Tidal Debris Candidates from the $\omega$ Centauri Accretion Event and its Role in Building Up the Milky Way Halo

Adrian M. Price-Whelan; Andrew C. Mason; Arik Mitschang; Borja Anguiano; Carlos Allende Prieto; Danny Horta; David L. Nidever; Katia Cunha; Ricardo P. Schiavon; Sten Hasselquist

REVIEW 4 major objections 5 minor 132 references

Tidal Debris Candidates from the $\omega$ Centauri Accretion Event and its Role in Building Up the Milky Way Halo

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The Milky Way field contains 463 stars chemically matched to Omega Centauri's core, likely tidal debris from its accretion event.

desk verdict A useful candidate catalog, but the boldest claims outrun what the classifier validation can support. read the letter →

arxiv 2505.08353 v1 pith:RXOUGCIQ submitted 2025-05-13 astro-ph.GA

Borja Anguiano , Arik Mitschang , Takanobu Kirihara , Yutaka Hirai , Danny Horta , Sten Hasselquist , Ricardo P. Schiavon , Steven R. Majewski

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Andrew C. Mason Adrian M. Price-Whelan Carlos Allende Prieto Verne Smith Katia Cunha David L. Nidever

This is my paper · ORCID

classification astro-ph.GA

keywords OmegaCentauritidaldebrischemicaltaggingAPOGEEsurveystellarhaloGaia-Sausage-EnceladusaccreteddwarfgalaxyN-bodysimulations

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that 463 field stars in the APOGEE survey carry a multi-element chemical fingerprint matching the core of the globular cluster $\Omega$ Centauri, at membership probability $P>0.8$, and that these stars are tidal debris from the $\Omega$ Centauri accretion event. If the identification holds, this is the largest chemically tagged census of such debris to date, and it recasts $\Omega$ Centauri as the stripped nucleus of a dwarf galaxy rather than an ordinary globular cluster. The paper also argues that most candidates move on the highly radial orbits of an accreted halo, that their chemistry is distinct from the Gaia-Sausage-Enceladus population, and that N-body simulations require a progenitor stellar mass of $\gtrsim 10^8\,M_\odot$.

What carries the argument

The central machinery is a chemical-tagging neural network: a fully connected multi-layer perceptron that takes thirteen APOGEE abundance ratios as input and outputs a membership probability for sharing the $\Omega$ Centauri core's abundance patterns, trained on 1,794 cluster stars against a negative sample of globular cluster, Magellanic Cloud, and Sagittarius stars. This network supplies the chemical tag that isolates the 463 candidates. The supporting machinery is an N-body model of a Plummer-sphere progenitor with mass $10^8\,M_\odot$, whose simulated stripped particles are matched to the candidates in sky coordinates, distance, proper motion, radial velocity, and energy-action space, where the radial action $J_R$ is used to classify debris as accreted-halo-like.

What would settle it

Run the same classifier on a sample of field stars with known unrelated origins, or on mock stellar populations built from APOGEE measurement errors, and count the fraction that pass $P>0.8$; if the field false-positive rate approaches the number of candidates, the chemical association collapses. Alternatively, measure abundances of elements excluded from the training set, such as barium or europium, for the 463 candidates and check whether they trace the $\Omega$ Centauri core distribution rather than the general halo.

Watch

Extended reading notes

Core claim

Using a neural-network classifier trained on 1,794 APOGEE spectra of the $\Omega$ Centauri core and a negative sample of 15,119 objects drawn from globular clusters, the Magellanic Clouds, and the Sagittarius system, the paper assigns every APOGEE field star a membership probability $P$ for sharing $\Omega$ Centauri's abundance patterns across thirteen abundance ratios and combinations. It reports 463 stars with $P>0.8$, 284 with $P>0.9$, and 186 with $P>0.95$, whose chemistry -- especially elevated C+N, Al, and Ce -- resembles the cluster's unusual populations. Most of these candidates have high radial action $J_R$ and sit in the accreted halo, while a minority show prograde or retrograde disk-like kinematics, which the paper interprets as stripping from an extended progenitor. Nearly all stars in a selected Gaia-Sausage-Enceladus sample have $P<0.1$, so the two structures appear chemically distinct, although the paper leaves open the possibility that GSE hosted $\Omega$ Centauri. An N-body model of a $10^8\,M_\odot$ Plummer progenitor reproduces the observed sky positions, distances, proper motions, radial velocities, and energy-action spread of the candidates, supporting a massive dwarf-galaxy origin.

