Chemodynamically Tagged Groups of CEMP Stars in the Halo of the Milky Way. I. Untangling the Origins of CEMP-s and CEMP-no Stars

The nature of the first generation of stars in the universe, the so-called Population III stars, is of primary interest in stellar and galactic archaeology. These stars are thought to have been massive and short-lived (Bromm et al. 1999; Omukai et al. 2005). Detailed models of rapidly rotating, ultra-metal-poor (UMP; [Fe/H] < −4.0) and hyper-metal-poor (HMP; [Fe/H] < −5.0) Population III stars (e.g., Meynet et al. 2006, 2010; Hirano et al. 2015; Maeder & Meynet 2015), as well as the so-called faint (mixing and fallback) supernova (SN) models (e.g., Umeda & Nomoto 2005; Nomoto et al. 2013; Tominaga et al. 2014), which can apply to somewhat higher metallicities, such as extremely metal-poor ([Fe/H] < −3.0) stars, produce prodigious amounts of CNO, capable of enriching the natal gas from which later generations of presently observed, long-lived, low-mass stars are formed. The initial mass function (IMF) of Population III stars and the nucleosynthesis pathways involved in their production of the elements incorporated into lower-mass next-generation (Population II) stars can thus be constrained from studies of carbon-enhanced metal-poor (CEMP) stars, providing essential information on early Galactic chemical evolution and on the nature of the very first stars.

Carbon can be also produced in significant amounts by low-mass (M < 1–3M_⊙) stars in their asymptotic giant branch (AGB) stage of evolution (e.g., Suda et al. 2004; Herwig 2005; Lucatello et al. 2005; Bisterzo et al. 2011; Starkenburg et al. 2014; Hansen et al. 2015). If such a star is a member of a binary (or multiple) system, the transfer of mass to a companion star via Roche lobe overflow (or more likely winds) allows the nucleosynthetic products of the donor (the erstwhile primary star) to be preserved on the surface of the receiving star (Stancliffe et al. 2007; Abate et al. 2015). If the receiving star has a mass M ≲ 0.7M_⊙, its lifetime exceeds the Hubble time and can be observed today.

The first spectroscopic surveys to assemble significantly large samples of very metal-poor (VMP; [Fe/H] < −2.0) Population II stars in the halo of the Milky Way (MW) were the HK (Beers et al. 1985, 1992) and Hamburg/ESO (Christlieb 2003) objective-prism surveys. Beers & Christlieb (2005) provided the basis for the modern nomenclature for describing stars of various (low) metallicities and suggested initial classifications based on their carbon and neutron-capture element abundances. Of particular interest to the present study are the various classes of CEMP stars, distinguished by their high level of carbonicity, [C/Fe] (originally set at [C/Fe] > +1.0, now usually taken to be [C/Fe] > +0.7).

Subsequent surveys, including the Sloan Digital Sky Survey (York et al. 2000) and its extensions (SEGUE, Yanny et al. 2009; SEGUE-2, Rockosi et al. 2022), AEGIS (Keller et al. 2007), LAMOST (Deng et al. 2012), and Pristine (Starkenburg et al. 2017), have greatly increased the number of recognized CEMP stars to many thousands.

CEMP stars have been demonstrated to increase in frequency with decreasing metallicity. They comprise approximately 30% of all stars with [Fe/H] < −2.0, 60% for [Fe/H] < −3.0, 80% for [Fe/H] < −3.5, and approaching 100% (see Caffau et al. 2011 for a possible exception) for [Fe/H] < −4.0 (see Figure 6 of Yoon et al. 2018). This fundamental result indicates that the most metal-poor CEMP stars may preserve the chemical-abundance signature of the very first generations of stars, making them extremely valuable for the purposes of stellar and galactic archaeology (Frebel & Norris 2015).

CEMP stars can be divided into multiple subclasses. Work subsequent to the original Beers & Christlieb (2005) classification has introduced a number of refinements; we refer the interested reader to the review by Frebel (2018). In the present work, we adopt the classifications listed in Table 1. The primary subclasses of interest in this paper are the CEMP-s stars, which exhibit overabundances of neutron-capture elements ([Ba/Fe] > +1.0, [Ba/Eu] > +0.5) associated with the production by the s-process, and the CEMP-no stars, which exhibit no enhancements of neutron-capture elements ([Ba/Fe] < 0.0).

It has also been demonstrated that the frequencies of CEMP-s and CEMP-no stars are not the same in different regions (and populations) of the MW. Specifically, CEMP-s stars are primarily associated with the metal-weak thick disk (MWTD) and inner-halo regions, while the bulk of the CEMP-no stars are found in the outer-halo region (Carollo et al. 2012, 2014; Lee et al. 2017, 2019; Yoon et al. 2018). These, and other authors, have pointed to this evidence as supporting differences in the formation and accretion histories of the various Galactic stellar populations.

Rossi et al. (2005) first pointed out that CEMP stars might not share a single nucleosynthetic origin, based on the apparent bimodal distribution of [C/Fe] and absolute carbon abundance, A(C), ⁹  at low metallicity (see their Figure 12). Later, Spite et al. (2013) and Bonifacio et al. (2015) presented evidence that there existed high and low "bands" in plots of A(C) versus [Fe/H] for main-sequence turnoff stars and mildly evolved subgiants, primarily associated with CEMP-s and CEMP-no stars, respectively.

The full richness of the behavior of CEMP stars in the A(C)–[Fe/H] space was revealed in Figure 1 of Yoon et al. (2016)—the so-called Yoon–Beers diagram, which separated CEMP stars into three morphological groups. Yoon et al. identified the great majority of CEMP-s stars as CEMP Group I stars, based on their distinctively higher A(C) compared to the CEMP-no stars, while most CEMP-no stars were classified as either CEMP Group II or Group III stars. The Group II stars exhibit a strong dependency of A(C) on [Fe/H], while the Group III stars show no such dependency. Based on this, and the clear differences between Group II and Group III stars in the A(Na)–A(C) and A(Mg)–A(C) spaces (Figure 4 of Yoon et al.), these authors argued for the existence of multiple progenitors and/or environments in which the CEMP-no stars formed.

Examination of the effects of dust cooling for varied compositions (e.g., carbon- versus silicate-based dust grains) could account for the formation of both the Group II and III CEMP-no stars (see, e.g., Chiaki et al. 2017). Simulations of Population III star enrichment by Sarmento et al. (2016) exhibited patterns in the A(C)–[Fe/H] space that can be associated with these same groups (see their Figure 13). Simulations of Population II star formation by Sharma et al. (2018b) show different formation pathways for Group I and Group II CEMP stars. It should be noted that Yoon et al. (2016) also pointed out that some CEMP stars exhibited anomalous abundance patterns within these different groups, such as stars with A(C)_c < 7.1 while [Ba/Fe] > 0.0 or A(C)_c > 7.1 while [Ba/Fe] < +1.0. Since the causes of these abundance patterns are not yet understood, their relative numbers are low compared to CEMP stars as a whole, and since not all of the CEMP stars have the abundance measurements required to determine their anomalous status, we make no distinctions between these stars in this work.

In light of the above, it is likely that at least some classes of CEMP stars (notably, CEMP-no stars, but also some CEMP-s stars) were not formed in situ in the Milky Way, but, rather, were born in low- and intermediate-mass satellite dwarf galaxies that were later accreted into it. According to early simulations (e.g., Helmi & de Zeeuw 2000), and many since, a large fraction (at least 50%) of Galactic accretion events can be recovered by applying clustering algorithms to the phase space of energies and other dynamical parameters of individual field stars. This opens the possibility of using a clustering approach to match CEMP stars formed in similar environments with each other by identifying them as members of individual Chemodynamically Tagged Groups (CDTGs), which we pursue in this paper.

A pilot effort illustrating the application of this approach to chemically peculiar stars in the halo of the MW was conducted by Roederer et al. (2018), specific to r-process-enhanced stars, based on a relatively small sample size of 35 such stars. The sample was expanded considerably (426 r-process-enhanced stars) by Gudin et al. (2021), who demonstrated clear evidence that r-process-enhanced stars shared common chemical-evolution histories, presumably in their parent dwarf galaxies. Shank et al. (2022a) analyzes a sample of ∼1700 r-process-enhanced stars, reaching similar conclusions.

Another recent work, Yuan et al. (2020), explored the clustering of a large data set of VMP MW halo stars. Through application of a trained neural network (STARGO), these authors successfully mapped dynamically tagged groups (DTGs) of VMP stars onto known more-massive substructures in the MW and identified new DTGs for future spectroscopic follow-up. Other recent examples of this approach include an analysis of HK/HES stars (Limberg et al. 2021), the Best and Brightest survey (Shank et al. 2022b), and stars from the RAVE survey (Shank et al. 2022).

In this work, we derive dynamical parameters for a sample of 572 (of an initial sample of 644) CEMP stars with available moderate- to high-resolution spectroscopy (R ≥ 4350).

