Galactic kinematics & dynamics from RAVE stars 3

We analyse the kinematics of ∼ 400 000 stars for which the RAdial Velocity Experiment (RAVE) has obtained spectra. These stars, half giants and half dwarfs, mostly lie within 2.5 kpc of the Sun. We decompose 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 the giants as a whole. Without binning the data 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, which have vertical velocity dispersion rising from 21 kms in the plane to ∼ 55 kms at |z| = 2kpc and radial velocity dispersion rising from 37 kms to 82 kms in the same interval. 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 vφ components in eight bins in the (R, z) plane. We compare the observed velocity distributions with the predictions of a published dynamical model fitted to the velocities of stars that lie within ∼ 150 pc of the Sun and star counts towards the Galactic pole. The predictions are remarkably successful. In particular, the model accurately reproduces the non-Gaussian nature of the vr and vz distributions. The theoretical vφ distributions for the cool dwarfs fit the data extremely well, while those for the hot dwarfs have displacements to low vφ that grow with |z| from very small values near the plane. At |z|>∼ 0.5 kpc, the theoretical vφ distributions for giants show a deficit of stars with large vφ. The theoretical vz distributions provide excellent fits to the data for all classes at all locations. At |z|>∼ 0.5 kpc, the observed vr distributions of giants become too narrow. We show that systematically over-estimating distances by 20 per cent introduces asymmetry into the model vr and vz distributions near the plane and by broadening those distributions far from the plane significantly improves the fits to the data. The ability of the dynamical model to give such a good account of a large body of data to which it was not fitted inspires confidence in the fundamental correctness of the assumed, disc-dominated, gravitational potential.