ON THE MICROLENSING OPTICAL DEPTH OF THE GALACTIC BAR

The microlensing probability (optical depth tau) towards the Galactic Centre carries information about the mass distribution of the Galatic bulge/bar, and so it can be used to constrain the very uncertain shape parameters of the bar. We find tau depends on the bar mass, radial pr ofile, angle, axis scalelengths and boxyness by a few simple analytica l formulae, which show: (1) tau is largest if the angle cc and the axi al ratio y(0)/x(0) conspire so that y(0)/x(0) = tan alpha. (2) At a fi xed field on the minor axis but away from the centre, boxy bars with a flat density profile tend to give a larger optical depth than ellipso idal bars with a steep profile. (3) Main-sequence sources should have a significantly lower (20-50 per cent lower) optical depth than red cl ump giants if main-sequence stars are not observed as deep as the brig ht clump giants. An application to four models constrained by the COBE maps shows most models produce optical depth 2 sigma lower than MACHO and OGLE observed values even with both a massive bar, 2.8 x 10(10) M (.), and a full disc. The high tau argues for a massive (> 2 x 10(10) M(.)) boxy bar with y(0)/x(0) approximate to tan alpha and alpha < 20 degrees and with a flat radial profile up to corotation.