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

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 afore-mentioned theory is examined by comparison with recent, accurate observational relationships in the M-dwarf domain. The mass function is shown to flatten out below $\sim 1 \msol$ but to keep rising down to the bottom of the main sequence. Combining the present determination below 1 $\msol$ and Scalo's (1986) mass function for larger masses, we show that the mass function is well described over the entire stellar mass range, from $\sim 100 \msol$ to $\sim 0.1 \msol$, by three functional forms, namely a two-segment power-law, a log-normal form or an exponential form, all normalized to the Hipparcos sample at 0.8 $\msol$. 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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