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Chemical tagging seeks to identify unique star formation sites frompresent-day stellar abundances. Previous techniques have treated each abundancedimension as being statistically independent, despite theoretical expectationsthat many elements can be produced by more than one nucleosynthetic process. Inthis work we introduce a data-driven model of nucleosynthesis where a set oflatent factors (e.g., nucleosynthetic yields) contribute to all stars withdifferent scores, and clustering (e.g., chemical tagging) is modelled by amixture of multivariate Gaussians in a lower-dimensional latent space. We usean exact method to simultaneously estimate the factor scores for each star, thepartial assignment of each star to each cluster, and the latent factors commonto all stars, even in the presence of missing data entries. We use aninformation-theoretic Bayesian principle to estimate the number of latentfactors and clusters. Using the second Galah data release we find that sixlatent factors are preferred to explain N = 2,566 stars with 17 chemicalabundances. We identify the rapid- and slow-neutron capture processes, as wellas latent factors consistent with Fe-peak and \alpha-element production, andanother where K and Zn dominate. When we consider N ~ 160,000 stars withmissing abundances we find another 7 factors, as well as 16 components inlatent space. Despite these components showing separation in chemistry that isexplained through different yield contributions, none show significantstructure in their positions or motions. We argue that more data, and jointpriors on cluster membership that are constrained by dynamical models, arenecessary to realise chemical tagging at a galactic-scale. We release softwarethat allows for model parameters to be optimised in seconds given a fixednumber of latent factors, components, and $10^7$ abundance measurements.

A data-driven model of nucleosynthesis with chemical tagging in a lower-dimensional latent space