The Milky Way Tomography with Sloan Digital Sky Survey. V. Mapping the Dark Matter Halo

We present robust constraints from the Sloan Digital Sky Survey (SDSS) on the shape and distribution of the dark matter halo within the Milky Way (MW). Using the number density distribution and kinematics of SDSS halo stars, we probe the dark matter distribution to heliocentric distances exceeding ~10 kpc and galactocentric distances exceeding ~20 kpc. Our analysis utilizes Jeans equations to generate two-dimensional acceleration maps throughout the volume; this approach is thoroughly tested on a cosmologically derived N-body+SPH simulation of a MW-like galaxy. We show that the known accelerations (gradients of the gravitational potential) can be successfully recovered in such a realistic system. Leveraging the baryonic gravitational potential derived by Bovy & Rix, we show that the gravitational potential implied by the SDSS observations cannot be explained, assuming Newtonian gravity, by visible matter alone: the gravitational force experienced by stars at galactocentric distances of ~20 kpc is as much as three times stronger than what can be attributed to purely visible matter. We also show that the SDSS data provide a strong constraint on the shape of the dark matter halo potential. Within galactocentric distances of ~20 kpc, the dark matter halo potential is well described as an oblate halo with axis ratio q^Φ _DM=0.7 +/- 0.1; this corresponds to an axis ratio q^ρ _DM∼ 0.4 +/- 0.1 for the dark matter density distribution. Because of our precise two-dimensional measurements of the acceleration of the halo stars, we can reject several MOND models as an explanation of the observed behavior.