Load-bearing premise

The load-bearing premise is that $\Omega$ Centauri's multi-element chemical fingerprint is rare enough in the APOGEE field that a classifier trained only on the cluster and a curated set of unrelated stars does not mislabel ordinary field stars as debris.

Editorial extensions

If this is right

A census of 463 chemically tagged debris candidates gives a far larger footprint of the Omega Centauri event than the known tidal tails, enabling tests of the progenitor's orbit and mass-loss history.
The dominance of high-$J_R$, accreted-halo orbits among the candidates implies that the debris has been dynamically heated and mixed into the halo, so the event contributed to building the stellar halo rather than only the disk.
The chemical separation from the Gaia-Sausage-Enceladus sample suggests at least two distinct accretion events helped shape the inner halo.
The presence of both prograde and retrograde disk-like debris requires a progenitor large enough to spill stars across the Galactic center at pericenter, supporting a dwarf-galaxy-scale original system.
The reported metal-poor, high-$\alpha$, chemically homogeneous plume is an additional ancient halo component, chemically independent of both GSE and Omega Centauri.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the same classifier were run against a field-only negative sample with a measured false-positive rate, the number of genuine debris stars could be substantially below 463, because unrelated metal-poor field stars may share the training chemistry.
Because the classifier is trained on the surviving core, debris stripped before Omega Centauri's later self-enrichment episodes would not carry today's fingerprint, so 463 is likely a lower-bound census of the original system, not the full extent of the event.
High-resolution follow-up of the 463 candidates in elements outside the training set, such as barium or europium, would provide an independent test of the association and could expose interlopers.
The same training scheme applied to other massive clusters with suspected dwarf-galaxy origins could map additional accretion events; the paper's inconclusive M54-Sagittarius test is a caution that the method's power depends on the uniqueness of each system's chemistry.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing is the catalog: 463 APOGEE field stars tagged at P>0.8 as ω Cen debris, with kinematics and N-body simulation. That is worth having. The paper also correctly asks whether ω Cen is GSE's stripped nucleus and finds the two chemically distinct in its classifier, with an appropriate hedge that a connection cannot be ruled out.

The soft spot is not small: the classifier's precision (~80%) is measured on curated negatives (GCs, LMC/SMC, Sgr) with a ~12% positive prior. In the APOGEE field, the prior is orders of magnitude lower—Figure 5 shows >99% of stars at P<0.01. There is no field-level false-positive estimate, so the purity of the 463 is unknown. The cluster validation (Figure 7) is not decisive for field stars, which are messier. And because [Fe/H] is an input feature, the P-[Fe/H] structure could partly trace known field components.

The plume is weaker: the abstract calls it 'chemically homogeneous' but no homogeneity test is shown, and the cut at P<0.1 makes 'distinct from ω Cen' at least partly a consequence of the selection. The N-body simulation is illustrative (single 1e8 M_sun, 1 kpc Plummer, no DM), not a fit; it shows a large progenitor can produce prograde debris but does not measure the mass.

The authors acknowledge the GC-separability issue themselves, which helps. But the abstract overclaims, and I would not trust the counts without a field-level contamination estimate.

Send it to review. The catalog is a dataset claim that needs vetting. Require major revision: add a field control, show plume homogeneity, soften the claims.

Referee Report

4 major / 5 minor

Summary. The paper trains a fully connected neural network on APOGEE DR17 multi-element abundances of the ω Cen core (1,794 stars after quality cuts) against a negative sample of globular-cluster, LMC/SMC, and Sagittarius stars, and uses the network output P to select 463 APOGEE field stars with P>0.8 as ω Cen tidal debris candidates (§3.1). The candidates are then analyzed in energy–action and orbital spaces, compared with a kinematically selected GSE sample (§4), and compared with a 500 Myr N-body simulation of a 10^8 M_sun Plummer progenitor in a static Milky Way potential (§5). The paper also reports a metal-poor high-α 'plume' in the P–[Fe/H] plane and concludes that ω Cen was an independent, massive dwarf-galaxy merger, while acknowledging that association with GSE cannot be ruled out.

