Rates for parallax-shifted microlensing events from ground-based observations of the Galactic bulge

The parallax effect in ground-based microlensing (ML) observations consists of a distortion to the standard ML light curve arising from the Earth's orbital motion. This can be used to partially remove the degeneracy among the system parameters in the event timescale, t(0). In most cases, the resolution in current ML surveys is not accurate enough to observe this effect, but parallax could conceivably be detected with frequent follow-up observations of ML events in progress, providing the photometric errors are small enough. We calculate the expected fraction of ML events where the shape distortions will be observable by such follow-up observations, adopting Galactic models for the lens and source distributions that are consistent with observed microlensing timescale distributions. We study the dependence of the rates for parallax-shifted events on the frequency of follow-up observations and on the precision of the photometry. For example, we find that for hourly observations with typical photometric 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 approximate to 10% of events overall), will give rise to a measurable parallax shift at the 95% confidence level. These fractions may be increased by improved photometric accuracy and increased sampling frequency. While long-duration events are favored, the surveys would be effective in picking out such distortions in events with timescales 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 higher parallax incidence is favored by mass functions with higher mean masses. Parallax measurements yield the reduced transverse speed, <(upsilon)over tilde> which gives both the relative transverse speed and lens mass as a function of distance. We give examples of the accuracies with which <(upsilon)over tilde> may be measured in typical parallax events. Fitting hit light curves, which may be shape-distorted (e.g., by parallax, blending, etc.), with only the three standard ML parameters can result in inferred values for these quantities that are significantly in error. Using our model, we study the effects of such systematic errors and find that, due primarily to blending, the inferred timescales from such fits, for events with disk lenses, tend to shift the event 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 slightly at both the low and high ends.