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

TL;DR

This study uses K-dwarf star data from SDSS/SEGUE to model the Galactic gravitational potential near the Sun, constraining the local dark matter density and total surface mass density through velocity and spatial distribution analysis.

Contribution

It provides new constraints on the local dark matter density and the Galactic mass distribution by applying the vertical Jeans Equation to a large, abundance-selected stellar sample.

Findings

Total surface mass density at 1 kpc is 67 ± 6 M_sun/pc^2.

Local dark matter density is 0.0065 ± 0.0023 M_sun/pc^3.

Disk scale height is constrained to less than 300 pc.

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 $67 \pm 6 M_{\odot} {\rm pc^{-2}}$ 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.