All Figures

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig1.eps}}\end{figure}$ Figure 1: Model star cluster specifications. Panel a): a random selection of n in the range $0\leq n\leq 1$ produces King-like RDPs in the range $0\leq R\leq\mbox{$R_{\rm t}$ }$ (see Eq. (2)). Panel b): Radially-variable mass function slopes $\left(\frac{dN}{dm}\propto m^{-(1+\chi)}\right)$ used in the models. Panel c): Padova isochrones used to simulate the mass-luminosity relation of the star cluster models. The 10 Gyr, $\mbox{$\rm [Fe/H]$ }=-1.5$ metallicity isochrone is adopted in the globular cluster models. Panel d): distribution of concentration parameters of the GCs in H03 with peaks at $c\approx1.6,~1.3,~{\rm and}~0.7$ . Panel e): model fraction of stars brighter than $M_J=M_{J_{TO}}+\Delta _{TO}$ . In all cases, the fraction of stars brighter than the TO ( M_{J_TO}) is below the $1\%$ level.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig2.eps}}\end{figure}$ Figure 2: A selection of RDPs ( top panels), MDPs ( middle) and 2MASS J magnitude SBPs ( bottom) that illustrate structural changes under different magnitude depths. Arbitrary units (au) are used both for the radial coordinate and projected area.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig3.eps}}\end{figure}$ Figure 3: Structural parameters of the GC models. Top panels: ratio of the tidal radius measured in profiles with a photometric depth $\rm\Delta _{TO}$ with respect to that derived from the deepest one, for the RDPs ( left panels), MDPs (vertical- middle) and SBPs ( right). Horizontal-middle panels: half-type radii. Bottom: core radii. TO values are indicated by the dotted line. Except for GC-C (uniform mass function), the remaining models present changes in radii in the RDPs and MDPs. SBP radii are essentially uniform.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig4.eps}}\end{figure}$ Figure 4: Same as Fig. 3 for the OC models. For comparison purposes, the y-scale is the same as in Fig. 3. Similarly to the GC models, radii changes are conspicuous in the RDPs and MDPs.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig5.eps}}\end{figure}$ Figure 5: GC model profiles. Ratio between the same type of radii as measured in RDPs and MDPs ( left panels) and RDPs and SBPs ( right panels). From top to bottom: tidal, half and core radii. TO values are indicated by the dotted line.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig6.eps}}\end{figure}$ Figure 6: Same as Fig. 5 for the OC models. For comparison purposes, the y-scale is the same as in Fig. 5.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig7.eps}}\end{figure}$ Figure 7: Top panels: relation of the half-type radii with the concentration parameter, for the RDPs ( left panel), MDPs ( middle) and SBPs ( right). For each model, R_h values increase for deeper profiles. Dashed line in panels a) and b): $R_h\sim c^2$ . In panel c): $\mbox{$R_{\rm hL}$ }\sim c$ . Bottom panels: concentration parameter as a function of photometric depth.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig8.eps}}\end{figure}$ Figure 8: Structural analysis of NGC 6397. Panel a): decontaminated CMD of a central ( $R<5\hbox {$^\prime $ }$ ) region. The reference magnitude $\mbox{$J$ }=15$ is indicated by the dashed-line. Shaded region: colour-magnitude filter. Background-subtracted RDPs for stars brighter than $\mbox{$J$ }<15+\Delta_{J15}$ , with $\Delta_{J15}=1,~0,~-1,~-2$ are shown in panels b) to d), respectively. The respective King-like fits (solid-line) together with the fit uncertainty (shaded region) are shown.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig9.eps}}\end{figure}$ Figure 9: Left panels: RDP and SBP structural radii of NGC 6397 as a function of $\Delta _{J15}$ , normalised to the values measured in the deepest profile. Right panels: RDP to SBP radii ratios (similar to Fig. 5).
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig2.eps}}\end{figure}$	Figure 2: A selection of RDPs ( top panels), MDPs ( middle) and 2MASS J magnitude SBPs ( bottom) that illustrate structural changes under different magnitude depths. Arbitrary units (au) are used both for the radial coordinate and projected area.
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig4.eps}}\end{figure}$	Figure 4: Same as Fig. 3 for the OC models. For comparison purposes, the y-scale is the same as in Fig. 3. Similarly to the GC models, radii changes are conspicuous in the RDPs and MDPs.
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig5.eps}}\end{figure}$	Figure 5: GC model profiles. Ratio between the same type of radii as measured in RDPs and MDPs ( left panels) and RDPs and SBPs ( right panels). From top to bottom: tidal, half and core radii. TO values are indicated by the dotted line.
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig6.eps}}\end{figure}$	Figure 6: Same as Fig. 5 for the OC models. For comparison purposes, the y-scale is the same as in Fig. 5.
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig7.eps}}\end{figure}$	Figure 7: Top panels: relation of the half-type radii with the concentration parameter, for the RDPs ( left panel), MDPs ( middle) and SBPs ( right). For each model, R_h values increase for deeper profiles. Dashed line in panels a) and b): $R_h\sim c^2$ . In panel c): $\mbox{$R_{\rm hL}$ }\sim c$ . Bottom panels: concentration parameter as a function of photometric depth.
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics{fig9.eps}}\end{figure}$	Figure 9: Left panels: RDP and SBP structural radii of NGC 6397 as a function of $\Delta _{J15}$ , normalised to the values measured in the deepest profile. Right panels: RDP to SBP radii ratios (similar to Fig. 5).
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