Gravitational microlensing and the structure of the inner Milky Way

We analyze the first-year MACHO collaboration observations of microlensing toward the Galactic center using a new direct likelihood technique that is sensitive to the distribution of the events on the sky. We consider the ful l set of 41 events and calculate the direct likelihood against a simply par ameterized Galactic model consisting of either a Gaussian or exponential ba r and a double exponential disk. Optical depth maps are calculated taking i nto account the contribution of both disk lenses and sources. We show that based on the presently available data, a slope in the optical depth has bee n clearly detected (3 sigma) in Galactic latitude and that there are indica tions of a small slope in Galactic longitude. We discuss limits 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 x 10(10) M-. at the 90% confidence level and that the bulge inclination angle is less than 30 degrees also at the 90% confidence level. The most likely bar mass is M- Bulge = 2.5 x 10(10) M-.. Such a high mass would imply a low MACHO fraction for the halo. We consider disk parameters and show that there are two dege neracies between the effects of a disk and those of a bar on the optical de pths. Finally, we discuss how to break these degeneracies and consider vari ous strategies for future microlensing observations.