Dynamically Tagged Groups of Metal-Poor Stars II. The Radial Velocity Experiment Data Release 6

Orbital characteristics based on Gaia Early Data Release 3 astrometric parameters are analyzed for ${\sim} 8,000$ metal-poor stars ([Fe/H] $\leq -0.8$) compiled from the RAdial Velocity Experiment (RAVE) Data Release 6. Selected as metal-poor candidates based on broadband photometry, RAVE collected moderate-resolution ($R \sim 7,500$) spectra in the region of the Ca triplet for these stars. About $20\%$ of the stars in this sample also have medium-resolution ($1,200 \lesssim R \lesssim 2,000$) validation spectra obtained over a four-year campaign from $2014$ to $2017$ with a variety of telescopes. We match the candidate stars to photometric metallicity determinations from the Huang et al. recalibration of the Sky Mapper Southern Survey Data Release 2. We obtain dynamical clusters of these stars from the orbital energy and cylindrical actions using the \HDBSCAN ~unsupervised learning algorithm. We identify $179$ Dynamically Tagged Groups (DTGs) with between $5$ and $35$ members; $67$ DTGs have at least $10$ member stars. Milky Way (MW) substructures such as Gaia-Sausage-Enceladus, the Metal-Weak Thick Disk, the Splashed Disk, Thamnos, the Helmi Stream, and LMS-1 (Wukong) are identified. Associations with MW globular clusters are determined for $10$ DTGs; no recognized MW dwarf galaxies were associated with any of our DTGs. Previously identified dynamical groups are also associated with our DTGs, with emphasis placed on their structural determination and possible new identifications. We identify chemically peculiar stars as members of several DTGs; we find $22$ DTGs that are associated with \textit{r}-process-enhanced stars. Carbon-enhanced metal-poor (CEMP) stars are identified among the targets with available spectroscopy, and we assign these to morphological groups following the approach given by Yoon et al.


