Constructing the Stellar Density Profile

For the purposes of determining radial profiles for NGC 6752, I rely on the V- and I-band data from the ACS Survey Catalogue, as this is the deepest available data set. Repeating the process using the WFC3/NUV catalogue gave the same overall shape, with a simple shift in density that was consistent at all radii. This indicates that depth is the dominant difference between the observed distributions.

The procedure I used is similar to that described by Djorgovski (1988). As shown in Figure 4.4, the catalogue is divided into concentric circles, centred on the cluster centre, increasing in radius by 50 pixels (2^′′) each step. Each annulus is split into eight equal sectors. Due to the off-centre location of the cluster centre on the chip, the number of segments which fell entirely on the chip in V- and I-band data ranges from 35 to 52, depending on the sector considered, while sectors in the NUV data contained 35 to 46 complete segments. The number of sources falling within a

120 Chapter 4. NGC 6752: The Colour-Magnitude Diagram and Radial Profile

0 0.5 1 1.5 2

0 0.2 0.4 0.6 0.8 1

Log(r) [arcseconds]

Figure 4.5: Completeness at different radii, for sources brighter than VST MAG= 19.7 mag, determined using the artificial star catalogue from the ACS Survey.

segment is divided by the area of the segment to give the stellar density.

The overall density for a given annulus is then computed as the average of the densities of the segments corresponding to that annulus. The error on the overall density of an annulus is the standard deviation of the densities in the annulus’ seg-ments. This is justified by the fact that the dominant error source is the discrete nature of the distribution; if there is an unusually dense region of stars in one seg-ment, that segment will contribute an artificially high number to the annulus, but the corresponding dispersion will also be larger.

In constructing the radial density profiles, I include all of the sources listed in the ACS Survey Catalogue (unlike in previous sections, in which only V- and I-band sources with a match in the WFC3 catalogues are included). This has a plate scale of 0.^′′05/pixel out to radius ≃ 101^′′. I limit the data to sources brighter than

≈ 2 mags below the MSTO, corresponding to to VST MAG= 19.7 mag, to reduce the likelihood of incompleteness impacting the results. I further correct for complete-ness using the artificial star catalogue for NGC 6752 that was created by Anderson et al. (2008) as part of the ACS Survey. Following their method, I consider a star to be recovered if the input and output fluxes agree to within 0.75 mag and the

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0 0.5 1 1.5 2

-0.5 0 0.5

1

Figure 4.6: Observed radial density profile using V- and I-band data from the ACS Survey Catalogue, based on the centre determined in Section 4.4.1. Blue, solid line: best-fit King model to the data for the overall observed density profile, with W0= 11, r_c= 9^′′, c= 2.547. The poor fit to the data indicates that the profile of NGC 6752 cannot be well modelled with a single King profile.

tions agree to within 0.5 pixels. Using the centre determined in Section 4.4.1 I test for completeness as a function of radius, for stars brighter than V_{ST MAG}= 19.7 mag.

As shown in Figure 4.5, I find that completeness is almost 100% at the edges of the images, and is over 50% even in the core. I correct the stellar densities using the fractions of artificial sources recovered at each radius.

The radial profile obtained using this method is plotted in Figure 4.6. The profile shows a continuing rise in density towards the centre of the cluster. This agrees with the findings of Ferraro et al. (2003a), and is contrary to the findings of Noy-ola & Gebhardt (2006), whose surface brightness profile showed a flat core within log(r) ≈ 0.^′′5. As shown in Table 4.4 and Figure 4.3, the centre used by Noyola &

122 Chapter 4. NGC 6752: The Colour-Magnitude Diagram and Radial Profile

This paper

Noyola & Gerbhardt (2006)

Figure 4.7: Radial density profile using different estimates of the centre position.

Black points: observed radial density profile using V- and I-band data from the ACS Survey Catalogue, based on the centre determined in Section 4.4.1. Red crosses: observed radial density profile using the same data, but using the centre estimate from Noyola & Gebhardt (2006). Note that the data in this figure are raw data, not corrected for completeness.

Gebhardt differed from ours by nearly 1^′′. Figure 4.7 shows the result of creating a radial density profile using this data but the centre given by Noyola & Gebhardt.

The majority of the profile is unchanged, but the density at the innermost measure-ment point is slightly lower, giving the impression of a flatter core. The difference between the radial profile found here and that of Noyola & Gebhardt could, there-fore, be partly due to the difference in the assumed centre positions. An alternative explanation is that there is a fundamental difference between the stellar density pro-file and surface brightness propro-file. D’Amico et al. (2002) showed that NGC 6752 has an usually high mass-to-light ratio(& 10), leading to a high proportion of

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tically faint sources in the core, which may contribute to the stellar density, but not the surface brightness.