Dynamically Tagged Groups of Very Metal-poor Halo Stars from the HK and Hamburg/ESO Surveys

Beginning almost fifty years ago with the pioneering work of Bond (1970, 1980) and Bidelman & MacConnell (1973), photographic objective-prism techniques have proven to be efficient sieves for identifying large numbers of stars that are metal deficient (and/or chemically peculiar). These efforts were expanded by the HK survey¹⁶ (Beers et al. 1985, 1992), and later by the HES survey (Christlieb et al. 2008), which included fainter stars, making it possible to explore deeper into the Galactic halo, where more metal-poor stars have been found. Both surveys sought to identify such stars via visual (HK) or automated (HES) inspection of the prism plates, searching for stars with weak, or absent, Ca ii K lines in their very low-resolution (R = λ/Δλ ∼ 300) spectra.

Over the past three decades, the metal-poor candidates identified in these surveys have been followed-up with medium-resolution (1200 ≲ R ≲ 2000) spectroscopy with a wide variety of telescopes and instruments. The typical spectral coverage of these spectra are 3500–5000 Å, although there was wide variation. The decisions as to which targets to observe are difficult to quantify, since many observers contributed to these efforts. In addition, in some cases, photometric information from independent efforts (HK), or taken directly from an approximate calibration of the prism spectra (HES), were obtained in advance of the spectroscopic follow-up. A complete description of the HK and HES candidate selection can be found in Beers et al. (1985, 1992) and Christlieb et al. (2008), respectively.

Metallicity ([Fe/H]) estimates were originally obtained by application of a number of techniques, initially based solely on the indices tracking the equivalent width of the Ca ii K line, as a function of measured or estimated color (often B − V; see Beers et al. 1990b). Later, techniques designed to obtain estimates of the carbonicity ([C/Fe]), based on the strength of the CH G-band feature at ∼4330 Å, were developed (see, e.g., Rossi et al. 2005; Placco et al. 2010, 2011, and references therein). Further refinements, including approaches to avoid difficulties involving the saturation of Ca ii K indexes at higher metallicities and/or lower temperatures were incorporated (see, e.g., Beers et al. 1999; Rossi et al. 2005). Many of these same techniques were used as the starting point for more modern pipelines used for similar medium-resolution spectra from SDSS (Lee et al. 2008a, 2008b) and LAMOST (Xiang et al. 2015).

One of the primary drivers for these endeavors was to develop lists of vetted VMP stars that served as input targets for large-scale high-resolution spectroscopic follow-up campaigns involving astronomers worldwide (e.g., the "Extremely Metal-poor Stars" program of Norris et al., e.g., Norris et al. 1996; the "First Stars" program of Cayrel et al., e.g., Hill et al. 2002; Cayrel et al. 2004; the CEMP stars follow-up program by Aoki et al., e.g., Aoki et al. 2007; the "Zero-Z" program of Cohen et al., e.g., Cohen et al. 2008). For almost two decades, the HK/HES surveys were responsible for the discovery of the majority of stars known with [Fe/H] < −3.0 (see Frebel et al. 2006; Placco et al. 2011; Roederer et al. 2014), including the first hyper metal-poor ([Fe/H] < −5.0) stars found in the Galactic halo (Christlieb et al. 2002; Frebel et al. 2005).

As the determinations of [Fe/H] (and [C/Fe]) for the HK/HES medium-resolution spectra were acquired over many years (some including photometric information, some not), with a variety of instruments and calibrations, for our present purpose, it is necessary to perform a homogeneous re-analysis. Of course, we now have available multiple new techniques, photometry, and high-resolution calibrations that can be brought to bear on this effort.

All estimates of stellar atmospheric parameters for our stars have been obtained by application of the n-SSPP pipeline (Beers et al. 2014, 2017), a modified version of the SEGUE Stellar Parameter Pipeline (SSPP; Lee et al. 2008a, 2008b, 2011, 2013). The n-SSPP is a compilation of routines that utilizes spectroscopic and photometric inputs to perform various estimates of the stellar parameters. It employs χ² minimization between the analyzed spectra and a dense grid of synthetic ones, as well as other techniques, where suitable, depending on the wavelength coverage of the input. Then, the best set of values is adopted. See also Placco et al. (2018, 2019) for recent applications of these methods to low-metallicity stars observed with a variety of instruments. The errors for effective temperatures (T_eff) and surface gravity ($\mathrm{log}g$) values are ±150 K and ±0.35 dex, respectively. The adopted solar abundances are from Asplund et al. (2009). The typical uncertainty for estimates of [Fe/H] and [C/Fe] is ±0.15–0.25 dex, depending on T_eff and signal-to-noise ratio. Comparisons between the metallicity and carbonicity values from the n-SSPP and those from high-resolution spectroscopy are published in Placco et al. (2014a); they are quite compatible (at the 1σ level).