Significance. If the 463 chemically tagged candidates are genuine, this would be the largest census of ω Cen tidal debris to date and would provide important dynamical evidence for a massive dwarf-galaxy progenitor, with consequences for the assembly history of the Milky Way halo. The use of the full APOGEE abundance vector, the explicit cross-validation on external clusters, and the plan to release the candidate table are clear strengths. However, the reliability of the central catalog is inferred only from curated negative classes whose separability the authors themselves acknowledge, and no field-level false-positive estimate is provided. Because the kinematic and N-body conclusions inherit the catalog, the significance of the paper is presently conditional. The 'plume' is also stated more strongly than demonstrated: its existence and chemical homogeneity are not tested. These issues are fixable with additional analysis, which is why I recommend major revision rather than rejection.

major comments (4)

[Section 3.1, Figs. 4 and 5] The central claim of '463 ω Cen debris candidates' rests on a classifier whose precision is measured only on a curated test set with a roughly 12% positive prior, while the actual APOGEE field has more than 99% of its stars at P<0.01 (Fig. 5). The negative training sample (globular clusters, LMC/SMC, Sagittarius) is more chemically coherent than the general field, and the paper explicitly acknowledges this for the globular clusters; the cluster-level validation in Fig. 7 therefore does not bound contamination in the field. Because [Fe/H] is an input feature and the P–[Fe/H] plane shows strong structure tracing known field components, the P>0.8 candidates could be, to zeroth order, the metal-poor tail of the field. Please provide a field-level false-positive estimate, for example by applying the tagger to an APOGEE field sample cross-matched with an independent origin indicator, or by a mock-contamination test that draws stars from field-like abundance distributions and reports the expected number of P>0.8 interlopers.
[Section 3.2, Fig. 5, and Abstract] The 'metal-poor high-α chemically homogeneous halo debris' (the plume) is selected by the cuts P<0.1 and −2.5<[Fe/H]<−1.9, but no significance test is given against a field population at the same metallicity, and no quantitative homogeneity statistic is reported. Calling this structure 'chemically homogeneous' in the abstract is therefore unsupported by the present evidence. In addition, because the plume is defined by P<0.1, its separation from the ω Cen core is partly by construction. Please add a null-hypothesis comparison, a scatter-versus-measurement-error test, and a statement of how the plume is distinguished from unrelated metal-poor halo stars, or soften the claim.
[Sections 5.1–5.2, Fig. 15] The conclusion that the ω Cen progenitor had a stellar mass ≳10^8 M_sun is inferred from a single N-body model with M=10^8 M_sun, scale radius 1 kpc, a pre-stripped dark matter halo, and a static Milky Way potential integrated for only 500 Myr. The comparison with a 10^6 M_sun model is useful, but it does not explore the sensitivity of the prograde Lz component to progenitor radius, density profile, pericentric history, or time dependence of the Galactic potential; the text itself concedes that periods of very small pericenter cannot be ruled out. As written, the mass inference is not robust. Please add a parameter study or an analytic bounding argument, or explicitly present the result as a single-model illustration with the strong caveats it requires.
[Section 4.1, Fig. 12] The statement that the GSE sample is chemically distinct from ω Cen is based on the same ω Cen-trained classifier, and the selected GSE sample is known to contain ω Cen debris and plume stars, as shown by the P>0.001 bump in the reverse CDF in the left panel of Fig. 12. The paper discusses this contamination qualitatively but does not quantify the fraction of the GSE sample affected or rerun the comparison after removing the ω Cen candidates and plume stars. Please quantify the contamination and report the comparison on a cleaned GSE sample before using this result to support the 'independent merger event' interpretation.

minor comments (5)

[Section 6] The text lists 'NGC 3101' among the four validation clusters; this should be NGC 3201, as in Fig. 7.
[Section 3.1] The statement 'In total we have 15119 objects that comprise the negative sample' is inconsistent with the sum of the stated components (1,454 + 5,434 + 400 = 7,288). Please correct the numbers or define explicitly what the 15,119 objects are, since the class balance enters the interpretation of the precision curve in Fig. 4.
[Table 2] The caption says the table shows the first four entries of the debris candidates, but the printed table lists only column descriptions; please include sample rows or change the caption to match the table contents.
[References] Several references are incomplete: Brown et al. (2018) contains a bare DOI, and Wilson et al. (2019) lists 'PASA, 999, 999'. These should be updated before resubmission.
[Section 3.1] The network is described as having three hidden layers (256, 128, and 32 units), but the text says 'for the two hidden layers, we use the Rectified Linear Unit'; please specify the activations for all three hidden layers for reproducibility.

