Testing the chemical homogeneity of chemically tagged dissolved birth
  clusters
  Chemically tagging stars back to common formation sites in the Milky Way and
establishing a high level of chemical homogeneity in these chemically tagged
birth clusters is crucial for understanding the chemical and dynamical history
of the Galactic disc. We constrain the intrinsic abundance scatter in 17 newly
chemically tagged dissolved birth clusters found in the APOGEE survey by
modelling APOGEE spectra as a one-dimensional function of initial stellar mass,
performing forward modelling of the observed stellar spectra, then comparing
the data and simulations using Approximate Bayesian Computation. We exemplify
this method with the well-known open clusters M67, NGC 6819, and NGC 6791. We
study 15 elements measured by APOGEE and find that, in general, we are able to
obtain very strong constraints on the intrinsic abundance scatter of most
elements in the chemically tagged birth clusters, with upper limits of
$\lesssim 0.02$ dex for C, $\lesssim 0.03$ dex for O, Mn, and Fe, $\lesssim
0.04$ dex for Si and Ni, and $\lesssim 0.05$ dex for N, Mg, and Ca. While we
find some evidence for a small amount of chemical inhomogeneity in the
remaining elements (i.e. Na, Al, S, K, Ti, and V), we are still able to obtain
similar or stronger limits compared to those found for open clusters,
consistent with previous findings. By strongly constraining their level of
chemical homogeneity, we can strengthen the statement that these groups of
stars represent birth clusters, with promising implications for future chemical
tagging studies.
