The Galactic Disk Mass Budget. I. Stellar Mass Function and Density

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Abstract
In this paper, we use the general theory worked out within the past few years for the structure and the evolution of low-mass stars to derive the stellar mass function in the Galactic disk down to the vicinity of the hydrogen-burning limit from the observed nearby luminosity functions. The accuracy of the mass-magnitude relationships derived from the aforementioned theory is examined by comparison with recent, accurate observational relationships in the M-dwarf domain. The mass function is shown to flatten out below ~1 M☉ but to keep rising down to the bottom of the main sequence. Combining the present determination below 1 M☉ and J. M. Scalo's mass function for larger masses, we show that the mass function is well described over the entire stellar mass range, from ~100 M☉ to ~0.1 M☉, by three functional forms, namely, a two-segment power law, a lognormal form, or an exponential form, all normalized to the Hipparcos sample at 0.8 M☉. Integration of this mass function yields a reasonably accurate census of the entire stellar population in the Galactic disk and its volume and surface mass density.
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