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

To constrain the Galactic gravitational potential near the Sun ($\sim$1.5 kpc), we derive and model the spatial and velocity distribution for a sample of 9000 K-dwarfs that have spectra from SDSS/SEGUE, which yield radial velocities and abundances ([Fe/H] & [$α$/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.