INTRODUCTION
Large-scale spectroscopic surveys conducted over the last few decades have allowed the structure, assembly, and chemical-evolution history of the Milky Way (MW) to be explored in great detail (York et al. 2000;Yanny et al. 2009;Cui et al. 2012). The spectra from such surveys provide important information about stellar atmospheres, in particular their chemical abundances, an important tool for determining the origin and evolution of the elements in the stellar populations of the Galaxy. The collected spectra can also provide radial velocity measurements, which are used as one of the 6-D astrometric parameters (along with position, distance, and proper motions) to derive the orbits of stars in a selected gravitational potential.
The Radial Velocity Experiment (RAVE; Steinmetz et al. 2006) is one of the largest contributors of such information. In the newest RAVE Data Release 6 (DR6; Steinmetz et al. 2020a) there are ∼ 450, 000 unique stellar objects with radial velocities available, with 95% having an accuracy better than 4.0 km s −1 . With such a large and homogeneous set of radial velocities available, RAVE provides the opportunity to study the MW through both their dynamics and chemical compositions. One of the first uses of RAVE to study MW dynamics was by Seabroke et al. (2008), who determined that there were no vertical tidal streams asso-ciated within the Solar Neighborhood, the region surveyed by RAVE Data Release 1 (DR1; Steinmetz et al. 2006). Also using RAVE DR1, Klement et al. (2008) discovered a new radial stream, while recovering previously known streams such as the Helmi Stream (Helmi et al. 1999). The stellar parameters obtained by RAVE have allowed astronomers to discover metal-poor stars ([Fe/H] 1 −1.0), as first reported by Fulbright et al. (2010) using both DR1 and Data Release 2 (DR2; Zwitter et al. 2008). Coşkunoǧlu et al. (2011Coşkunoǧlu et al. ( , 2012, Bilir et al. (2012), Duran et al. (2013), and Karaali et al. (2014) employed kinematics and stellar parameters from RAVE to determine estimates of the Local Standard of Rest, radial and vertical metallicity gradients, and space velocity components for the thin and thick disk of the Galaxy. Antoja et al. (2012) was one of the first to probe beyond the Solar Neighborhood in search of kinematic groups using RAVE. These authors reidentified some known groups, such as Hercules, while also recovering new kinematic over-densities, revealing nonaxisymmetric groups present in the MW. Utilizing the full RAVE Data Release 4 (DR4; Kordopatis et al. 2013), Binney et al. (2014) was able to compare the kinematics of stars within 2 kpc of the Sun to dynamical models, showing remarkable consistency for the velocity components of the sample.
The advent of Gaia (Gaia Collaboration et al. 2016a) has provided proper motions and parallax-based distances for an unprecedented number of stars. Using both Gaia Data Release 1 (DR1; Gaia Collaboration et al. 2016b) and RAVE DR4, Helmi et al. (2017) argued that the stellar halo was built solely by mergers and had a dominant retrograde-velocity component. Using the same data sets, Robin et al. (2017) were able to constrain the formation histories of the thin and thick disks. Recently, Li et al. (2020) employed RAVE Data Release 5 (DR5; Kunder et al. 2017) and Gaia Data Release 2 (DR2; Gaia Collaboration et al. 2018) to discover new structures in the MW using dynamical quantities such as the orbital energy and angular momentum, which offer insight into the structures' origins.
When Galactic satellites are accreted and dispersed into the MW, the energies and dynamical actions of their member stars are expected to resemble those of their parent progenitor satellites (Helmi et al. 1999). The seminal work of Roederer et al. (2018) employed un-supervised clustering algorithms, an approach that has proven crucial to determine structures in the MW that are not revealed through large-scale statistical sampling methods. These authors were able to collect 35 chemically peculiar (r -process-enhanced) stars and determine their orbits. With these data in hand, multiple clustering tools were applied to the orbital energy and actions to determine stars with similar orbital characteristics. This study revealed eight dynamical groupings comprising between two and four stars each. The small dispersion of each group's metallicity was noted, and accounted for by reasoning that each group was associated with a unique satellite accretion event. Yuan et al. (2020a) utilized the self-organizing map neural network routine StarGO (Yuan et al. 2018) on the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Cui et al. 2012) Data Release 3 (Li et al. 2018) stellar survey. These authors used StarGO to examine the very metal-poor ([Fe/H] −1.8) stars to seek dynamical clusters based on the derived energy, angular momentum, and polar and azimuthal (E,L,θ,φ) parameters. From this prescription, the authors identified 57 dynamically tagged groups (DTGs), of which most were associated with GSE or Sequoia (Myeong et al. 2019), while 18 were new structures not previously associated with known large-scale substructures. Limberg et al. (2021a) constructed DTGs from metal-poor stars in the HK (Beers et al. 1985(Beers et al. , 1992 and Hamburg/ESO (Christlieb et al. 2008) surveys using the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN; Campello et al. 2013) algorithm over the orbital energy and cylindrical action space. Their clustering procedure was able to identify 38 DTGs, with 10 of those being newly identified substructures. Gudin et al. (2021) extended the work by Roederer et al. (2018), using a much larger sample of r -process-enhanced stars (see their Table 1 for definitions). Also utilizing the HDBSCAN algorithm, 30 Chemo-Dynamically Tagged Groups (CDTGs) 2 were discovered. Their analysis revealed statistically significant similarities in the dispersions of stellar metallicity, carbon abundance, and r -process-element ([Sr/Fe], [Ba/Fe], and [Eu/Fe]) abundances, strongly suggesting that these stars experienced similar chemical-evolution histories in their progenitor galaxies.
This work aims to analyze the DTGs present among stars in RAVE Data Release 6 (DR6; Steinmetz et al.  Schlegel et al. (1998), and recalibrated by Schlafly & Finkbeiner (2011), is shown in the background on a gray scale with darker regions corresponding to larger reddening. 2020a), focusing on metal-poor ([Fe/H] ≤ −0.8) stars. The procedures employed closely follow the work of Shank et al. (2021), hereafter referred to as Paper I in this series, which considered DTGs found in the sample of the Best & Brightest selection of Schlaufman & Casey (2014). The association of our identified DTGs with recognized Galactic substructures, previously known DTGs/CDTGs, globular clusters, and dwarf galaxies is explored, with the most interesting stellar populations being noted for future high-resolution follow-up studies.
This paper is outlined as follows. Section 2 describes the RAVE DR6 sample, along with their associated astrometric parameters and the dynamical parameters. The clustering procedure is outlined in Section 3. Section 4 explores the clusters and their association to known MW structures. Finally, Section 5 presents a short discussion and perspectives on future directions.

DATA
The RAVE DR6 survey (Steinmetz et al. 2020a) forms the basis for the compilation of our data set. We construct three samples, the Full Sample, the Initial Sample, and the Final Sample, which are described in the following sections.

