Fig. 4: The natural correlation between the fraction of FRs and the binary fraction.

a Fraction of fast-spinning BSSs, f_FR (with v sin i ≥ 40 km/s; grey circles) plotted as a function of the global binary fraction²⁵, f_BIN (ω Centauri is lacking because no reliable estimates of its binary fraction are available in the literature). Errors computed following the Poisson statistics are also reported. The dashed line is the best fit to the data, while the solid line traces the equation obtained by combining the two best-fit relations shown in panel b. b The relations linking the fraction of binaries f_BIN (grey circles in the top panel) and the fraction of fast-rotating BSSs f_FR (grey circles in the bottom panel) to the cluster central density (log ρ₀ in units of L_⊙/pc³). The small empty circles in the top panel are the data for a sample of 59 Galactic GCs²⁵. The solid lines are the best linear fits to the data (see Supplementary Table 3 for the values of the fit parameters and uncertainties).