On the local dark matter density

Jo Bovy, Scott Tremaine

Published 2012-05-17, updated 2012-06-29Version 2

An analysis of the kinematics of 412 stars at 1-4 kpc from the Galactic mid-plane by Moni Bidin et al. (2012) has claimed to derive a local density of dark matter that is an order of magnitude below standard expectations. We show that this result is incorrect and that it arises from the assumption that the mean azimuthal velocity of the stellar tracers is independent of Galactocentric radius at all heights. We substitute the assumption, supported by data, that the circular speed is independent of radius in the mid-plane. We demonstrate that the assumption of constant mean azimuthal velocity is implausible by showing that it requires the circular velocity to drop more steeply than allowed by any plausible mass model, with or without dark matter, at large heights above the mid-plane. Using the approximation that the circular velocity curve is flat in the mid-plane, we find that the data imply a local dark-matter density of 0.008 +/- 0.003 Msun/pc^3 = 0.3 +/- 0.1 GeV/cm3, fully consistent with standard estimates of this quantity. This is the most robust direct measurement of the local dark-matter density to date.