UNIFICATION OF THE NEARBY AND PHOTOMETRIC STELLAR LUMINOSITY FUNCTIONS

We introduce a model Galactic field low-mass stellar population that h as a proportion of binary systems as observed, with a mass ratio distr ibution consistent with observational constraints. The model single-st ar and system luminosity function agrees with the nearby and the Malmq uist-corrected photometric luminosity function, respectively. We tabul ate the model luminosity functions in the photometric V, I, and K band s, and in bolometric magnitudes. Unresolved binary systems are thus a natural explanation for the difference between the nearby and photomet ric luminosity functions. A local overdensity of faint stars need not be postulated to account for the difference and is very unlikely. We s tress that the nearby luminosity function can only be used to weakly c onstrain the stellar mass function below 0.5 M. because of the small s ample size. The photometric luminosity function can only be used to pu t lower limits on the stellar mass function because most binary system s are not resolved. Taken together, however, the nearby and photometri c stellar luminosity function data do not imply a mass function with a peak at a mass of 0.2-0.3 M.. Instead, the data are consistent with a power-law mass function between 0.08 M. and 0.5 M.. We urge researche rs to use only star count data that are properly corrected for all con tributions to cosmic scatter, photometric uncertainties, and unresolve d binaries, and to be aware of the severe limitations of theoretical m ass-luminosity relations for low-mass stars, when drawing conclusions about structure in the stellar mass function.