SIMBAD references

Most transit microlensing events due to very low mass lens objects suffer from extreme finite-source effects. While modelling their light curves, there is a known continuous degeneracy between their relevant lensing parameters, i.e. the source angular radius normalized to the angular Einstein radius ρ_⋆, the Einstein crossing time t_E, the lens impact parameter u₀, the blending parameter, and the stellar apparent magnitude. In this work, I numerically study the origin of this degeneracy. I find that these light curves have five observational parameters (i.e. the baseline magnitude, the maximum deviation in the magnification factor, the full width at half-maximum $\rm {FWHM}=2 \mathit{ t}_{\rm {HM}}$, the deviation from a top-hat model, and the time of the maximum time derivative of microlensing light curves $T_{\rm {max}}=t_{\rm E}\sqrt{\rho _{\star }^{2}-u_{0}^{2}}$). For extreme finite-source microlensing events due to uniform source stars, we get t_HM ≃ T_max and the deviation from the top-hat model tends to zero, which both cause the known continuous degeneracy. When either ρ_⋆ ≲ 10 or the limb-darkening effect is considerable, t_HM and T_max are two independent observational parameters. I use a numerical approach, i.e. random forests containing 100-120 decision trees, to study how these observational parameters are efficient in yielding the lensing parameters. These machine learning models find the mentioned five lensing parameters for finite-source microlensing events from uniform and limb-darkened source stars with the average R²-scores of 0.87 and 0.84, respectively. R²-score for evaluating the lens impact parameter gets worse on adding limb darkening, and for extracting the limb-darkening coefficient itself this score falls as low as 0.67.