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 with spectra from SDSS/SEGUE , which yield radial velocities and abundances ( [ Fe/H ] & [ \alpha /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 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 mass scale height \lesssim 300 pc and the total surface mass density to be 67 \pm 6 ~ { } M _ { \odot } { pc ^ { -2 } } at |z| = 1.0 kpc of which the contribution from all stars is 42 \pm 5 ~ { } ~ { } M _ { \odot } { pc ^ { -2 } } ( presuming a contribution from cold gas of 13 ~ { } M _ { \odot } { pc ^ { -2 } } ) .
We find significant constraints on the local dark matter density of 0.0065 \pm 0.0023 ~ { } M _ { \odot } { pc ^ { -3 } } ( 0.25 \pm 0.09 ~ { } { GeV cm ^ { -3 } } ~ { } ) .
Together with recent experiments this firms up the best estimate of 0.0075 \pm 0.0021 ~ { } M _ { \odot } { pc ^ { -3 } } ( 0.28 \pm 0.08 ~ { } { GeV cm ^ { -3 } } ~ { } ) , consistent with global fits of approximately round dark matter halos to kinematic data in the outskirts of the Galaxy .