MOA-II Galactic microlensing constraints: the inner Milky Way has a low dark matter fraction and a near maximal disc

Microlensing provides a unique tool to break the stellar to dark matter degeneracy in the inner Milky Way. We combine N-body dynamical models fitted to the Milky Way's Boxy/Peanut bulge with exponential disc models outside this, and compute the microlensing properties. Considering the range of models consistent with the revised MOA-II data, we find low dark matter fractions in the inner Galaxy: at the peak of their stellar rotation curve a fraction f_v = (0.88 ± 0.07) of the circular velocity is baryonic (at 1σ, f_v > 0.72 at 2σ). These results are in agreement with constraints from the EROS-II microlensing survey of brighter resolved stars, where we find f_v = (0.9 ± 0.1) at 1σ. Our fiducial model of a disc with scale length 2.6 kpc, and a bulge with a low dark matter fraction of 12 per cent, agrees with both the revised MOA-II and EROS-II microlensing data. The required baryonic fractions, and the resultant low contribution from dark matter, are consistent with the NFW profiles produced by dissipationless cosmological simulations in Milky Way mass galaxies. They are also consistent with recent prescriptions for the mild adiabatic contraction of Milky Way mass haloes without the need for strong feedback, but there is some tension with recent measurements of the local dark matter density. Microlensing optical depths from the larger OGLE-III sample could improve these constraints further when available.