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Large star-to-star abundance variations are direct evidence of multiplestellar populations in Galactic globular clusters (GCs). The main and mostwidespread chemical signature is the anti-correlation of the stellar Na and Oabundances. The interquartile range (IQR) of the [O/Na] ratio is well suited toquantifying the extent of the anti-correlation and to probe its links to globalcluster parameters. However, since it is quite time consuming to obtain preciseabundances from spectroscopy for large samples of stars in GCs, here we showempirical calibrations of IQR[O/Na] based on the O, Na abundances homogeneouslyderived from more than 2000 red giants in 22 GCs in our FLAMES survey. We finda statistically robust bivariate correlation of IQR as a function of the totalluminosity (a proxy for mass) and cluster concentration c. Calibrated andobserved values lie along the identity line when a term accounting for thehorizontal branch (HB) morphology is added to the calibration, from which weobtained empirical values for 95 GCs. Spreads in proton-capture elements O andNa are found for all GCs in the luminosity range from Mv=-3.76 to Mv=-9.98.This calibration reproduces in a self-consistent picture the link of abundancevariations in light elements with the He enhancements and its effect on thestellar distribution on the HB. We show that the spreads in light elements seemalready to be dependent on the initial GC masses. The dependence of IQR onstructural parameters stems from the well known correlation between c and Mv,which is likely to be of primordial origin. Empirical estimates can be used toextend our investigation of multiple stellar populations to GCs in externalgalaxies, up to M31, where even integrated light spectroscopy may currentlyprovide only a hint of such a phenomenon.

Empirical estimates of the Na-O anti-correlation in 95 Galactic globular clusters