Quantifying Chemical Tagging: Towards Robust Group Finding in the Galaxy
  The first generation of large-scale chemical tagging surveys, in particular
the HERMES/GALAH 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 database 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.
