Dynamical Relics of the Ancient Galactic Halo

We employ the neural-network-based clustering method StarGO (Yuan et al. 2018) to find substructures that are clustered in energy and integrals of motion space. We calculate the orbital energy in the gravitational potential of McMillan (2017) using AGAMA (Vasiliev 2019). The energy (E) and components of the angular momentum (L_x, L_y, L_z) are approximately conserved, even if the potential is not spherical (e.g., Helmi & de Zeeuw 2000). Specifically, a network of 100 × 100 neurons are trained by the VMP halo catalog in the (E, L, θ, ϕ) space, where

$$\begin{eqnarray}&&\theta =\arccos ({L}_{z}/L),\quad \quad \phi =\arctan ({L}_{x}/{L}_{y}).\end{eqnarray} \tag{ 1 }$$

We briefly summarize the neural-network learning process and group identification procedure below; a more detailed description is available in Yuan et al. (2019).

Each grid point of the map shown in the middle panel of Figure 1 hosts a neuron, which has a weight vector with the same dimension as the input vector. The values for all the weight vectors are initially randomized. For any given star from the sample, we find the neuron having the closest weight vector to its input vector. This neuron is referred to as its best-matching unit (BMU). The unsupervised learning is performed by updating the weight vector of every neuron of the map closer to the input vector of the given star. The learning effectiveness of each neuron depends on its distance from the BMU on the map. The neighboring neurons of the BMU learn more effectively by updating their weight vectors much closer to the input vector compared to neurons located farther away. All the neurons change their weight vectors from the previous values for every input star. One iteration finishes after all the stars are input into the neural network once. After a sufficient number of iterations, the weight vectors converge and the final map becomes self-organized. Therefore, the entire learning process is called a self-organizing map. The difference in weight vectors between neighboring neurons is defined as u. The trained neural network can be quantified by a 100 × 100 matrix of u_mtx. The distribution of all the elements of the matrix is shown in the left panel of Figure 1.

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In the middle panel of Figure 1, we highlight neurons with u < u_16% and u < u_40% with yellow and light blue, respectively. They represent neurons that, judged by similarity, lie in the top 16% and 40%, respectively. For comparison, neurons with u > u_80% are colored gray; these have similarities in weight vectors that lie in the bottom 20%. The different sets of neurons are associated with stars having correspondingly similar or dissimilar features in the input space. The most prominent structure revealed by the trained neuron map is the nearly diagonal boundary. Most of the neurons with high similarities (the yellow and light-blue patches) reside in the lower left and upper right corners separated by the gray boundary line. Neurons in these two regions correspond to stars with negative and positive ϕ, which is the azimuthal phase angle of angular momentum (see the first row of Figure 2). Stars in the region of low absolute values of θ (inclination angle of the angular momentum) are clearly separated into two sets, depending on their values of ϕ. The angular momenta of these stars are in nearly opposite directions; thus, their BMUs sit on opposite sides of the nearly diagonal boundary line. Those stars with high absolute values of θ are close in angular momentum directions; they are found in the upper region of the neuron map in the top left panel of Figure 2.

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Besides the diagonal boundary line, we can also see that the boundaries separate several white patches into isolated islands (see the upper left corner in the middle panel of Figure 1). Neurons in the islands have more similar weight vectors compared to those in their surroundings. We take a slice of the neuron map at ${y}_{\mathrm{map}}=72$, shown as the blue line, and plot the values of u along the grid point of x_map in the right panel of Figure 1. We fill the area above the curve with u < u_16% and u < u_40% with yellow and light blue, respectively. These regions represent the range of x_map of the slice crossing the colored patches of the neuron map. Similarly, the area under the curve with u > u_80% is filled with gray, denoting the range of the slice in the gray region. The red horizontal line shows the defined boundary at u_80%. As can be seen, the isolated islands containing both light-blue and yellow patches around the left edge of the map (x_map = 0, y_map ∼ 72) correspond to the deep valley in the (x_map, u) plot.

The group identification algorithm is performed by gradually decreasing the value of the defined boundary until isolated islands appear in the middle panel of Figure 1. This is equivalent to lowering the red line in the right panel until the valley is separated by gray peaks for slices from all directions across that island. Intuitively, we consider that the input data space is composed of star clusters overlapping with each other. By taking a 1D slice of the neuron map, they are shown as valleys. If the valleys have lower values of u in slices from all directions, they correspond to isolated islands in the neuron map. The goal of the group identification is to find the critical value of u that can pick out these structures. We then try to obtain the most complete member list for each group and check its significance and level of contamination for validation during the second step (see details in Section 3.2). We begin to find islands at the 90th percentile of the distribution of u, u_90%, and perform the group identification all the way to the 5th percentile, u_5%.

