Constraints on the Shape of the Milky Way Dark Matter Halo from Jeans
  Equations Applied to SDSS Data
  We search for evidence of dark matter in the Milky Way by utilizing the
stellar number density distribution and kinematics measured by the Sloan
Digital Sky Survey (SDSS) to heliocentric distances exceeding ~10 kpc. We
employ the cylindrically symmetric form of Jeans equations and focus on the
morphology of the resulting acceleration maps, rather than the normalization of
the total mass as done in previous, mostly local, studies. Jeans equations are
first applied to a mock catalog based on a cosmologically derived N-body + SPH
simulation, and the known acceleration (gradient of gravitational potential) is
successfully recovered. The same simulation is also used to quantify the impact
of dark matter on the total acceleration. We use Galfast, a code designed to
quantitatively reproduce SDSS measurements and selection effects, to generate a
synthetic stellar catalog. We apply Jeans equations to this catalog and produce
two-dimensional maps of stellar acceleration. These maps reveal that in a
Newtonian framework, the implied gravitational potential cannot be explained by
visible matter alone. The acceleration experienced by stars at galactocentric
distances of ~20 kpc is three times larger than what can be explained by purely
visible matter. The application of an analytic method for estimating the dark
matter halo axis ratio to SDSS data implies an oblate halo with q_DM = 0.47 +/-
0.14 within the same distance range. These techniques can be used to map the
dark matter halo to much larger distances from the Galactic center using
upcoming deep optical surveys, such as LSST.