Circularity Check

1 steps flagged · score 3.0 of 10

Central 463-candidate census is a supervised classifier output and not circular, but the C+N and Al 'hallmark' trends used as evidence are input features to the same classifier, making that confirmation circular.

self definitional [Section 3.1 (model input list) and Section 3.2 / Figure 6 discussion]
"we use the following individual abundances measured in the APOGEE spectra for our exercise: [C/Fe], [N/Fe], [O/Fe], [Mg/Fe], [Al/Fe], [Si/Fe], [Mn/Fe], [Ni/Fe], [Fe/H], [CI/Fe], [Na/Fe], [K/Fe], [Ca/Fe], [Co/Fe], [Ce/Fe]. ... A good number of the debris candidates are clearly enhanced in C+N, Al abundances with respect to the rest of the debris population and most of the Galactic halo. ... The hallmark C+N and Al trends are potential evidence that an extended part of the ω Cen tidal debris stream has been found."

The neural-network membership probability P is a function of the input abundances, which include [C/Fe], [N/Fe], and [Al/Fe] (Table 1 lists C, N, Al among the model inputs). Selecting stars with P > 0.8 therefore selects stars whose C+N and Al patterns lie near the ω Cen training distribution. Reporting that the candidates are 'clearly enhanced in C+N, Al' and treating the 'hallmark C+N and Al trends' as independent 'potential evidence' that tidal debris has been found is a validation of the selection using the same features that define the selection; by construction, high-P candidates resemble ω Cen in those dimensions. This does not make the census itself circular, but this particular confirmation is.

full rationale

The core claim — 463 field stars with P > 0.8 — is the output of a supervised neural-network classifier trained on APOGEE ω Cen core abundances (Section 3.1). That is the operational definition of weak chemical tagging, not a hidden reuse of the target as input. The GSE comparison is an independent application of the same classifier to a kinematically selected sample, and the N-body mass inference compares a 10^8 Msun model with a 10^6 Msun model rather than fitting to the candidate list. The one genuine circularity is the paper's use of C+N and Al enhancements as confirmatory evidence, even though C, N, and Al are among the classifier's input features; that step is self-definitional but is an aside rather than the basis of the census. The absence of a field-level false-positive rate for the 463 candidates is a real contamination risk, but it is a statistical validity concern, not a circularity of the derivation chain.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The central claim nests on the uniqueness of ω Cen's chemical pattern (axiom 1), which the paper's own cited literature questions. The candidate list is classification output, not a physical derivation. The N-body mass inference relies on assumed model parameters (mass 10^8, radius 1 kpc), making the '≳10^8 M_sun' conclusion model-conditioned. The plume is a box-selected structure without a significance test, though it connects to prior l'itoi detections.

free parameters (6)

P > 0.8 membership threshold = 0.8
The threshold for 'debris candidate' is selected based on the inverse CDF analysis in §3.2 (Figure 7), which favors P>0.6; the paper then uses P>0.8 without formal optimization. Counts (463/284/186) depend on this choice.
Neural network architecture and hyperparameters = 256-128-32 units, ReLU, MSE, gradient descent
Hand-chosen model settings in §3.1; no ablation or tuning curve is shown, and performance likely depends on them.
Negative sample composition = 15,119 stars (1,454 GC + 5,434 LMC/SMC + 400 Sgr + others)
The negative training set in §3.1 is built from specific programs; the classifier boundary depends on this sample, which does not explicitly include field halo/disk stars.
N-body progenitor mass = 1e8 M_sun (comparison run 1e6 M_sun)
The Plummer model in §5.1 is constructed with total mass 10^8 M_sun and scale radius 1 kpc; the conclusion that the progenitor was ≳10^8 M_sun is effectively derived from this assumed input in §6.
N-body scale radius and DM-stripped assumption = 1 kpc, no DM
§5.1: progenitor dwarf galaxy as Plummer model; the inferred requirement that the radius exceed ~1 kpc to produce prograde debris depends on this choice.
Plume selection cuts = P<0.1, [Fe/H]<-2.0 (also -2.5<[Fe/H]<-1.9)
§3.2.1: the metal-poor 'plume' is defined by these cuts; the claim that it is a distinct debris structure depends on this arbitrary box selection.

