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.