This paper is outlined as follows. Section 2 describes the assembly of this sample, along with the adopted distance estimates, radial velocities, proper motions, and the subset of chemical abundances we consider. We also briefly describe the nature of this sample in this section. Section 3 provides a brief overview of the HDBSCAN clustering method we employ and the results of its application to the CEMP sample. Section 4 examines the CDTGs based on the MW substructures and globular clusters that are associated with our CDTGs. In Section 5 we perform a statistical analysis of our results and demonstrate the likely shared chemical-enrichment history of the members of the individual CDTGs. We also consider the nature of CDTGs based on the clustering of Group I and Group II CEMP stars in the Yoon–Beers diagram. Section 6 considers the astrophysical implications of our results and provides perspectives for future studies. Section 7 summarizes our final results.

A compilation of CEMP stars with abundance analyses based on high-resolution spectroscopy was published by Yoon et al. (2016), and it serves as the basis for this work. We also include CEMP surveys with similar analyses—Sakari et al. (2018), Hansen et al. (2018), Ezzeddine et al. (2020), Holmbeck et al. (2020), Rasmussen et al. (2020), Zepeda et al. (2022), Pristine (Lucchesi et al. 2022), and GALAH (Buder et al. 2021).

Note that we have chosen to exclusively adopt reported abundances based on the local thermodynamical equilibrium (LTE) assumption. Exploration of the effects of the non-LTE assumption, in particular on the abundance estimates for carbon, can and will be undertaken in the future. Popa et al. (2023) have outlined an approach for obtaining non-LTE corrections specifically for the CH molecular feature (G band), upon which the great majority of present high-resolution analyses depend for estimates of carbon. This is expected to lead to a correction grid covering large ranges of stellar parameters, which will be of general utility. Note that Popa et al. (2023) specifically caution against the naive combination of non-LTE corrections with 3D effects, as some have attempted in the past; the 3D corrections are still in their relative infancy and ideally need to be carried out in conjunction with non-LTE assumptions, not separately.

The use of large-scale photometric surveys, e.g., J-PLUS (Cenarro et al. 2019) and S-PLUS (Mendes de Oliveira et al. 2019), will be crucial for the identification of many additional relatively bright CEMP stars for future high-resolution spectroscopic follow-up. Whitten et al. (2019, 2021) have already explored methodology for extracting estimates of [Fe/H] and [C/Fe] from the narrow- and broadband photometry that they provide. Y. Huang et al. (2023, in preparation) is in the process of extending the elemental-abundance information in these surveys to encompass estimates not only for [Fe/H] and [C/Fe], but for [N/Fe], [Mg/Fe], and [Ca/Fe] as well.

2.1. Construction of the Initial Sample

The data used in this work were assembled from the literature, including the sources cited in Yoon et al. (2016), JINABase (Abohalima & Frebel 2018), the SAGA database (Suda et al. 2008), and a number of other recent sources. We included stars with estimated stellar parameters, [Fe/H], and [C/Fe], at a minimum. When available, we also tabulated the [Mg/Fe] ratio and the neutron-capture elemental-abundance ratios [Sr/Fe], [Y/Fe], [Ba/Fe], and [Eu/Fe]. Duplicates were then removed, retaining the observations of a given star with the higher spectroscopic resolution and additional elemental abundances (in particular n-capture species) available. It is unavoidable that the methods used by the different sources are quite inhomogeneous; for this reason, we choose not to combine the reported stellar parameter or abundance information when multiple sources exist for a given star.

We then removed stars that did not satisfy [C/Fe]_c > +0.7, obtained by applying the carbon-abundance correction scheme for evolution on the giant branch (Placco et al. 2014). Following these cuts, our initial sample consists of 644 stars. This sample includes stars with 3540 ≤ T_eff (K) ≤ 7100, surface gravity $-0.30\leqslant \mathrm{log}g\leqslant 5.07$, −7.80 ≤ [Fe/H] ≤ −1.13, and +0.71 ≤ [C/Fe]_c ≤ + 4.39. The spatial distribution of the stars in our initial sample of CEMP stars is shown in Figure 1. Table 11 in the Appendix lists the various data for these stars. The full table is available in machine-readable format.

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Figure 2 provides histograms of the full set of elemental-abundance ratios considered in the present work.

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The Yoon–Beers diagram of A(C)_c versus [Fe/H] for these stars is shown in Figure 3, corrected from the observed value to account for the depletion of carbon on the giant branch following Placco et al. (2014). The definitions of CEMP morphological groups were originally presented in Yoon et al. (2016), based on the level of [Ba/Fe]. These same authors demonstrated that similar assignments can be carried out using a separation based on A(C)_c   (and [Fe/H]) alone. As not all of our CEMP stars have available measured [Ba/Fe], we base our morphological group assignments purely on corrected carbon abundances, A(C)_c , [C/Fe]_c , and [Fe/H]. To account for the errors in these measurements and the lack of clear delineations between the groups, we use definitions with some overlap. We assign CEMP groups as follows: Stars with [Fe/H] > −4 and A(C)_c > 6.75 are Group I stars, stars with A(C)_c < 7.25 and [C/Fe]_c < +2.25 are Group II stars, and all other stars are assigned to Group III. With these definitions, we have 443 Group I stars (271 Group I only stars), 363 Group II stars (191 Group II only stars), and 10 Group III stars. For convenience, a list of the stars with their adopted CEMP Group status and a summary of their available elemental-abundance ratios is provided in Table 2. Note that this table includes all stars in the initial sample of CEMP stars. Those that are removed in the assembly of the final sample, as described below, are listed with an asterisk following their names.

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Table 2. Identified CEMP Stars and Their Group Associations

Name	Group	Teff (K)	log g	[Fe/H]	[C/Fe]c	A(C)c	[Mg/Fe]	[Sr/Fe]	[Y/Fe]	[Ba/Fe]	[Eu/Fe]
HD 224959	I	5050	2.100	−2.42	+2.04	8.05	+0.39	+1.50	...	+2.07	+2.01
SDSS J000219.87+292851.8	I	6150	4.000	−3.26	+2.63	7.80	+0.36	+0.27	...	+1.83	...
BPS CS 29503−0010	I	6050	3.660	−1.70	+1.65	8.38	...	+1.13	...	+1.81	+1.69
HE 0002−1037	I	4673	1.280	−3.75	+3.43	8.11	...	...	...	...	...
BPS CS 31070−0073*	I/II	6190	3.860	−2.55	+1.34	7.22	+0.53	+1.75	...	+2.28	+2.74
HE 0007−1832	I	6500	3.800	−2.79	+2.79	8.43	+0.55	+0.08	...	+0.04	<+1.70
HE 0010−3422	I	5400	3.100	−2.78	+1.93	7.58	+0.34	+0.77	...	+1.46	+1.64
HE 0012−1441	I	5750	3.500	−2.52	+1.71	7.62	+0.83	...	...	+1.10	...
HE 0013−0257	II	4500	0.500	−3.82	+0.93	5.54	+0.68	−0.46	...	−1.16	<+0.67
HE 0015+0048	II	4600	0.900	−3.07	+1.27	6.63	+0.65	−1.07	...	−1.18	<+0.75
HE 0017−4346	I	6198	3.800	−3.07	+3.02	8.38	+0.86	+0.84	...	+1.23	<+0.99
HE 0017+0055	I	4261	0.800	−2.47	+2.80	8.76	...	...	...	+2.30	+2.14
SMSS J002148.06−471132.1	II	4765	1.400	−3.17	+0.78	6.04	+0.43	+0.02	...	−1.18	<+0.50
2MASS J00224486−1724290*	II	4765	1.550	−4.05	+2.07	6.45	+1.03	−0.73	...	−1.10	+0.25
SDSS J002314.00+030758.0*	III	5997	4.600	−5.80	+3.76	6.39	+3.33	...	...	...	...
HE 0024−2523	I	6625	4.300	−2.72	+2.69	8.40	+0.71	+0.44	...	+1.41	<+0.07
BPS CS 22882−0012	I/II	6290	3.800	−2.75	+1.10	6.78	+0.36	+0.56	...	+0.61	<+1.23
BPS CS 31062−0050	I	5600	3.000	−2.32	+2.12	8.23	+0.59	+0.96	...	+2.35	+1.87
2MASS J00305267−1007042	I/II	4831	1.480	−2.35	+0.88	6.96	+0.24	+0.50	...	−0.71	+0.00
SDSS J003602.17−104336.2	I	6500	4.500	−2.50	+2.37	8.30	+0.27	−0.13	...	+0.37	...
RAVE J003946.9−684957	II	4631	1.160	−2.62	+0.73	6.54	...	+0.43	...	−0.10	−0.38
BPS CS 29497−0030	I	7000	4.000	−2.52	+2.37	8.28	+0.35	+1.30	...	+2.75	+1.71
BPS CS 29497−0034	I	4800	1.800	−2.90	+2.78	8.31	+0.70	+1.05	...	+1.98	+1.79
G270−51	I	6000	3.800	−2.74	+2.39	8.08	+0.43	+0.18	...	+1.96	+1.39
2MASS J00453930−7457294	I	4947	2.010	−2.00	+0.99	7.42	...	+0.83	...	+0.37	+0.55

Note. Stars with names that end with * are not in the final sample.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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2.2. Construction of the Final Sample

2.2.1. Radial Velocities, Distances, and Proper Motions

To obtain the dynamical information for our initial sample, we cross-matched our stars with Gaia EDR3 (Gaia Collaboration et al. 2016, 2021), supplemented by recent radial-velocity information from Gaia DR3 (Babusiaux et al. 2022), in order to obtain radial velocities, parallaxes, and proper motions. When an accurate radial velocity was available from the spectroscopic surveys (which applies to all but a handful of cases), we use it if there was no Gaia radial velocity (RV). For stars with available source radial velocities, Figure 4 compares these values with those having Gaia radial velocities. If the spectroscopic source radial velocities differed from those reported by Gaia by more than 15 km s⁻¹ (45 stars), the star was removed from further analysis, as many are suspected to be binaries.