After the unsupervised learning process, we can map different data sets to the trained neural network by matching input vectors to the BMUs. By this means, we are able to obtain the relationship between the new data set and the trained network. The methodology of this procedure is illustrated in detail in Yuan et al. (2019), where it is used to show that the Cetus Stream is associated with the globular cluster NGC 5824. Here, we apply the same approach to map additional catalogs (APOGEE, r-process-enhanced stars, and CEMP stars) onto the trained map, as well as to quantify the significance, contamination, and confidence level of the identified groups.

The algorithm is summarized in the following steps. For a given group ${ \mathcal G }$, which has n ≥ 5 star members, extracted from the VMP sample (${ \mathcal S }$) with a total of ${ \mathcal N }$ stars, we proceed as follows:

• 1.  
  Obtain the probability density functions (pdf's) for energy E, modulus of angular momentum L, and its direction θ and ϕ by Gaussian kernel density estimation.
• 2.  
  Draw a random sample (${ \mathcal S }1$) of 5000 stars according to the pdf's from 1.
• 3.  
  Find the BMU for every star from ${ \mathcal S }1$ on the trained neuron map, and obtain the stars associated with group ${ \mathcal G }$ on the map.
• 4.  
  Calculate the 4D distance between member stars of ${ \mathcal G }$ and their BMUs. Obtain the largest distance for ${ \mathcal G }$ denoted by u_vw,max.
• 5.  
  Calculate the 4D distance between stars from ${ \mathcal S }1$ associated with ${ \mathcal G }$ and their BMUs, which is referred to as u_vw. Retain the stars with u_vw ≤ u_vw,max, n₁. Thus, the probability of the retained stars is p = n₁/5000.
• 6.  
  Calculate the binomial probability ${ \mathcal P }$ of detecting a group with more than n stars from the total sample of ${ \mathcal N }$ stars, given the probability p. If 1 – ${ \mathcal P }\geqslant 99.73 \%$, the significance of ${ \mathcal G }$ is larger than 3σ, and we consider it as a possible detected group.
• 7.  
  If ${ \mathcal G }$ is a possible detected group, we estimate the contamination fraction from ${ \mathcal S }1$, which is defined as ${{ \mathcal F }}_{c}=p/(n/{ \mathcal N })$. ${ \mathcal G }$ is considered as valid if ${{ \mathcal F }}_{c}\leqslant 40 \%$.

After obtaining all of the valid groups, the same approach is utilized to check the confidence of membership. For ${ \mathcal G }$, we first generate 100 Monte Carlo realizations for each group member and denote this sample as ${{ \mathcal S }}_{\mathrm{MC}}$. This is done by considering the observational uncertainties in the 5D astrometric parameters together with the covariance matrix, as well as the uncertainty in radial velocity. Applying steps 1–5 to ${{ \mathcal S }}_{\mathrm{MC}}$, we obtain the probability (p_MC) of the Monte Carlo realizations that are associated with ${ \mathcal G }$, which quantifies the confidence level of a given group member. The overall confidence level of ${ \mathcal G }$ is estimated by averaging p_MC for all the members, as listed in Table 1. For example, DTG-52 has the lowest confidence level, 39%, among all the groups. This value means that its groups members have a 39% chance, on average, to be identified as members of DTG-52, taking into account the observational errors.

