Globular cluster star classification: application to M13
  Starting from recent determination of Fe, O, Na abundance on a restricted
sample (N=67) of halo and thick disk stars, a natural and well motivated
selection criterion is defined for the classification of globular cluster
stars. An application is performed to M13 using a sample (N=112) for which Fe,
O, Na abundance has been recently inferred from observations. A comparison is
made between current and earlier M13 star classification. Both O and Na
empirical differential abundance distributions are determined for each class
and 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
procedure is repeated with regard to four additional classes according if
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 AF and CE stage. Within
the errors, the oxygen slope for CE stage is equal and opposite in sign with
respect of the sodium slope for AF stage, while the contrary holds in dealing
with the oxygen slope for AF stage with respect to the sodium slope for CE
stage. In the light of simple models of chemical evolution applied to M13, the
O-Na anticorrelation and the primordial to current M13 mass ratio are
discussed. 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.
