ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: in concert. The quantification of the abundance uncertainties included S/N-dependent cross-validation and an error rescaling for some elements, exploiting the fact that abundance estimates for member stars of open clusters should on average not differ by less than their uncertainties. This provided a set of APOGEE-derived abundances that is unprecedented in its (pertinent) combination of quality, quantity, and homogeneity. We only considered stars with very similar stellar parameters, giants in a restricted T eff and log g range; we have 90 spectra across seven open clusters and thousands of “field stars” with the same data, S/N, and data analysis. For all of these stars, we have individual abundances for 20 elements (Fe, C, N, O, Na, Mg, Al, Si, S, K, Ca, Ti, V, Mn, Ni, P, Cr, Co, Cu, and Rb), with a median precision of 0.03 dex. We characterize these abundances by their values [X/Fe], except for iron, where we use [Fe/H]. On this basis, we undertook an extensive analysis of the chemical (in-)homogeneity of stars within an open cluster, testing the standard assumption that such stellar “birth siblings” were formed at the same time from chemically homogeneous material. This should result in identical element abundances, including those elements (e.g., C and N), whose photospheric abundance has been altered in giants by mass/age-dependent dredge-up. We confirm that the abundances of cluster member stars typically agree with each other within their small (0.03 dex) uncertainties, as had been found before (see Section 1 ). Moving beyond, we explicitly determined the intrinsic dispersion in these abundances, or derived upper limits for them. We found that (at least in the best sampled clusters), the abundance dispersions are essentially zero, with typical upper limits of ∼0.03 dex. However, there are exceptions: some elements in some clusters show small but significant dispersion, attributable to a subset of member stars. To quantify the abundance similarity among stars of known common birth origin (cluster members) to the (dis-)similarity among field stars, we compared the abundances among pairs of stars. It was tempting to define a distance measure in the high-dimensional space of element abundances, but the “curse of dimensionality” makes distance in a 20 dimensional space very dependent on prior assumptions about distance distributions once the distances become comparable to the measurement uncertainties. Therefore, we resorted to a simple statistic, , quantifying the likelihood of the 20 observed abundances (differences) for any pair of stars, assuming their intrinsic abundances were identical. When we construct for intracluster pairs of stars, we find that its median is similar to , again illustrating the level of chemical homogeneity within clusters. Yet, about 20% of intracluster star pairs have , indicating significant abundance differences in one or more elements. We find open clusters to be mostly, but not exclusively,