We use the kinematics of \sim 200 000 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 ( ( 6 \pm 0.9 ) \times 10 ^ { 10 } { M } _ { \odot } ) , and the surface density within 0.9 { kpc } of the plane ( ( 69 \pm 10 ) { M } _ { \odot } { pc } ^ { -2 } ) are almost independent of the ( oblate ) halo ’ s 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 Galaxy ’ s mass is baryonic .
If the halo is flattened , the baryons contribute even less strongly to the local radial force and to the Galaxy ’ s mass .
The dark-matter density at the location of the Sun is 0.0126 q ^ { -0.89 } { M } _ { \odot } { pc } ^ { -3 } = 0.48 q ^ { -0.89 } \hbox { 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 ( { \bf 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 .