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Yule-Simpson's paradox in Galactic Archaeology
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
Microsoft Academic Graph classification: Metallicity Astrophysics Simpson's paradox Galaxy Stars Physics Galaxy formation and evolution Radius Flattening Milky Way
QB, QC, Space and Planetary Science, Astronomy and Astrophysics, Astrophysics - Astrophysics of Galaxies, Astrophysics of Galaxies (astro-ph.GA), FOS: Physical sciences, ABUNDANCES [GALAXY], DISC [GALAXY], EVOLUTION [GALAXY], KINEMATICS AND DYNAMICS [GALAXY], STELLAR CONTENT [GALAXY], //purl.org/becyt/ford/1.3 [https], //purl.org/becyt/ford/1 [https]
QB, QC, Space and Planetary Science, Astronomy and Astrophysics, Astrophysics - Astrophysics of Galaxies, Astrophysics of Galaxies (astro-ph.GA), FOS: Physical sciences, ABUNDANCES [GALAXY], DISC [GALAXY], EVOLUTION [GALAXY], KINEMATICS AND DYNAMICS [GALAXY], STELLAR CONTENT [GALAXY], //purl.org/becyt/ford/1.3 [https], //purl.org/becyt/ford/1 [https]
Microsoft Academic Graph classification: Metallicity Astrophysics Simpson's paradox Galaxy Stars Physics Galaxy formation and evolution Radius Flattening Milky Way
- National Scientific and Technical Research Council Argentina
- Liverpool John Moores University United Kingdom
- Leibniz Association Germany
- Leibniz Institute for Astrophysics Potsdam Germany
121113
Adibekyan V. Z., Sousa S. G., Santos N. C., Delgado Mena E., Gonzalez Hernandez J. I., Israelian G., Mayor M., Khachatryan G., 2012, A&A, 545, A32
Adibekyan V. Z., et al., 2013, A&A, 554, A44
Allende Prieto C., Kawata D., Cropper M., 2016, A&A, 596, A98
Anders F., et al., 2014, A&A, 564, A115
Anders F., Chiappini C., Santiago B. X., Matijevic G., Queiroz A. B., Steinmetz M., 2018, A&A, submitted, arXiv:1803.09341
Aumer M., White S. D. M., 2013, MNRAS, 428, 1055
Aumer M., White S. D. M., Naab T., Scannapieco C., 2013, MNRAS, 434, 3142
Bensby T., Lind K., 2018, A&A, 615, A151
Bergemann M., et al., 2014, A&A, 565, A89
Binney J., 2013, New Astron. Rev., 57, 29
- National Scientific and Technical Research Council Argentina
- Liverpool John Moores University United Kingdom
- Leibniz Association Germany
- Leibniz Institute for Astrophysics Potsdam Germany
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