How Many Elements Matter?

Some studies of stars' multielement abundance distributions suggest at least 5-7 significant dimensions, but others show that many elemental abundances can be predicted to high accuracy from [Fe/H] and [Mg/Fe] (or [Fe/H] and age) alone. We show that both propositions can be, and are, simultaneously true. We adopt a machine-learning technique known as normalizing flow to reconstruct the probability distribution of Milky Way disk stars in the space of 15 elemental abundances measured by APOGEE. Conditioning on T (eff) and logg minimizes the differential systematics. After further conditioning on [Fe/H] and [Mg/Fe], the residual scatter for most abundances is sigma([X/H]) less than or similar to 0.02 dex, consistent with APOGEE's reported statistical uncertainties of similar to 0.01-0.015 dex and intrinsic scatter of 0.01-0.02 dex. Despite the small scatter, residual abundances display clear correlations between elements, which we show are too large to be explained by measurement uncertainties or by the finite sampling noise. We must condition on at least seven elements to reduce the correlations to a level consistent with the observational uncertainties. Our results demonstrate that cross-element correlations are a much more sensitive probe of a hidden structure than dispersion, and they can be measured precisely in a large sample even if the star-by-star measurement noise is comparable to the intrinsic scatter. We conclude that many elements have an independent story to tell, even for the mundane disk stars and elements produced by the core-collapse and Type Ia supernovae. The only way to learn these lessons is to measure the abundances directly, and not merely infer them.

Automated summary

Studies have shown that the multielement abundance distributions of stars can be accurately predicted from a small number of elements. However, there are significant correlations between residual abundances, which cannot be explained solely by measurement uncertainties. By conditioning on at least seven elements, these correlations can be reduced to a level consistent with observational uncertainties. This demonstrates that cross-element correlations are a valuable probe of hidden structures and can be precisely measured in large samples.