The RVs have been measured with the line-by-line and cross-correlation techniques (Beers et al. 1999, 2014, 2017) and are precise to 10–15 km s⁻¹. Figure 2 shows the comparison between our measured RVs and those from Gaia DR2 (when available). The shaded areas represent the 1σ and 2σ ranges, where σ is the biweight scale (Beers et al. 1990a). This metric is more suitable, since the distribution of residuals is affected by occasional outliers. Many of the larger differences are likely due to the presence of binary systems or problems with the wavelength calibration of the medium-resolution spectra for individual stars. We remove any stars residing outside this 2σ region from our analysis, whenever Gaia RVs are available for comparison. Even though other sources of RVs are usable for part (∼20%) of our sample, we have decided to retain these directly measured values in order to preserve the homogeneity of our uncertainties, and avoid introducing unnecessary biases.

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To construct our initial sample, we first remove apparent white dwarfs or other warm objects, such as subdwarf B stars, spectra with clear Ca ii K-line core emission features, or spectral defects in the wavelength region of the Ca ii K/H lines (3900 Å–4000 Å). For objects with more than a single observation, we adopt the median of the estimated metallicities. We then exclude anything bluer than the main-sequence turnoff by limiting our sample to T_eff < 7000 K. Note that this temperature cutoff still includes a number of halo blue stragglers and horizontal-branch stars. Finally, we have selected objects with [Fe/H] ≤ −1.8, as these will include VMP stars within the expected error bars on the metallicity estimates. We refer to all of these stars below as VMP stars. This results in a total initial sample of 4443 VMP stars.

Note that the initial sample includes a small fraction (∼15%) of stars—primarily used for parameter calibration and/or short lists of candidate halo stars from other samples—that were observed with the same resolving power and wavelength coverage as the HK/HES stars during the course of the main follow-up effort (see Figure 3). These other small samples include data from: (i) Beers et al. (2001), comprising cooler stars from the Edinburgh-Cape Blue Object Survey (indicated by the prefix "EC" in our sample); (ii) Beers et al. (2002), comprising candidate metal-poor stars identified close to the Galactic plane in the Luminous Stars Extension survey (identified with the prefix "LSE" in our sample); (iii) Rhee (2001), comprising metal-poor candidates (primarily cooler giants) identified from digital scans of the HK survey plates with the Automatic Plate Machine facility in Cambridge, UK (Rhee et al. 1999), known as the HK II survey (identified with the prefix "II" in our sample); (iv) Frebel et al. (2006; see also Beers et al. 2017), comprising bright metal-poor candidates from the HES plates; and (v) Beers et al. (2014), comprising metal-poor candidates selected by Bidelman & MacConnell (1973; see also Norris et al. 1985). For simplicity of notation, we refer to the full sample as the VMP HK/HES sample (listed in Appendix A.1; Table 5).

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We cross-match the VMP HK/HES sample with Gaia DR2 to obtain accurate proper motions, where available. We combine these data with distances from Anders et al. (2019), estimated with the StarHorse code (Queiroz et al. 2018, 2020) in a Bayesian framework. The 50th percentile of these distance distributions are compatible with the inverse of the Gaia parallaxes within 2–3 kpc from the Sun, but can be used when the reported Gaia parallax is either negative or missing. Finally, we have restricted our sample to stars with relative distance errors smaller than 20% of their nominal values, assuming Gaussian distributions according to its 16th and 84th percentiles. This cut yields heliocentric distances ≲5 kpc (Figure 3), with few exceptions. Out of these stars, the vast majority (∼97%) have re-normalized unit weight errors within the recommended interval (RUWE < 1.4; Lindegren et al. 2018), which can be used to obtain reliable dynamical-parameter estimates.

We have adopted a velocity of the local standard of rest (LSR) of V_LSR = 232.8 km s⁻¹ (McMillan 2017), and a peculiar motion of the Sun with respect to the LSR of (U,V,W)_⊙ = (11.1,12.24,7.25) km s⁻¹ (Schönrich et al. 2010). Then, the position on the sky, distance, proper motions, and RVs of the stars are converted to the Cartesian Galactic phase-space positions and velocities using Astropy Python tools (Astropy Collaboration et al. 2013, 2018). Finally, we have made a cut in velocity, $| V-{V}_{\mathrm{LSR}}| \gt 210$ km s⁻¹, to primarily retain stars from the halo. Applying this criterion leaves a final sample of 1540 likely VMP HK/HES halo stars with data suitable for dynamical analysis (these are listed, along with the adopted dynamical parameters, in Appendix A.2; Table 6).

