Lensing of unresolved stars towards the Galactic Bulge

This paper presents an analysis of lensing of unresolved background stars. Previous calculations of the lensing rates and optical depths considered only resolved stars. However, if a faint unresolved star lens is close enough to a resolved star, the event will be seen by the microlensing experiments and attributted to the bighter star. The blending biases the duration, making the contribution of the unresolved stars very significant for short events. It is especially annoying, because this contribution is confused with lensing by brown dwarfs. The exact rates of these blended events are extremly sensitive to the limiting magnitude achieved in the microlensing search. Appropriate calculations of the optical depth and rates are provided here, and illustrated in the case of the DUO and OGLE experiments. The additional contribution of unresolved stars is very significant. It probably explains the high optical depth and rates observed towards the Galactic Bulge. The blended unresolved event can be identified using either the color shift or the light curve shape. However, neither of these two methods is apropriate to identify a large number of blended events towards the Bulge. In some case of good photometry and small impact parameter an indentification is possible. This is illustrated by the case of the OGLE 5 event, which clearly appears as a case of lensing of an unresolved star. The recent results obtained by the PLANET collaboration indicate that a high resolution and dense sampling of the light curve is possible, and will probably provide a very interesting possibility to correct the blending bias, as demonstrated for OGLE 5. This possiblity, is certainly better than a statistical estimation of the lensing rates, which are always prone to some uncertainty. But, at this time, the analysis of Microlensing events found in the various microlensing experiments requires the uses of modelisations of the contribution of unresolved stars. Send offprint requests to: C. Alard