Quantifying chemical tagging: Towards robust group finding in the Galaxy

The first generation of large-scale chemical tagging surveys, in particular the High Efficiency and Resolution Multi-Element Spectrograph (HERMES)/Galactic Archaeology with HERMES million star survey, promises to vastly expand our understanding of the chemical and dynamical evolution of the Galaxy. This, however, is contingent on our ability to confidently perform chemical tagging on such a large data set. Chemical homogeneity has been observed across a range of elements within several Galactic open clusters, yet the level to which this is the case globally, and particularly in comparison to the scatter across clusters themselves, is not well understood. The patterns of elements in coeval cluster members, occupying a complex chemical abundance space, are rooted in the evolution, ultimately the nature of the very late stages, of early generations of stars. The current astrophysical models of such stages are not yet sufficient to explain all observations, combining with our significant gaps in the understanding of star formation, makes this a difficult arena to tackle theoretically. Here, we describe a robust pair-wise metric used to gauge the chemical difference between two stellar components. This metric is then applied to a data base of high-resolution literature abundance sources to derive a function describing the probability that two stars are of common evolutionary origin. With this cluster probability function, it will be possible to report a confidence, grounded in empirical observational evidence, with which clusters are detected, independent of the group finding methods. This formulation is also used to probe the role of chemical dimensionality, and that of individual chemical species, on the ability of chemical tagging to differentiate coeval groups of stars.