Empirical estimates of the Na-O anti-correlation in 95 Galactic globular
  clusters
  Large star-to-star abundance variations are direct evidence of multiple
stellar populations in Galactic globular clusters (GCs). The main and most
widespread chemical signature is the anti-correlation of the stellar Na and O
abundances. The interquartile range (IQR) of the [O/Na] ratio is well suited to
quantifying the extent of the anti-correlation and to probe its links to global
cluster parameters. However, since it is quite time consuming to obtain precise
abundances from spectroscopy for large samples of stars in GCs, here we show
empirical calibrations of IQR[O/Na] based on the O, Na abundances homogeneously
derived from more than 2000 red giants in 22 GCs in our FLAMES survey. We find
a statistically robust bivariate correlation of IQR as a function of the total
luminosity (a proxy for mass) and cluster concentration c. Calibrated and
observed values lie along the identity line when a term accounting for the
horizontal branch (HB) morphology is added to the calibration, from which we
obtained empirical values for 95 GCs. Spreads in proton-capture elements O and
Na 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 abundance
variations in light elements with the He enhancements and its effect on the
stellar distribution on the HB. We show that the spreads in light elements seem
already to be dependent on the initial GC masses. The dependence of IQR on
structural parameters stems from the well known correlation between c and Mv,
which is likely to be of primordial origin. Empirical estimates can be used to
extend our investigation of multiple stellar populations to GCs in external
galaxies, up to M31, where even integrated light spectroscopy may currently
provide only a hint of such a phenomenon.
