We use the kinematics of $sim200,000$ giant stars that lie within $sim 1.5$ kpc of the plane to measure the vertical profile of mass density near the Sun. We find that the dark mass contained within the isodensity surface of the dark halo that passes
through the Sun ($(6pm0.9)times10^{10},mathrm{M_odot}$), and the surface density within $0.9$ kpc of the plane ($(69pm10),mathrm{M_odot,pc^{-2}}$) are almost independent of the (oblate) halos axis ratio $q$. If the halo is spherical, 46 per cent of the radial force on the Sun is provided by baryons, and only 4.3 per cent of the Galaxys mass is baryonic. If the halo is flattened, the baryons contribute even less strongly to the local radial force and to the Galaxys mass. The dark-matter density at the location of the Sun is $0.0126,q^{-0.89},mathrm{M_odot,pc^{-3}}=0.48,q^{-0.89},mathrm{GeV,cm^{-3}}$. When combined with other literature results we find hints for a mildly oblate dark halo with $q simeq 0.8$. Our value for the dark mass within the solar radius is larger than that predicted by cosmological dark-matter-only simulations but in good agreement with simulations once the effects of baryonic infall are taken into account. Our mass models consist of three double-exponential discs, an oblate bulge and a Navarro-Frenk-White dark-matter halo, and we model the dynamics of the RAVE stars in the corresponding gravitational fields by finding distribution functions $f(mathbf{J})$ that depend on three action integrals. Statistical errors are completely swamped by systematic uncertainties, the most important of which are the distance to the stars in the photometric and spectroscopic samples and the solar distance to the Galactic centre. Systematics other than the flattening of the dark halo yield overall uncertainties $sim 15$ per cent.
We construct new estimates on the Galactic escape speed at various Galactocentric radii using the latest data release of the Radial Velocity Experiment (RAVE DR4). Compared to previous studies we have a database larger by a factor of 10 as well as re
liable distance estimates for almost all stars. Our analysis is based on the statistical analysis of a rigorously selected sample of 90 high-velocity halo stars from RAVE and a previously published data set. We calibrate and extensively test our method using a suite of cosmological simulations of the formation of Milky Way-sized galaxies. Our best estimate of the local Galactic escape speed, which we define as the minimum speed required to reach three virial radii $R_{340}$, is $533^{+54}_{-41}$ km/s (90% confidence) with an additional 5% systematic uncertainty, where $R_{340}$ is the Galactocentric radius encompassing a mean over-density of 340 times the critical density for closure in the Universe. From the escape speed we further derive estimates of the mass of the Galaxy using a simple mass model with two options for the mass profile of the dark matter halo: an unaltered and an adiabatically contracted Navarro, Frenk & White (NFW) sphere. If we fix the local circular velocity the latter profile yields a significantly higher mass than the un-contracted halo, but if we instead use the statistics on halo concentration parameters in large cosmological simulations as a constraint we find very similar masses for both models. Our best estimate for $M_{340}$, the mass interior to $R_{340}$ (dark matter and baryons), is $1.3^{+0.4}_{-0.3} times 10^{12}$ M$_odot$ (corresponding to $M_{200} = 1.6^{+0.5}_{-0.4} times 10^{12}$ M$_odot$). This estimate is in good agreement with recently published independent mass estimates based on the kinematics of more distant halo stars and the satellite galaxy Leo I.
