This paper investigates the discrepancy between recent measurements of the density profile of the globular cluster 47 Tucanae 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 .
( 1992 ) used pre-refurbishment Wide Field/Planetary Camera 1 ( WFPC1 ) V -band images to derive r _ { core } = 23 ^ { \prime \prime } \pm 2 ^ { \prime \prime } . [ Calzetti et al .
( 1993 ) ] suggested that the density profile is instead a superposition of two King profiles , one with a small , 8 ^ { \prime \prime } core radius and the other with a 25 ^ { \prime \prime } core radius , based on U -band Faint Object Camera ( FOC ) images .
More recently , [ De Marchi et al .
( 1996 ) ] have used deep WFPC1 U -band images to derive r _ { core } = 12 ^ { \prime \prime } \pm 2 ^ { \prime \prime } .
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 r _ { core } \sim 12 ^ { \prime \prime } 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 _ { core } = 18 ^ { \prime \prime } .

( 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 which is well fit by r _ { core } = 22 ^ { \prime \prime } \pm 2 ^ { \prime \prime } .

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 areal coverage than the WFPC1 and FOC data sets ; the WFPC2-based density profile supports the above conclusions , yielding r _ { core } = 24 \farcs 0 \pm 1 \farcs 9 .