assumptions (5)

domain assumption Chemical abundance patterns of ω Cen are conserved and sufficiently unique for tagging
The entire candidate selection in §3.1 assumes stripped ω Cen stars retain their core abundance patterns and that no other field population shares the same multi-element pattern. The paper itself cites Garcia-Dias et al. (2019) and Casamiquela et al. (2021) showing overlapping chemical signatures between birth sites, undermining strong tagging.
domain assumption APOGEE abundance measurements are reliable across S/N 40-300 and the full parameter range
§2.1: ω Cen training stars span S/N 40-300 and [Fe/H] -2.3 to -0.5; the model assumes ASPCAP abundances are on the same system for field giants and cluster stars.
domain assumption The Bovy (2015) gravitational potential accurately represents the Milky Way for orbit/action calculations
§2: gala actions and orbits adopt this potential; all kinematic conclusions (high JR, E-Lz diagrams, GSE selection) depend on it.
domain assumption The Horta et al. (2023) E-Lz selection provides a representative GSE sample
§4.1: the GSE sample is taken from Horta et al. (2023) based on E-Lz; the authors note this selection is biased and contaminated, affecting the claim that GSE is chemically distinct from ω Cen.
ad hoc to paper Static potential and short integration for N-body
§5.1: the MW potential is fixed, progenitor DM is assumed stripped before the simulation, and only 500 Myr are integrated; these simplify the problem but could alter the debris distribution and prograde fraction.

invented entities (1)

Metal-poor high-α 'plume' debris independent evidence
purpose: Identified as a likely accreted halo component, possibly a major building block of the MW halo, chemically distinct from GSE and ω Cen.
Naidu et al. (2020) reported l'itoi, a retrograde metal-poor high-α debris; the plume extends this to include prograde members, but the specific claim of a larger prograde+retrograde structure is new and not independently confirmed.

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Pith. "Pith review of Tidal Debris Candidates from the $\omega$ Centauri Accretion Event and its Role in Building Up the Milky Way Halo." pith.science (2026). https://pith.science/paper/RXOUGCIQ

@misc{pith2026250508353,
  author       = {Pith},
  title        = {Pith review of: Tidal Debris Candidates from the $\omega$ Centauri Accretion Event and its Role in Building Up the Milky Way Halo},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RXOUGCIQ}},
  note         = {Machine review of arXiv:2505.08353}
}

abstract

We identify stellar tidal debris from the $\omega$ Centauri ($\omega$ Cen) system among field stars in the APOGEE survey via chemical tagging using a neural network trained on APOGEE observations of the $\omega$ Cen core. We find a total of 463 $\omega$ Cen debris candidates have a probability $P > 0.8$ of sharing common patterns in their chemical abundances across a range of individual elements or element combinations, including [C+N], O, Mg, Al, Si, Ca, Ni, and Fe. Some debris candidates show prograde or retrograde disk-like kinematics, but most show kinematics consistent with the accreted halo, showing high radial actions, $J_{R}$, values. We find that a sample of Gaia-Sausage-Enceladus (GES) members are chemically distinct from the $\omega$ Cen core, suggesting that $\omega$ Cen is associated to an independent merger event shaping the Milky Way halo. However, a connection between GSE and $\omega$ Cen cannot be ruled out. A detailed comparison with $N$-body simulations indicates that the $\omega$ Cen progenitor was a massive dwarf galaxy ($\gtrsim 10^8 M_{\odot}$). The existence of a metal-poor high-$\alpha$ chemically homogeneous halo debris is also reported.

