The Gravitational Potential Near the Sun From SEGUE K-dwarf Kinematics
  To constrain the Galactic gravitational potential near the Sun ($\sim$1.5
kpc), we derive and model the spatial and velocity distribution for a sample of
9000 K-dwarfs that have spectra from SDSS/SEGUE, which yield radial velocities
and abundances ([Fe/H] & [$\alpha$/Fe]). We first derive the spatial density
distribution for stars of three abundance-selected sub-populations by
accounting for the survey's selection function. The vertical profile of these
sub-populations are simple exponentials and their vertical dispersion profile
is nearly isothermal. To model these data, we apply the `vertical' Jeans
Equation, which relates the observable tracer number density and vertical
velocity dispersion to the gravitational potential or vertical force. We
explore a number of functional forms for the vertical force law, and fit the
dispersion and density profiles of all abundance selected sub-populations
simultaneously in the same potential, and explore all parameter co-variances
using MCMC. Our fits constrain a disk {\it mass} scale height $\lesssim$ 300 pc
and the total surface mass density to be $67 \pm 6 M_{\odot} {\rm pc^{-2}}$ at
$|z| = 1.0$ kpc of which the contribution from all stars is $42 \pm 5 M_{\odot}
{\rm pc^{-2}}$ (presuming a contribution from cold gas of $13 M_{\odot} {\rm
pc^{-2}}$). We find significant constraints on the local dark matter density of
$0.0065\pm0.0023 M_{\odot} {\rm pc^{-3}}$ ($0.25\pm0.09 {\rm GeV cm^{-3}} $).
Together with recent experiments this firms up the best estimate of
$0.0075\pm0.0021 M_{\odot} {\rm pc^{-3}}$ ($0.28\pm0.08 {\rm GeV cm^{-3}} $),
consistent with global fits of approximately round dark matter halos to
kinematic data in the outskirts of the Galaxy.
