Distribution functions for the Milky Way

Analytic distribution functions (DFs) for the Galactic disc are discussed. The DFs depend on action variables and their predictions for observable quantities are explored under the assumption that the motion perpendicular to the Galactic plane is adiabatically invariant during motion within the plane. A promising family of DFs is defined that has several adjustable parameters. A standard DF is identified by adjusting these parameters to optimise fits to the stellar density in the column above the Sun, and to the velocity distribution of nearby stars and stars ~1 kpc above the Sun. The optimum parameters imply a radial structure for the disc which is consistent with photometric studies of the Milky Way and similar galaxies, and that 20 per cent of the disc's luminosity comes from thick disc. The fits suggest that the value of the V component of the Sun's peculiar velocity should be revised upwards from 5.2 km/s to ~11 km/s. It is argued that the standard DF provides a significantly more reliable way to divide solar-neighbourhood stars into members of the thin and thick discs than is currently used. The standard DF provides predictions for surveys of stars observed at any distance from the Sun. It is anticipated that DFs of the type discussed here will provide useful starting points for much more sophisticated chemo-dynamical models of the Milky Way.