tokens: regression with an objective datapoint rejection, which models the outlier distribution. The method infers the parameters of the linear fit together with the mean and variance of the distribution of outliers as well as the number of outliers at the same time. The model is run through 50 000 MCMC realizations, taking the maximum of the posterior distribution and the standard deviation as the best values of the slope, intercept, and their uncertainties. We did not attempt to perform the fits when the number of stars with abundances is smaller than 15 or when the uncertainties in the abundances are greater than 0.05 dex. In Fig. 10 we plotted some examples of the differential element abundance pairs δ X 1 vs. δ X 2 . The full matrix of differential abundances for the three clusters are found in Figs. B.3 – B.5 . We also overplotted the obtained fits. For the Hyades, we obtain statistically significant correlations (larger than 3 σ ) of all pairs of abundances that we analyze. Some elements with larger intrinsic uncertainties (e.g., Ba, Nd, Cu) tend to present less significant correlations. For the other two clusters, we have a smaller sample of stars selected as most probable members and larger uncertainties in the abundance measures. The less significant fit is the one of Na I vs. Mn I in NGC 2632, which has a posterior with two peaks. For Ruprecht 147, two fits involving Si I have lower significances than 3 σ . In Fig. 10 we see no dependence of the differential abundance pairs with respect to T eff , showing that all types of stars correlate in the same way. Fig. 10. Left : δ Ti vs. δ Si. Right : δ Mg vs. δ Fe, rows correspond to the three clusters. Color represents effective temperature. Translucid lines are the resulting linear fit according to the obtained posterior distribution in the intercept and the slope. The slope and its uncertainty is indicated in each panel. For the Hyades, a large number of slopes were retrieved, so we computed the compatibility among all of them within the quoted uncertainties: (i) The fits involving Cu I and Ba II that have non-Gaussian posterior distributions tend to not be incompatible with the others. However, in these cases, uncertainties are not well represented by the standard deviation. (ii) In the case of Nd II , all the slopes are larger than 3 σ when compared to most of the other cases. We attribute this to the larger uncertainties of this element in comparison with the others, which makes the dispersion in its dimension increase, and thus increase the value of the slope. (iii) We find compatible slopes for all other pairs of elements. This indicates that the differences in star-by-star abundance are due to a zero-point difference in the overall metallicity among the stars in the cluster, with no variation depending on the chemical element. 6.3.2. Comparison with synthetic data To better interpret our results, we generated a set of simulated spectra of stars in two cases: a chemically homogeneous
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