Table 1.  VMP Groups

uthr	${ \mathcal G }$	n	${{ \mathcal F }}_{{\rm{c}}}$	Confidence	Substructure
u1(90th)	DTG-1	9	0%	85%	Helmi? (vz > 0)
u2(84th)	DTG-2	8	0%	82%	Cand14?
u3(80th)	DTG-3	38	1%	94%	Helmi (vz < 0)
	DTG-4	20	37%	98%	Sequoia
	DTG-5	6	0%	87%	Sequoia
	DTG-6	8	8%	92%	Rg5
u4(70th)	DTG-7	8	25%	69%	Sausage
	DTG-8	7	19%	78%	New, Polar
u5(65th)	DTG-9	9	33%	68%	Sausage
u6(57th)	DTG-10	5	0%	70%	Rg5
	DTG-11	15	0%	91%	Cand10?
	DTG-12	7	19%	91%	Sausage
	DTG-13	15	22%	99%	Sausage
	DTG-14	10	13%	81%	Sausage
	DTG-15	7	9%	78%	New, Polar
u7(50th)	DTG-16	5	0%	80%	Sausage
	DTG-17	7	8%	58%	Sausage
	DTG-18	16	16%	66%	Sausage
u8(45th)	DTG-19	25	28%	86%	New, Pg
u9(40th)	DTG-20	4	13%	66%	Sausage
	DTG-21	44	33%	93%	New, Rg
	DTG-22	27	29%	94%	New, Rg
	DTG-23	7	19%	79%	Rg5
	DTG-24	6	11%	77%	New, Rg
u10(30th)	DTG-25	6	22%	71%	Sausage
	DTG-26	9	22%	90%	Sausage
	DTG-27	13	31%	79%	Sausage
	DTG-28	20	16%	95%	New, Rg
uthr	${ \mathcal G }$	n	${{ \mathcal F }}_{{\rm{c}}}$	Confidence	Substructure
u10(30th)	DTG-29	74	35%	93%	New, Rg
	DTG-30	15	26%	86%	Sausage
	DTG-31	25	24%	95%	Sausage
	DTG-32	14	14%	81%	Sausage
	DTG-33	37	25%	88%	New, Rg
u11(20th)	DTG-34	8	0%	83%	New, Polar
	DTG-35	11	6%	85%	New, Polar
	DTG-36	8	8%	82%	New, Polar
	DTG-37	5	13%	65%	Sausage
	DTG-38	171	31%	93%	Sausage
	DTG-39	8	22%	97%	New, Polar
	DTG-40	17	18%	82%	Sausage
	DTG-41	22	9%	94%	Sausage
	DTG-42	11	12%	84%	Sausage
u12(10th)	DTG-43	8	14%	84%	New, Polar
	DTG-44	14	9%	87%	New, Polar
	DTG-45	25	15%	85%	New, Polar
	DTG-46	25	10%	90%	Sausage
	DTG-47	9	26%	87%	Sausage
	DTG-48	14	17%	88%	Sausage
	DTG-49	5	0%	91%	Sausage
	DTG-50	18	11%	74%	Sausage
	DTG-51	7	8%	68%	New, Polar
	DTG-52	4	0%	39%	Rg5
	DTG-53	5	11%	56%	Rg5
	DTG-54	4	0%	97%	New, Polar
	DTG-55	9	22%	82%	Sausage
	DTG-56	5	0%	89%	Sausage
u13(5th)	DTG-57	17	3%	80%	Sausage

Note. The values of u_thr denoted by the percentiles in the brackets are listed in the first column. For each group ${ \mathcal G }$, n is the number of valid members, ${{ \mathcal F }}_{{\rm{c}}}$ denotes the contamination fraction, and the confidence level is defined in Section 3.2. New groups are classified into retrograde (Rg), polar, and prograde (Pg). Two groups may be associated with candidate groups found by Myeong et al. (2018a).

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Adopting the same approach, the trained neuron map enables us to find the associated group members from the APOGEE halo sample, as well as from the r-process-enhanced star and CEMP star catalogs. Similarly, we generate 1000 Monte Carlo realizations for each star in a new sample and apply steps 1–5 to that. We obtain the probability (p_APOGEE, p_r, and p_CEMP) of the Monte Carlo realizations that are associated with ${ \mathcal G }$. We consider the star to be a valid member of ${ \mathcal G }$ if its probability is greater than 25%.

The progenitor of the Gaia Sausage is believed to be very substantial, possibly comparable in mass to the Large Magellanic Cloud (Belokurov et al. 2018). For example, there are up to ∼20 potential globular clusters showing typical chemodynamical characteristics of the Gaia Sausage (Myeong et al. 2018b, 2019). The detritus of the Gaia Sausage extends out to galactocentric radii of ∼30 kpc (Iorio & Belokurov 2019), which corresponds to the break radius in the stellar halo. Deason et al. (2013) predicted that the break radius was the apocentric pileup caused by the early accretion of a massive satellite, and this was subsequently confirmed to be the Gaia Sausage in Deason et al. (2018). Evidence from the break radius in the relative age profile, as determined from BHB photometry (Whitten et al. 2019), also supports the idea that the inner halo is formed through a few prominent mergers, particularly the Gaia Sausage event. The progenitor galaxy has been wholly destroyed, yet it is still only partially phase mixed in the inner halo, with clouds, shells, and feathers associated with its dismemberment. With such an enormous progenitor, we expect our algorithm to identify substructures within the Gaia Sausage, as well as detritus flung out of the nascent Milky Way disk by its impact.

