Globular Cluster Star Classification: Application to M13

Starting from recent determination of Fe, O, Na abundances on a restricted sample (N = 67) of halo and thick disk stars, a natural and well motivated selection criterion is defined for the classification globular cluster stars. An application is performed to M13 using a sample (N = 113) for which Fe, O, Na abundances have been recently inferred from observations. A comparison is made between the current and earlier M13 star classifications. Both O and Na empirical differential abundance distributions are determined for each class and for the whole sample (with the addition of Fe in the last case) and compared with their theoretical counterparts due to cosmic scatter obeying a Gaussian distribution whose parameters are inferred from related subsamples. The occurrence of an agreement between the empirical and theoretical distributions is interpreted as absence of significant chemical evolution and vice versa. The procedure is repeated with regard to four additional classes depending on whether oxygen and sodium abundance is above (stage CE) or below (stage AF) a selected threshold. Both O and Na empirical differential abundance distributions, related to the whole sample, exhibit a linear fit for the AF and CE stage. Within the errors, the oxygen slope for the CE stage is equal and of opposite sign with respect to the sodium slope for AF stage, while the contrary holds when dealing with the oxygen slope for the AF stage with respect to the sodium slope for the CE stage. In the light of simple models of chemical evolution applied to M13, oxygen depletion appears to be mainly turned into sodium enrichment for [O/H]≥ -1.35 and [Na/H]≤ -1.45, while one or more largely preferred channels occur for [O/H]< -1.35 and [Na/H]> -1.45. In addition, the primordial to the current M13 mass ratio can be inferred from the true sodium yield in units of the sodium solar abundance. Though the above results are mainly qualitative due to large (-+1.5 dex) uncertainties in abundance determination, still the exhibited trend is expected to be real. The proposed classification of globular cluster stars may be extended in a twofold manner, namely to: (i) elements other than Na and Fe and (ii) globular clusters other than M13.