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To constrain the Galactic gravitational potential near the Sun ($\sim$1.5kpc), we derive and model the spatial and velocity distribution for a sample of9000 K-dwarfs that have spectra from SDSS/SEGUE, which yield radial velocitiesand abundances ([Fe/H] & [$\alpha$/Fe]). We first derive the spatial densitydistribution for stars of three abundance-selected sub-populations byaccounting for the survey's selection function. The vertical profile of thesesub-populations are simple exponentials and their vertical dispersion profileis nearly isothermal. To model these data, we apply the `vertical' JeansEquation, which relates the observable tracer number density and verticalvelocity dispersion to the gravitational potential or vertical force. Weexplore a number of functional forms for the vertical force law, and fit thedispersion and density profiles of all abundance selected sub-populationssimultaneously in the same potential, and explore all parameter co-variancesusing MCMC. Our fits constrain a disk {\it mass} scale height $\lesssim$ 300 pcand 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 $13 M_{\odot} {\rmpc^{-2}}$). 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 tokinematic data in the outskirts of the Galaxy.

The Gravitational Potential Near the Sun From SEGUE K-dwarf Kinematics