Gravitational lensing of fast radio bursts: prospects for probing microlens populations in lensing galaxies

Gravitational lensing by a stellar microlens of mass $M$ forms two images separated by micro-arcseconds on the sky and has a time delay of $2\times10^{-5}(M/{\rm M_\odot})$ seconds. Although we cannot resolve such micro-images in the sky, they could be resolved in time if the source is a fast radio burst (FRB). In this work, we study the magnification ($|μ|$) and time delay~($t_d$) distributions of micro-images led by different microlens populations. We find that, in microlensing of typical strongly lensed (macro-)images in galaxy lenses, micro-images stemmed from a population of stellar mass microlenses in the $[0.08, 1.5]\:{\rm M_\odot}$ range and a second (dark) microlens population in $[10^{-3} - 10^{-2}]\:{\rm M_\odot}$ range reside in different parts of $|μ|-t_d$ plane. For the global minimum macro-image, due to low stellar mass density, we find that the stellar population leads to peaks in autocorrelation at ${>}10^{-6}$ seconds, whereas the secondary population leads to peaks at ${<}10^{-6}$ seconds, allowing us to differentiate different microlens populations. However, an increase in stellar density introduces new peaks at ${<}10^{-6}$ seconds, which can pollute the inference about the presence of multiple microlens populations. In addition, we also show that the number of micro-images, hence the number of peaks in the autocorrelation, is also sensitive to the underlying stellar mass function, allowing us to constrain the stellar initial mass function (IMF) with FRB microlesning in the future. This work is a first step towards using FRB lensing to probe the microlens population within strong lenses, and more detailed studies are required to assess the effect of various uncertainties that we only discussed qualitatively.