Using Astrometry to Deblend Microlensing Events

We discuss the prospect of deblending microlensing events by observingastrometric shifts of the lensed stars. Since microlensing searches aregenerally performed in very crowded fields, it is expected that stars will beconfusion limited rather than limited by photon statistics. By performingsimulations of events in crowded fields, we find that if we assume a dark lensand that the lensed star obeys a power law luminosity function, $n(L)\proptoL^{-\beta}$, over half the simulated events show a measurable astrometricshift. Our simulations included 20000 stars in a $256\times 256$ Nyquistsampled CCD frame. For $\beta=2$, we found that 58% of the events weresignificantly blended $(F_{\ast}/F_{tot}\leq 0.9)$, and of those, 73% had alarge astrometric shift $(\geq 0.5 pixels)$. Likewise, for $\beta=3$, we foundthat 85% of the events were significantly blended, and that 85% of those hadlarge shifts. Moreover, the shift is weakly correlated to the degree ofblending, suggesting that it may be possible not only to detect the existenceof a blend, but also to deblend events statistically using shift information.Comment: 24 pages, 7 postscript Figure