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Distance estimates for our stars were obtained using StarHorse (Anders et al. 2022). When the relative error from StarHorse exceeded 30%, we used the Bailer-Jones (Bailer-Jones et al. 2021) estimates, unless its relative error was also greater than 30%, in which case we removed the star from the sample. Figure 5 shows the distance estimates from both methods for stars in the initial sample. Note that three stars with unusually high, and likely suspect, distances were removed from the final sample.

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2.2.2. Dynamical Parameters

We employ the Action-based GAlaxy Modeling Architecture ¹⁰  (AGAMA) package (Vasiliev 2018), which uses the radial velocities, distances, and proper motions of stars to derive orbital parameters for stars in the initial sample. We use the same solar position, solar peculiar motions, ¹¹  and gravitational potential (McMillan 2017) as used in Shank et al. (2022b). To obtain errors for these estimates, we assume the errors in the input quantities are normally distributed. Then we obtain orbital parameters by finding the mean and standard deviation of the values from 1000 runs of AGAMA sampling from the distributions for our inputs.

Figure 6 presents histograms of the derived estimates of r_peri, r_apo, and ${Z}_{\max };$ stars that were unbound from the Galaxy (E > 0 km² s⁻²) are not included. All of the stars have r_peri distances inside of 20 kpc. As can be appreciated from inspection, the distributions of these parameters are quite similar across the Group I and Group II subsamples. There are too few Group III stars to make meaningful interpretations at present.

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The stars with AGAMA results consistent with being bound to the Galaxy comprise our final sample, which includes a total of 572 stars. Table 12 in the Appendix lists the various data for these stars. The full table is available in machine-readable format.

Figure 7 is a Toomre Diagram of the stars in the final sample. For this sample, 64% of the stars are on prograde orbits, while 36% are on retrograde orbits. When we consider the stars that are assigned (unique) morphological groups, Group I stars are 62%/38% prograde/retrograde. Group II stars are 68%/32% prograde/retrograde. The Group III stars are 75%/25% prograde/retrograde. Note that not all stars in the final sample have morphological groups assigned, so these numbers are based on the subset that do.

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To perform our clustering exercise, we employ HDBSCAN ¹²  (Campello et al. 2013). This method groups data by density in the phase space considered (orbital energies and cylindrical actions), then places the clusters into a hierarchy based on how they change when the requisite density belonging to a cluster changes. We refer the interested reader to Campello et al. (2013) and Shank et al. (2022b) for a full description of HDBSCAN. In our use of this algorithm, we set the following parameters: min_cluster_size = 3, min_samples = 3, cluster_selection_method = ''leaf,'' prediction_data=True, Monte Carlo samples set at 1000, and minimum confidence set to 20%. The min_cluster_size determines how small the clusters can be. The min_samples parameter can be adjusted to account for different noise levels in the data. By choosing cluster_selection_method = ''leaf'' we allow HDBSCAN to make smaller clusters with tighter orbital-parameter values. With the prediction_data = True, the method has memory of the nominal clusters for each run in the Monte Carlo procedure. Full descriptions of these input choices of parameters can be found in Shank et al. (2022b).

Table 3 lists the 40 identified CDTGs, along with the number of members, assigned confidence values, and associations with previously identified DTGs and CDTGs, as described below. Note that, even though we set the minimum confidence for cluster identification to 20.0%, the smallest confidence in this table is 35.5%; most are much higher. The average confidence level for the 40 CDTGs is 77.1%.

Table 4 provides a listing of the individual members of the identified CDTGs from the application of HDBSCAN, along with the available elemental-abundance ratios considered in this paper. The biweight location and scale, analogous to the mean and standard deviation, for the abundances within each CDTG are shown in bold at the end of each listing. In addition, any stars that are associated with DTGs, CDTGs, globular clusters, or dwarf galaxies identified in previous works are listed at the beginning of each CDTG in the table.

Table 5 lists the mean values, along with the associated dispersions, of the dynamical parameters for the CDTGs. The number of stars in each CDTG is indicated by the N Stars column.