Construction of the Full Sample
Of the 322, 367 unique stars in RAVE DR6 that have acceptable quality-flags from the MADERA stellar parameter pipeline (Steinmetz et al. 2020b), photometric metallicity and temperature estimates are taken from the SkyMapper Southern Survey (SMSS; Wolf et al. 2018) Data Release 2 (DR2; Onken et al. 2019). These estimates are derived by the procedure described in Huang et al. (2021b) and explained below. Metal-poor candidate stars from RAVE are also taken from the sample in Placco et al. (2018) whose authors explored the nature of the RAVE stellar parameters with a corresponding set of spectroscopic parameters, also explained below. The validation spectra from Placco et al. (2018) 3 were then used to determine the stellar atmospheric parameters and elemental abundances for the stars using the non-SEGUE Stellar Parameter Pipeline (n-SSPP; Beers et al. 2014Beers et al. , 2017, following the procedures described in Paper I. The parameters obtained are the effective temperature (T eff Spec ), surface gravity (log g), and metallicity ([Fe/H] Spec ), while the elemental abundances are the carbon abundance ([C/Fe]), and the α-element abundance ([α/Fe]). The carbon abundance is then adjusted, using the prescription outlined in Placco et al. (2014), to account for the depletion of carbon along the red giant branch. This corrected carbon abundance ([C/Fe] c ) is used as the star's natal carbon abundance. The average errors adopted for each of the stellar parameters for the spectra with S/N ∼ 30 are ±150 K for T eff ; ±0.35 dex for log g, and ±0.20 dex for [Fe/H], [C/Fe], and [α/Fe], with values for each star listed in Table 8 in the Appendix (See Lee et al. 2008 for more information on the errors). Note that the elemental abundances reported here supersede those published in Placco et al. (2018) The rest of our sample is assembled from recent photometric estimates of temperature, luminosity classes, and metallicity for candidate stars from the RAVE DR6 survey based on the procedure described by Huang et al. (2021b). This study made use of recalibrated zero-points (Huang et al. 2021a) in the narrow-and medium-band photometry obtained by the Sky Mapper Southern Survey (SMSS; Wolf et al. 2018) Data Release 2 (DR2; Onken et al. 2019), along with broad-band photometry from Gaia EDR3 (Gaia Collaboration et al. 2021). The average errors adopted for each of the stellar parameters for the photometric portion of the sample are ±62 K for T eff , and ±0.13 dex for [Fe/H], with values for each star listed in Table 8 in the Appendix (See Huang et al. 2021b for more information on the errors). Huang et al. (2021b) have compared the photometric estimates of T eff and [Fe/H] from their catalog with several mediumresolution studies (including stars from the Pristine Survey follow-up reported by Aguado et al. 2019, and from the Best & Brightest sample reported by Limberg et al. 2021b) and high-resolution studies that employed near-IR spectroscopy from APOGEE DR14 (Abolfathi et al. 2018) and DR16 (Ahumada et al. 2020), as well as optical high-resolution spectroscopy from a number of individual papers, and find generally excellent agreement. A total of 8205 stars have available photometric estimates of effective temperature and metallicity within desired ranges ([Fe/H] P hot ≤ −0.8 and 4250 ≤ T eff,Phot (K) ≤ 7000); 1303 of these stars also have available mediumresolution spectra. The total number of stars available is 8675, when duplicates are properly taken in considera- tion between the spectroscopic and photometric sources through the process discussed in the next section.
We refer to these stars as the Full Sample. The spatial distribution of the Full Sample in Galactic coordinates can be seen in Figure 1. Figure 2 compares the distributions of apparent magnitudes and colors for the Full Sample stars, as described in more detail below. Trimming of this sample to obtain a subset of stars suitable for our dynamical analysis is described below for the Initial Sample.

Construction of the Initial Sample
The metallicities from both RAVE DR6 and SMSS DR2 photometric estimates were available to construct the Initial Sample. Here we explore the comparison between the two metallicity sets and provide reasoning on our selection methods.

Metallicities
Comparisons of the metallicity estimates of the RAVE values to those with updated spectroscopic stellar parameters revealed a significant dispersion among the RAVE measurements, as can be appreciated in the left panel of Figure 3. The comparison between the photometric estimates of the metallicity and the spectroscopic metallicity is shown in the same figure in the right panel. The biweight (see Beers et al. 1990) estimates of offsets and scale in the residuals between the RAVE DR6 metallicities and the spectroscopic metallicities (in the sense [Fe/H] RAV E − [Fe/H] Spec ) is µ = +0.32 dex and σ = 0.57 dex, respectively, while the biweight offset and scale in the residuals between the photometric metallicities and spectroscopic metallicities (in the sense [Fe/H] P hot − [Fe/H] Spec ) determined from the validation spectra is µ = +0.12 dex and σ = 0.30 dex, respectively. Based on these behaviors, we decided to use the photometric determinations based on the recalibrated SMSS DR2 from Huang et al. (2021b) for the present analysis, rather than the RAVE DR6 estimates.

