Compact binaries through a lens: Silent versus detectable microlensing for the LIGO-Virgo-KAGRA gravitational wave observatories

Abstract

Massive objects located between Earth and a compact binary merger can act as gravitational lenses magnifying signals and improving the sensitivity of gravitational wave detectors to distant events. Depending on the parameters of the system, a point-mass lens between the detector and the source can either lead to a smooth frequency-dependent amplification of the gravitational wave signal, or magnification combined with the appearance of a second image that interferes with the first creating a regular, predictable pattern. We map the increase in the signal to noise ratio for upcoming LIGO-Virgo-KAGRA (LVK) observations as a function of the mass of the lens 𝑀𝐿 and a dimensionless source position 𝑦 for any point-mass lens between the detector and the binary source. To quantify detectability, we compute the optimal match between the lensed waveform and the waveforms in the unlensed template bank and provide a map of the match. The higher the mismatch with unlensed templates, the more detectable lensing is. Furthermore, we estimate the probability of lensing, and find that the redshift to which binary mergers are visible with the LVK increases from 𝑧≈1 to 𝑧≈3.2 for a total detected mass 𝑀det=120⁢𝑀⊙. The overall probability of lensing is <20% of all detectable events above the threshold SNR for 𝑀det=120⁢𝑀⊙ and <5% for more common events with 𝑀det=60⁢𝑀⊙. We find that there is a selection bias for detectable lensing that favors events that are close to the line of sight 𝑦≲0.5. Black hole binary searches could thus improve their sensitivity by taking this bias into account. Moreover, the match, the signal-to-noise ratio increase due to lensing, and the probability of lensing are only weakly dependent on the noise curve of the detector with very similar results for both the O3 and predicted O4 noise power spectral densities. These results are upper limits that assume all dark matter is composed of 300⁢𝑀⊙ point-mass lenses.