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

Studies of the disc main-sequence luminosity function using photometric and kinematic absolute magnitude calibration methods result in significantly different estimates of the number density of very faint (MV > + 14) dwarfs. We have used numerical techniques to investigate the biases affecting the latter method, using observational data to constrain the simulations. These show that distant, high-velocity subdwarfs make a substantial contribution to deep proper-motion surveys. Indeed, analysis of these surveys represents an effective method of determining the halo luminosity function, with our results suggesting that this may be flatter than the disc function. The inclusion of these halo stars accounts for the substantially higher space densities of low-luminosity dwarfs derived by Luyten compared with kinematically unbiased photometric surveys.