Color-magnitude diagram and luminosity function of M4 near the hydrogen-burning limit

A proper-motion separation of M4 members from field stars, using deep Hubble Space Telescope observations separated by a time baseline of 5 yr, allows us to study a pure sample of cluster main-sequence stars almost to the minimum mass for hydrogen burning. High-precision photometry shows how badly current theoretical models fail to reproduce the color-magnitude diagram of low-mass stars of moderate metallicity ([M/H]similar or equal to -1). This inability of theory to reproduce the luminosity-color relation casts doubt on the theoretical mass-luminosity relation, which is needed to convert the observed luminosity function (LF) into a mass function (MF) as well as to convert our locally determined LF into a global MF. To the extent that we trust theoretical M-L relations for such transformations, we obtain a flat MF from the LF, and some indication that theoretical masses might be too low at a given luminosity, near the H-burning limit.