Table 5. Cluster Dynamical Parameters Determined by AGAMA

Cluster	N Stars	(〈vr 〉, 〈vϕ 〉, 〈vz 〉)	(〈Jr 〉, 〈Jϕ 〉, 〈Jz 〉)	〈E〉	〈ecc〉
		(${\sigma }_{\langle {v}_{r}\rangle }$, ${\sigma }_{\langle {v}_{\phi }\rangle }$, ${\sigma }_{\langle {v}_{z}\rangle }$)	(${\sigma }_{\langle {J}_{r}\rangle }$, ${\sigma }_{\langle {J}_{\phi }\rangle }$, ${\sigma }_{\langle {J}_{z}\rangle }$)	σ〈E〉	σ〈ecc〉
		(km s−1)	(kpc km s−1)	(105 km2 s−2)
CDTG-1	17	(56.3, 154.2, −11.2)	(161.2, 1273.1, 63.0)	−1.642	0.38
		(74.3, 18.2, 50.3)	(61.8, 69.6, 40.1)	0.024	0.07
CDTG-2	12	(−18.5, −88.6, −19.1)	(291.4, −562.3, 83.2)	−1.824	0.63
		(84.5, 25.3, 40.9)	(80.3, 87.1, 41.9)	0.040	0.07
CDTG-3	11	(−15.6, −134.2, −95.6)	(156.7, −911.0, 707.2)	−1.534	0.37
		(104.5, 48.2, 170.6)	(79.4, 178.2, 128.5)	0.041	0.11
CDTG-4	10	(−60.3, 69.3, −62.1)	(396.6, 550.6, 165.3)	−1.722	0.70
		(91.0, 21.5, 75.7)	(27.5, 93.6, 44.6)	0.021	0.03
CDTG-5	10	(−63.4, −13.5, 67.3)	(314.9, −63.4, 628.9)	−1.728	0.72
		(93.0, 22.3, 139.7)	(42.5, 146.9, 53.5)	0.024	0.06
CDTG-6	10	(1.4, −120.7, −13.2)	(137.0, −875.8, 266.7)	−1.704	0.41
		(55.7, 26.5, 119.5)	(69.3, 140.7, 99.1)	0.049	0.10
CDTG-7	9	(2.2, 33.6, 26.5)	(499.3, 259.5, 74.2)	−1.814	0.84
		(61.2, 15.2, 78.2)	(71.1, 119.0, 29.5)	0.018	0.08
CDTG-8	9	(148.2, −22.6, −13.2)	(811.8, −186.6, 20.3)	−1.678	0.92
		(35.4, 10.4, 37.3)	(51.7, 88.7, 63.9)	0.036	0.04
CDTG-9	9	(60.4, 100.0, −68.5)	(180.3, 699.4, 584.0)	−1.620	0.44
		(56.5, 33.0, 174.3)	(45.3, 55.8, 90.2)	0.038	0.06
CDTG-10	8	(53.3, 111.9, 3.6)	(242.0, 879.4, 144.2)	−1.707	0.52
		(55.4, 7.3, 64.6)	(8.3, 47.9, 29.2)	0.022	0.01
CDTG-11	8	(8.4, 27.1, 10.8)	(400.9, 146.8, 183.3)	−1.861	0.88
		(133.7, 18.4, 89.6)	(58.7, 84.3, 33.8)	0.050	0.06
CDTG-12	7	(−37.2, 83.2, −16.2)	(268.9, 604.6, 302.0)	−1.715	0.58
		(90.8, 8.7, 81.3)	(40.1, 60.3, 52.2)	0.018	0.03
CDTG-13	7	(−15.9, 188.7, −2.2)	(31.8, 1552.4, 37.3)	−1.634	0.17
		(18.5, 2.5, 37.0)	(7.5, 61.9, 28.3)	0.024	0.03
CDTG-14	7	(−2.8, 15.9, −218.0)	(246.5, −7.9, 1410.4)	−1.454	0.44
		(123.0, 89.4, 76.2)	(87.1, 440.2, 105.3)	0.055	0.06
CDTG-15	6	(−67.5, 73.2, −95.7)	(455.8, 413.2, 972.8)	−1.487	0.60
		(123.5, 54.2, 131.9)	(113.3, 176.5, 49.1)	0.051	0.10
CDTG-16	6	(−31.1, 51.3, 23.1)	(810.1, 457.0, 188.6)	−1.530	0.83
		(174.9, 15.7, 78.6)	(16.7, 63.8, 59.7)	0.035	0.03
CDTG-17	6	(−155.2, −21.4, 58.9)	(1284.8, −158.1, 515.3)	−1.368	0.95
		(153.1, 8.7, 144.5)	(72.6, 80.5, 97.6)	0.028	0.03
CDTG-18	6	(87.8, −12.0, 165.9)	(148.8, −90.4, 1917.9)	−1.407	0.30
		(113.5, 20.8, 214.4)	(163.8, 187.0, 113.4)	0.049	0.14
CDTG-19	5	(17.5, 178.6, 41.8)	(42.1, 1122.0, 197.8)	−1.703	0.20
		(45.7, 34.7, 112.3)	(33.6, 21.2, 4.2)	0.020	0.09
CDTG-20	5	(51.6, 29.9, 3.2)	(618.5, 279.8, 194.6)	−1.682	0.86
		(56.3, 12.5, 78.7)	(21.6, 138.9, 16.6)	0.033	0.06
CDTG-21	5	(−18.4, −128.9, 28.0)	(254.5, −901.7, 80.4)	−1.688	0.54
		(96.6, 15.6, 66.9)	(28.0, 79.0, 43.4)	0.033	0.00
CDTG-22	5	(−41.8, 74.5, 95.7)	(76.0, 287.0, 491.7)	−1.873	0.44
		(21.6, 29.1, 29.9)	(33.2, 45.6, 70.7)	0.058	0.07
CDTG-23	5	(38.0, 85.6, 60.9)	(77.4, 420.3, 672.2)	−1.739	0.34
		(98.2, 3.3, 144.4)	(68.7, 45.7, 61.4)	0.017	0.20
CDTG-24	5	(17.8, 232.0, 0.9)	(59.1, 1995.8, 57.5)	−1.503	0.20
		(63.5, 19.8, 54.5)	(7.3, 144.6, 44.5)	0.015	0.02
CDTG-25	4	(−12.9, −8.6, 40.5)	(1279.9, −127.7, 98.7)	−1.454	0.92
		(181.4, 17.7, 44.1)	(80.3, 214.4, 21.3)	0.041	0.02
CDTG-26	4	(9.9, −22.5, 4.1)	(113.7, −164.1, 983.4)	−1.672	0.38
		(117.7, 28.2, 176.3)	(50.9, 207.4, 27.6)	0.039	0.08
CDTG-27	4	(43.5, 282.5, −3.3)	(224.6, 2492.1, 54.7)	−1.340	0.34
		(49.8, 38.6, 38.8)	(54.5, 100.3, 33.6)	0.034	0.04
CDTG-28	4	(−124.6, −22.5, −23.8)	(145.5, −57.3, 113.6)	−2.174	0.84
		(24.1, 31.3, 81.8)	(61.2, 98.6, 4.1)	0.026	0.02
CDTG-29	4	(−118.0, 12.5, −46.0)	(711.6, 95.5, 55.7)	−1.739	0.93
		(34.3, 13.2, 27.8)	(19.6, 110.1, 14.3)	0.011	0.05
CDTG-30	4	(−10.9, −11.4, 58.0)	(1167.6, −104.5, 801.2)	−1.338	0.89
		(233.9, 12.6, 160.9)	(87.7, 128.6, 35.8)	0.023	0.03
CDTG-31	4	(160.9, 21.2, −13.7)	(978.3, 164.9, 314.1)	−1.503	0.94
		(47.6, 2.9, 122.9)	(59.5, 53.2, 43.3)	0.048	0.02
CDTG-32	4	(62.7, 124.8, −34.3)	(519.3, 1062.6, 255.6)	−1.509	0.61
		(142.4, 43.6, 94.7)	(104.0, 82.1, 21.4)	0.031	0.05
CDTG-33	4	(35.7, −67.7, 21.4)	(889.2, −573.3, 91.3)	−1.503	0.83
		(219.1, 17.6, 67.2)	(20.8, 148.6, 31.4)	0.035	0.04
CDTG-34	3	(129.6, 26.3, −70.7)	(1593.8, 181.2, 63.7)	−1.345	0.93
		(277.3, 44.7, 19.3)	(67.9, 393.4, 16.2)	0.036	0.04
CDTG-35	3	(69.8, −2.8, −17.6)	(663.7, −22.2, 37.7)	−1.814	0.98
		(39.7, 3.9, 25.7)	(22.1, 31.4, 13.4)	0.014	0.01
CDTG-36	3	(19.5, 12.3, 8.0)	(516.0, 81.5, 103.8)	−1.851	0.95
		(97.3, 8.8, 53.2)	(34.3, 59.3, 23.3)	0.021	0.03
CDTG-37	3	(5.9, 189.1, 32.9)	(38.6, 891.0, 181.2)	−1.796	0.23
		(51.9, 17.9, 78.0)	(21.9, 59.6, 22.5)	0.023	0.07
CDTG-38	3	(32.0, 111.4, 41.5)	(174.9, 701.8, 63.1)	−1.861	0.49
		(27.3, 8.8, 26.3)	(18.5, 61.3, 5.5)	0.024	0.04
CDTG-39	3	(−222.0, 88.6, −25.1)	(860.9, 548.3, 377.3)	−1.456	0.80
		(64.6, 30.7, 95.3)	(38.1, 36.5, 42.0)	0.016	0.01
CDTG-40	3	(61.2, −116.4, 55.7)	(389.1, −1050.4, 96.5)	−1.599	0.58
		(105.2, 19.8, 23.5)	(20.4, 95.9, 50.0)	0.014	0.03

A machine-readable version of the table is available.

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4.1. Milky Way Substructures

We check each CDTG for association with known MW substructures. These associations are based on the stellar orbital parameters as well as the chemical abundances of individual stars in the CDTGs. To find these associations, we employ the substructure criteria from Naidu et al. (2020). Each substructure has specific dynamical and chemical criteria, and CDTGs are associated with these substructures when the criteria are met. To see exactly how these criteria are applied, we refer the interested reader to Shank et al. (2022a). We found that 25 of the 40 CTDGs had associated substructures: Gaia-Sausage-Enceladus (GSE), LMS-1 (Wukong), the MWTD, Thamnos, I'itoi, and the Splashed Disk listed in Table 6. This table provides the numbers of stars in the CDTGs associated with each substructure, the means and dispersions of their chemical abundances, and the means and dispersions of their dynamical parameters. The Lindblad diagram and projected-action plot for these substructures is shown in Figure 8. The CDTGs found to be associated with known MW substructures and globular clusters are listed in Table 7.

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Table 6. Identified Milky Way Substructures

Substructure	N Stars	〈[Fe/H]〉	〈[C/Fe]c〉	〈[Mg/Fe]〉	〈[Sr/Fe]〉	〈[Y/Fe]〉	〈[Ba/Fe]〉	〈[Eu/Fe]〉	(〈vr 〉, 〈vϕ 〉, 〈vz 〉)	(〈Jr 〉, 〈Jϕ 〉, 〈Jz 〉)	〈E〉	〈ecc〉
									(${\sigma }_{\langle {v}_{r}\rangle }$, ${\sigma }_{\langle {v}_{\phi }\rangle }$, ${\sigma }_{\langle {v}_{z}\rangle }$)	(${\sigma }_{\langle {J}_{r}\rangle }$, ${\sigma }_{\langle {J}_{\phi }\rangle }$, ${\sigma }_{\langle {J}_{z}\rangle }$)	σ〈E〉	σ〈ecc〉
									(km s−1)	(kpc km s−1)	(105 km2 s−2)
GSE	99	−2.52	+1.31	+0.40	+0.29	+0.07	+0.38	+0.64	(−11.6, 17.9, 2.6)	(701.8, 104.8, 233.4)	−1.666	0.85
		0.55	0.73	0.22	0.74	0.22	+1.00	0.62	(152.1, 48.1, 89.3)	(351.2, 305.5, 217.2)	0.195	0.10
Thamnos	15	−2.35	+1.27	+0.30	−0.10	NaN	+0.62	+0.68	(−15.0, −124.0, −0.2)	(177.9, −915.3, 201.7)	−1.702	0.43
		0.30	0.53	0.28	1.33	NaN	+1.11	0.54	(69.3, 23.0, 102.0)	(75.9, 146.9, 117.9)	0.043	0.10
LMS-1	15	−3.11	+1.44	+0.54	−0.27	NaN	−0.05	+0.41	(9.1, 99.1, −50.5)	(293.2, 579.4, 742.5)	−1.567	0.52
		0.78	0.63	0.30	1.05	NaN	+1.35	0.57	(106.7, 47.7, 137.7)	(152.1, 185.2, 201.7)	0.077	0.11
I'itoi	11	−2.71	+1.57	+0.41	+0.18	+0.20	+0.53	+0.58	(−21.7, −136.7, −37.7)	(184.5, −901.1, 711.1)	−1.531	0.38
		0.33	0.74	0.06	0.35	0.00	+1.35	1.00	(93.8, 45.0, 148.4)	(98.2, 172.7, 116.5)	0.040	0.11
Splashed Disk	5	−2.69	+1.23	+1.17	−0.18	+0.09	−0.03	+0.88	(−22.8, 81.7, 62.3)	(85.0, 312.2, 463.9)	−1.873	0.45
		0.63	0.90	0.59	0.26	0.34	+0.98	0.39	(39.0, 23.7, 116.6)	(27.3, 57.5, 54.5)	0.055	0.07
MWTD	3	−2.28	+1.35	+0.36	+0.33	NaN	+0.33	+0.51	(32.0, 111.4, 41.5)	(174.9, 701.8, 63.1)	−1.861	0.49
		0.20	0.79	0.01	0.27	NaN	+0.68	0.27	(27.3, 8.8, 26.3)	(18.5, 61.3, 5.5)	0.024	0.04

