Statistics of magnification for extremely lensed high redshift stars

Microlensing of stars in strongly lensed galaxies can lead to temporary extreme magnification factors ($\mu\!>\!1000$), enabling their detection at high redshifts. Following the discovery of Icarus, several stars at cosmological distances ($z\!>\!1$) have been observed using the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST). This emerging field of gravitational lensing holds promise to study individual high redshift stars. Also offers the opportunity to study the substructure in the lens plane with implications for dark matter models, as more lensed stars are detected and analysed statistically. Due to the computational demands of simulating microlensing at large magnification factors, it is important to develop fast and accurate analytical approximations for the probability of magnification in such extreme scenarios. In this study, we consider different macro-model magnification and microlensing surface mass density scenarios and study how the probability of extreme magnification factors depends on these factors. To achieve this, we create state of the art large simulations of the microlensing effect in these scenarios. Through the analysis of these simulations, we derive analytical scaling relationships that can bypass the need for expensive numerical simulations. Our results are useful to interpret current observations of stars at cosmic distances which are extremely magnified and under the influence of microlenses.