In this work, we demonstrate a smoking-gun method to detect lensed gravitational waves from binary neutron stars through a measurement of their “tidal effects.”
When a gravitational wave is lensed, it can undergo magnification. Usually, identifying lensing magnification from gravitational waves is not possible because it only introduces an overall shift in the gravitational wave’s amplitude. Due to the change in the gravitational-wave amplitude, the binary neutron star will simply appear more massive than it truly is, but no unique lensing signature can be extracted from such a “mass bias.”
However, gravitational-wave measurements combined with the so-called equation-of-state of neutron stars allow us to estimate the binary neutron star mass from the gravitational waves in a “secondary way,” which would render feasible a robust check for the lensing magnification.
By measuring the tidal effects of binary neuron stars, we can perform Bayesian analysis to estimate the source-frame masses that are not subjected to the above “mass bias.” We show that if the two mass measurements disagree with each other, then we can conclude that the event must be lensed. Indeed, a “lensed” binary neutron star would resemble an apparently massive binary neutron star merger with the tidal effects of a lower mass binary neutron star.
Using the methodologies we present in this paper, we can test if future gravitational-wave observations of neutron star mergers are lensed. The method could likely be applied in Einstein Telescope or LISA based on the current best models for the binary neutron star and lens populations. We also perform the lensing test on the GW190425, a LIGO/Virgo detection of a gravitational wave from a massive binary neutron star merger, finding no evidence favoring the lensed hypothesis, consistent with the expectation.