The Palomar/MSU Nearby Star Spectroscopic Survey. IV. The Luminosity Function in the Solar Neighborhood and M Dwarf Kinematics

Abstract

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 VC 2 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( M V ), for stars with absolute magnitudes between -1 and +17. Using empirical and semiempirical mass- M V relations, we transform Φ( M V ) 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 M ⊙ < M < 0.7 M ⊙ ), and the local mass density of main-sequence stars is ∼0.031 M ⊙ 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 M ⊙ . Finally, the ( U , W ) velocity distributions of both the VC 2 sample and the fainter ( M V > 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.