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

Abstract

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 $67\pm 6M_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$ at $|z|=1.0$ kpc of which the contribution from all stars is $42\pm 5M_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$ (presuming a contribution from cold gas of $13M_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$). We find significant constraints on the local dark matter density of $0.0065\pm 0.0023M_{\odot }\mathrm{p}{\mathrm{c}}^{-3}$ ($0.25\pm 0.09\mathrm{GeVc}{\mathrm{m}}^{-3}$). Together with recent experiments this firms up the best estimate of $0.0075\pm 0.0021M_{\odot }\mathrm{p}{\mathrm{c}}^{-3}$ ($0.28\pm 0.08\mathrm{GeVc}{\mathrm{m}}^{-3}$), consistent with global fits of approximately round dark matter halos to kinematic data in the outskirts of the Galaxy.

46 pages, 13 figures, 1 table, accepted for publication in The Astrophysical Journal

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