For the mapping of RPE stars onto our DTGs, carried out in Section 7, we have adopted the recent compilation of r-I and r-II stars from Gudin et al. (2020). The majority of these objects come from the R-Process Alliance data releases (Hansen et al. 2018; Sakari et al. 2018; Ezzeddine et al. 2020; Holmbeck et al. 2020), complemented with additional data from JINAbase (Abohalima & Frebel 2018). These stars are all metal-poor ([Fe/H] < −1.0) and at least moderately enriched in r-process elements ([Eu/Fe] > +0.3; [Ba/Eu] < 0.0). We do not apply the [Fe/H] ≤ −1.8 cut since these stars are already chemically peculiar, independently of their metallicities. For consistency, we have used the same kinematic criteria described in Section 2.3, but keeping stars with relative distance errors up to 30%, which avoids constraining our sample too much. These larger errors in distances lead to increasing uncertainties in the dynamical parameters. However, since we employ a statistical method for the cluster assignment, such errors will propagate into smaller membership probabilities, which we independently evaluate (Section 4). Our more rigorous selection yielded a total sample of 305 RPE stars for dynamical analyses.

The identification of DTGs was carried out using the clustering algorithm Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN;¹⁸ Campello et al. 2015), implemented in Python by McInnes et al. (2017).

HDBSCAN has been developed to work with an initially unknown total number of groups, having variable shapes and density contrasts. Another important feature is that HDBSCAN is robust in the presence of noisy data; there is no dependence on the underlying assumption of smooth background models in energy-action space that past works relied upon to deal with this challenge. It is also convenient that the fundamental hyper-parameter that HDBSCAN requires to operate is the minimum number of elements to form a valid group (min_cluster_size), which is physically meaningful.

HDBSCAN constructs a hierarchical cluster tree based on the estimated local densities for each point in the multidimensional parameter space. Two points are considered connected if they form a dense region in this parameter space. The clusters are likely to be real if they are persistent for different density thresholds, from very low to very high. These can be interpreted as persistent clusters (with a min_cluster_size) with less-likely members falling out of them as they move through the hierarchical tree. This exercise ensures that the resulting groups are very stable.

We have chosen min_cluster_size = 5 and cluster_selection_method = "leaf" as input parameters in order to build the cluster hierarchy tree. This choice, in particular the "leaf" mode, is optimized for the detection of fine-grained substructures in favor of larger ones. After testing with the algorithm, we have noticed that the overall behavior of the groups does not change significantly with min_cluster_size. Essentially, smaller clumps are erased when this parameter is increased, as expected. Therefore, we have avoided smaller values for the min_cluster_size, as that could lead to an unrealistic number of groups. We have also avoided values that are too large, as that would not be in keeping with our objective of finding small groups that could have originated from low-mass systems. The larger substructures in our data can still be mapped out following the execution of the procedure, assembled from the smaller, robust ones (Section 5). This choice is also consistent with the work of both Yuan et al. (2020b) and Myeong et al. (2018a), who accepted groups containing at least four and five members, respectively, making our study comparable to theirs. Again, we note that the clusters are built exclusively from the VMP sample. The RPE stars are mapped onto the groups only after the cluster assignment has already been completed.

Although we expect clusters identified by HDBSCAN to be quite stable, we still need to assess the statistical significance of the groups against variations in the dynamical properties of each member star due to their estimated uncertainties. We have sampled 1000 sets of (E, J_R, J_ϕ, J_z) from the 16th and 84th percentiles of each quantity for each star in a Monte Carlo framework. Then, we throw these perturbed data sets back into the hierarchical tree, and re-evaluate their cluster assignments. An object is considered a valid member of a given group if it was assigned at least 200 times to the same cluster out of the 1000 Monte Carlo realizations. We take this to indicate that the star presents at least a 20% membership probability. We define the confidence level of a given group (see Table 1) as the average membership probability of its member stars.

Application of this method results in the identification of 38 significant DTGs,¹⁹ comprising ∼400 stars (27% of the final sample). The characteristics of each DTG are listed in Table 1, and are represented with different symbols in Figure 5. Those with qualitatively similar dynamical properties are shown with similar colors. The number of stars in each dynamical group ranges from 5 to 30. The one with the highest confidence level is DTG-10 (94%). The DTGs with the lowest confidence are DTG-12 and DTG-23, both at 39%. Just over half (23/38; 60%) are retrograde ($\langle {J}_{\phi }\rangle \lt 0$). We compare our results to those from the literature and further discuss the nature of our DTGs in Sections 5 and 6.

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The structure known as GSE has been suggested to be the remnant of the last large-scale merging event experienced by the Galaxy (Belokurov et al. 2018; Haywood et al. 2018; Helmi et al. 2018), containing the majority of the accreted stars in the nearby halo. Its members form a well-defined sequence in the color–magnitude diagram presented in Gaia Collaboration et al. (2018b) for stars with halo-like kinematics. They also exhibit typically low metallicities ([Fe/H] ≲ −0.7; Di Matteo et al. 2019) and α-element abundance ratios (Hayes et al. 2018; Mackereth et al. 2019; also noted earlier on by Nissen & Schuster 2010). These stars are distinguishable in velocity space, as they form an extended distribution in v_R (velocity toward the radial direction of the cylindrical coordinate system) around an azimuthal velocity (v_ϕ) close to zero (Koppelman et al. 2018; Feuillet et al. 2020), which translates into highly eccentric orbits (Naidu et al. 2020). Moreover, stars from the GSE progenitor are usually old (≳10 Gyr; Gallart et al. 2019; Bonaca et al. 2020), and its (proposed) globular clusters form a tight age–metallicity relation (Myeong et al. 2018b, 2019; Massari et al. 2019; Kruijssen et al. 2020).

