Spiral arms, bar shape and bulge microlensing in the Milky Way

A new model for the luminosity distribution in the inner Milky Way is found, using a nonparametric penalized maximum-likelihood algorithm to deproject a dereddened COBE/ DIRBE L-band map of the inner Galaxy. The model is also constrained by the apparent magnitude (line-of-sight) distributions of clump giant stars in certain bulge fields. An important new feature is the inclusion of a spiral arm model in the disc. Spiral arms make the model appear broader on the sky: thus our bar is more elongated than in previous eight-fold symmetric models. They also lead to a smoother disc model interior to the Sun. The bar length is approximate to3.5 kpc. and its axis ratios are 1 : (0.3-0.4) : 0.3. independent of whether the spiral arm model is four-armed or two-armed. The larger elongation in the plane makes it possible to reproduce the observed clump giant distributions as well. With only the surface brightness data, a small model degeneracy is found even for fixed orientation of the bar, amounting to about +/- 0.1 uncertainty in the in-plane axial ratio. Including the clump giant data removes most of this degeneracy and also places additional constraints on the orientation angle of the bar. We estimate 15degrees less than or similar to phi(bar) less than or similar to 30degrees, with the best models obtained for 20degrees less than or similar to phi(bar) less than or similar to 25degrees. We use our reference model to predict a microlensing optical depth map towards the bulge. normalizing its mass by the observed terminal velocity curve. For clump giant sources at (l, b) = 3.degrees9, -3.degrees8) we find tau(-6) = tau/10(-6) = 1.27, within 1.8sigma of the new MACHO measurement given by Popowski et al. The value for all sources at (l, b) = (2.degrees68, - 3.degrees35) is tau(-6) = 1.1. still >3sigma away from the published MACHO DIA value. The dispersion of these values within our models is = 10 per cent. Because the distribution of sources is well fitted by the near-infrared model, increasing the predicted optical depths by >20 per cent will be difficult. Thus the high value of the measured clump giant optical depth argues for a near-maximal disc in the Milky Way.