Gravitational Lensing of Gravitational Waves: Effect of microlens population in lensing galaxies

We analyse the effects of microlensing in the LIGO/Virgo frequency band due to a population of stellar-mass microlenses and study their implications for strongly lensed gravitational wave (GW) signals. We consider a wide range of strong lensing magnifications and the corresponding surface densities of the microlens population found in lensing galaxies, and use them to generate realisations of the amplification factor. The methodologies for simulating amplification curves for both type-I (minima) and type-II (saddle) images are also discussed. We find that, on average, the presence of microlens population introduces a net amplification (de$-$amplification) in minima (saddle points) type of images in the LIGO frequency range. With increasing microlens density, the overall scatter and distortions increase and become significant from relatively lower frequencies. Comparison between IMFs suggests that although the differences are not significant in typical cases, the bottom-heavy IMF tends to show a steeper rise in the scatter due to microlensing at higher frequencies compared to a bottom-light IMF. However, with the increase in the strong lensing magnification, the effects of microlensing become increasingly significant regardless of other parameters, such as the microlens density, type of images or the IMF of the population. Hence, for microlensing features to be notable in GW signal, the strong lensing magnification needs to be substantial. In some extreme cases of strong lensing magnification ($\sim100$), the mismatch between lensed and unlensed waveforms of compact binary coalescences can reach as high as $\sim6\%$. While for most of the typical microlens densities and strong lensing magnifications the mismatch remains less than $1\%$ (showing that the waveforms will not miss detection by LIGO/Virgo, in general), nevertheless their inferred source parameters may still be affected.