Hs. Zhao et Sd. Mao, ON THE MICROLENSING OPTICAL DEPTH OF THE GALACTIC BAR, Monthly Notices of the Royal Astronomical Society, 283(4), 1996, pp. 1197-1213
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.