At 10 different threshold values of u_thr, we find 27 DTGs of 498 stars (see Table 2), all of which have high eccentricities ($\langle e\rangle \gtrsim 0.7$) and little or no net rotational velocity. We associate DTGs with the Gaia Sausage if they additionally have large radial motions with $\langle {J}_{{\rm{R}}}\rangle \gt 500$ kpc km s⁻¹ and small $\langle {J}_{{\rm{z}}}\rangle \ \lt$ 500 kpc km s⁻¹. This yields the blue groups shown in Figures 4 and 6. Although some other DTGs may have high-eccentricity members with e ≈ 0.7, we are able to distinguish them from the Gaia Sausage groups based on the action constraints. There are comparable numbers of DTGs that have slightly prograde and retrograde orbits, consistent with the almost head-on encounter originally postulated in Belokurov et al. (2018). These DTGs also have different orbital energies, from −2 × 10⁵ to −1.3 × 10⁵ km² s⁻², consistent with different pieces of the debris from a single, almost radial merger event.

We check the members of the Gaia Sausage groups from APOGEE data, shown as the blue diamonds in Figure 7. They clearly separate into two groupings in the metallicity−abundance plot. The subgroups on the low-α track are from the progenitor satellite itself. Their chemistry is consistent with that of typical dwarf galaxies. Another subgroup is clustered in the high-α region, which represents the typical chemistry of the thick disk. These stars with high eccentricities and high α are probably disk stars splashed up by the Gaia Sausage merger event, evidence for which has been presented elsewhere (Di Matteo et al. 2018; Belokurov et al. 2019). Similarly, we highlight the high-eccentricity region (e ≥ 0.7) by light-blue shading in the top panel, and we plot them with the same color in the bottom panel. Just as pointed out above, these high-eccentricity stars are populated in both sequences in the metallicity−abundance plot. This is clear evidence of significant disk splash due to this major merger event. This agrees with the two α sequences of the kinematically hot halo decomposed from their distributions in color–magnitude diagrams (Gallart et al. 2019). For the low-α sequence, there appears a hint of a change in gradient at [Fe/H] = −1.3, as also seen by Mackereth et al. (2019). High-eccentricity halo stars with [Fe/H] ≳ −1.0 belong almost wholly to the high-α sequence.

The profusion of retrograde stars in the stellar halo has long been a puzzle (Carollo et al. 2007; Majewski et al. 2012). Myeong et al. (2018c) identified a series of high-significance retrograde substructures in the Gaia data, which they called Rg1 to Rg7. Subsequently, some of these (Rg1–Rg4 and Rg6) were associated with six retrograde globular clusters, including two enormous ones, FSR 1758 and ω Centauri. The latter has been suggested by multiple authors to be the core of a nucleated dwarf galaxy (Bekki & Freeman 2003; Bekki & Norris 2006; Joo & Lee 2013). This is consistent with the wreckage of another dwarf galaxy—the Sequoia—which came in on a strongly retrograde orbit, disgorging globular clusters and debris throughout the inner Galaxy (Myeong et al. 2019).

We find 13 very retrograde groups (DTG-4, DTG-5, DTG-6, DTG-10, DTG-21, DTG-22, DTG-23, DTG-24, DTG-28, DTG-29, DTG-33, DTG-52, and DTG-53), identified with six threshold values (u₃, u₆, u₉, u₁₀, u₁₁, and u₁₂). By comparing the reported substructures from Myeong et al. (2019) with the action-space map shown in Figure 4, we are able to clearly associate DTG-4 and DTG-5 with Sequoia (plotted in green symbols), which has 26 stars in total. The Sequoia groups have eccentricity e ≈ 0.5 and inclination angle i ≈ 160°. They are also highly retrograde, with $\langle {v}_{\phi }\rangle \approx -270$ km s⁻¹.

