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 non-parametric 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 disk. 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 disk model interior to the Sun. The bar length is ≈ 3.5 kpc and its axis ratios are 1:(0.30.4):0.3, independent of whether the spiral arm model is 4-armed or 2-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 bar’s orientation angle. We estimate 15 deg ∼< φbar ∼< 30 deg, with the best models obtained for 20 deg ∼< φbar ∼< 25 deg. We use our reference model to predict a microlensing optical depth map towards the bulge, normalising its mass by the observed terminal velocity curve. For clump giant sources at (l, b) = (3.9 deg,−3.8 deg) we find τ−6 ≡ τ/10−6 = 1.27, within 1.8σ of the new MACHO measurement given by Popowski et al. The value for all sources at (l, b) = (2.68 deg,−3.35 deg) is τ−6 = 1.1, still > 3σ away from the published MACHO DIA value. The dispersion of these τ−6 values within our models is ' 10%. Because the distribution of sources is well-fit by the NIR model, increasing the predicted optical depths by > 20% will be difficult. Thus the high value of the measured clump giant optical depth argues for a near-maximal disk in the Milky Way.