Local stellar kinematics from Hipparcos data

From the parallaxes and proper motions of a kinematically unbiased subsample of the Hipparcos Catalogue, we have re‐determined as a function of colour the kinematics of main‐sequence stars.  Whereas the radial and vertical components of the mean heliocentric velocity of stars show no trend with colour, the component in the direction of Galactic rotation nicely follows the asymmetric drift relation, except for stars bluer than B  −  V  = 0.1 mag. Extrapolating to zero dispersion yields, for the velocity of the Sun with respect to the local standard of rest (LSR) in km s −1 , U 0  = 10.00 ± 0.36 (radially inwards), V 0  = 5.25 ± 0.62 (in the direction of Galactic rotation) and W 0  = 7.17 ± 0.38 (vertically upwards).  Parenago's discontinuity is beautifully visible in a plot of velocity dispersion against colour: the dispersion, which is essentially constant for late spectral types, decreases towards early spectral types blueward of B  −  V  ≈ 0.61 mag.  We determine the velocity dispersion tensor σ 2 as function of colour. The mixed moments involving vertical motion are zero within the errors, while σ 2 xy is non‐zero at about (10 km s −1 ) 2 independently of colour. The resulting vertex deviations are about 20° for early‐type stars and 10° ± 4° for old‐disc stars. The persistence of the vertex deviation to late‐type stars implies that the Galactic potential is significantly non‐axisymmetric at the solar radius. If spiral arms are responsible for the non‐axisymmetry, they cannot be tightly wound.  Except for stars bluer than B  −  V = 0.1 mag, the ratios of the principal velocity dispersions are given by σ 1 :σ 2 :σ 3  ≈ 2.2 : 1.4 : 1, while the absolute values increase with colour from σ 1  ≈ 20 km s −1 at B  −  V  = 0.2 mag to σ 1  ≈ 38 km s −1 at Parenago's discontinuity and beyond. These ratios imply significant heating of the disc by spiral structure and that R 0 / R d  ≃ 3 to 3.5, where R d is the scalelength of the disc.