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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.