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Table 7. Associations of Identified CDTGs

Structure	Reference	Associations	Identified CDTGs
MW Substructure	Naidu et al. (2020)	GSE	4, 5, 7, 8, 11, 16, 17, 20, 25, 28, 29, 30, 31, 33, 34, 35, 36, 39
		LMS-1	9, 15
		Thamnos	6, 21
		I'itoi	3
		MWTD	38
		Splashed Disk	22

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4.1.1. Gaia-Sausage-Enceladus

One of the earliest known mergers, GSE, is thought to have been accreted by the MW about 10 Gyr ago (Helmi 2020). It is also the largest known merger and the most populated substructure in this work, with 99 CEMP stars in 18 different CDTGs. While the metallicity distribution function (MDF) for GSE peaks near [Fe/H] ∼ −1.2, the CEMP stars associated with GSE exhibit a biweight location and scale (robust alternatives to the mean and standard deviation) of 〈[Fe/H]〉 = −2.52 (σ = 0.55 dex). Our GSE stars also show a biweight location and scale of 〈[Mg/Fe]〉 = +0.40 (σ = 0.22 dex), which is higher than GSE's value (+0.21; Naidu et al. 2022). Based on these differences, it is likely that the low-metallicity tail of GSE comprises CEMP stars with elevated [Mg/Fe] abundances.

4.1.2. LMS-1 (Wukong)

We found two CDTGs in the substructure LMS-1, with a total of 15 stars. LMS-1 was found to be the most metal-poor substructure by Malhan et al. (2022), so finding this large number of CEMP stars might be expected, given the increasing frequency of CEMP stars with declining metallicity. The CEMP stars associated with LMS-1 belong to all three CEMP Group morphologies. We found three UMP ([Fe/H] < −4) stars associated with LMS-1. No other substructure has more than two stars at or below [Fe/H] < −4, and there was only one such star in a CDTG without an associated substructure. Based on this, UMP stars are likely much more common in LMS-1 than in other recognized MW substructures, despite the mean of −1.58 reported by Naidu et al. (2022) for the substructure as a whole. For our sample, we found 〈[Fe/H]〉 = −3.11 with a large dispersion of σ = 0.78 dex.

4.1.3. Thamnos

Thamnos is believed to have formed from the merging of a relatively small satellite (stellar mass <5 × 10⁶ M_⊙) with the MW (Helmi 2020). It is particularly interesting how low in energy the stars in this structure are, considering how deep in the MW it resides. This has been used to argue that the merger occurred very early in the MW's history (Bonaca et al. 2020; Kruijssen et al. 2020). We found 2 CDTGs associated with Thamnos, with 15 total CEMP stars, including both Group I and Group II CEMP morphologies. The stars in Thamnos have the second highest mean metallicity (〈[Fe/H]〉 = −2.35) among those with substructure associations, with a dispersion σ = 0.30 dex.

4.1.4. The Metal-weak Thick Disk

The MWTD has been argued to have formed from either a merger scenario, possibly related to GSE, or the result of old stars born within the solar radius migrating out to the solar position due to tidal instabilities within the MW (Carollo et al. 2019). However, several recent papers, including Carollo et al. (2019), An & Beers (2020), Dietz et al. (2021), and Mardini et al. (2022), have presented evidence that the MWTD is an independent structure from the canonical thick disk and thus may have arisen independently.

We found one CDTG of CEMP stars associated with this substructure, with a combined total of three stars. As expected, these stars occupy the low-metallicity tail of the MWTD MDF, with a biweight location and scale of 〈[Fe/H]〉 = −2.28 (σ = 0.20 dex). The CEMP stars associated with the MWTD have a [Mg/Fe] biweight location and scale (〈[Mg/Fe]〉 +0.36, σ = 0.01 dex) that is quite similar to the stars in GSE.

4.1.5. I'itoi

The substructure I'itoi has several possible formation scenarios suggested in the literature, associating it with other halo substructures, including Sequoia and Thamnos (Naidu et al. 2020). We found one CDTG in I'itoi that contains a total of 11 stars, including both Group I and Group II morphologies. We found I'itoi to be the second most metal-poor substructure among our associations, 〈[Fe/H]〉 = −2.71) with a dispersion of σ = 0.33 dex.

4.2. Splashed Disk

4.3. Previously Identified Dynamically Tagged Groups and Stellar Associations

4.4. Globular Clusters and Dwarf Galaxies

5.1. Statistical Framework

5.2. Important Caveats

5.3. Results

We now consider how to account for the observed behaviors of the CDTGs in our study, emphasizing the likely differences in the astrophysical origins of Group I (primarily CEMP-s) stars and Group II (primarily CEMP-no) stars.

Numerous studies support the binary mass-transfer scenario for the production of carbon for Group I stars. The work of Lucatello et al. (2005), Starkenburg et al. (2014), and Hansen et al. (2016a) showed that most CEMP-s stars are in fact members of binary systems, confirming results that apply to stars over a wide range of metallicities (e.g., Abate et al. 2013, 2015; Lee et al. 2014). Some have argued that this mechanism is responsible for the carbon enhancement in all CEMP stars. Hansen et al. (2016b) showed that Group II CEMP stars are not often associated with binary status. In contrast, Arentsen et al. (2019) suggested that they may be wide (long-period) binaries and thus difficult to detect with a limited number of radial-velocity measurements. Suda et al. (2004) and Komiya et al. (2007, 2020) have argued that mass transfer from a long-period binary companion could explain the origin of the Group II CEMP stars. The recent work by Aguado et al. (2022) used carbon isotropic ratios to show that, for the mega metal-poor ([Fe/H] = −6.2) star SMSS 1605–1443, which we would classify as a Group III CEMP-no star, the carbon was not produced and transferred from an AGB binary companion.

There are also a variety of proposed mechanisms for producing carbon-enriched material for Group II stars in the early universe, including massive rapidly rotating stars and various SN scenarios (Umeda & Nomoto 2003, 2005; Chieffi & Limongi 2004; Iwamoto et al. 2005; Meynet et al. 2006,2010; Nomoto et al. 2006; Tominaga et al. 2007, 2014; Heger & Woosley 2010; Limongi & Chieffi 2012; Ishigaki et al. 2014; Choplin et al. 2016; Salvadori et al. 2016; Kobayashi et al. 2020).

If the mass-transfer scenario applies to both Groups I and II CEMP CDTGs, they should both exhibit large dispersions in their corrected carbon-abundance distributions, as they would be due to local, and not global, pollution events. A change in the abundances of a single star (or even multiple stars) in a CDTG would not affect the rest of the stars, leading to a wide dispersion in the elemental abundances. Based on our statistical analysis of the Group I and II CEMP dynamical clusters, this interpretation is unlikely, as they exhibit quite different behaviors. In particular, the small, and statistically significant, dispersion of the observed corrected carbon abundances within the Group II CDTGs points to the carbon coming from the environment that the stars formed in, rather than from enriched material transferred from binary companions. The dispersion in the mean [C/Fe]_c for Group II CDTGs is already at the measurement limit for the observations, so it does not appear plausible to explain this low dispersion with anything but natal carbon abundances.

Note that the models described by Komiya et al. (2020) could produce carbon enhancements at low metallicity without considering a significant mass transfer, if some of their uncertain modeling parameters are considered. As they point out, the Fe yield of faint (mixing and fallback) SNe is highly affected by the ejection factor, which controls the fraction of materials ejected from the region between the mass cut and the outer boundary of the mixing region. Also, [C/Fe] ratios could be affected by the diffusion coefficient, the amount of mass swept up by SNe, and the nature of the IMF. Their optimum model, with lower swept-up mass and diffusion coefficient, could reproduce the trend of [C/Fe], while this model overproduces stars with [Fe/H] < −4 (Figure 14 of Komiya et al. 2020).

Taking into account these uncertainties, the contradiction between our results and the mass-transfer scenario might be mitigated. Komiya et al. (2020) only studied the effect of mass transfer in models without faint SNe. If they include mass transfer in models that include faint SNe, they would not need to assume a high rate of binary mass transfer to explain CEMP-no stars. In this case, the mass transfer, even if it occurs, may not significantly affect the low observed dispersion of carbon in Group II CDTGs.

Our results suggest the hypothesis that Group II CEMP stars are formed from the gas enriched by rapidly rotating massive stars or the ejecta of SNe with large carbon enhancements and depleted Fe production. Faint (mixing and fallback) SNe are one of the astrophysical candidates that have been suggested to be responsible (Umeda & Nomoto 2003, 2005; Iwamoto et al. 2005; Tominaga et al. 2007; Ishigaki et al. 2014). These SNe eject a small amount of Fe due to the large amount of fallback, resulting in ejecta with large [C/Fe] abundance ratios. Indeed, Tominaga et al. (2007) successfully reproduced the observed abundance pattern of the CEMP-no star CS 29498-043 (Aoki et al. 2004) with their 25 M_☉ faint SN model. Thus, although the predicted [C/Fe] ratios are highly dependent on the choice of uncertain parameters, the ejecta from faint SNe could serve as one of the primary production sites for Group II CEMP stars.

