The stellar mass function at low luminosities

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Abstract
We have combined the most recent studies of the stellar luminosity function to derive the mass function for stars in the mass range |$1.0\gt M/{M}_{\odot}\gt0.08$|⁠. Our analysis shows the importance of using bolometric magnitudes in investigations of cool, late-type stars. The well-established ‘Wielen dip’ at |${M}_{V}\simeq +7$| carries over into the bolometric function, which peaks at |${M}_\text{bol} \sim + 9.5$|⁠. However, we also find evidence for a second minimum at |${M}_\text{bol} \sim + 12.5$| 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 |$\sim 0.09\,{M}_{\odot}\,\text{pc}^{-3}$| and the missing mass remains unfound.

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