Parameters
The comparison between metallicity determinations from both the spectroscopic and photometric estimates can be appreciated in Figure 4. The biweight estimators of location and scale for the metallicity residuals determined from the medium-resolution spectra and the photometric metallicity yield µ = +0.12 dex and σ = 0.30 dex. As noted by Huang et al. (2021b), stars that have enhanced carbon often estimated photometric metallicities that are somewhat higher than the spectroscopic determinations, due to molecular carbon features affecting the blue narrow/medium-band filters v and u from SMSS (particularly for cooler carbon-enhanced stars). Stars with [C/Fe] c > +0.7, which we define as carbonenhanced metal-poor (CEMP) stars are indicated with red circles around the dots shown in the bottom panel   of Figure 4. We note that, when these stars are removed from the sample, similar offsets and residuals are found as for the entire sample.
From inspection of this figure, there appears to be a systematic discrepancy in the metallicity estimates in the metal-rich region. As in Paper I, we attribute this to difficulties encountered by the n-SSPP estimates 5 , rather than the photometric estimates, which have been shown by Huang et al. (2021b) to have excellent performance in this metallicity regime. As noted below, we only retain stars with [Fe/H] ≤ −0.8 in the Final Sample, so these stars will not greatly affect our subsequent analysis. Figure 5 shows the distributions of [Fe/H] and T eff estimates obtained from the photometric and spectroscopic sub-samples. As can be appreciated from inspection of this figure, although these subsets are similarly distributed over T eff (right panel), the majority of the the stars in the spectroscopic validation sample have [Fe/H] −1.8 (left panel), resulting from the selection of very low-metallicity candidates for the validation process.
For stars that have both spectroscopic and photometric stellar parameters, we perform a procedure to obtain the parameters available to produce final adopted  Table 10 of the Appendix.
The stars from the Full Sample were then crossmatched with Gaia Early Data Release 3 (EDR3; Gaia Collaboration et al. 2021) using a 5 radius to find their 6-D astrometric parameters. To validate the match for each star, confirmation was performed by checking that the stellar magnitudes agreed to within 0.5 mag between the sources. The Full Sample was mostly taken from V magnitudes supplied by the AAVSO Photometric All Sky Survey (APASS; Henden & Munari 2014) Data Release 9 (DR9; Henden et al. 2016), with various other sources listed in the Appendix tables supplying the rest. The corresponding matches were then compared with the V magnitude utilizing the transformation from Gaia magnitudes G, G BP , and G RP in EDR3 provided in Table C.2 of Riello et al. (2021). A comparison of the magnitudes and colors for the photometric and spectroscopic subsets can be seen in Figure 2. From inspection of the figure, although the relative numbers differ, the distributions are similar to one another.

Construction of the Final Sample
Once stars from the Full Sample are matched with those from Gaia EDR3, dynamical parameters for stars in the Initial Sample can be recovered and used to construct the Final Sample.

Radial Velocities, Distances, and Proper Motions
Radial velocities, parallaxes, and proper motions for each star are taken from Gaia EDR3, when available. Note that the radial velocities for the stars in Gaia EDR3 are available for about 87% of the Full Sample. Typical errors for Gaia EDR3 radial velocities are ∼1 km s −1 . The top panel of Figure 8 shows a histogram of the residual differences between the RAVE DR6 radial velocities and the Gaia EDR3 values. The biweight location and scale of these differences are µ = −0.1 km s −1 and σ = 2.5 km s −1 , respectively. The bottom panel of this figure shows the residuals between the RAVE DR6 and Gaia EDR3 radial velocities, as a function of the Gaia radial velocities. The blue dashed line is the biweight location, while the shaded regions represent the first (1σ) and second (2σ) biweight scale ranges. We expect that many of the stars with residuals outside the 2σ range are binaries, causing an improper measurement of the systemic radial velocities.
The distances to the stars are determined either through the StarHorse distance estimate (Anders et al. 2021) or the Bailer-Jones distance estimate (BJ21; Bailer-Jones et al. 2021). Parallax values in our Full Sample from EDR3 have an average error of around 0.04 mas. The StarHorse and BJ21 distances are determined by a Bayesian approach utilizing the EDR3 parallax, magintude, and color (Anders et al. 2021;Bailer-Jones et al. 2021). The errors are presented for each star in the tables provided in the Appendix. We prioritize the StarHorse distances when the relative error (the error divided by the reported value), , is < 30%. If the StarHorse relative error is ≥ 30%, then we adopt the BJ21 distance if the relative error is < 30%. If only one distance estimator is available, then we adopt it. If both distances, or the only available distance, have ≥ 30%, then we discard the star from the dynamical analysis below. Note that in Figure 9 the StarHorse and BJ21 approaches produce similar distances, especially when the distance is smaller than 5 kpc. A comparison between Figure 9 and Figure 8 in Paper I clearly shows the improvement in the distance estimators when the StarHorse distances are used in comparison to the Gaia EDR3 inverse-parallax distances employed in Paper I. The proper motions in our Full Sample from Gaia EDR3 have an average error of 39 µas yr −1 .

