Color-Magnitude Diagram and Luminosity Function of M4 near the Hydrogen-burning Limit

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Abstract
A proper-motion separation of M4 members from field stars, using deep HST observations separated by a time base-line of 5 years, 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] ~ -1). This inability of theory to reproduce the luminosity-radius 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.
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