Resolving the Controversy over the Core Radius of 47 Tucanae (NGC 104)1,2

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Abstract
This paper investigates the discrepancy between recent measurements of the density profile of the globular cluster 47 Tuc that have used Hubble Space Telescope data sets. A large core radius would support the long‐held view that 47 Tuc is a relaxed cluster, while a small core radius may indicate that it is in a post–core‐collapse phase or possibly even on the verge of core collapse, as suggested by a variety of unusual objects—millisecond pulsars, X‐ray sources, high‐velocity stars—observed in the core of the cluster. Guhathakurta et al. used pre‐refurbishment Wide Field Planetary Camera 1 (WFPC1) V‐band images to derive rcore = 23'' ± 2''. Calzetti et al. suggested that the density profile is instead a superposition of two King profiles, one with a small,8'' core radius and the other with a 25'' core radius, based on U‐band Faint Object Camera (FOC) images. More recently, De Marchi et al. have used deep WFPC1 U‐band images to derive rcore = 12'' ± 2''. The cluster centers used in these studies are in agreement with one another; differences in the adopted centers are not the cause of the discrepancy. Our independent analysis of the data used by De Marchi et al. reaches the following conclusions: 1. De Marchi et al.'s rcore ~ 12'' value is spuriously low, a result of radially varying bias in the star counts in a magnitude‐limited sample; photometric errors and a steeply rising stellar luminosity function cause more stars to scatter across the limiting magnitude into the sample than out of it, especially near the cluster center, where crowding effects are most severe. 2. Changing the limiting magnitude to the main‐sequence turnoff, away from the steep part of the luminosity function, partially alleviates the problem and results in rcore = 18''. 3. Combining such a limiting magnitude with accurate photometry derived from point‐spread function fitting, instead of the less accurate aperture photometry employed by De Marchi et al., results in a reliable measurement of the density profile that is well fitted by rcore = 22'' ± 2''. The Calzetti et al. FOC‐based density profile measurement is also likely to have been biased by a poor choice of limiting magnitude and large radially varying photometric errors associated with aperture photometry. Archival Wide Field Planetary Camera 2 (WFPC2) data are used to derive a star list with a higher degree of completeness, greater photometric accuracy, and wider area coverage than the WFPC1 and FOC data sets; the WFPC2‐based density profile supports the above conclusions, yielding rcore = 240 ± 19.
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