Dynamical Parameters
The orbital characteristics of the stars are determined using the Action-based GAlaxy Modelling Architecture 6 (AGAMA) package (Vasiliev 2019), using the same Solar positions and peculiar motions described in Paper I 7 . The MW gravitational potential we adopt is the MW2017 potential (McMillan 2017), also described in Paper I. The 6D astrometric parameters, determined in Section 2, are run through the orbital integration process in AGAMA using the same procedure outlined in Paper I to calculate the orbital energy, cylindrical positions and velocities, angular momentum, cylindrical actions, and eccentricity. See Paper I for definitions of these orbital parameters.
The above procedure obtains the orbital parameters if the astrometric parameters are precisely described by the given values. However, these values have errors associated with them, so a method must be developed to estimate the errors in the orbital parameters. This is accomplished through a Monte Carlo sampling over the errors in the astrometric parameters. The procedure that we employ to determine the orbital errors using Monte Carlo sampling is described in detail in Paper I.
An inspection is performed to identify stars that are not suitable for the following dynamical analysis. The Initial Sample of 8377 stars contains stars that are unbound from the MW (E> 0), along with stars that do not have the full 6-D astrometric parameters of position, radial velocity, distance, and proper motions were then cut. Finally, in order to obtain accurate orbital dynamics, we remove 401 stars with differences in their RAVE DR6 radial velocities compared to the Gaia radial velocities that lie outside the 15 km s −1 range. Most of these stars are expected to be binaries. Application of this cut leaves a total sample of 7957 stars to perform the following analysis. The dynamical parameters of the stars with orbits determined are listed in Table 9 in the Appendix; we refer to this as the Final Sample. Figure 10 provides histograms of r apo (top), r peri (middle), and Z max (bottom) for the Final Sample. From inspection of this figure, it is clear that the majority of the stars in this sample occupy orbits that take them inside the inner-halo region, but they also explore regions well into the outer-halo region, up to ∼ 50 kpc away.
3. CLUSTERING PROCEDURE Helmi & de Zeeuw (2000) were among the first to suggest the use of integrals of motion, in their case orbital energy and angular momenta, to find substructure in the MW using the precision measurements of next-generation surveys that were planned at the time. McMillan & Binney (2008) suggested the use of actions as a complement to the previously suggested orbital energy and angular momenta, with only the vertical angular momentum being invariant in an axisymmetric potential. Most recently, many authors have employed the orbital energy and cylindrical actions (E,J r ,J φ ,J z ) to determine the substructure of the MW using Gaia measurements (Helmi et al. 2017;Myeong et al. 2018a,b;Roederer et al. 2018;Naidu et al. 2020;Yuan et al. 2020b,a;Gudin et al. 2021;Limberg et al. 2021a;Shank et al. 2021).
As described in Paper I, we employ HDBSCAN in order to perform a cluster analysis over the orbital energy and cylindrical actions from the Final Sample obtained through the procedure outlined in Section 2.3. The HDBSCAN algorithm 8 operates through a series of calculations that are able to separate the background noise from denser clumps of data in the dynamical parameters. We utilize the following parameters described in Paper I:~min_cluster_size = 5, min_samples = 5,~cluster_selection_method = 'leaf',~prediction_data =~True , Monte Carlo samples at 1000, and minimum confidence set to 20%. Table 1 provides a listing of the Dynamically Tagged Groups (DTGs) identified by this procedure, along with their numbers of member stars, confidence values, and associations described below. Note that, although a minimum confidence value of 20% was employed, the actual minimum value found for these DTGs is 23.9%. The DTGs and CDTGs are identified using the nomenclature introduced by Yuan et al. (2020a), to which we refer the interested reader.  Table 4 lists the derived dynamical parameters derived by AGAMA used in our analysis.

STRUCTURE ASSOCIATIONS
Associations between the newly identified DTGs are now sought between known MW structures, including large-scale substructures, previously identified dynamical groups, stellar associations, globular clusters, and dwarf galaxies.

Milky Way Substructures
Analyzing the orbital energy and actions is not sufficient to determine separate large-scale substructures. Information on the elemental abundances is crucial due to the differing star-formation histories of the structures, which can vary in both mass and formation redshift (Naidu et al. 2020). The outline for the prescription used to determine the structural associations with our DTGs is described in Naidu et al. (2020), and explained in detail in Paper I. Simple selections are performed based on physically motivated choices for each substructure, excluding previously defined substructures, as the process iterates to decrease contamination between substructures. Following their procedures, we find 6 predominant MW substructures associated with our DTGs, listed in Table 5. This table provides the numbers of stars in each substructure, the mean and dispersion of their chemical abundances, and the mean and dispersion of their dynamical parameters for each substructure. The Lindblad diagram and projected-action plot for these substructures is shown in Figure 11.

