Globular Cluster Intrinsic Iron Abundance Spreads: II. Protocluster
  Metallicities and the Age-Metallicity Relations of Milky Way Progenitors
  Intrinsic iron abundance spreads in globular clusters, although usually
small, are very common, and are signatures of self enrichment: some stars
within the cluster have been enriched by supernova ejecta from other stars
within the same cluster. We use the Bailin (2018) self enrichment model to
predict the relationship between properties of the protocluster -- its mass and
the metallicity of the protocluster gas cloud -- and the final observable
properties today -- its current metallicity and the internal iron abundance
spread. We apply this model to an updated catalog of Milky Way globular
clusters where the initial mass and/or the iron abundance spread is known to
reconstruct their initial metallicities. We find that with the exception of the
known anomalous bulge cluster Terzan 5 and three clusters strongly suspected to
be nuclear star clusters from stripped dwarf galaxies, the model provides a
good lens for understanding their iron spreads and initial metallicities. We
then use these initial metallicities to construct age-metallicity relations for
kinematically-identified major accretion events in the Milky Way's history. We
find that using the initial metallicity instead of the current metallicity does
not alter the overall picture of the Milky Way's history, since the difference
is usually small, but does provide information that can help distinguish which
accretion event some individual globular clusters with ambiguous kinematics
should be associated with, and points to potential complexity within the
accretion events themselves.
