Ari Buchalter

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 Earths orbital motion. This can be used to partially remove the degeneracy among the system parameters in the event timescale, t0. 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 ≈ 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 t0 ≈ 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, , which gives both the relative transverse speed and lens mass as a function of distance. We give examples of the accuracies with which may be measured in typical parallax events. Fitting ML 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 ≈ 10% toward shorter t0. Events where the lens resides in the bulge are essentially unaffected. In both cases, the impact parameter distribution is depressed slightly at both the low and high ends.

Rates for color shifted microlensing events

If the objects responsible for gravitational microlensing (ML) of Galactic-bulge stars are faint dwarfs, then blended light from the lens will distort the shape of the ML light curve and shift the color of the observed star during the event. The resolution in current surveys is not accurate enough to observe this effect, but it should be detected with frequent and precise followup observations. We calculate the expected rates for ML events where the shape distortions will be observable by such followup observations, assuming that the lenses are ordinary main-sequence stars in a bar and in the disk. We study the dependence of the rates for color-shifted (CS) events on the frequency of followup observations and on the precision of the photometry for a variety of waveband pairings. We find that for hourly observations in

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and

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with typical photometric errors of 0.01 mag, 28\% of the events where a main-sequence bulge star is lensed, and 7\% of the events where the source is a bulge giant, will give rise to a measurable CS at the 95\% confidence level. For observations in

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V

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, the fractions become 18\% and 5\%, respectively, but may be increased to 40\% and 13\% by improved photometric accuracy and increased sampling frequency. We outline how the mass, distance, and transverse speed of the lens can be obtained, giving examples of typical errors. We discuss how CS events can be distinguished from events where the source is blended with a binary companion.