tokens: to a predicted final binding energy equal to E bin ∼ 2.4 E bin,0 in very good agreement with what shown in Fig. 7 . 3.3 Radial variation of the binary fraction Fig. 8 shows the radial profiles of the binary fraction (defined as the ratio of the number of binaries for each population to the total number of binaries and single stars in the cluster) for all binaries, for FG binaries, and for SG binaries. The low ionization rate of the compact binaries we are considering, facilitates the central accumulation of binaries segregating from the outer regions and results into an increasing binary fraction in the cluster inner regions. It is interesting to note that the evolved binary fraction radial profiles are in general qualitative agreement with those found in the recent observational study of Milone et al. ( 2016 ). Figure 8. Time evolution of the radial profiles of the binary fraction (defined as the ratio of the number of binaries to the total number of binaries and single stars) for the model MPr5f1x3-800. Each profile is calculated by combining three snapshots around the time indicated in the legend. Top, middle, and bottom panels show, respectively, the profiles for all the binaries, for FG binaries, and for SG binaries. The horizontal dashed line in the top panel shows the initial binary fraction. The three panels of Fig. 9 show the cumulative and the differential radial profiles of SG-to-FG binary ratio and the differential SG-to-FG ratio for single stars. The interplay among ionization, ejection and segregation towards the inner regions results into a progressive decrease of the SG-to-FG binary number ratio in the cluster inner regions. The global SG-to-FG binary number ratio decreases with time due to the dominant effect of the preferential ionization or ejection of SG binaries; it is interesting to note that this is opposite to what happens to the global SG-to-FG number ratio for single stars which increases with time because for single stars the preferential evaporation of FG stars (see also Vesperini et al. 2013 ) drives the evolution of this number ratio. Figure 9. Time evolution of the radial profile of the cumulative number ratio of SG to FG binaries (top panel), the differential SG-to-FG binary number ratio (middle panel), and the differential number ratio of SG to FG single stars (bottom panel) for the model MPr5f1x3-800. Lines with different colour and style correspond to the different times indicated in the legend, and the horizontal lines show the global SG-to-FG ratio for binaries (middle panel) and single stars (bottom panel). (Each profile has been calculated using three combined snapshots around the times indicated in the legend.) As shown in Fig. 9 , the SG-to-FG binary number ratio depends on the distance from the cluster centre. It is important to identify the radius R glob , where the local SG-to-FG ratio is equal to the global value of this ratio. In paper I , we have already shown that R glob depends on the initial
ner_tags: O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O