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Resolving the Controversy Over the Core Radius of 47 Tucanae (NGC 104)

This paper investigates the discrepancy between recent measurements of the density profile of the globular cluster 47 Tuc that have used HST data sets. Guhathakurta et al. (1992) used pre-refurbishment WFPC1 V-band images to derive r_c = 23" +/- 2". Calzetti et al. (1993) suggested that the density profile is a superposition of two King profiles (r_c = 8" and r_c = 25") based on U-band FOC images. De Marchi et al. (1996) used deep WFPC1 U-band images to derive r_c = 12" +/- 2". Differences in the adopted cluster 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 r_c ~ 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 r_c = 18". (3) Combining such a limiting magnitude with accurate photometry derived from PSF fitting, instead of the less accurate aperture photometry employed by De Marchi et al., results in a reliable measurement of the density profile which is well fit by r_c = 22" +/- 2". Archival WFPC2 data are used to derive a star list with a higher degree of completeness, greater photometric accuracy, and wider areal coverage than the WFPC1 and FOC data sets; the WFPC2-based density profile supports the above conclusions, yielding r_c = 24" +/- 1.9".