In order to identify potential members of GSE among our DTGs, we establish that these groups must display $\langle e\rangle \geqslant 0.8$ (see Figure 6). This criterion is similar to that of Naidu et al. (2020) and Bonaca et al. (2020). These authors have shown that stars in this range of e compose a well-behaved, strongly peaked metallicity distribution. The requirement that e ≥ 0.8 had already been suggested by Myeong et al. (2018b), who considered the distribution of globular clusters and halo stars in action space, and Mackereth et al. (2019), who analyzed the α-element abundance ratios of such high-eccentricity stars. In total, 13 of our DTGs (comprising 173 stars; Table 2) can be attributed to GSE (blue circles in the top row of Figure 5). Application of this selection yields a mean radial action $\langle {J}_{R}\rangle \gtrsim 450$ kpc km s⁻¹ for each associated group. Additionally, our selected groups are contained within $-600\lesssim \langle {J}_{\phi }\rangle$ (kpc km s⁻¹) < +500 (similar to Feuillet et al. 2020). The dynamical nature of GSE can be visualized in the projected action-space diagram shown in Figure 6 (top panel).

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Table 2.  Larger Substructures in the VMP HK/HES Sample

Substructure	Associated DTGs	Members	$\langle E\rangle$	($\langle {J}_{R}\rangle ,\langle {J}_{\phi }\rangle ,\langle {J}_{z}\rangle$)	$\langle e\rangle$	$\langle i\rangle$	($\langle {v}_{R}\rangle$, $\langle {v}_{\phi }\rangle$, $\langle {v}_{z}\rangle$)	Median [Fe/H]
			σE	(${\sigma }_{{J}_{R}}$, ${\sigma }_{{J}_{\phi }}$, ${\sigma }_{{J}_{z}}$)	σe	σi	(${\sigma }_{{v}_{R}}$, ${\sigma }_{{v}_{\phi }}$, ${\sigma }_{{v}_{z}}$)	MAD[Fe/H]
			(km2 s−2)	(kpc km s−1)		(deg)	(km s−1)	(dex)
GSE	11,20,21,23,24,28,29,	173	−1.7 × 105	(826,−108 , 57)	0.90	103	(−7, −14, 2)	−2.2
	30,34,35,36,37,38		1.4 × 104	(318, 229, 39)	0.05	39	(162, 28, 49)	0.3
Sequoia	1,5	19	−1.2 × 105	(916, −2496, 111)	0.54	163	0, −301, −39)	−2.2
			1.5 × 104	(576, 389, 73)	0.14	6	(150, 44, 83)	0.4
HStr	3	18	−1.3 × 105	(321, 1153, 1210)	0.40	62	(−46, 144, −198)	−2.3
			3.3 × 103	(132, 134, 183)	0.08	3	(98, 16, 167)	0.5
Thamnos	25,26,31,32,33	53	−1.7 × 105	(200, −1066, 59)	0.44	159	(−4, −136, 6)	−2.2
			5.7 × 103	(99, 276, 41)	0.14	10	(70, 36, 55)	0.3

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The GSE substructure, as we have defined it, presents stars with orbital inclinations ($i={\cos }^{-1}\left({L}_{z}/L\right)$, where L_z is the vertical component of the total angular momentum, L) spanning all possible values. In the i versus e space, it shows a "boomerang-like" shape in the top panel of Figure 6, concentrated toward high values of e. This substructure presents characteristic v_ϕ and v_R that overlap with those from the SD (Bonaca et al. 2017; Di Matteo et al. 2019; Belokurov et al. 2020; An & Beers 2020; Amarante et al. 2020a, 2020b). However, the average metallicity of the SD is $\langle$[Fe/H]$\rangle$ ≈ −0.5. Since our stars are all VMP, we expect minimal contamination from this source.

The velocity space of GSE is shown in Figure 7. As previously mentioned, this substructure presents an almost null net rotation with small dispersion ($\langle {v}_{\phi }\rangle \approx -14$ km s⁻¹; ${\sigma }_{{v}_{\phi }}=28$ km s⁻¹). An interesting feature is that our velocity distribution in the radial direction is continuous, occupying $-300\lt \langle {v}_{R}\rangle$ (km s⁻¹) < +300. This is very similar to the aforementioned characteristically huge spread in v_R presented by Belokurov et al. (2018) and others since (e.g., Koppelman et al. 2018 and Feuillet et al. 2020). The importance of GSE to the halo is further examined in Section 7.

