LUMINOSITY FUNCTIONS FOR VERY LOW MASS STARS AND BROWN DWARFS

We have made a theoretical investigation of the luminosity function for low-mass objects with the aim of constraining the stellar initial mass function at the low-mass end. We have examined how luminosity functions for low-mass stars are affected by (1) star formation histories, (2) brown dwarf and pre-main-sequence cooling rates and main-sequence mass luminosity relations, and (3) the initial mass function (IMF). In order to determine cooling rates and the mass-luminosity relation, we have made a new series of evolutionary calculations for very low mass stars and brown dwarfs in the range (0.05 M. < M < 0.50 M.). We have constructed model luminosity functions for specific comparison with the results of four recent observational surveys. Our work affirms the likelihood that the stellar mass function in the solar neighborhood is increasing at masses near the bottom of the main sequence and perhaps at lower masses. Observational searches published to date are not complete enough to characterize the mass function in the substellar region. We find that in the most optimistic case, brown dwarfs contribute half of the local missing disk mass. The actual contribution is likely to be considerably less. As an aid to future observational programs, we make predictions of the form of the luminosity function in low-luminosity regimes currently being probed by infrared searches