The fraction of first- and second-generation stars in globular clusters - I. The case of NGC 6752
We present a new method to estimate the fraction of stars with chemical composition of first and second(s) generation(s) currently hosted in Galactic globular clusters (GCs). We compare cluster and field stars of similar metallicity in the [Fe/H]-[Na/H] plane. Since the phenomenon of multiple populations is only restricted to the cluster environment, the number of GC stars whose location coincides with that of field stars provides the fraction of first generation stars in that cluster. By exclusion, the fraction of second generation stars is derived. We assembled a dataset of 1891 field stars of the thin disk, thick disk, and halo of the Milky Way in the metallicity range -3.15 <= [Fe/H] <= +0.48 dex and with Na abundance from high resolution spectra. They are mostly dwarfs, but include also giants. Considering only the range in metallicity spanned by most GCs extensively studied for the Na-O anticorrelation (-2.36 <= [Fe/H] <= -0.33 dex), we have 804 stars. The total sample is homogeneized by offsets in [Fe/H] and [Na/H] with respect to a reference sample using the same line list and NLTE correction for Na adopted in a recent extensive survey of GC stars. This fully accounts for offsets among analyses due to different temperature scales, line lists, adopted (or neglected) corrections for departures from LTE. We illustrate our method estimating the fraction of first and second generation stars in the well studied GC NGC 6752. As a by-product, the comparison of [Na/H] values in GC and field stars suggests that at least two classes of old stellar systems probably contributed to the halo assembly: one group with characteristics similar to the currently existing GCs, and the other more similar to the present-day dwarf satellite galaxies.