We apply a new method to determine the local disc matter and dark halo matter density to kinematic and position data for \sim 2000 K dwarf stars taken from the literature .
Our method assumes only that the disc is locally in dynamical equilibrium , and that the ‘ tilt ’ term in the Jeans equations is small up to \sim 1 kpc above the plane .
We present a new calculation of the photometric distances to the K dwarf stars , and use a Monte Carlo Markov Chain to marginalise over uncertainties in both the baryonic mass distribution , and the velocity and distance errors for each individual star .
We perform a series of tests to demonstrate that our results are insensitive to plausible systematic errors in our distance calibration , and we show that our method recovers the correct answer from a dynamically evolved N-body simulation of the Milky Way .
We find a local dark matter density of \rho _ { \mathrm { dm } } = 0.025 ^ { +0.014 } _ { -0.013 } M _ { \odot } pc ^ { -3 } ( 0.95 ^ { +0.53 } _ { -0.49 } GeV cm ^ { -3 } ) at 90 % confidence assuming no correction for the non-flatness of the local rotation curve , and \rho _ { \mathrm { dm } } = 0.022 ^ { +0.015 } _ { -0.013 } M _ { \odot } pc ^ { -3 } ( 0.85 ^ { +0.57 } _ { -0.50 } GeV cm ^ { -3 } ) if the correction is included .
Our 90 % lower bound on \rho _ { \mathrm { dm } } is larger than the canonical value typically assumed in the literature , and is at mild tension with extrapolations from the rotation curve that assume a spherical halo .
Our result can be explained by a larger normalisation for the local Milky Way rotation curve , an oblate dark matter halo , a local disc of dark matter , or some combination of these .