There is another slightly less retrograde substructure, Rg5, from Myeong et al. (2019), shown as red polygonal boxes in Figure 4, as well as in the top row of Figure 6. We find five groups (DTG-6, DTG-10, DTG-23, DTG-52, and DTG-53) of 33 stars, marked by magenta triangles, that have a very good match with these boxes and thus are likely associated with Rg5. In contrast to Sequoia, Rg5 has lower eccentricity (e ≈ 0.3) and inclination angle (i ≈ 120°) and is less retrograde, with $\langle {v}_{\phi }\rangle \approx -90$ km s⁻¹. Rg5 has two components of v_z, depending on the sign, which are centered at 168 and −183 km s⁻¹, respectively. Notice also that the Sequoia groups have higher orbital energy than Rg5, so the two substructures are well separated in the projected space of energy and azimuthal action.

The remaining six retrograde DTGs all have lower orbital energy than Sequoia (E ≤ −1.6 × 10⁶ km² s⁻²) but more retrograde orbits than Rg5, as shown in the (J_ϕ, E) space in the second row of Figure 6. Some of these groups may be from the same progenitor, but without chemical information it is hard to be certain. These groups are separated crudely into two sets, colored with coral and cyan, due to their differences in inclination angles, as shown in the top right panel of Figure 5. The coral groups (DTG-21, DTG-24, and DTG-29) have the same mean inclination angle (i ≈ 160°) as the Sequoia groups. The cyan groups (DTG-22, DTG-28, and DTG-33) appear to be more diffuse, with slightly lower inclination angles (i ≈ 130°–145°). The average rotational velocities of these two sets are −120 and −100 km s⁻¹, respectively. The coral groups have almost zero mean vertical velocity, whereas the cyan groups have two disjointed portions, with v_z centered at 96 and −111 km s⁻¹, respectively. Both sets partially overlap with the two retrograde substructures with slightly larger rotational velocities reported by Koppelman et al. (2019a). Both of these two sets of groups occupy the same corner region of very retrograde orbits as Sequoia in the action-space map (see the right panel of Figure 4). It is possible that some of these DTGs are the low-energy debris from Sequoia.

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We also look for the associated APOGEE members for all of the retrograde DTGs. None of the stars can be associated with Rg5, which implies that it is likely a VMP-dominated substructure (Myeong et al. 2018c, e.g.,). There are three stars (green triangles) belonging to Sequoia. Two of them have [Mg/Fe] measurements and sit in the low-α region. We find 20 members for the coral groups and 9 members for the cyan groups. There are two α-rich members for both sets, which are stars that originated from the disk. Excepting these stars, the majority are metal-poor stars with [Fe/H] < −1.0, which appear to follow the low-α sequence of a typical dwarf galaxy. However, we are not able to confirm that they follow the same track of [Mg/Fe] versus [Fe/H] from the available abundance data. Further high-resolution spectroscopic studies are crucial to verify the hypothesis that they are from the same merger event.

This is one of the earliest pieces of halo substructure to be found kinematically. Helmi et al. (1999) first discovered a stream composed of eight stars in Hipparcos data. When this was supplemented with an extended data set of metal-poor halo stars (Chiba & Beers 2000), the stream was identified as having 12 members, separated into 3 stars with positive v_z and 9 stars with negative v_z. This appeared to be a vindication of the power of searches in angular momentum space, which associated two different sets of debris in velocity space with the same substructure. Helmi (2008) later provided a simulation that showed a possible interpretation of the data as the partially phase-mixed debris of a heavily disrupted satellite. Depending on the relative location of observer to the cloud of debris, we may expect to observe the debris as two separate velocity groups.

Subsequently, Myeong et al. (2018a) rediscovered the stream in their search for substructures in velocity space using Gaia DR1 data, cross-matched with the SDSS spectroscopic survey. They labeled it S2, as its connection with the structure found by Helmi et al. (1999) was not immediately apparent. A total of 73 stars were found in a striking, well-defined, and kinematically cold stream with prominent negative v_z motion, which could correspond to the negative v_z portion of the simulation from Helmi (2008). S2 revealed a clear stream feature for the first time—the substructure was extended along the direction of its streaming motion. They fitted a model to S2 and argued that its progenitor had a total mass of ∼10⁹ M_⊙ and a stellar mass of ∼10⁶ M_⊙, making it comparable to a present-day dSph like Draco. Myeong et al. (2018c) searched for substructures in action space, and S2 was once again recovered. Since the actions can be considered as a set of integrals of motion, a group of stars with positive v_z motion (with comparable action variables) were also included as potential members in addition to the prominent negative v_z stream. However, the positive v_z portion appears more diffuse, without clear features in configuration space. The metallicity distribution function of S2 is peaked at [Fe/H] = −1.9 with a dispersion of 0.23 dex, ranging from −2.65 to −1.3 (Myeong et al. 2018c).

