Tracing birth properties of stars with abundance clustering
  To understand the formation and evolution of the Milky Way disk, we must
connect its current properties to its past. We explore hydrodynamical
cosmological simulations to investigate how the chemical abundances of stars
might be linked to their origins. Using hierarchical clustering of abundance
measurements in two Milky Way-like simulations with distributed and steady star
formation histories, we find that abundance clusters of stars comprise
different groups in birth place ($R_\text{birth}$) and time (age). Simulating
observational abundance errors (0.05 dex), we find that to trace discrete
groups of ($R_\text{birth}$, age) requires a large vector of abundances. Using
15-element abundances (Fe, O, Mg, S, Si, C, P, Mn, Ne, Al, N, V, Ba, Cr, Co),
up to $\approx$ 10 clusters can be defined with $\approx$ 25% overlap in
($R_\text{birth}$, age). We build a simple model to show that it is possible to
infer a star's age and $R_\text{birth}$ from abundances with precisions of
$\pm$0.06 Gyr and $\pm$1.17 kpc respectively. We find that abundance clustering
is ineffective for a third simulation, where low-$\alpha$ stars form
distributed in the disc and early high-$\alpha$ stars form more rapidly in
clumps that sink towards the galactic center as their constituent stars evolve
to enrich the interstellar medium. However, this formation path leads to large
age-dispersions across the [$\alpha$/Fe]-[Fe/H] plane, which is inconsistent
with the Milky Way's observed properties. We conclude that abundance clustering
is a promising approach toward charting the history of our Galaxy.