Gaia-Sausage-Enceladus
The most populated substructure is Gaia-Sausage-Enceladus (GSE), which contains 523 member stars. GSE is thought to be a remnant of an earlier merger that distributed a significant number of stars throughout the inner halo of the MW (Belokurov et al. 2018;Helmi et al. 2018). The action space determined by the member stars exhibits an extended radial component, a null azimuthal component within errors, and a null vertical component. These orbital properties are the product of the high-eccentricity selection of the DTGs, and agree with previous findings of GSE orbital characteristics when using other selection criteria Myeong et al. 2018a;Limberg et al. 2021a).
The [Fe/H] of GSE found in our work is rather metal poor ([Fe/H] ∼ −1.5), consistent with studies of its metallicity in dynamical groupings, even though our sample contains more metal-rich stars that could have been associated with GSE (Gudin et al. 2021;Limberg et al. 2021a). The stars that form DTGs in GSE tend to favor the more metal-poor tail of the substructure, which is also seen in previous DTG analysis. The [α/Fe] of GSE exhibits a relatively low level, consistent with the low-Mg structure detected by Hayes et al. (2018) and with Mg levels consistent with accreted structures simulated by Mackereth et al. (2019). The α-element enhancement seen in GSE is due to accretion of older stellar populations, consistent with known element abundance patterns. We also obtain a [C/Fe] Figure 11 how GSE occupies a large region of the Lindblad diagram, concentrated in the planar and radial portions of the projected-action plot.

The Metal-Weak Thick Disk
The second-most populated substructure is the Metal-Weak Thick Disk (MWTD), which contains 119 member stars. The MWTD is thought 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). The non-existent radial and vertical velocity components, as well as the large posi-      (2020) and Dietz et al. (2021) have presented evidence that the MWTD is an independent structure from the TD. The distribution in [Fe/H] and mean velocity space represents a stellar population consistent with the high-Mg population (Hayes et al. 2018), with the mean α-element abundance being similar within errors. The [C/Fe] c abundance is also given for the MWTD, and shows an enhancement in carbon, possibly pointing to a relation with the strongly prograde CEMP structure found in Dietz et al. (2021), which was attributed to the MWTD population. Notice in Figure 11 how the MWTD occupies a higher energy component of the disk (the gray dots mostly positioned with prograde orbits) in the Lindblad diagram.

The Splashed Disk
The third-most populated substructure is the Splashed Disk (SD), which contains 56 member stars. The SD is thought to be a component of the primordial MW disk that was kinematically heated during the GSE merger event Di Matteo et al. 2019;Belokurov et al. 2020). The mean velocity components of the SD are consistent with a null radial and vertical velocity, while showing a large positive azimuthal velocity consistent with disk-like stars. The mean eccentricity of these stars is consistent with disk-like orbits. The SD consists of the most metal-rich substructure identified here. The high [α/Fe] abundances for the SD shows that these stars are old, and they could be the result of a possible merger event, such as the one that created GSE. The [C/Fe] c abundance for the SD are high, which is in conjunction with the high mean α-element abundances. Notice in Figure 11 how the SD overlaps with the MWTD. This is due to the selection criteria only using metallicity and α-element abundances to determine the SD stars (Naidu et al. 2020). Considering the SD is thought to be composed of stars that have been heated due to the GSE merger event, the positions of the SD stars in the Lindblad diagram does not show a relatively large deviation from disk-like orbits. More associations with the SD are needed to make any definitive claims.

Thamnos
The fourth-most populated substructure is Thamnos, which contains 40 member stars. Thamnos was proposed by Koppelman et al. (2019b) as a merger event that populated these stars in a retrograde orbit that is similar to TD stars. The low energy and strong retrograde rotation suggest that Thamnos merged with the MW long ago (Koppelman et al. 2019b). Here we find a similar low mean orbital energy and strong mean retrograde motion, and we recover as strong a retrograde motion as in Koppelman et al. (2019b), within errors. The low mean metallicity, consistent with the value reported by Limberg et al. (2021a), and elevated [C/Fe] c of these stars also supports the merger being ancient. The [α/Fe] is high, also suggesting an old population, consistent with Kordopatis et al. (2020). Notice in Figure 11 how Thamnos occupies a space that could be described as a retrograde version of disk stars.

The Helmi Stream
The second-to-least populated substructure is the Helmi Stream (HS), which contains 12 member stars. The HS is one of the first detected dynamical substructures in the MW using integral of motions (Helmi et al. 1999). The HS has a characteristically high vertical velocity, which separates it from other stars that lie in the disk, and can be seen in the sample here. The large uncertainty on vertical velocity of the HS members corresponds to the positive and negative vertical velocity components of the stream, with the negative vertical velocity population dominating, consistent with the members determined here (Helmi 2020 Limberg et al. (2021c) noted that the metallicity range of HS is more metal-poor than previously expected, with stars reaching down to [Fe/H] ∼ −2.5, which is consistent with the results presented here. Notice in Figure 11 how the HS occupies a relatively isolated space in the Lindblad diagram, thanks to the large vertical velocity of the stars providing the extra energy compared to the other disk stars.