After Gaia DR2, Koppelman et al. (2019b) used its cross-match with APOGEE, RAVE, and LAMOST to identify more possible members. They drew a rectangular selection box in the space (${L}_{z},{L}_{\perp }=\sqrt{{L}_{x}^{2}+{L}_{y}^{2}})$ to claim nearly 600 members of the stream, although of course this includes some contaminants from other halo stars that enter the box. They argued that the metallicity distribution ranges from [Fe/H] = −2.3 to 0.0 and peaks at [Fe/H] = −1.5 (see Figure 10 of Koppelman et al. 2019b). The authors considered the stars with [Fe/H] ≳ −0.5 to be likely contaminants. Their N-body simulations favored a system with a stellar mass of ∼10⁸ M_⊙ accreted 5–8 Gyr ago. This is significantly larger than suggested by Myeong et al. (2018a). In their picture, the progenitor is a substantial dwarf galaxy, contributing approximately 15% of its mass in stars.

Based on the velocity properties of the 38 member stars of DTG-3 (see Table 2), it can be readily confirmed as the analog of S2 (Myeong et al. 2018a), similar to the negative v_z part of the simulation of Helmi (2008). On the other hand, DTG-1 (with nine stars) is a more diffuse substructure with positive v_z motion, similar to the positive v_z group mentioned above. It has slightly higher energy and a larger radial motion than DTG-3, as can be noted from the plots in the second row of Figure 6. The pole of its angular momentum vector is also reversed because of the opposite sign of v_z. There appear to be two possibilities. First, such differences could arise if DTG-1 was stripped at an earlier pericentric passage from the same progenitor as DTG-3. Alternatively, DTG-1 may have a different origin than DTG-3 entirely, in which case DTG-3 would be the residue of a less massive dwarf. High-resolution spectroscopic data should allow us to verify which of these hypotheses is more probable.

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The metallicity distribution function of this substructure can be examined here by using the map of the APOGEE halo sample onto the trained neuron network. This is shown in Figure 7, with the two possible portions of the stream represented by orange triangles and circles. From the metallicity−abundance plot, they appear to be mostly α-poor, and the metallicity distribution is truncated at [Fe/H] ≲ −1.3. The metal-rich star at [Fe/H] ≈ −0.6 is a clear contaminant, judged from its [Mg/Fe] and its orbital rotation velocity v_ϕ, which marks it as a member of the thick disk.

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Compared with the rest of the groups, DTG-2 (brown) and DTG-19 (yellow) are very prograde. Both have moderate eccentricity (e ≈ 0.6–0.8) but lowish inclinations (i ≈ 30°). They are both populated with stars having inward and outward v_R. This is typical of highly disrupted substructures, in which there may be multiple, coexisting wraps. The rotational velocity of DTG-19 is ≈80 km s⁻¹, which is characteristic of the metal-weak thick disk. The two clumps of DTG-19 with opposite v_R are centered at ≈140 and ≈−157 km s⁻¹, respectively. DTG-2 has a larger $\langle {v}_{\phi }\rangle \approx 150$ km s⁻¹, as compared to DTG-19, as well as larger radial action and higher orbital energy. Both groups are in the region close to the disk stars in the (J_ϕ, E) space. In the top row of Figure 5, as well as in the second row of Figure 6, we have plotted the substructure Candidate Group 14 from Myeong et al. (2018c) as a red polygon. The latter plots especially suggest that DTG-2 is likely the same substructure as Candidate Group 14.

Although DTG-2 and DTG-19 have lower eccentricities than the Gaia Sausage groups, they are still high compared to typical disk stars. It is difficult to trace their origins from dynamics only; thus, we look for chemical abundance information via their associated members from APOGEE. We find three candidate members associated with DTG-2 and five with DTG-19. From Figure 5, we see that these members have orbital eccentricities, around 0.6–0.8. Two of the three DTG-2 members and three of the five DTG-19 members sit in the region associated with the thick-disk system in the abundance versus metallicity plot. The other three stars from these two groups are VMP, so their abundances will have larger uncertainties. Although the sample size of APOGEE members is small, the [Mg/Fe] values of DTG-2 and DTG-19 favor the scenario that they are associated with the splashed or heated disk component arising from the Gaia Sausage merger event (Di Matteo et al. 2018; Belokurov et al. 2019).

