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Abstract The element abundance pattern found in Milky Way disk stars is close to two-dimensional, dominated by production from one prompt process and one delayed process. This simplicity is remarkable, since the elements are produced by a multitude of nucleosynthesis mechanisms operating in stars with a wide range of progenitor masses. We fit the abundances of 14 elements for 48,659 red-giant stars from APOGEE Data Release 17 using a flexible, data-drivenK-process model—dubbedKPM. In our fiducial model, withK= 2, each abundance in each star is described as the sum of a prompt and a delayed process contribution. We find thatKPMwithK= 2 is able to explain the abundances well, recover the observed abundance bimodality, and detect the bimodality over a greater range in metallicity than has previously been possible. We compare to prior work by Weinberg et al., finding thatKPMproduces similar results, but thatKPMbetter predicts stellar abundances, especially for the elements C+N and Mn and for stars at supersolar metallicities. The model fixes the relative contribution of the prompt and delayed processes to two elements to break degeneracies and improve interpretability; we find that some of the nucleosynthetic implications are dependent upon these detailed choices. We find that moving to four processes adds flexibility and improves the model’s ability to predict the stellar abundances, but does not qualitatively change the story. The results ofKPMwill help us to interpret and constrain the formation of the Galaxy disk, the relationship between abundances and ages, and the physics of nucleosynthesis. 

Abstract 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 groups of chemically similar stars comprise different groups in birth place (R_birth) and time (age). Simulating observational abundance errors (0.05 dex), we find that to trace distinct groups of (R_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 ≈10 groups can be defined with ≈25% overlap in (R_birth, age). We build a simple model to show that in the context of these simulations, it is possible to infer a star’s age andR_birthfrom abundances with precisions of ±0.06 Gyr and ±1.17 kpc, respectively. We find that abundance clustering is ineffective for a third simulation, where low-αstars form distributed in the disk and early high-αstars form more rapidly in clumps that sink toward the Galactic center as their constituent stars evolve to enrich the interstellar medium. However, this formation path leads to large age dispersions across the [α/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.