Parallax Effect in Microlensing Events due to Free-Floating Planets

Abstract

One of most important applications of microlensing observations is detecting free-floating planets(FFPs). The time scale of microlensing due to FFPs ($t_{\rm E}$) is short (a few days). Discerning the annual parallax effect in observations from these short-duration events by one observer is barely possible, though their parallax amplitude is larger than that in common events. In microlensing events due to FFPs, the lens-source relative trajectory alters because of the observer's motion by $\boldsymbol{\delta u}$. This deviation is a straight line if $t_{\rm E} \ll P_{\oplus}$, and its size is $\delta u\propto \pi_{\rm{rel}}$ ($P_{\oplus}$ is the observer's orbital period). So, most of observed microlensing events due to close FFPs have simple Paczy\'nsky lightcurves with indiscernible and valuable parallax. To evaluate destructive effects of invisible parallax in such events, we simulate $\sim9650$ microlensing events due to FFPs with $t_{\rm E}<10$ days that are observed only by The Nancy Grace Roman Space Telescope(\wfirst). We conclude that in half of these microlensing events the missing parallax alters the real lightcurves, changing their shape and derived properties(by $\Delta \chi^{2}\gtrsim100$). By fitting Paczy\'nski lightcurves to these affected events we evaluate the relative and dimensionless deviations in the lensing parameters from their real values ($\delta t_{\rm E}, \delta \rho_{\star}, ...$). We conclude that around $46$ FFPs which are discovered by \wfirst\ have lightcurves highly affected by invisible parallax with $\delta t_{\rm E}>0.1~\rm{and}~\delta \rho_{\star}>0.1$. Our study reveals the importance of simultaneous and dense observations of microlensing events viewed by \wfirst\ by other observers rotating the Sun in different orbits.