The vertical force in the Solar Neighbourhood using red clump stars in TGASxRAVE - Constraints on the local dark matter density

We investigate the kinematics of red clump stars in the Solar Neighbourhood by combining data from TGAS and RAVE to constrain the local dark matter density. After calibrating the absolute magnitude of red clump stars, we characterize their velocity distribution over a radial distance range of $6$-$10$ kpc and up to $1.5$ kpc away from the Galactic plane. We then apply the axisymmetric Jeans equations on subsets representing the thin and thick disks to determine the (local) distribution of mass near the disk of our Galaxy. Our kinematic maps are well-behaved permitting a straightforward local determination of the vertical force, which we find to be $K_z^{\rm thin} = -2454 \pm 619$ and $K_z^{\rm thick} = -2141 \pm 774$ $(\mathrm{km/s})^2 \! /\mathrm{kpc}$ at $1.5$ kpc away from the Galactic plane for the thin and thick disk samples and for thin and thick disk scale heights of 0.28 kpc and 1.12 kpc respectively. These measurements can be translated into a local dark matter density $\rho_\textrm{DM} \sim 0.018 \pm 0.002 M_\odot/\textrm{pc}^3$. The systematic error on this estimate is much larger than the quoted statistical error, since even a 10% difference in the scale height of the thin disk leads to a 30% change in the value of $\rho_\textrm{DM}$, and a nearly equally good fit to the data.