Previously Identified Dynamically Tagged Groups and Stellar Associations
Separately, we can compare the newly identified DTGs in this work with other dynamical groups identified by previous authors. We take the mean group properties used to detect the previously identified groups and compare them to the mean and dispersion for the dynamical parameters of our identified DTGs. Stellar associations are also considered, allowing the identification of stars in our sample that belong to previously identified groups. For details on the previous work used in this process, see Paper I. The resulting dynamical associations between our identified DTGs and previously identified groups (along with substructure and globular cluster associations, see Section 4.3) are listed in Table 6. Table 2 lists the individual stellar associations for each of our DTGs.
One example of associations of identified DTGs with past groups is DTG-42. This DTG was associated with the Helmi Stream through the procedure outlined in Naidu et al. (2020) (see Section 4.1 for more details). There were four stars associated with this DTG through a 5 radius search of the DTG member stars. Two of the stars belong in HK18:Green, and the other two belong in NB20:H99, both of which are associated with the Helmi Stream . DTG-42 is also dynamically associated with GM18a:S2, GM18b:S2, DG21:CDTG-15, and GL20:DTG-3, all of which were identified as part of the Helmi Stream (Myeong et al. 2018a,b;Gudin et al. 2021;Limberg et al. 2021a). DG21:CDTG-15 was originally associated with GL20:DTG-3 as well by the authors, further strengthening our associations (Gudin et al. 2021).
An interesting DTG associated with the GSE is DTG-7, which has multiple previously identified groups and stars associated with them. Taking a closer look at DTG-7, we can find three stellar associations between this group and DG21:CDTG-1, and one stellar association each in IR18:E and EV21:NGC 4833, a globular cluster (Gudin et al. 2021;Roederer et al. 2018;Vasiliev & Baumgardt 2021). Again DG21:CDTG-1 is found associated with IR18:E by the authors, and even though we have a stellar association with EV21:NGC 4833, we do not find a strong dynamical association between DTG-7 and the globular cluster (Gudin et al. 2021;Vasiliev & Baumgardt 2021). DTG-7 is dynamically associated with GC21:Sausage, DG21:CDTG-1, GL21:DTG-37, DS21:DTG-43, again all of which are associated to GSE by their authors (Cordoni et al. 2021;Gudin et al. 2021;Limberg et al. 2021a;Shank et al. 2021).
The only DTG with multiple associations related to the MWTD is DTG-14. Stellar associations with DG21:CDTG-6 and HL19:GL-1 were found, with neither of them having associations to large-scale substructure by their authors (Gudin et al. 2021;Li et al. 2019). Dynamical associations with both HL19:GL-1 and DS21:DTG-2 are found with DTG-14. Interestingly, since we use the same procedure outlined by Shank et al. (2021), those authors found that DS21:DTG-2 is also associated with both HL19:GL-1 and DG21:CDTG-6 along with the MWTD. These associations across multiple papers show how powerful these identifications are when identifying past structures, such as the unidentified DG21:CTDG-6 and HL19:GL-1 as candidate MWTD associations.
DTG-102 is an interesting case, since we have associated it with Thamnos, and there are 3 stellar associations with previously identified groups along with one dynamical association. There were two stellar associations between DTG-102 and HL20:GR-2, which was not identified by the authors (Li et al. 2020). DG21:CDTG-2 had a stellar association and was also dynamically associated with DTG-102 while being identified as a part of Thamnos by the authors (Gudin et al. 2021).
Another use of the stellar associations comes from the suggestion by Roederer et al. (2018), strengthened by Gudin et al. (2021), that dynamical groups of stars have a statistically significant correlation between their elemental abundances. This is of importance to discover new chemically peculiar stars, particularly r-processenhanced stars. Out of our DTGs, there are 22 associations between known r-process-enhanced stars and our discovered DTGs. The member stars in these DTGs provide interesting candidates for high-resolution spectroscopic follow-up, due to the increased likelihood of the other members comprising chemically peculiar stars, especially in terms of r-process enhancement (Roederer et al. 2018;Gudin et al. 2021).

