Hubble Space TelescopeObservations of the Main Sequence of M4

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Abstract
We present new results from a photometric study of the main-sequence stars in M4 (NGC 6121=C1620-264), the closest globular cluster to the Sun. Multifield, multiepoch observations at approximately 1, 2, and 6 core radii were obtained with WFPC2 on the Hubble Space Telescope through either the F606W filter or the F555W (V) and F814W (I) filters. The multiepoch observations allowed us to clean the data on the basis of proper motion and thus separate cluster from field stars or extragalactic objects. In all the fields the cluster main sequence can be traced to at least V = 27.0, but there remains a trail of stars to the limit of the data near V = 30 in the deepest outer field. There is no evidence that we have reached the end of the hydrogen-burning main sequence in any of our fields; however, there is some indication that very few stars remain to be detected in the deepest data. A study of the scatter about the cluster main sequence yields a surprisingly small and variable binary fraction: fb 2% in the inner parts of the cluster, falling to the 1% range outside. However, with one possible exception, no stars in the 6 core radius field exhibit photometric variability on timescales of a few hours through a few days. For the currently visible main-sequence stars, the cluster mass function (MF) is very flat (α = 0.1) in the outer field and flattens further in the inner fields, suggesting well-developed mass segregation. The observed variation in the MF is broadly consistent with isotropic, multimass Michie-King models. Because we have a large sample of white dwarfs in the outer field, we are able to show that the cluster IMF above 0.8 M⊙ was considerably steeper than the present-day MF for low-mass stars. Two appendices are included in this contribution. The first is a detailed discussion of the techniques used to reduce the data, while the second provides a direct comparison between the cluster stars and those belonging to the inner spheroid of the Galaxy. This yields a relative distance between the cluster, dc, and the Galactic center, Ro, of Ro/dc = 4.36 ± 0.13. With our subdwarf-based estimate of dc = 1.73 ± 0.09 kpc to M4, we find Ro = 7.5 ± 0.6 kpc.

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