Figures

Figures reproduced from arXiv: 2505.08353 by the authors.

**Figure 1.** — Gaia-based color-magnitude diagram of the ω Cen system, with the APOGEE targets marked, color-coded by the ASPCAP-derived [Fe/H]. APOGEE observations are covering the wide distribution of the ω Cen red-giant branch stars and also the wide metallicity spread. We make use of the last SDSS-IV public release of data from the APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP, Garc´ıa P´erez et al. 201… view at source ↗

**Figure 2.** — Top panel: Normalized fraction of the metallicity distribution function of ω Cen populations for the APOGEE (black) and Johnson & Pilachowski (2010, “JP10”) (red) sample. There is an agreement between the APOGEE and JP10 [Fe/H] distributions. Bottom panel: Histogram of the discrepancies between the [Fe/H] measurements from APOGEE spectra and the values from JP10. The two independent measurements show good agreem… view at source ↗

**Figure 3.** — Distributions of the chemical tagging model negative training sample (solid black line), compared to the ω Cen subsample that represent the positive training data (dashed red line) and the full APOGEE sample (grey line) for six individual abundances. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Recall 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Precision [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: — Neural network model performance. The best model recall and precision are plotted for P > Pthresh from 0 to 1 at intervals of 0.01. The dashed grey horizontal line at 0.12 represents a random uneducated model. Our best fit does substantially better, achieving close t…

**Figure 5.** Figure 5: shows the stellar APOGEE [Fe/H] as a function of ω Cen chemically tagged membership probability. In this figure, we clearly detect the structure related to the MW disk and halo at very low probabilities. We also have a prominent over-density close to P ∼ 1 and rangin…

**Figure 6.** Figure 6: — Chemical abundance patterns of select elements for ω Cen debris candidates as compared to the MW. The debris candidates are color-coded by the ω Cen membership probabilities, and we only show candidates where P > 0.8 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: — Inverse cumulative distribution functions for the ω Cen membership probability for four distinct clusters (NGC104, NGC3201, NGC2808, and NGC6121), as well as ω Cen itself (black line). We also present the CDF for every member of the globular cluster listed in APOGEE …

**Figure 8.** Figure 8: — ω Cen membership probability as a function of [Fe/H], energy-action spaces and the [Fe/H] - [Mg/Fe] plane. Left-hand panels: the orange color in these panels highlights the selection of P < 0.1 and −1.9 < [Fe/H] < − 0.9. There are clearly three structures, a metal-we…

**Figure 9.** Figure 9: — ω Cen membership probability as a function of [Fe/H], energy-action spaces and the [Fe/H] - [Mg/Fe] plane for the ω Cen debris candidates with P > 0.8. The Lindblad diagram reveals that most of the debris lie within the accreted halo with some having disk-like kinema…

**Figure 10.** Figure 10: — In the top panels we have the maximum height achieved above the Galactic plane Zmax versus the orbital eccentricities for P < 0.1 and -1.9 < [Fe/H] < -0.9 (left) and P > 0.8 (right), where ω Cen core is marked with a red X. The lower panel also shows the apocenter w…

**Figure 11.** Figure 11: — Best model recall and precision are plotted for P > Pthresh from 0 to 1 at intervals of 0.01. The dashed grey horizontal line at 0.12 represents a random uneducated model. The model is not helpful at discriminating M54, therefore any predictions would not be meaning…

**Figure 12.** Figure 12: — Left panel: Reverse cumulative distribution functions for the ω Cen membership probability for the selected GSE sample (blue line) and the ω Cen members (green line). Note the “bump” in the GSE sample for P > 0.001, those are ω Cen debris members and the metal-poor …

**Figure 13.** Figure 13: — Distribution of the simulated ω Cen debris in (a) declination, (b) heliocentric distance, proper motion in (c) α and (d) δ, and (e) radial velocity as a function of α. The colors represent the mass fraction in each region normalized by the total mass of the ω Cen p…

**Figure 15.** Figure 15: — Left panel: the distribution of the ω Cen debris in the Lindblad diagram. Right panel: the distribution in the energyaction space. The cyan points indicate the ω Cen membership candidates where the P > 0.8. in other elements between ω Cen and these clusters, the mo…

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