The age of the solar neighbourhood

High-quality Hipparcos data for a complete sample of nearly 12 000 main-sequence and subgiant stars, together with Padua isochrones, are used to constrain the star formation history of the solar neigbourhood and the processes that stochastically accelerate disc stars. The velocity dispersion of a coeval group of stars is found to increase with time from ∼8 km s-1 at birth as t0.33. In the fits, the slope of the initial mass function (IMF) near 1 M⊙ proves to be degenerate with the rate at which the star formation rate declines. If the slope of the IMF is to lie near Salpeter's value, -2.35, the star formation rate has to be very nearly constant. The age of the solar neighbourhood is found to be 11.2 ± 0.75 Gyr with remarkably little sensitivity to variations in the assumed metallicity distribution of old disc stars. This age is only a gigayear younger than the age of the oldest globular clusters when the same isochrones and distance scale are employed. It is compatible with current indications of the redshift of luminous galaxy formation only if there is a large cosmological constant. A younger age is formally excluded because it provides a poor fit to the number density of red stars. Since this density is subject to a significantly uncertain selection function, ages as low as 9 Gyr are plausible even though they lie outside our formal error bars