Prograde orbits with strong radial motion match the description of the recently claimed Nyx substructures from Necib et al. (2019a, 2019b). These two streams have oppositely directed subgroups, centered on v_R at ≈156 and ≈−124 km s⁻¹, respectively, with rotational velocities of 141 and 120 km s⁻¹. The similarities between the velocities of the Nyx substructures with the two prograde DTGs suggest that they too may be aspects of the same Splashed Disk phenomenon.

The remaining groups all have relatively polar orbits. They are roughly separated into three different sets in the third row of Figure 6. The maroon group (DTG-11) has slightly higher J_z and E, whereas the orange groups and the purple groups are similar but have different signs of J_ϕ. The orange groups (DTG-8, DTG-36, DTG-44, DTG-54, and DTG-55) are slightly retrograde, while the purple groups (DTG-15, DTG-34, DTG-35, DTG-39, DTG-43, DTG-45, and DTG-51) are slightly prograde.

From velocity space, we see that DTG-11 has a prominent vertical motion, with $\langle {v}_{z}\rangle$ = 230 km s⁻¹, but almost zero rotation. It has a very polar orbit, which moves almost in the (x, z)-plane, perpendicular to the plane of the Galactic disk. The orbital inclination is about 90°, and the eccentricity is low, e ≈ 0.3. DTG-11 almost connects with the orange and purple sets. The latter two have opposite inclination angle offsets, ≈20° compared to DTG-11, and extended ranges of eccentricity. They are less polar than DTG-11, as clearly shown in Figure 5.

From the distribution of DTG-11 in action space, it probably is an associated substructure with one of the metal-poor Candidate Groups from Myeong et al. (2018c), who found a number of polar groups with low mean metallicity, such as Candidate 10 with $\langle [\mathrm{Fe}/{\rm{H}}]\rangle \approx -2.0$. Notice that all of the polar DTGs overlap with the Gaia Sausage groups in the (J_ϕ, E) space but have much more polar orbits. They may nonetheless be associated with the Gaia Sausage, but they were perhaps stripped off earlier when its orbit was less eccentric. The simulations of Amorisco (2017) show that massive satellites can lose their angular momentum to dynamical friction and gradually become more radial. The earlier stripped material may therefore have significant angular momentum, even if the final merger event is almost head-on.

From the APOGEE data, we find two members for the orange groups and 12 members for the purple groups. For both sets, half of the members reside in the low-α sequence, while the other half are in the high-α sequence. Although the metal-poor purple set appears to follow the lower-α track compared to the Gaia Sausage stars, more members with detailed abundance measurements are required to verify their origin. Similar to the retrograde groups, the α-rich members originated from the thick-disk system.

We find that four r-II stars in total are associated with two of the DTGs. CS 31082−001 and J2357−0052 are associated with DTG-10. We plot them by star symbols in dynamical space; they are seen to be well within the box of the Rg5 group from Myeong et al. (2018c) in Figures 4 and 6. Both stars have very low metallicities, [Fe/H] = −2.78 and −3.36, respectively, and stand out compared to other r-II stars. First, both stars have an extreme enhancement of r-process elements, with [Eu/Fe] = +1.65 and +1.92, respectively. These exceed the nominal criteria of [Eu/Fe] ≥ +1.0 required for r-II stars (Beers & Christlieb 2005). In fact, among extremely metal-poor stars ([Fe/H] < −3.0), SDSS J2357−0052 is currently one of the most r-process-enhanced stars known (Suda et al. 2008). CS 31082−001, on the other hand, is one of the best-studied r-II stars, with detailed abundances for 26 heavy elements beyond Sr, including the actinides Th and U. This star was the first example of a subclass of r-process-enhanced stars with Th and U abundances that are unexpectedly high, relative to Eu, referred to as "actinide-boost" stars (Hill et al. 2002). It is not currently known if SDSS J2357−0052 is also an actinide-boost star, as there is only a relatively high upper limit on [Th/Fe] (<+2.74; Aoki et al. 2010), and no measurement of U, available. Clearly, this star is of great interest for further study. Interestingly, based on the clustering of 35 highly r-process-enhanced stars with $[\mathrm{Eu}/\mathrm{Fe}]\geqslant +0.7$ in the (E, J_r, J_ϕ, J_z) space, these two stars belongs to the same Group C from Roederer et al. (2018). This is consistent with our findings that they are dynamically associated with the same substructure, Rg5.

