The luminosity function for low mass stars.

This paper describes a photometric survey for late M-dwarfs from COSMOS measures of R- and I-band UK Schmidt plates. The survey covers some 85 square degrees and includes about 500 M-stars within 100 pc. The luminosity function is sampled down to M_R ≈ 17. In addition, spectra have been obtained for the six reddest stars, which have confirmed the low temperatures deduced from the photometry. Proper motions for two-thirds of the sample stars have been measured and indicate that the reddest stars are younger than the sample as a whole. The observed luminosity function has been compared with theoretical functions from the literature. There are some puzzling discrepancies for the more luminous stars, but there is unambiguous evidence for a steadily rising mass function towards the sample limit and the observations suggest that the local missing mass is in the form of low luminosity stars. The evolutionary status of the low luminosity stars in the sample is examined in the light of two hypotheses.