Gravitational Microlensing and the Structure of the Inner Milky Way

We analyze the first-year MACHO collaboration observations of microlensingtowards the Galactic center using a new direct likelihood technique that issensitive to the distribution of the events on the sky. We consider the fullset of 41 events, and calculate the direct likelihood against asimply-parameterized Galactic model consisting of either a gaussian orexponential bar and a double exponential disk. Optical depth maps arecalculated taking into account the contribution of both disk lenses andsources. We show that based on the presently available data, a slope in theoptical depth has been clearly detected ($3\sigma$) in Galactic latitude andthat there are indications of a small slope in Galactic longitude. We discusslimits that can be set on the mass, angle and axis ratio of the Galactic bulge.We show that based on microlensing considerations alone, $M_{Bulge}>1.5\times10^{10}\Msol$ at the 90\% confidence level and that the bulge inclination angleis less than $30 \deg$ also at the 90\% confidence level. The mostly likely barmass is $M_{Bulge}=3.5\times10^{10}\Msol$. Such a high mass would imply a lowMACHO fraction for the halo. We consider disk parameters and show that thereare two degeneracies between the effects of a disk and those of a bar on theoptical depths. Finally, we discuss how to break these degeneracies andconsider various strategies for future microlensing observations.