Constraining the lensing of binary neutron stars from their stochastic background

TL;DR

This paper estimates the likelihood of gravitational lensing affecting binary neutron star signals detectable by LIGO and Virgo, concluding such events are extremely rare at current sensitivities and unlikely in the near future.

Contribution

It extends previous formalism to binary neutron star lensing, providing the first estimates of resolvable lensed BNS events constrained by current non-detections.

Findings

Lensed BNS events with magnification >1.02 are less than 7×10⁻⁸ at current sensitivities.

Current non-detection constrains the rate of resolvable lensed BNS events.

Future sensitivities may improve detection prospects but remain limited.

Abstract

Gravitational wave (GW) transients from binary neutron star (BNS) coalescences can, in principle, be subject to gravitational lensing thereby increasing the amplitude and signal-to-noise ratio. We estimate the rate of lensed BNS events resolvable by LIGO and Virgo and find that it is constrained by the current non-detection of a stochastic GW background. Following closely the formalism we developed (10.1103/PhysRevLett.125.141102) in the context of binary black hole lensing, we show that at current sensitivities the fraction of BNS coalescences with lensing magnifications $\mu> 1.02$ is less than $\sim 7\times 10^{-8}$ and therefore such events should not be expected in the near future. We also make predictions for projected future sensitivities.