Orbital motion effects in astrometric microlensing

We investigate lens orbital motion in astrometric microlensing and its detectability. In microlensing events, the light centroid shift in the source trajectory (the astrometric trajectory) falls off much more slowly than the light amplification as the source distance from the lens position increases. As a result, perturbations developed with time such as lens orbital motion can make considerable deviations in astrometric trajectories. The rotation of the source trajectory due to lens orbital motion produces a more detectable astrometric deviation because the astrometric cross-section is much larger than the photometric one. Among binary microlensing events with detectable astrometric trajectories, those with stellar-mass black holes have most likely detectable astrometric signatures of orbital motion. Detecting lens orbital motion in their astrometric trajectories helps to discover further secondary components around the primary even without any photometric binarity signature as well as resolve close/wide degeneracy. For these binary microlensing events, we evaluate the efficiency of detecting orbital motion in astrometric trajectories and photometric light curves by performing Monte Carlo simulation. We conclude that astrometric efficiency is 87.3 per cent whereas the photometric efficiency is 48.2 per cent.Comment: 9 pages, 8 figures, accepted for publication in MNRA

Polarimetry microlensing of close-in planetary systems

A close-in giant planetary (CGP) system has a net polarization signal whose value varies depending on the orbital phase of the planet. This polarization signal is either caused by the stellar occultation or by reflected starlight from the surface of the orbiting planet. When the CGP system is located in the Galactic bulge, its polarization signal becomes too weak to be measured directly. One method for detecting and characterizing these weak polarization signatures due to distant CGP systems is gravitational microlensing. In this work, we focus on potential polarimetric observations of highly-magnified microlensing events of CGP systems. When the lens is passing directly in front of the source star with its planetary companion, the polarimetric signature caused by the transiting planet is magnified. As a result some distinct features in the polarimetry and light curves are produced. In the same way microlensing amplifies the reflection-induced polarization signal. While the planet-induced perturbations are magnified, whenever these polarimetric or photometric deviations vanish for a moment the corresponding magnification factor or the polarization component(s) is equal to the related one due to the planet itself. In order to evaluate the observability of such systems through polarimetric or photometric observations of high-magnification microlensing events, we simulate these events by considering confirmed CGP systems as their source stars and conclude that the efficiency for detecting the planet-induced signal with the state-of-the-art polarimetric instrument (FORS2/VLT) is less than 0.1 %. Consequently, these planet-induced polarimetry perturbations can likely be detected under favorable conditions by high-resolution and short-cadence polarimeters of the next generation.Comment: 9 pages, 7 figures, one tabl

Numerically studying the degeneracy problem in extreme finite-source microlensing events

Most transit microlensing events due to very low-mass lens objects suffer from extreme finite-source effects. While modeling 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 $\rho_{\star}$, the Einstein crossing time $t_{\rm E}$, the lens impact parameter $u_{0}$, 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 5 observational parameters (i.e., the baseline magnitude, the maximum deviation in the magnification factor, the Full Width at Half Maximum $\rm{FWHM}=2 t_{\rm{HM}}$, the deviation from top-hat model, 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 $t_{\rm{HM}}\simeq T_{\rm{max}}$, and the deviation from the top-hat model tends to zero which both cause the known continuous degeneracy. When either $\rho_{\star}\lesssim10$ or the limb-darkening effect is considerable $t_{\rm{HM}}$, and $T_{\rm{max}}$ 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 5 lensing parameters for finite-source microlensing events from uniform, and limb-darkened source stars with the average $R^{2}$-scores of $0.87$, and $0.84$, respectively. $R^{2}$-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 $0.67$.Comment: 10 pages, 6 figure