THE DISTRIBUTION OF LOW-MASS STARS IN THE GALACTIC DISC

We quantify the complex interdependence of stellar binarity, the stell ar mass-luminosity relation, the mass function, the colour-magnitude r elation and Galactic disc structure, all of which must be understood w hen analysing star-count data and stellar luminosity functions. We der ive a mass-M(V) relation and a model for the change of stellar luminos ity with changes in chemical abundance and age. Combination of this wi th detailed modelling of all astrophysical and observational contribut ions to the Malmquist scatter allows us to model star-count data witho ut approximating Malmquist corrections. We show for the first time tha t a single mass function and normalization explain the stellar distrib ution towards both Galactic poles, as well as the distribution of star s within a distance of 5.2 pc of the Sun. The initial mass function ca n be approximated by xi(m)is-proportional-to m(-alpha) with alpha3 alm ost-equal-to 2.7 for stars more massive than 1M., alpha2 almost-equal- to 2.2 in the mass range 0.5 less-than-or-equal-to m less-than-or-equa l-to 1 M. and 0.70 < alpha1 < 1.85 in the range 0.0 8 < m less-than-or -equal-to 0. 5 M . If the stars at a distance of about 1 00 pc from th e Galactic mid-plane have a metallicity smaller by about 0.1 dex than do the stars near the plane used to calibrate the mass-M(V) and colour -magnitude relations, then both the stars within 5.2 pc of the Sun and the star-count data reaching to a photometric distance of 130 pc lead to a low-mass power-law index of alpha1 almost-equal-to 1.5. The chan ge in the power index at 0.5 M, may indicate a characteristic mass-sca le in the star formation process. Our model is most consistent with th e data if the proportion of binaries among 'stars' is larger than 5 0 per cent and if the component masses are uncorrelated. The possible de cline of the proportion of binaries with increasing absolute magnitude , observed in the solar neighbourhood, is in agreement with our models . Two features in the luminosity function for low-mass stars are unive rsal, being solely the result of stellar physics. These features are a flattening at M(V) almost-equal-to 7 and a conspicuous maximum at M(V ) almost-equal-to 12. Binary stars cause the system luminosity functio n derived from photographic surveys to decrease uniformly with increas ing magnitude relative to the single-star luminosity function, but bot h show the same general features. The solar neighbourhood mass density in main-sequence stars with masses between 0.08 and 100 M. is rho = 0 .05 +/- 0.01 M. pc-3, of which main-sequence stars less massive than t he Sun contribute about 80 per cent. These estimates explicitly includ e the effects of binaries. Unresolved binaries cause the apparent disc scaleheight to decrease with decreasing mass to a value of almost-equ al-to 150 pc for star-count data in the colour range 4 < V - I < 4.5 i f all 'stars' are unresolved binaries with uncorrelated component mass es. The vertical structure of the Galactic disc is not well described by a single exponential within a few hundred pc of the plane. Neglect of this can lead to a spurious apparent correlation between stellar ma ss and disc scaleheight.