Gaia astrometry and APOGEE spectroscopy (APOGEE, the Apache Point Observatory Galactic Evolution Experiment, a high-resolution near-infrared spectroscopic survey of Milky Way stars) have shown that the kinematically defined substructures of the Milky Way's stellar halo (Sequoia, Thamnos, the Helmi streams, Heracles) are not chemically pure populations: each contains large fractions of stars chemically compatible with the Gaia-Sausage-Enceladus (GSE) merger, with the heated indigenous disc, and with Sagittarius or omega Centauri debris. Mori et al. (2025) quantified this contamination star-by-star with Gaussian Mixture Models in a 7-dimensional abundance space and concluded that none of these substructures is a unique population with its own origin. Their analysis leaves a precise open problem: can such multidimensional chemical compatibility be converted into secure genetic (common-progenitor) attributions rather than coincidental chemical convergence, how robust are the compatibility classifications to thresholds, training samples and abundance sets, and how extensively does Sagittarius debris contaminate the energy-angular-momentum (E−LzE-L_z) selections that define GSE and the other substructures?

Background

In the current picture of galaxy formation, large galaxies grow by accreting smaller galaxies, whose tidally stripped stars remain recognizable in the stellar halo as kinematic substructures. The Milky Way's dominant accreted component is Gaia-Sausage-Enceladus (GSE), the remnant of a massive merger about 8-10 billion years ago, identified as a concentration of stars on eccentric, low-angular-momentum orbits. Several smaller named substructures are defined almost purely by kinematic cuts in the plane of orbital energy EE and vertical angular momentum LzL_z (an 'integral-of-motion' space in which long-lived debris tends to cluster): the retrograde (orbiting counter to the Galaxy's rotation, i.e. at negative LzL_z), high-energy Sequoia; the low-energy, retrograde Thamnos; the Helmi streams (stars on tightly inclined orbits identified by angular-momentum components); and the very low-energy Heracles (a compact inner-halo structure whose standard selection additionally imposes chemical cuts). omega Centauri is a globular cluster widely suspected to be the stripped nucleus of a dwarf galaxy, and the Sagittarius dwarf galaxy (Sgr) is currently being tidally disrupted, wrapping the Galaxy in an enormous stellar stream. Because a massive merger redistributes stars across the E−LzE-L_z plane while the indigenous Galactic disc is kinematically heated into halo-like orbits, every kinematically defined sample is expected to be a mixture. Chemical abundances (ratios such as [Mg/Fe], [Al/Fe], [Mn/Fe] for elements produced by different nucleosynthetic channels) are dynamically unbiased tags: a star's abundance pattern records the star-formation and chemical-enrichment history of its birth galaxy, so stars born in the same system should share multidimensional abundance patterns. Mori et al. (2025) applied Gaussian Mixture Models (GMMs, probabilistic density models that assign each star a probability of belonging to a reference population) trained on GSE samples selected with the kinematic definitions of Koppelman et al. 2019 ('K19') or Massari et al. 2019 ('M19'), and on a metal-poor disc sample ([Fe/H] ≤ -0.6 in the analyzed v1), to APOGEE DR17 spectra (DR17 is APOGEE's 17th data release) of stars selected from Gaia EDR3 (the early third data release of the Gaia astrometry mission) in each substructure's kinematic box. They found that large fractions of every substructure are chemically compatible with GSE (Sequoia at the ~50-66% level, which they argue points to a shared origin with GSE), that Thamnos' cleaned remnant overlaps omega Centauri abundances, that the cleaned Helmi streams overlap Sagittarius, and that GSE itself is contaminated by Sagittarius stars. Their mean-abundance predecessor, Horta et al. (2023), had found several substructures chemically indistinguishable from GSE by comparing mean abundance ratios, a method that by construction cannot detect mixtures. The interpretation problem is that chemical compatibility is not genetic proof: independent satellites of similar mass and star-formation history may converge to similar abundance patterns, and integrals of motion are not conserved through massive mergers, so present-day E−LzE-L_z position does not tag birth site. Later high-resolution studies sharpen rather than settle this: Matsuno et al. (2022) found Sequoia chemically distinct from Gaia-Enceladus at metallicities -1.8 < [Fe/H] < -1.4 (in tension with a shared origin), while the Helmi streams become chemically indistinguishable from Gaia-Enceladus above [Fe/H] ~ -1.5 despite being a separate structure; dedicated Thamnos studies disagree on whether its stars are mostly heated in-situ halo (Ceccarelli et al. 2025), a very metal-poor ex-situ population like the stars of the Cetus-Palca stream, a low-luminosity accreted stellar stream (Xie et al. 2026), or omega Centauri debris (Mori et al. 2025); and simulations (Garcia-Bethencourt et al. 2023) show that separate GE and Sequoia progenitors can reproduce the observed chemical and dynamical properties. On the Sagittarius side, DESI K-giant work (Kizhuprakkat et al. 2026) found that distance-error-convolved Sgr stars spill onto the retrograde periphery of GSE and may contaminate kinematically selected GSE samples, but a precise mapping of Sgr debris at varying energies and longitudes, and its quantified impact on the standard substructure selections, does not exist. The Deason & Belokurov (2024) review of Gaia-era Galactic archaeology explicitly flags that chemical indistinguishability of substructures may or may not imply common origin and that 'care must be taken in defining distinct substructures in the halo'.

Problem Statement

Determine the progenitor identity of the kinematically defined Galactic halo substructures (Sequoia, Thamnos, the Helmi streams, Heracles, and GSE itself), by solving three linked questions left open by the chemical-decoding analysis of Mori et al. (2025): (1) Robustness of the classification - building on the GMM threshold (5/10/15/20 percentile) and GSE training-definition (Koppelman-2019 vs Massari-2019 vs Horta-2023) tests already performed by Mori et al. (2025), establish how the star-by-star chemical-compatibility fractions and the membership assignments of the cleaned populations further depend on the abundance set used and on extending the metal-poor disc training model above its current metallicity limit ([Fe/H] ≤ -0.6 in v1, -0.8 in v3), and enlarge the samples so that the small cleaned populations (the metal-rich minority in Sequoia, the Thamnos and omega Centauri candidates) admit definitive attribution. (2) Sagittarius debris mapping - precisely map Sagittarius debris across the E-Lz plane at varying energies and longitudes (in the solar-neighborhood spectroscopic sample, complementing the distant-halo distance-error spillover found in DESI data) and quantify how much it contaminates the GSE selection and each other standard substructure definition. (3) Genetic origin versus convergent chemical evolution - establish criteria by which multidimensional chemical compatibility between two substructures can be attributed to a common progenitor rather than to independent satellites that happened to undergo similar chemical evolution. All three components serve one objective: a secure, contamination-corrected attribution of the stars in each kinematically defined substructure to distinct progenitors (or to GSE, heated-disc, Sagittarius, or omega Centauri contamination), i.e. a reliable census of the Milky Way's accretion events.

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