature for a source transverse velocity of ∼1800 km s ^−1 . This is comparable to the velocity dispersion of large galaxy clusters. Assuming the same population distribution, the most likely source parameters of μ = 100 and z _S = 1.4 are always expected to showcase detectable dephasing imprints for A# sensitivity, provided they are moving with transverse velocities larger than ∼ 2000 km s ^−1 . 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.

Keywords

• Gravitational wave astronomy
• Gravitational waves
• Neutron stars
• Gravitational lensing
• Strong gravitational lensing