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Speculation that a substantial, strongly retrograde merger event could have contributed stars to the Galactic halo began to appear many years ago (Norris & Ryan 1989; Carollo et al. 2007, 2010; Beers et al. 2012). Further evidence came with the discovery of the massive globular cluster FSR 1758 (Cantat-Gaudin et al. 2018; Barbá et al. 2019). Myeong et al. (2018c) revealed an excess of stars with highly energetic, very retrograde orbits in the Galactic halo with metallicities of −1.9 < [Fe/H] < −1.3. Building on that, Myeong et al. (2018d) discovered a profusion of small dynamical groups of stars in this region of the (E, J_ϕ) space (and called them Rg1-4 and Rg6).

Based on the above, Myeong et al. (2019) argued that this population of stars originated from a merger event they referred to as Sequoia. These authors also claimed that a dynamically cohesive group of globular clusters (including FSR 1758) were associated to Rg1-4 and Rg6. So far, other independent analyses recognized additional Sequoia debris (Koppelman et al. 2019a; Massari et al. 2019; Matsuno et al. 2019; Dietz et al. 2020; Yuan et al. 2020b, 2020a; Monty et al. 2020; Naidu et al. 2020).

Among our dynamical groups, DTG-1 and DTG-5 (comprising a total of 19 stars, with a high confidence level, ∼75%) can be readily identified as part of the Sequoia remnant. These DTGs have $\langle E\rangle =-1.2\times {10}^{5}$ km² s² and $\langle {J}_{\phi }\rangle \approx -2500$ kpc km s⁻¹, so they are well within the interval established by Myeong et al. (2019). DTG-1 and DTG-5 also spread through many different values of J_R (in line with Myeong et al. 2018d), and exhibit low average vertical action: $\langle {J}_{z}\rangle \,\approx 145$ kpc km s⁻¹. We revisit the Sequoia event, and its possible connection to RPE stars, in Section 7.

The Helmi Stream (HStr) was one of the first dynamical groups to be found. Helmi et al. (1999) analyzed astrometric data of a small sample of metal-poor ([Fe/H] < −1.6) stars from the Hipparcos Catalog (Perryman et al. 1997), and found that some of these were significantly clumped in angular-momentum space. Further members were added by Chiba & Beers (2000) and other works since (e.g., Koppelman et al. 2018; Myeong et al. 2018a). One distinguishing aspect of this stream is that the majority of its members exhibit negative v_z, although some have positive v_z. This feature has been interpreted as the partially phase-mixed fragments of a (now) shredded satellite (Helmi 2008). The discovery of such a group, with apparently disconnected blobs in velocity space, is a demonstration of the power of searches in the integrals-of-motion space. More recent studies have focused on the chemical aspects of this substructure (Roederer et al. 2010; Aguado et al. 2020), confirming its ancient nature from its low typical metallicity (−3.0 ≲ [Fe/H] ≲ −1.5), its profile in [α/Fe] (with a "knee" at [Fe/H] ≈ −2.0), and predominance of the r-process contribution to the enrichment of neutron-capture elements ([Sr/Ba] ≲ 0.0) in the low-metallicity regime. However, the complicated story of the HStr and its progenitor is still under scrutiny (and debate; see, e.g., Koppelman et al. 2019b), and its characterization is far from being complete.

Inspection of the first row of Figure 5 allows for the immediate association of one of our larger (18 stars) and high-confidence (88%) dynamical groups (DTG-3) with the HStr. This connection is in agreement with the selection criteria delineated by Koppelman et al. (2019b). Independent efforts converge on an azimuthal velocity of $\langle {v}_{\phi }\rangle \approx 150$ km s⁻¹ for this stream (Beers et al. 2017; Gaia Collaboration et al. 2018c; Koppelman et al. 2018; Myeong et al. 2018a), which is compatible with our findings ($\langle {v}_{\phi }\rangle =144$ km s⁻¹; ${\sigma }_{{v}_{\phi }}\,=16$ km s⁻¹). Crucially, our DTG-3 has members that are detached in the vertical component of velocity (upper right panel of Figure 7), with the great majority presenting v_z < 0, which is expected for the canonical HStr. The potential enrichment of the HStr members in neutron-capture elements via the r-process is further explored in Section 7.

Koppelman et al. (2019a) suggested that another substantial, very retrograde substructure exists in the Galactic halo, which they named Thamnos. It resides in the same corner region in the projected action-space map as Sequoia (Figure 6, top panel). However, there is a marked difference in orbital energy between Thamnos and Sequoia (upper left pane of Figure 5). The Thamnos event can be described, then, as a low-energy counterpart of Sequoia. These authors further suggested that this substructure could possibly be divided into two pieces, Thamnos 1 (Th. 1), highly retrograde and with lower metallicity, and Thamnos 2 (Th. 2), moderately retrograde and more metal-rich.