Several studies have attempted to explain CEMP-no star formation solely from SN ejecta (e.g., Salvadori et al. 2015; Sarmento et al. 2016, 2019; Chiaki et al. 2017, 2020; de Bennassuti et al. 2017; Sharma et al. 2018a, 2018b; Hartwig & Yoshida 2019). Using the eagle cosmological hydrodynamical simulation (Schaye et al. 2015), Sharma et al. (2018b) found that low-metallicity core-collapse SNe with low Fe yields contribute to forming CEMP-no stars. Stars formed from such SNe exhibited high [C/Fe] and low [C/O], similar to CEMP-no stars' observed properties. Hartwig & Yoshida (2019) proposed a new scenario for forming CEMP-no stars. Their analytical estimates have shown that such stars could be formed from the carbon-rich material before those formed from carbon-normal gas in the inhomogeneous interstellar medium, due to the shorter cooling time of the carbon-enhanced gas. In this manner, CEMP-no stars could be formed from carbon-normal SNe.

Our results clearly favor one or more of the rapidly rotating massive-star and SNe scenarios, rather than the binary mass-transfer scenario(s). Note that, as shown in Table 10, the dispersion of [Mg/Fe] for the Group II CEMP stars is of marginal statistical significance, as reflected in the GEAD probability, unlike the highly significant behavior of [C/Fe]_c . While core-collapse SNe synthesize Mg, the lack of strong significance in [Mg/Fe] does not rule out this hypothesis for the stars in group Group II CDTGs, in part due to the limited number of Group II CDTGs (five) with measured [Mg/Fe] dispersions in our sample. Recent cosmological zoom-in simulations of MW-like galaxies show a low expected scatter of [Mg/Fe] in low-mass disrupted dwarf galaxies (Hirai et al. 2022), which would make detecting the similarities difficult.

Taking the available evidence as a whole, informed by the work in the current paper, we propose that most of the CEMP stars in Group II CDTGs (primarily CEMP-no stars) are formed from rapidly rotating, high-mass stars or the ejecta of various SNe, while stars in Group I CDTGs (primarily CEMP-s stars) are formed from binary mass transfer from an evolved companion. To confirm and refine these ideas, future studies need to explore the chemical nature of CDTGs with other elements and conduct more comprehensive galaxy-formation simulations with improved modeling of CEMP star formation.

In this work, we have assembled a sample of CEMP stars with elemental abundances for a select number of species derived from moderate- to high-resolution spectroscopy. We then derived space velocities for the sample to estimate each star's dynamical parameters (E, J_r , J_ϕ , J_z ) using AGAMA. Dynamical clustering of this sample using HDBSCAN resulted in the identification of 40 CDTGs. We found CDTGs to be associated with the following MW substructures: GSE, LMS-1, Thamnos, the MWTD, the SD, and I'itoi. We only found a few CEMP CDTGs (four) to be associated with globular clusters, consistent with many previous claims of the lack of carbon-enhanced stars in these dense environments.

Finally, we separated the full sample of stars with available dynamical parameters into the CEMP morphological groups in the Yoon–Beers diagram of A(C)_c versus [Fe/H] and repeated the clustering exercise. Although the numbers of such clusters are reduced in total, the CEMP Group I CDTGs exhibit high [C/Fe]_c dispersions, leading to the interpretation that the stars in these groups (primarily CEMP-s) likely arise from local enrichment events, such as mass transfer, in environments with extended star formation. In stark contrast, the CEMP Group II CDTGs exhibit such small dispersions in [C/Fe]_c that we argue they cannot have arisen from local events but formed instead from natal gas enriched by high-mass early-generation rapidly rotating stars or SN explosions in environments that did not support extended star formation, such as low-mass satellite galaxies.

We thank an anonymous referee for comments that helped clarify our presentation. J.Z., T.C.B., D.S., D.G., Y.H., J.Y., M.M., C.P., T.P., and S.C. acknowledge partial support for this work from grant PHY 14-30152; Physics Frontier Center/JINA Center for the Evolution of the Elements (JINA-CEE), and OISE-1927130: The International Research Network for Nuclear Astrophysics (IReNA), awarded by the US National Science Foundation. Y.H. is partly supported by JSPS KAKENHI grant Nos. JP21J00153, JP20K14532, JP21H04499, JP21K03614, and JP22H01259. The work of V.M.P. is supported by NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

Here we present the tables for the initial sample of CEMP stars (Table 11) and the final sample of CEMP stars (Table 12). The full tables are available only in machine-readable format.

Table 11. Description of the Initial Sample of CEMP Stars

Column	Field	Unit	Description
1	Name	⋯	The name of the star as given by the reference
2	Source ID	⋯	The Gaia EDR3 Source ID of the star
3	RA	(J2000)	The R.A. of the star given in hours:minutes:seconds
4	DEC	(J2000)	The decl. of the star given in degrees:minutes:seconds
5	Vmag	⋯	The V magnitude of the star as given by the Vmag reference
6	Gmag	⋯	The Gaia G mean magnitude of the star as given by the Gaia Source ID
7	GBP − GRP	⋯	The Gaia BP − RP color mean magnitude of the star as given by the Gaia Source ID
8	Vmag (Gaia)	⋯	The V magnitude of the star as determined by the transformations from G mag to V mag
			using V = G + 0.02704 − 0.01424 ∗ (BP − RP) + 0.2156 ∗ (BP − RP)2 −
			0.01426(BP − RP)3 given by Riello et al. (2021)
9	RV	(km s−1)	The radial velocity as given by the RV reference
10	Error	(km s−1)	The radial velocity error as given by RV reference
11	RVGaia	(km s−1)	The radial velocity as given by the Gaia Source ID
12	Error	(km s−1)	The radial-velocity error as given by the Gaia Source ID
13	Parallax	(mas)	The parallax as given by the Gaia Source ID
14	Error	(mas)	The parallax error as given by the Gaia Source ID
15	Distance	(kpc)	The inverse parallax distance (1/Parallax)
16	Error	(kpc)	The inverse parallax distance error (Parallaxerror/(Parallax2))
19	Relative Error	⋯	The relative error of the corrected distance as given by Gaia
20	Distance BJ21	(kpc)	The 50th percentile distance as given by Bailer-Jones et al. (2021) based on the Gaia Source ID
21	Error	(kpc)	The 50th percentile error as estimated by the 84th percentile distance and the 16th percentile
			distance as given by Bailer-Jones et al. (2021) based on the Gaia Source ID ((dist84-dist16)/2)
22	RelativeError	⋯	The relative error of the 50 percentile distance as given by Bailer-Jones et al. (2021) based on
			the Gaia Source ID
23	Distance StarHorse	(kpc)	The 50 percentile distance as given by Anders et al. (2022) based on the Gaia Source ID
24	Error	(kpc)	The 50 percentile error as estimated by the 84 percentile distance and the 16 percentile
			distance as given by Anders et al. (2022) based on the Gaia Source ID ((dist84-dist16)/2)
25	Relative Error	⋯	The relative error of the 50 percentile distance as given by Anders et al. (2022) based on the
			Gaia Source ID
26	PMRA	(mas yr−1)	The proper motion in the R.A. as given by the Gaia Source ID
27	Error	(mas yr−1)	The proper motion error in the R.A. as given by the Gaia Source ID
28	PMDEC	(mas yr−1)	The proper motion in the decl. as given by the Gaia Source ID
29	Error	(mas yr−1)	The proper motion error in the decl. as given by the Gaia Source ID
30	Correlation Coefficient	⋯	The correlation coefficient between the proper motion in R.A. and the proper
			motion in decl. as given by the Gaia Source ID
31	Teff	(K)	The effective temperature of the star as given by the reference
32	log g	(cgs)	The surface gravity of the star as given by the reference
33	[Fe/H]	⋯	The metallicity of the star as given by (log (Fe)–log (Fe)⊙)
			(solar value of 7.5 taken from Asplund et al. 2009)
34	log (Fe)	⋯	The logarithmic iron abundance of the star as given by the reference
35	[C/Fe]	⋯	The carbon-abundance ratio of the star as given by (log (C)–log
			(C)⊙–[Fe/H]) (solar value of 8.43 taken from Asplund et al. 2009)
36	log (C)	⋯	The logarithmic carbon abundance of the star as given by the reference
37	[C/Fe]c	⋯	The carbon-abundance ratio corrected for evolutionary effects from Placco et al. (2014)
38	ACc	⋯	The absolute carbon corrected for evolutionary effects from Placco et al. (2014) ([C/Fe]c
			+ [Fe/H] + log (C)⊙) (solar value of 8.43 taken from Asplund et al. 2009)
39	CARDET	⋯	Flag with "D" if the carbon-abundance ratio ([C/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
40	[Mg/Fe]	⋯	The magnesium-abundance ratio of the star as given by (log (Mg)–log
			(Mg)⊙–[Fe/H]) (solar value of 7.60 taken from Asplund et al. 2009)
41	log (Mg)	⋯	The logarithmic magnesium abundance of the star as given by the reference
42	MAGDET	⋯	Flag with "D" if the magnesium-abundance ratio ([Mg/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
43	[Sr/Fe]	⋯	The strontium abundance ratio of the star as given by (log (Sr)–log
			(Sr)⊙–[Fe/H]) (solar value of 2.87 taken from Asplund et al. 2009)
44	log (Sr)	⋯	The logarithmic strontium abundance of the star as given by the reference
45	STRDET	⋯	Flag with "D" if the strontium abundance ratio ([Sr/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
46	[Y/Fe]	⋯	The yttrium abundance ratio of the star as given by (log (Y)–log
			(Y)⊙–[Fe/H]) (solar value of 2.21 taken from Asplund et al. 2009)
47	log (Y)	⋯	The logarithmic yttrium abundance of the star as given by the reference
48	YTTDET	⋯	Flag with "D" if the yttrium abundance ratio ([Y/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
49	[Ba/Fe]	⋯	The barium abundance ratio of the star as given by (log (Ba)–log
			(Ba)⊙–[Fe/H]) (solar value of 2.18 taken from Asplund et al. 2009)
50	log (Ba)	⋯	The logarithmic barium abundance of the star as given by the reference
51	BARDET	⋯	Flag with "D" if the barium abundance ratio ([Ba/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
52	[Eu/Fe]	⋯	The europium abundance ratio of the star as given by (log (Eu)–log
			(Eu)⊙–[Fe/H]) (solar value of 0.52 taken from Asplund et al. 2009)
53	log (Eu)	⋯	The logarithmic europium abundance of the star as given by the reference
54	EURDET	⋯	Flag with "D" if the europium abundance ratio ([Eu/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by reference
55	Class	⋯	The class for the star, as given by Table 1
56	Reference	⋯	The reference for the star
57	Vmag Reference	⋯	The reference for the V magnitude of the star
58	Distance AGAMA	⋯	The reference for the distance used in AGAMA (StarHorse prioritized over BJ21 unless
			StarHorse distance has a relative error greater than 0.3, if both have a relative error greater
			than 0.3 we adopt no distance estimate)

