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

Abstract

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 <it>COBE/ DIRBE L</it>-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 ≈3.5 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 15°≲<it>φ</it><inf>bar</inf>≲30°, with the best models obtained for 20°≲<it>φ</it><inf>bar</inf>≲25°. 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 (<it>l</it>,<it>b</it>)=(3<f>°<inf>.</inf></f>9, −3<f>°<inf>.</inf></f>8) we find <it>τ</it><inf>−6</inf>≡<it>τ</it>/10−6=1.27, within 1.8<it>σ</it> of the new MACHO measurement given by Popowski et al. The value for all sources at (<it>l</it>,<it>b</it>)=(2<f>°<inf>.</inf></f>68, −3<f>°<inf>.</inf></f>35) is <it>τ</it><inf>−6</inf>=1.1, still >3<it>σ</it> away from the published MACHO DIA value. The dispersion of these <it>τ</it><inf>−6</inf> 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.