From our analysis, a total of five dynamical groups could be associated with this substructure, two of them with Th. 1 (DTG-25 and DTG-26) and the other three with Th. 2 (DTG-31, DTG-32, and DTG-33). Since Th. 1 and Th. 2 have been proposed to share the same progenitor, we present them as a single cohesive substructure (orange hexagons; top row of Figure 5). Thamnos can be differentiated from GSE as having predominantly retrograde motion ($\langle i\rangle \approx 160^\circ ;$ $\langle {J}_{\phi }\rangle \approx -1000$ kpc km s⁻¹) and lower eccentricity ($\langle e\rangle =0.44;$ $\langle {J}_{R}\rangle \approx 200$ kpc km s⁻¹). These values are in agreement with the limits independently proposed by Naidu et al. (2020).

We note that the proliferation of small dynamical groups of stars in the low-energy, highly retrograde corner of the (E, J_ϕ) space has also been pointed out by Yuan et al. (2020b) in their own inspection of a VMP sample (their ZY20:DTG-21/24/29; see their Figure 6). Their DTGs are also comparable to ours in J_R and J_z. It is possible that many (if not all) of the groups reported by both works are pieces of the same larger substructure. This hypothesis is attractive, since it has been shown that Thamnos has a metallicity distribution that preferentially occupies the VMP regime (Koppelman et al. 2019a; Helmi 2020; Naidu et al. 2020). Thus, it would be natural to find it from examination of VMP stellar samples.

Our findings corroborate the claims that Sequoia and Thamnos are well separated in their binding energies, as can be seen from the upper left panel of Figure 5. If one were to assume that they originated from the same merger event, it would imply that the progenitor was at least as massive as that of GSE, in conflict with their lower metallicities. For the purpose of confirming the nature of these substructures, one requires not only reliable metallicities, but other chemical abundances, especially of the α-elements, in order to explore their chemical-evolution and star formation histories. It is clear from the ongoing discussions about Sequoia/Thamnos in the literature just how difficult it is to disentangle the formation history of the Galactic halo in terms of its clumps, streams, over-densities, and their respective progenitors.

Besides the HStr (DTG-3), other dynamical groups stand out from the rest as having predominantly polar orbits (Table 3). One of these is DTG-2 (sky-blue hexagons; second row of Figure 5). This DTG has been segregated from the rest of the polar groups as it exhibits $\langle {J}_{R}\rangle \gt \langle {J}_{\phi }\rangle ;$ it has eight members and a high confidence level (87%). One of the distinctive features of DTG-2 can be appreciated from its distribution in velocity space (Figure 7). Much like the HStr, we notice that this group is split into two blobs of v_z, one positive and one negative. We note that this DTG exhibits the highest absolute value of vertical velocity ($\left|{v}_{z}\right|\approx 300$ km s⁻¹) out of our groups. This DTG might also be a fragmented piece of the low-mass stellar-debris stream LMS-1 (Wukong), recently discovered by Yuan et al. (2020a). These authors also argued that this substructure would be reasonably metal-poor ([Fe/H] ≲ −1.5), in keeping with our VMP selection. Further discussion on the nature of DTG-2 is presented in Section 7.