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 12. Description of the Final Sample

Column	Field	Unit	Description
1	Name	⋯	The name of the star as given by the reference
2	Source ID	⋯	The Gaia EDR3 Source ID of the star
3	RA	(J2000)	The R.A. of the star given in hours:minutes:seconds
4	DEC	(J2000)	The decl. of the star given in degrees:minutes:seconds
5	Vmag	⋯	The V magnitude of the star as given by the Vmag reference
6	Gmag	⋯	The Gaia G mean magnitude of the star as given by the Gaia Source ID
7	GBP − GRP	⋯	The Gaia BP − RP color mean magnitude of the star as given by the Gaia Source ID
8	Vmag (Gaia)	⋯	The V magnitude of the star as determined by the transformations from G mag to
			V mag using V=G + 0.02704 − 0.01424 ∗ (BP − RP) + 0.2156 ∗ (BP − RP)2 −
			0.01426(BP − RP)3 given by Riello et al. (2021)
9	RV	(km s−1)	The radial velocity as given by the RV reference
10	Error	(km s−1)	The radial-velocity error as given by the RV reference
11	RVGaia	(km s−1)	The radial velocity as given by the Gaia Source ID
12	Error	(km s−1)	The radial-velocity error as given by the Gaia Source ID
13	Parallax	(mas)	The parallax as given by the Gaia Source ID
14	Error	(mas)	The parallax error as given by the Gaia Source ID
15	Distance	(kpc)	The inverse parallax distance (1/Parallax)
16	Error	(kpc)	The inverse parallax distance error (Parallaxerror/(Parallax2))
17	Relative Error	⋯	The relative error of the corrected distance as given by Gaia
18	Distance BJ21	(kpc)	The 50 percentile distance as given by Bailer-Jones et al. (2021) based on
			the Gaia Source ID
19	Error	(kpc)	The 50 percentile error as estimated by the 84 percentile distance and the 16
			percentile distance as given by Bailer-Jones et al. (2021) based on the Gaia Source ID
			((dist84-dist16)/2)
20	Relative Error	⋯	The relative error of the 50 percentile distance as given by Bailer-Jones et al. (2021)
			based on the Gaia Source ID
21	Distance StarHorse	(kpc)	The 50 percentile distance as given by Anders et al. (2022) based on the Gaia Source ID
22	Error	(kpc)	The 50 percentile error as estimated by the 84 percentile distance and the 16 percentile
			distance as given by Anders et al. (2022) based on the Gaia Source ID ((dist84-dist16)/2)
23	Relative Error	⋯	The relative error of the 50 percentile distance as given by Anders et al. (2022) based on
			the Gaia Source ID
24	PMR.A.	(mas yr−1)	The proper motion in the R.A. as given by the Gaia Source ID
25	Error	(mas yr−1)	The proper motion error in the R.A. as given by the Gaia Source ID
26	PMdecl.	(mas yr−1)	The proper motion in the decl. as given by the Gaia Source ID
27	Error	(mas yr−1)	The proper motion error in the decl. as given by the Gaia Source ID
28	Correlation Coefficient	⋯	The correlation coefficient between the
			proper motion in R.A. and the proper motion
			in decl. as given by the Gaia Source ID
29	Teff	(K)	The effective temperature of the star as given by the reference
30	log g	(cgs)	The surface gravity of the star as given by the reference
31	[Fe/H]	⋯	The metallicity of the star as given by (log (Fe)–log (Fe)⊙)
			(solar value of 7.5 taken from Asplund et al. 2009)
32	log (Fe)	⋯	The logarithmic iron abundance of the star as given by the reference
33	[C/Fe]	⋯	The carbon-abundance ratio of the star as given by (log (C)–log
			(C)⊙–[Fe/H]) (solar value of 8.43 taken from Asplund et al. 2009)
34	log (C)	⋯	The logarithmic carbon abundance of the star as given by the reference
35	[C/Fe]c	⋯	The carbon-abundance ratio corrected for evolutionary effects from Placco et al. (2014)
36	ACc	⋯	The absolute carbon corrected for evolutionary effects from Placco et al. (2014) ([C/Fe]c
			+ [Fe/H] + log (C)⊙) (solar value of 8.43 taken from Asplund et al. 2009)
37	CARDET	⋯	Flag with "D" if the carbon-abundance ratio ([C/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
38	[Mg/Fe]	⋯	The magnesium-abundance ratio of the star as given by (log (Mg)–log
			(Mg)⊙–[Fe/H]) (solar value of 7.60 taken from Asplund et al. 2009)
39	log (Mg)	⋯	The logarithmic magnesium abundance of the star as given by the reference
40	MAGDET	⋯	Flag with "D" if the magnesium-abundance ratio ([Mg/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
41	[Sr/Fe]	⋯	The strontium abundance ratio of the star as given by (log (Sr)–log
			(Sr)⊙–[Fe/H]) (solar value of 2.87 taken from Asplund et al. 2009)
42	log (Sr)	⋯	The logarithmic strontium abundance of the star as given by the reference
43	STRDET	⋯	Flag with "D" if the strontium abundance ratio ([Sr/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
44	[Y/Fe]	⋯	The yttrium abundance ratio of the star as given by (log (Y)–log
			(Y)⊙–[Fe/H]) (solar value of 2.21 taken from Asplund et al. 2009)
45	log (Y)	⋯	The logarithmic yttrium abundance of the star as given by the reference
46	YTTDET	⋯	Flag with "D" if the yttrium abundance ratio ([Y/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
47	[Ba/Fe]	⋯	The barium abundance ratio of the star as given by (log (Ba)–log
			(Ba)⊙–[Fe/H]) (solar value of 2.18 taken from Asplund et al. 2009)
48	log(Ba)	⋯	The logarithmic barium abundance of the star as given by the reference
49	BARDET	⋯	Flag with "D" if the barium abundance ratio ([Ba/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
50	[Eu/Fe]	⋯	The europium abundance ratio of the star as given by (log (Eu)–log
			(Eu)⊙–[Fe/H]) (solar value of 0.52 taken from Asplund et al. 2009)
51	log (Eu)	⋯	The logarithmic europium abundance of the star as given by the reference
52	EURDET	⋯	Flag with "D" if the europium abundance ratio ([Eu/Fe]) is detected by the reference and "U"
			if an upper limit by the reference and "L" if a lower limit by the reference and "X" if none is
			detected by the reference
53	Class	⋯	The class for the star, as given by Table 1
54	Reference	⋯	The reference for the star
55	Vmag Reference	⋯	The reference for the V magnitude of the star
56	Distance AGAMA	⋯	The reference for the distance used in AGAMA (StarHorse prioritized over BJ21 unless
			StarHorse distance has a relative error greater than 0.3, if both have a relative error greater
			than 0.3 we adopt no distance estimate)
57	(vr, vϕ , vz)	(km s−1)	The cylindrical velocities of the star as given by AGAMA
58	Error	(km s−1)	The cylindrical velocity errors of the star as given by Monte Carlo sampling through AGAMA
59	(Jr, Jϕ , Jz)	(kpc km s−1)	The cylindrical actions of the star as given by AGAMA
60	Error	(kpc km s−1)	The cylindrical action errors of the star as given by Monte Carlo sampling through AGAMA
61	Energy	(km2 s−2)	The orbital energy of the star as given by AGAMA
62	Error	(km2 s−2)	The orbital energy error of the star as given by Monte Carlo sampling through AGAMA
63	rperi	(kpc)	The Galactic pericentric distance of the star as given by AGAMA
64	Error	(kpc)	The Galactic pericentric distance error of the star as given by Monte Carlo sampling through
			AGAMA
65	rapo	(kpc)	The Galactic apocentric distance of the star as given by AGAMA
66	Error	(kpc)	The Galactic apocentric distance error of the star as given by Monte Carlo
			sampling through AGAMA
67	${Z}_{\max }$	(kpc)	The maximum height above the Galactic plane of the star as given by AGAMA
68	Error	(kpc)	The maximum height above the Galactic plane error of the star as given by Monte Carlo
			sampling through AGAMA
69	Eccentricity	⋯	The eccentricity of the star given by (rapo − rperi)/(rapo +
			rperi) through AGAMA
70	Error	⋯	The eccentricity error of the star as given by Monte Carlo sampling through AGAMA

