Yule-Simpson's paradox in Galactic Archaeology

Abstract

Simpson's paradox, or Yule-Simpson effect, arises when a trend appears in different subsets of data but disappears or reverses when these subsets are combined. We describe here seven cases of this phenomenon for chemo-kinematical relations believed to constrain the Milky Way disk formation and evolution. We show that interpreting trends in relations, such as the radial and vertical chemical abundance gradients, the age-metallicity relation, and the metallicity-rotational velocity relation (MVR), can lead to conflicting conclusions about the Galaxy past if analyses marginalize over stellar age and/or birth radius. It is demonstrated that the MVR in RAVE giants is consistent with being always strongly negative, when narrow bins of [Mg/Fe] are considered. This is directly related to the negative radial metallicity gradients of stars grouped by common age (mono-age populations) due to the inside out disk formation. The effect of the asymmetric drift can then give rise to a positive MVR trend in high-[alpha/Fe] stars, with a slope dependent on a given survey's selection function and observational uncertainties. We also study the variation of lithium abundance, A(Li), with [Fe/H] of AMBRE:HARPS dwarfs. A strong reversal in the positive A(Li)-[Fe/H] trend of the total sample is found for mono-age populations, flattening for younger groups of stars. Dissecting by birth radius shows strengthening in the positive A(Li)-[Fe/H] trend, shifting to higher [Fe/H] with decreasing birth radius; these observational results suggest new constraints on chemical evolution models. This work highlights the necessity for precise age estimates for large stellar samples covering wide spatial regions.

13 p., 7 Fig., Accepted to MNRAS

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• Unveiling the time evolution of chemical abundances across the Milky Way disk with APOGEE
• Milky Way Analogues in MaNGA: Multi-Parameter Homogeneity and Comparison to the Milky Way
• The GALAH Survey: Temporal Chemical Enrichment of the Galactic Disk
• On the Flaring of Thick Disc of Galaxies: Insights from Simulations
• Elemental abundances distributions in (R, $V_{\varphi }$) plane with LAMOST DR5 and Gaia DR2
• Disk flaring with TNG50: diversity across Milky Way and M31 analogs
• Using heritability of stellar chemistry to reveal the history of the Milky Way
• The vertical structure of the spiral galaxy NGC 3501: first stages of the formation of a thin metal-rich disc
• Quantifying chemical and kinematical properties of Galactic disks
• DoGR: Disaggregated Gaussian Regression for Reproducible Analysis of Heterogeneous Data