On the Microlensing Optical Depth of the Galactic Bar

The microlensing probability (optical depth τ) toward the Galactic center carries information about the mass distribution of the Galactic bulge/bar, so can be used to constrain the very uncertain shape parameters of the Galactic bar. In this paper we study a family of bar models with tunable triaxiality, boxyness and radial profile to span the range of plausible density models of the Galactic bar. It also includes four models that were used to fit to the COBE maps by Dwek et al (1995). We find the optical depth on the minor axis of the whole family of models and in special cases the whole microlensing map of the bulge/bar are given by simple analytical formulae. The formulae show the following dependence of the optical depth on the bar mass, radial profile, angle, axis scale lengths and boxyness. (1) τ is proportional to the mass of the bar, M . (2) τ falls along the minor axis with a gradient determined by the density profile and boxyness of the bar. (3) Going from an oblate bulge to a triaxial bar, the optical depth increases only if α < 45, where α is the angle between the bar’s major axis and our line of sight to the center. (4) Among bars with different degree of triaxiality, τ is the largest when the bar axis ratio y0 x0 = tanα, where y0, x0 are the bar scale lengthes on the short and long axes in the Galactic plane respectively. (5) At a fixed field on the minor axis but away from the center, boxy bars with a flat density profile tend to give a larger optical depth than ellipsoidal bars with a steep profile. (6) Main sequence sources should have a significantly lower (20-50% lower)