Rates for Parallax‐shifted Microlensing Events from Ground‐based Observations of the Galactic Bulge

The parallax effect in ground-based microlensing (ML) observations consistsof a distortion to the standard ML light curve arising from the Earth's orbitalmotion. In most cases, the resolution in current ML surveys is not accurateenough to observe this effect, but parallax could conceivably be detected withfrequent followup observations of ML events in progress. We calculate theexpected fraction of events where parallax distortions will be detected by suchobservations, adopting Galactic models consistent with the observed MLtimescale ($t_0$) distributions. We study the dependence of the rates forparallax-shifted events on the sampling frequency and on the photometricprecision. For example, we find that for hourly observations with typicalphotometric errors of 0.01 mag, 6\% of events where the lens is in the bulge,and 31\% of events where the lens is in the disk, (or $\approx 10$\% of eventsoverall) will give rise to a measurable parallax shift at the 95\% confidencelevel. These fractions may be increased by improved photometric accuracy andincreased sampling frequency. Parallax measurements yield the reducedtransverse speed, $\tilde{v}$, which gives both the relative transverse speedand lens mass as functions of distance. We give examples of the accuracies withwhich $\tilde{v}$ may be measured in typical parallax events. Using only the 3standard ML parameters to fit ML light curves which may be shape-distorted byparallax or blending, can result in incorrect inferred values for thesequantities. We find that the inferred timescales from such fits tend to shiftthe event duration distribution by $\approx 10$\% towards shorter $t_0$ forevents with disk lenses, but do not affect bulge lenses. In both cases, theimpact-parameter distribution is depressed slightly at the low and high ends.Comment: 25 pages, 7 Postscript figure