Table 3.  New DTGs in the VMP HK/HES Sample and Their Likely Associations

DTG	Association	Members	$\langle E\rangle$	($\langle {J}_{R}\rangle$, $\langle {J}_{\phi }\rangle$, $\langle {J}_{z}\rangle$)	$\langle e\rangle$	$\langle i\rangle$	($\langle {v}_{R}\rangle$, $\langle {v}_{\phi }\rangle$, $\langle {v}_{z}\rangle$)	Median [Fe/H]
			σE	(${\sigma }_{{J}_{R}}$, ${\sigma }_{{J}_{\phi }}$, ${\sigma }_{{J}_{z}}$)	σe	σi	(${\sigma }_{{v}_{R}}$, ${\sigma }_{{v}_{\phi }}$, ${\sigma }_{{v}_{z}}$)	MAD[Fe/H]
			(km2 s−2)	(kpc km s−1)		(deg)	(km s−1)	(dex)
2	Newa	8	−1.3 × 105	(690, 293, 1878)	0.57	83	(52, 35, 74)	−2.4
			5.7 × 103	(277, 189, 102)	0.05	4	(158, 19, 292)	0.4
4	New	8	−1.5 × 105	(85, 330, 1535)	0.23	80	(−19, 46, −44)	−2.5
			2.8 × 103	(89, 122, 110)	0.13	3	(104, 13, 237)	0.4
8	ZY20:DTG-35	14	−1.6 × 105	(173, 361, 1039)	0.40	77	(−11, 48, 51)	−2.5
			3.7 × 103	(110, 106, 99)	0.12	4	(102, 14, 192)	0.4
9	New	7	−1.6 × 105	(93, 25, 1299)	0.32	89	(−28, 3, 139)	−2.2
			2.7 × 103	(63, 80, 66)	0.09	3	(77, 10, 145)	0.2
13	ZY20:DTG-39	6	−1.7 × 105	(299, 159, 709)	0.62	82	(16, 20, 88)	−2.3
			1.7 × 103	(82, 68, 70)	0.08	3	(65, 9, 114)	0.5
6	Rg5	6	−1.5 × 105	(82, −1046, 787)	0.23	123	(−75, −140, −126)	−2.7
			2.7 × 103	(67, 60, 41)	0.11	2	(58, 30, 152)	0.3
7	New	7	−1.5 × 105	(644, −500, 471)	0.75	115	(−37, −62, −54)	−2.5
			4.2 × 103	(118, 54, 45)	0.04	4	(200, 9, 134)	0.4
12	New	6	−1.5 × 105	(576, −868, 285)	0.66	134	(−43, −108, 112)	−2.3
			3.7 × 103	(191, 62, 84)	0.09	6	(204, 14, 53)	0.4
14	New	11	−1.7 × 105	(370, −326, 431)	0.70	109	(6, −41, 18)	−2.4
			1.4 × 103	(78, 101, 61)	0.07	7	(51, 14, 126)	0.4
16	ZY20:DTG-33	5	−1.6 × 105	(161, −683, 482)	0.44	120	(−12, −83, −40)	−2.4
			1.8 × 103	(84, 94, 73)	0.11	3	(41, 15, 154)	0.3
18	ZY20:DTG-33	8	−1.7 × 105	(473, −450, 278)	0.73	119	(−31, −64, −69)	−2.2
			2.1 × 103	(60, 82, 35)	0.05	6	(149, 30, 58)	0.2
19	New	6	−1.6 × 105	(339, −1108, 209)	0.53	143	(85, −133, −2)	−2.4
			1.9 × 103	(52, 58, 14)	0.04	2	(104, 11, 130)	0.6
22	ZY20:DTG-33	7	−1.7 × 105	(353, −780, 297)	0.59	131	(−40, −111, −34)	−2.2
			1.2 × 103	(62, 65, 28)	0.04	5	(156, 34, 110)	0.4
10	New	5	−1.4 × 105	(701, 1496, 46)	0.64	13	(134, 182, −19)	−2.1
			1.5 × 103	(86, 80, 43)	0.03	6	(192, 20, 26)	0.2
15	New	6	−1.5 × 105	(555, 1110, 146)	0.63	34	(68, 140, 34)	−2.2
			3.5 × 103	(92, 55, 43)	0.03	5	(203, 15, 102)	0.2
27	ZY20:DTG-19	13	−1.7 × 105	(617, 590, 25)	0.77	26	(−16, 73, −17)	−2.2
			8.3 × 102	(47, 62, 12)	0.03	10	(171, 8, 40)	0.2
17	New	18	−1.7 × 105	(223, 577, 545)	0.51	64	(7, 4, 0)	−2.3
			2.7 × 103	(47, 63, 58)	0.05	2	(94, 18, 145)	0.4

Note. The DTGs are ordered by their numbers, but are kept grouped according to their qualitatively similar dynamical properties, as in Section 6.

^aTentative association with other reported substructure (Section 6.1).

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The remaining polar groups are DTG-4/8/9/13 (green symbols; bottom row of Figure 5). They are also mildly prograde (v_ϕ ≈ +50 km s⁻¹; Figure 7), and present characteristically low radial actions ($\langle {J}_{R}\rangle \leqslant 300$ kpc km s⁻¹; Figure 6). Out of these, DTG-8 and DTG-13 could be readily associated with ZY20:DTG-35 and ZY20:DTG-39 from Yuan et al. (2020b), respectively. These authors also identified many prograde polar groups. Future studies might reveal if this excess of polar VMP clumps could be the debris of a larger substructure or a superposition of individual small accreted systems.

Some of our DTGs have been classified as being predominantly prograde (Table 3). Three of these are DTG-10/15/27 (red triangles; bottom row of Figure 5). The orbits of their member stars lie close to the Galactic plane ($\langle {J}_{z}\rangle \,\lesssim 150$ kpc km s⁻¹; Figure 6), and exhibit moderate average eccentricities ($\langle e\rangle \geqslant 0.6;$ Figure 6). All of these groups are also distinguishable from their kinematics; they present negative and positive blobs in v_R (Figure 7). However, DTG-10 and DTG-15 are rotating much faster around the Galactic center ($\langle {v}_{\phi }\rangle \gtrsim +140$ km s⁻¹; $\langle {J}_{\phi }\rangle \gtrsim +1100$ kpc km s⁻¹) than DTG-27 ($\langle {v}_{\phi }\rangle \approx +70$ km s⁻¹; $\langle {J}_{\phi }\rangle \approx +600$ kpc km s⁻¹). The rotational motions of DTG-10/15 are compatible with the value suggested for the MWTD (Carollo et al. 2019; An & Beers 2020). Comparison with both Carollo et al. (2014) and Beers et al. (2014) also points to similarities in (E, J_ϕ), but the Galactic gravitational-potential model used by these authors is different from ours, so this should be taken with caution. In addition, our kinematic cut (Section 2.3) should yield minimal contamination from stellar populations with disk-like orbits.