Using the SDSS-Gaia halo sample, Myeong et al. (2018c) show that Rg5 has very low mean metallicity ([Fe/H] = −2.16). According to the universal relation between stellar mass and metallicity for dwarf galaxies from Kirby et al. (2013), the progenitor of Rg5 is likely a very low mass dwarf galaxy with stellar mass of 10³–10⁶ M_⊙, such as a UFD. Our findings of the two r-II members with extremely low metallicities also favor the scenario of a very low mass progenitor. Intriguingly, the absolute abundance of Eu in both the r-II stars in DTG-10 are identical (within 1σ) with values of $\mathrm{log}\epsilon (\mathrm{Eu})=-0.92\pm 0.19$ and −0.76 ± 0.11. This is consistent with uniform enrichment of a low-mass dwarf galaxy by a single r-process event, similar to Reticulum II (Ji et al. 2016; Roederer et al. 2016).

Two additional r-II stars, J00405260−5122491 and 2MASS J2256−0719, are found to be associated with DTG-38. Similar to DTG-10, the absolute abundances of Eu in the r-II stars are identical to each other. But unlike DTG-10, the metallicities of the r-II stars are very similar ($[\mathrm{Fe}/{\rm{H}}]\sim -2.2$), but much higher compared to DTG-10. Interestingly, the metallicities of the r-II stars in DTG-38 are similar to the typical metallicity of r-process-enhanced stars reported in classical dwarf spheroidals, such as Fornax (Letarte et al. 2010; Lemasle et al. 2014) and Draco (Cohen & Huang 2009). This is consistent with DTG-38 being the debris from a more massive system such as the Gaia Sausage.

CEMP stars are important tracers of very early nucleosynthesis and are more numerous than r-process-enhanced stars. They are frequently separated into subclasses according to their neutron-capture element abundances (Beers & Christlieb 2005). CEMP-s stars exhibit enhancements in their s-process elements, especially in Ba, and are frequently found to have radial velocity variations (Starkenburg et al. 2014; Hansen et al. 2016b). Their high C and s-process element abundances can be understood as a result of the mass transfer from an evolved binary companion. CEMP-i (formerly referred to as CEMP-r/s) stars have higher r-process-element abundances than CEMP-s stars, but they are also likely to be the result of binary interaction. Their abundance pattern is well described by neutron-capture reactions in an "intermediate" neutron density environment (Hampel et al. 2016). On the other hand, CEMP-no stars show no enhancement in their neutron-capture elements, with a clearly lower binary frequency than CEMP-s stars (Hansen et al. 2016a). Their C excess is generally attributed to nucleosynthesis pathways associated with the very first stars to be born in the universe (Iwamoto et al. 2005; Meynet et al. 2006). We are able to find nine CEMP stars associated with four existing substructures and five associated with the newly identified ones.

The Gaia Sausage groups are associated with six CEMP stars of different subclasses (CEMP-i, CEMP-s, and CEMP-no). DTG-13 hosts one CEMP-s star and one CEMP-i star. DTG-38, which is associated with two r-II stars, also has one CEMP-s and one CEMP-no star. We find one CEMP-s star in Rg5 and one in each of the five new DTGs (DTG-29, DTG-28, DTG-33, DTG-19, DTG-45). Among these CEMP-s stars, the one associated with DTG-29 is relatively metal-rich ([Fe/H] = −1.59).

Although CEMP-s stars constitute a substantial subgroup in the stellar halo (Yoon et al. 2019), only one is known in all of the dwarf galaxies (Frebel et al. 2014). No CEMP-i stars have yet been found in dwarfs. Our findings encourage the study of the birthplace of these heavy-element enriched CEMP stars in the stellar halo by tracing their dynamical origins. Overall, all the CEMP-no associated in our study are found in substructures from classical dwarf galaxies. The Helmi Stream and Sequoia have one CEMP-no star each, and the Gaia Sausage has two CEMP-no stars. Three of these four CEMP-no stars have [Fe/H] ≈ −2.0. Observationally speaking, we see more CEMP-no stars in this metallicity regime in classical dSph galaxies, compared to UFDs (see Figure 1 of Yoon et al. 2019), though this may just reflect the fact that this is the "metal-rich" tail of the MDF of UFDs.