RATES FOR PARALLAX-SHIFTED MICROLENSING EVENTS FROM GROUND-BASED OBSERVATIONS OF THE GALACTIC BULGE

The parallax effect in ground-based microlensing (ML) observations con sists of a distortion to the standard ML light curve arising from the Earth's orbital motion. This can be used to partially remove the degen eracy among the system parameters in the event timescale, t(0). In mos t cases, the resolution in current ML surveys is not accurate enough t o observe this effect, but parallax could conceivably be detected with frequent follow-up observations of ML events in progress, providing t he photometric errors are small enough. We calculate the expected frac tion of ML events where the shape distortions will be observable by su ch follow-up observations, adopting Galactic models for the lens and s ource distributions that are consistent with observed microlensing tim escale distributions. We study the dependence of the rates for paralla x-shifted events on the frequency of follow-up observations and on the precision of the photometry. For example, we find that for hourly obs ervations with typical photometric errors of 0.01 mag, 6% of events wh ere the lens is in the bulge, and 31% of events where the lens is in t he disk (or approximate to 10% of events overall), will give rise to a measurable parallax shift at the 95% confidence level. These fraction s may be increased by improved photometric accuracy and increased samp ling frequency. While long-duration events are favored, the surveys wo uld be effective in picking out such distortions in events with timesc ales as low as t(0) approximate to 20 days. We study the dependence of these fractions on the assumed disk mass function and find that a hig her parallax incidence is favored by mass functions with higher mean m asses. Parallax measurements yield the reduced transverse speed, <(ups ilon)over tilde> which gives both the relative transverse speed and le ns mass as a function of distance. We give examples of the accuracies with which <(upsilon)over tilde> may be measured in typical parallax e vents. Fitting hit light curves, which may be shape-distorted (e.g., b y parallax, blending, etc.), with only the three standard ML parameter s can result in inferred values for these quantities that are signific antly in error. Using our model, we study the effects of such systemat ic errors and find that, due primarily to blending, the inferred times cales from such fits, for events with disk lenses, tend to shift the e vent duration distribution by approximate to 10% toward shorter t(0). Events where the lens resides in the bulge are essentially unaffected. In both cases, the impact parameter s distribution is depressed sligh tly at both the low and high ends.