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset images: 1 2

We show the results obtained for the Group I CDTGs (Table 13), their dynamical parameters (Table 14), and the means, dispersions, and IQRs of the CDTGs (Table 15). Similar tables for the Group II CDTGs are provided in Tables 16–18, respectively.

Table 14. Group I Cluster Dynamical Parameters Determined by AGAMA

Cluster	N Stars	(〈vr 〉, 〈vϕ 〉, 〈vz 〉)	(〈Jr 〉, 〈Jϕ 〉, 〈Jz 〉)	〈E〉	〈ecc〉
		(${\sigma }_{\langle {v}_{r}\rangle }$, ${\sigma }_{\langle {v}_{\phi }\rangle }$, ${\sigma }_{\langle {v}_{z}\rangle }$)	(${\sigma }_{\langle {J}_{r}\rangle }$, ${\sigma }_{\langle {J}_{\phi }\rangle }$, ${\sigma }_{\langle {J}_{z}\rangle }$)	σ〈E〉	σ〈ecc〉
		(km s−1)	(kpc km s−1)	(105 km2 s−2)
CDTG-1-GI	11	(−22.4, −93.1, 8.4)	(286.4, −634.0, 84.8)	−1.805	0.61
		(86.1, 32.4, 56.4)	(132.1, 197.4, 26.6)	0.035	0.13
CDTG-2-GI	8	(9.9, 155.4, 12.4)	(184.6, 1280.6, 69.5)	−1.648	0.42
		(84.4, 19.5, 46.6)	(61.3, 62.0, 38.6)	0.029	0.07
CDTG-3-GI	7	(−17.9, 82.1, −19.7)	(392.9, 686.7, 116.0)	−1.723	0.67
		(87.8, 17.6, 43.1)	(38.9, 73.8, 40.0)	0.026	0.03
CDTG-4-GI	6	(12.3, 73.9, −133.1)	(197.1, 648.9, 563.0)	−1.630	0.47
		(34.3, 1.6, 13.3)	(50.1, 92.5, 116.6)	0.060	0.04
CDTG-5-GI	6	(−10.2, 188.8, −8.9)	(31.8, 1543.6, 40.6)	−1.641	0.17
		(16.1, 2.3, 30.9)	(6.0, 48.5, 30.2)	0.027	0.02
CDTG-6-GI	6	(61.5, 40.2, −25.7)	(417.0, 221.0, 1338.0)	−1.441	0.50
		(163.0, 65.8, 165.9)	(259.5, 191.1, 140.4)	0.063	0.13
CDTG-7-GI	5	(−56.6, −137.3, −129.6)	(168.9, −918.9, 826.6)	−1.482	0.38
		(87.5, 48.7, 67.9)	(131.5, 170.5, 43.4)	0.006	0.14
CDTG-8-GI	5	(−16.0, 45.8, 30.6)	(448.1, 373.5, 96.8)	−1.799	0.78
		(77.7, 4.8, 43.2)	(23.3, 85.5, 20.6)	0.011	0.04
CDTG-9-GI	5	(−66.1, 18.4, 56.8)	(211.7, 130.2, 2001.7)	−1.308	0.32
		(127.8, 38.2, 291.2)	(257.9, 327.0, 30.3)	0.019	0.17
CDTG-10-GI	4	(−21.2, 18.5, −97.6)	(828.2, 121.9, 233.3)	−1.597	0.94
		(178.8, 5.7, 84.8)	(62.9, 32.2, 24.8)	0.027	0.01
CDTG-11-GI	4	(−4.1, 245.7, 13.0)	(57.9, 2028.9, 42.9)	−1.496	0.20
		(55.3, 18.4, 29.1)	(6.7, 76.8, 31.0)	0.012	0.02
CDTG-12-GI	4	(−100.5, −21.6, 81.1)	(1195.5, −244.1, 683.1)	−1.338	0.89
		(128.5, 0.7, 137.7)	(94.2, 170.4, 72.5)	0.039	0.04
CDTG-13-GI	4	(−12.1, 13.1, −67.9)	(491.5, 96.7, 232.5)	−1.789	0.92
		(52.3, 12.6, 38.1)	(23.2, 93.2, 23.1)	0.024	0.05
CDTG-14-GI	3	(−51.7, −27.2, −1.2)	(1234.7, −322.1, 97.5)	−1.449	0.92
		(164.9, 6.9, 32.9)	(85.5, 70.6, 24.0)	0.038	0.02
CDTG-15-GI	3	(−8.3, 63.5, −38.5)	(306.6, 405.4, 90.8)	−1.881	0.71
		(60.7, 6.3, 48.7)	(22.9, 39.8, 30.8)	0.020	0.05
CDTG-16-GI	3	(87.5, 32.5, −11.8)	(614.9, 299.5, 204.5)	−1.669	0.86
		(26.3, 14.0, 84.7)	(18.2, 155.8, 13.2)	0.037	0.07

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Table 17. Group II Cluster Dynamical Parameters Determined by AGAMA

Cluster	N Stars	(〈vr 〉, 〈vϕ 〉, 〈vz 〉)	(〈Jr 〉, 〈Jϕ 〉, 〈Jz 〉)	〈E〉	〈ecc〉
		(${\sigma }_{\langle {v}_{r}\rangle }$, ${\sigma }_{\langle {v}_{\phi }\rangle }$, ${\sigma }_{\langle {v}_{z}\rangle }$)	(${\sigma }_{\langle {J}_{r}\rangle }$, ${\sigma }_{\langle {J}_{\phi }\rangle }$, ${\sigma }_{\langle {J}_{z}\rangle }$)	σ〈E〉	σ〈ecc〉
		(km s−1)	(kpc km s−1)	(105 km2 s−2)
CDTG-1-GII	10	(−17.0, 88.7, 1.6)	(230.6, 587.7, 262.0)	−1.754	0.57
		(86.2, 26.2, 82.4)	(95.1, 66.3, 97.0)	0.069	0.09
CDTG-2-GII	8	(−60.2, −49.4, 166.6)	(309.5, −323.5, 641.9)	−1.691	0.61
		(84.6, 36.8, 28.4)	(69.3, 242.8, 37.9)	0.093	0.10
CDTG-3-GII	4	(−33.5, 64.4, 6.4)	(406.1, 542.0, 63.7)	−1.771	0.72
		(14.6, 10.3, 60.8)	(23.0, 85.1, 42.9)	0.020	0.04
CDTG-4-GII	4	(−20.8, 44.9, −10.9)	(613.8, 354.4, 66.7)	−1.728	0.83
		(135.8, 7.9, 14.1)	(71.6, 41.1, 68.7)	0.021	0.01
CDTG-5-GII	4	(0.4, 169.3, −45.9)	(76.3, 1314.0, 80.8)	−1.649	0.25
		(1.3, 19.9, 13.1)	(59.8, 65.5, 33.5)	0.009	0.11
CDTG-6-GII	3	(−25.3, 19.5, −20.7)	(569.7, 146.3, 46.6)	−1.829	0.90
		(59.1, 7.8, 48.5)	(40.9, 58.8, 19.7)	0.012	0.06
CDTG-7-GII	3	(5.0, 45.8, 14.2)	(775.0, 425.4, 102.9)	−1.600	0.83
		(151.5, 7.1, 52.6)	(46.8, 29.4, 42.3)	0.044	0.02
CDTG-8-GII	3	(17.6, 125.8, 20.0)	(343.9, 1182.7, 66.3)	−1.595	0.53
		(97.2, 4.2, 39.8)	(40.6, 114.6, 47.9)	0.028	0.03
CDTG-9-GII	3	(−82.1, 124.4, −83.6)	(396.7, 610.2, 902.0)	−1.475	0.55
		(85.6, 40.8, 109.0)	(94.2, 185.1, 52.5)	0.035	0.05

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