Galactic kinematics and dynamics from RAVE stars

We analyse the kinematics of ~400000 RAVE stars. We split the sample into hot and cold dwarfs, red-clump and non-clump giants. The kinematics of the clump giants are consistent with being identical with those of non-clump giants. We fit Gaussian velocity ellipsoids to the meridional-plane components of velocity of each star class and give formulae from which the shape and orientation of the velocity ellipsoid can be determined at any location. The data are consistent with the giants and the cool dwarfs sharing the same velocity ellipsoids; sigma_z rises from 21 kms in the plane to sim 55 kms at |z|=2 kpc, while sigma_r rises from 37 kms to 82 kms. At (R,z) the longest axis of one of these velocity ellipsoids is inclined to the Galactic plane by an angle ~0.8 arctan(z/R). We use a novel formula to obtain precise fits to the highly non-Gaussian distributions of v_phi components. We compare the observed velocity distributions with the predictions of a dynamical model fitted to the velocities of stars that lie within ~150 pc of the Sun and star counts towards the Galactic pole. The model accurately reproduces the non-Gaussian nature of the v_r and v_z distributions and provides excellent fits to the data for v_z at all locations. The model v_phi distributions for the cool dwarfs fit the data extremely well, while those for the hot dwarfs have displacements to low v_phi that grow with |z| from very small values near the plane. At |z|>0.5 kpc, the theoretical v_phi distributions for giants show a deficit of stars with large v_phi and the model v_r distributions are too narrow. Systematically over-estimating distances by 20 per cent introduces asymmetry into the model v_r and v_z distributions near the plane and but significantly improves the fits to the data at |z|>0.5 kpc. The quality of the fits lends credence to the assumed, disc-dominated, gravitational potential