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THE GRAVITATIONAL POTENTIAL NEAR THE SUN FROM SEGUE K-DWARF KINEMATICS

To constrain the Galactic gravitational potential near the Sun (∼1.5 kpc), we derive and model the spatial and velocity distributions for a sample of 9000 K-dwarfs with spectra from SDSS/SEGUE, which yield radial velocities and abundances ([Fe/H] and [α/Fe]). We first derive the spatial density distribution for three abundance-selected sub-populations of stars accounting for the survey's selection function. The vertical profiles 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, fit the dispersion and density profiles of all abundance-selected sub-populations simultaneously in the same potential, and explore all parameter co-variances using a Markov Chain Monte Carlo technique. Our fits constrain a disk mass scale height ≲ 300 pc and the total surface mass density to be 67 ± 6 M☉ pc−2 at |z| = 1.0 kpc of which the contribution from all stars is 42 ± 5 M☉ pc−2 (assuming a contribution from cold gas of 13 M☉ pc−2). We find significant constraints on the local dark matter density of 0.0065 ± 0.0023 M☉ pc−3 (0.25 ± 0.09 GeV cm−3). Together with recent experiments this firms up the best estimate of 0.0075 ± 0.0021 M☉ pc−3 (0.28 ± 0.08 GeV cm−3), consistent with global fits of approximately round dark matter halos to kinematic data in the outskirts of the Galaxy.