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 refine 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, Φ(MV), for stars with absolute magnitudes between -1 and +17. Using empirical and semiempirical mass-MV relations, we transform Φ(MV) to the present-day mass function, ψ(M) (=dN/dM). Depending on the mass-luminosity calibration adopted, ψ(M) can be represented by either a two-component or a three-component power law. In either case, the power-law index α has a value of ~1.3 at low masses (0.1 Msolar<M<0.7 Msolar), and the local mass density of main-sequence stars is ~0.031 Msolar pc-3. We have converted ψ(M) to an estimate of the initial mass function, Ψ(M), by allowing for stellar evolution, the density law perpendicular to the plane, and the local mix of stellar populations. The results give α=1.1-1.3 at low masses and α=2.5-2.8 at high masses, with the change in slope lying between 0.7 and 1.1 Msolar. Finally, the (U,W) velocity distributions of both the VC2 sample and the fainter (MV>4) stars in the Hipparcos 25 pc sample are well represented by two-component Gaussian distributions, with ~10% 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.Based partly on observations made at the 60 inch (1.5 m) telescope at Palomar Mountain, which is jointly owned by the California Institute of Technology and the Carnegie Institution of Washington.