Gravitational Lensing of Gravitational Waves: Effect of Microlens Population in Lensing Galaxies

Abstract: With increasing sensitivities of the current ground-based gravitational-wave (GW) detectors, the prospects of detecting a strongly lensed GW signal are going to be high in the coming years. When such a signal passes through an intervening lensing galaxy or galaxy cluster, the embedded stellar-mass microlenses lead to interference patterns in the signal that may leave observable signatures. In this work, we present an extensive study of these wave effects in the LIGO/Virgo frequency band ($10$-$10^4$ Hz) due to the presence of the microlens population in galaxy-scale lenses for the first time. We consider a wide range of strong lensing (macro) magnifications and the corresponding surface microlens densities found in lensing galaxies and use them to generate realisations of the amplification factor. The methodologies for simulating amplification curves for both types of images (minima and saddle points) are also discussed. We then study how microlensing is broadly affected by the parameters like macro-magnifications, stellar densities, the initial mass function (IMF), types of images, and microlens distribution around the source. In general, with increasing macro-magnification values, the effects of microlensing become increasingly significant regardless of other parameters. Mismatch analysis between the lensed and the unlensed GW waveforms from chirping binaries suggests that, while inferring the source parameters, microlensing can not be neglected for macro-magnification $\gtrsim 15$. Furthermore, for extremely high macro-magnifications $\gtrsim 100$, the mismatch can even exceed $5\%$, which can result in both a missed detection and, consequently, a missed lensed signal.