The infrared luminosity function for low-mass stars

We present the first infrared observational luminosity functions (LFs) for M dwarfs towards the South Galactic Pole (SGP) and the Hyades cluster. We also give a definitive compilation of new and published VRIJHK data for 200 parallax stars, for deriving photometric parallaxes in such studies. Two-colour near-infrared/infrared diagrams of these data are used to demonstrate metallicity and gravity effects, and show that I–J is the purest temperature colour index. An MJ:I–J relation is given using high-quality trigonometric parallaxes from the new Yale catalogue. We describe the corrections to the LFs that are necessary to allow for magnitude errors (Malmquist effects), which have been incorrectly applied in recent determinations. Within the errors, the LFs for the Hyades cluster and the SGP are indistinguishable, although the faintest stars seen at the SGP cannot be detected by this work at the distance of the cluster. This implies that the mass functions of the field and this, relatively young, cluster are indistinguishable at low stellar masses. The peak in the LF for stars with masses ∼0.2 M⊙ is seen at all wavelengths, and for smaller masses the LF decreases, reaching a minimum at ∼0.1 M⊙, The infrared data indicate that there is a subsequent rise in the LF, and hence the mass function, for stars in the solar neighbourhood with masses close to the hydrogen-burning limit. Although it is uncertain whether or not the faintest objects observed are ‘brown dwarfs’, the fact that the mass function rises implies that low-mass objects may yet make up the local missing mass.