The Palomar/MSU nearby star spectroscopic survey. IV. The luminosity function in the solar neighborhood and M dwarf kinematics

We have used new astrometric and spectroscopic observations to re ne the volume-complete sample of M dwarfs defined in previous papers in this series. With the addition of Hipparcos astrometry, our revised VC2 sample includes 558 main-sequence stars in 448 systems. Analysis of that data set shows no evidence of any systematic kinematic bias. Combining those data with a Hipparcos-based sample of AFGK dwarfs within 25 pc of the Sun, we have derived the solar neighborhood luminosity function, Phi(M-V), for stars with absolute magnitudes between -1 and +17. Using empirical and semiempirical mass-M-V relations, we transform Phi(M-V) to the present-day mass function, psi(M)(=dN/dM). Depending on the mass-luminosity calibration adopted, psi(M) can be represented by either a two-component or a three-component power law. In either case, the power-law index alpha has a value of similar to1.3 at low masses (0.1 M-circle dot<M<0.7 M-circle dot), and the local mass density of main-sequence stars is similar to0.031 M-circle dot pc(-3). We have converted psi(M) to an estimate of the initial mass function,Psi(M), by allowing for stellar evolution, the density law perpendicular to the plane, and the local mix of stellar populations. The results give alpha=1.1-1.3 at low masses and alpha=2.5-2.8 at high masses, with the change in slope lying between 0.7 and 1.1 M-circle dot. Finally, the (U, W) velocity distributions of both the VC2 sample and the fainter (M-V>4) stars in the Hipparcos 25 pc sample are well represented by two-component Gaussian distributions, with similar to10% of the stars in the higher velocity dispersion component. We suggest that the latter component is the thick disk, and we offer a possible explanation for the relatively low velocity dispersions shown by ultracool dwarfs.