The stellar mass function at low luminosities

We have combined the most recent studies of the stellar luminosity function to derive the mass function for stars in the mass range <f>$1.0\\gt M/{M}_{\\odot}\\gt0.08$</f>. Our analysis shows the importance of using bolometric magnitudes in investigations of cool, late-type stars. The well-established ‘Wielen dip’ at <f>${M}_{V}\\simeq +7$</f> carries over into the bolometric function, which peaks at <f>${M}_\\text{bol} \\sim + 9.5$</f>. However, we also find evidence for a second minimum at <f>${M}_\\text{bol} \\sim + 12.5$</f> and a subsequent rise to fainter luminosities. The stellar mass-luminosity relation is poorly defined at these luminosities, but the continuity of the HR diagram provides a strong argument that none of the isolated low-luminosity stars found to date are brown dwarfs. Under this interpretation, the observed mass density locally is <f>$\\sim 0.09\\,{M}_{\\odot}\\,\\text{pc}^{-3}$</f> and the missing mass remains unfound.