New light on faint stars. IV - Proper motion surveys and the luminosity function

The application of photometric and kinematic absolute magnitude calibration methods to the disk main sequence luminosity function yields significantly different estimates of the number density of very faint dwarf stars. Numerical techniques are presently used to investigate the biases affecting the latter method, using observational data (which show that distant high velocity subdwarfs make a substantial contribution to deep proper motion surveys) as a constraint on simulations. An analysis of these surveys offers an effective method for the determination of the halo luminosity function, and the results obtained suggest that this function may be flatter than that of the disk. The inclusion of these halo stars accounts for the higher space densities of low luminosity dwarf stars derived by Luyten (1925), by comparison with kinematically unbiased photometric surveys.