The more modest rotation of DTG-27 makes it overlap with both the SD and ZY20:DTG-19 (Yuan et al. 2020b) in v_ϕ and v_R. In Section 5.1, we argued that stars from the SD should represent only a minor contamination in our VMP sample, since its metallicity is $\langle$[Fe/H]$\rangle \approx -0.5$. Indeed, these objects should not affect our definition of a large substructure such as GSE, but they could produce a small clump like DTG-27. The recent demonstration that a meaningful population of extremely and ultra-metal-poor stars ([Fe/H] ≤ −3.0 and ≤−4.0, respectively) permeates the Galactic thin and thick disks (Sestito et al. 2019, 2020; Di Matteo et al. 2020) underscores the possibility that these VMP stars could have acquired halo kinematics from dynamical heating mechanisms. The nature of DTG-27 is further discussed in Section 7.

The final prograde DTG out of our dynamical groups is DTG-17. Its stars are represented as yellow diamonds in the second row of Figure 5. This is a new group with 18 members (67% confidence). Considering kinematics, this DTG is similar to the green polar groups (DTG-4/8/9/13; Section 6.1). However, since its $\langle {J}_{\phi }\rangle \gt \langle {J}_{z}\rangle$, we present it as a predominantly prograde one. We note that Yuan et al. (2020b) also found some DTGs in this region of the energy-action space (see their Figure 6). Detailed chemical abundances from future spectroscopic efforts might hint at the origin of this excess of prograde VMP dynamical groups.

The majority of our new DTGs have retrograde orbits, many of which can be attributed to either Sequoia (Section 5.2) or Thamnos (Section 5.4). However, a total of eight dynamical groups are apparently unrelated to any of these better-known substructures (Table 3). The first of these is DTG-6 (orange diamonds; bottom row of Figure 5). Its stars are very retrograde ($\langle {J}_{\phi }\rangle \approx -1000$ kpc km s⁻¹), but exhibit moderate energy ($\langle E\rangle \approx -1.5\times {10}^{5}$ km² s²). This DTG occupies the same region as the Rg5 substructure proposed by Myeong et al. (2018d), and is likely associated with it. A more in-depth examination of DTG-6/Rg5 is presented in Section 7.

The remaining retrograde DTGs are presented as purple symbols in the middle row of Figure 5. These are DTG-7/12/14/16/18/19/22. We note that this large set of DTGs occupies an intermediate region of the (E, J_ϕ) space, between GSE and Thamnos. Therefore, it is difficult to disentangle their origins from dynamics alone. For instance, DTG-7 and DTG-12 have mean radial actions in the range of GSE ($\langle {J}_{R}\rangle \,\gtrsim 500$ kpc km s⁻¹), but their large values of vertical and retrograde motions, respectively, make them incompatible with this larger substructure. We revisit DTG-7 in Section 7. A similarly large set of VMP dynamical groups has already been reported by Yuan et al. (2020b). Among these, ZY20:DTG-33 strongly overlaps with three of our own DTGs (DTG-16, DTG-18, and DTG-22). Apparently, this region of the energy-action space is preferentially occupied by VMP stellar clumps; other searches, without [Fe/H] selection cuts, failed to recognize any cohesive substructures occupying it. Nevertheless, we are in urgent need of chemical-abundance information (e.g., α-elements) for the members of these DTGs in order to test whether or not these might be the remnants of low-mass system(s) that merged into the Galaxy.

Table 5 provides the relevant information for the initial sample (Section 2), as well as their derived atmospheric parameters, including metallicity (in the form of [Fe/H]) and carbonicity ([C/Fe]). We note that a small fraction (∼3%) of these stars are quite cool and carbon enhanced, with T_eff ≤ 4500 K and [C/Fe] (and/or [C/Fe]_c) ≥ +0.7. Caution is urged when considering the listed values of [Fe/H], [C/Fe], and [C/Fe]_c for these stars, due to the presence of "carbon-veiling" in cooler CEMP stars, which depresses the continuum in the region of the Ca ii K line that has a dominant influence on the metallicity estimation (see discussion in Yoon et al. 2020). These effects can be mitigated by application of procedures similar to those described in Yoon et al., which are currently being refined, and will be employed for the present data in the near future.

The first column of the table lists the 2MASS (Skrutskie et al. 2006) names, when available. The second and third columns list the HK and HES names. Other names for stars that do not appear in 2MASS or the HK and/or HES surveys are provided in the fourth column. The V-band magnitude is listed as well, based on information reported in the literature, supplemented, where needed, with transformed values from Gaia DR2 photometry (Evans et al. 2018), or estimated from the HES prism plates.

Table 6 provides the stars contained in the final sample (Section 2). The measured RVs (corrected to the heliocentric frame) from the medium-resolution spectroscopy are listed, along with the Gaia DR2 values, where available. The StarHorse distance estimates and their relative errors are from Anders et al. (2019), as described in Section 2.3. Proper motions are taken from Gaia Collaboration et al. (2018a). The primary derived dynamical properties used in our analysis (Section 3) are also listed.