The Lower Main Sequence and Mass Function of the Globular Cluster Messier 4

The deepest optical image ever in a globular star cluster, a Hubble Space Telescope 123 orbit exposure in a single field of Messier 4, was obtained in two filters (F606W, F814W) over a 10 week period in early 2001. A somewhat shallower image obtained in 1995 allowed us to select out cluster and field objects via their proper-motion displacement, resulting in remarkably clean color-magnitude diagrams that reach to V = 30, I = 28. The cluster main-sequence luminosity function contains very few stars fainter than MV = 15.0, MI = 11.8, which, in both filters, is more than 2 mag brighter than our limit. This is about the faintest luminosity seen among field Population II subdwarfs of the same metallicity. However, there remains a sprinkling of potential cluster stars to lower luminosity all the way down to our limiting magnitudes. These latter objects are significantly redder than any known metal-poor field subdwarf. Comparison with the current generation of theoretical stellar models implies that the masses of the lowest luminosity cluster stars observed are near 0.09 M☉. We derive the mass function of the cluster in our field and find that it is very slowly rising toward the lowest masses with no convincing evidence of a turnover even below 0.1 M☉. The formal slope between 0.65 and 0.09 M☉ is α = 0.75 (Salpeter of 2.35) with a 99% confidence interval of 0.55-1.05. A consistency check between these slopes and the number of observed cluster white dwarfs yields a range of possible conclusions, one of which is that we have indeed seen the termination of the white dwarf cooling sequence in M4.