Title: Starcounts Redivivus II: Deep Starcounts with Keck and HST and the Luminosity Function of the Galactic Halo

Abstract: We have combined deep starcount data with Galaxy model predictions to investigate how effectively such measurements probe the faint end of the halo luminosity function. We have tested a number of star/galaxy classification techniques using images taken in 0.5 arcsecond seeing with LRIS on the Keck telescope, and we find that different combinations of these techniques can produce variations of 10 \% in the inferred starcounts at R=22.5 and 30 \% at R=24.5 magnitudes. The decreasing average angular size of galaxies with fainter magnitude effectively limits ground-based work to R $<$ 25.5 magnitudes. The higher angular resolution provided by HST allows one to probe at least 2 magnitudes fainter, but the small field-size is a significant limitation. In either case, our models show that the contribution from halo subdwarfs is effectively limited to colours of (R-I) $<$ 1.0, with the redder stars being members of the Galactic disk. The apparent increase in number density for M$_V > 10$ in the derived luminosity function is a result of contributions from disk stars at fainter absolute magnitudes and does not provide evidence for an upturn in the halo subdwarf mass function. Indeed, starcount data alone are {\it not} an effective method of probing the shape of the halo luminosity function close to the hydrogen-burning limit. Finally, we examine how the Hubble Deep Field observations can be used to constrain the contribution of various stellar components to the dark-matter halo.