Discerning Parallax Amplitude in Astrometric Microlensing

Abstract

Gravitational microlensing is a powerful method for discovering Isolated Stellar-Mass Black Holes(ISMBHs). These objects make long-duration microlensing events. To characterize these lensing objects by fully resolving the microlensing degeneracy, measurements of parallax and astrometric deflections are necessary. Microlensing events due to ISMBHs have considerable astrometric deflections, but small parallax amplitudes as $\pi_{\rm E} \propto 1/\sqrt{M_{\rm l}}$, where $M_{\rm l}$ is the lens mass. We numerically investigate the possibility of inferring parallax amplitude from astrometric deflection in microlensing events due to ISMBHs. The parallax amplitude in astrometric deflections is proportional to the relative parallax $\pi_{\rm{rel}}$, which means (i) does not strongly depend on $M_{\rm l}$, and (ii) increases in microlensing observations toward the Magellanic Clouds(MCs). We assume these events are potentially detected in upcoming microlensing surveys-(1): the \wfirst\ observations of the Galactic bulge (GB), and (2): the LSST observations of the Large MC(LMC)-, and the Extremely Large Telescope (ELT) follows up them with one data point every ten days. We evaluate the probability of inferring parallax amplitude from these observations by calculating the Fisher/Covariance matrices. For GB, the efficiencies for discerning parallax amplitudes with a relative error $<4\%$ through astrometric, and photometric observations are $3.8\%$, and $29.1\%$, respectively. For observations toward the LMC, these efficiencies are $41.1\%$, and $23.0\%$, respectively. Measuring parallax amplitude through astrometric deflections is plausible in the GB events with the lens distance $\lesssim 2.7$kpc, and in the LMC halo-lensing. The ELT telescope by monitoring long-duration microlensing events can detect astrometric deflections, and their parallax-induced deviations.