Globular Clusters and Dwarf Galaxies
Both globular clusters and dwarf galaxies have been shown to play an important role in the formation of chemically peculiar stars (Ji et al. 2016;Myeong et al. 2018c). Globular clusters can also be a good indicator of galaxy-formation history based on their metallicities and orbits (Woody & Schlaufman 2021). From the work of Vasiliev & Baumgardt (2021), we can compare the dynamical properties of 170 globular clusters to those of the DTGs we identify. The procedure that is employed is the same one used for previously identified groups and stellar associations introduced in Sec. 4.2. The dynamics for 45 dwarf galaxies of the MW (excluding the Large Magellanic Cloud, Small Magellanic Cloud, and Sagittarius) are also explored. Paper I contains details of the orbits of the globular clusters and dwarf galaxies. The same procedure used for previously identified groups was then applied to determine whether a DTG was dynamically associated to the dwarf galaxy. Stellar associations were also determined for both globular clusters and dwarf galaxies in the same manner as previously identified groups.
The above comparison exercise led to 10 globular cluster associations, with 8 being unique. For a breakdown of which globular clusters are associated with our DTGs, see Table 6. Ryu 879 (RLGC 2) has three DTG associations which agree with each other in mean metallicity ( [Fe/H] ∼ −1.7). The mean metallicity agrees with the discovery of the globular cluster Ryu 879 (RLGC 2) within errors (Ryu & Lee 2018).The rest of the globular cluster associations are each associated with only one DTG in this work. We identify IC 1257, NGC 6284, and NGC 6356 through dynamical association, while NGC 4833, NGC 5139 (ωCen), NGC 6397, and NGC 6752 are identified through stellar association. Even though the matched stars in these globular clusters would have individually been associated with the globular cluster orbital parameters, the overall DTG did not possess sufficiently similar orbital characteristics to be associated.    , 8, 17, 24, 28, 30, 45, 50, 57, 58, 66, 75 79, 80, 92, 98, 115, 134, 135, 136, 142, 146 Note-We draw attention to the associations with CDTGs from Gudin et al. (2021) and Roederer et al. (2018) due to their enhancement in r-process abundances.
The DTGs associated with globular clusters are expected to have formed in chemically similar birth environments; this is mostly supported through the similar chemical properties of the DTGs. Associations of globular clusters with Galactic substructure have been made by Massari et al. (2019). These authors did not analyze Ryu 879 (RLGC 2), since the globular cluster was only recently discovered at the time of the publication. IC 1257, NGC 6284, and NGC 4833 were identified to GSE by both our identification and Massari et al. (2019) (see DTG-66, DTG-141, and DTG-7 respectively). NGC 6356 was identified as Thamnos by our determinations, while Massari et al. (2019) found it to be associated to the main disk which we do not consider as part of the substructure routine, though it should be pointed out that Thamnos has the dynamics of a higher-energy retrograde disk similar to the MWTD (Koppelman et al. 2019b). NGC 5139 (ω Cen) was identified as being associated with GSE or Sequoia by Massari et al. (2019), and our associations did recover this match to GSE (see . NGC 6397 and NGC 6752 are not associated to any substructure by our procedure (see DTG-55 and DTG-33, respectively), but Massari et al. (2019) find them associated to the main disk, which is not a part of the substructure routine.
We did not identify any associations of DTGs to the sample of (surviving) MW dwarf galaxies, either through stellar associations, or through the dynamical association procedure described above. Nevertheless, some of the DTGs identified by our analysis may well be associated with dwarf galaxies that have previously merged with the MW.
The analysis on the global properties of the identified DTGs that was explored in Section 6 of Paper I is foregone in this analysis due to the small number of DTGs that have sufficient C and α-element abundances to derive meaningful conclusions. Attention to the small number of DTGs that do meet these requirements are listed in Table 3.

DISCUSSION
We have assembled a Full Sample of 8675 stars from the RAVE DR6 survey (Steinmetz et al. 2020a) with available estimates of [Fe/H], and in some cases, with [C/Fe] and [α/Fe].
The Initial Sample contained 8377 stars, with 4250 ≤ T ef f (K) ≤ 7000 and [Fe/H] ≤ −0.8, 106 of which we identify as CEMP stars ([C/Fe] c > +0.7); these are listed in Table 10 in the Appendix. These stars are of interest due to their enhanced carbon and association to morphological groups described in Yoon et al. (2016). Based on their classification scheme, there are approximately 50 Group I CEMP stars, 55 Group II CEMP stars, and 5 Group III CEMP stars, with a number of stars that have ambiguous classifications. This list provides a useful reference for high-resolution follow-up targets, some of which has already begun (e.g., Rasmussen et al. 2020 andZepeda et al. 2021).
The Final Sample of 7957 metal-poor stars had sufficient radial velocity and astrometric information from which orbits were constructed, in order to determine Dynamically Tagged Groups (DTGs) in orbital energy and cylindrical action space with the HDBSCAN algorithm. We chose HDBSCAN as the clustering algorithm due to precedence within the literature (Koppelman et al. 2019b;Gudin et al. 2021;Limberg et al. 2021a;Shank et al. 2021), and its ability to extract clusters of stars over the energy and action space. Other clustering algorithms have been considered in the past, such as agglomerative clustering, affinity propogation, K-means, and mean-shift clustering (Roederer et al. 2018), along with friends-of-friends (Gudin et al. 2021).
We recover 179 DTGs that include between 5 and 35 members, with 67 DTGs containing at least 10 member stars. These DTGs were associated with MW substructure, resulting in the identification of the Gaia-Sausage-Enceladus, the Metal-Weak Thick Disk, the Splashed Disk, Thamnos, the Helmi Stream, and LMS-1 (Wukong). A total of 8 unique globular clusters were associated with 10 different DTGs, while no surviving dwarf galaxies were determined to be associated with the identified DTGs. Previously identified groups were found to be associated with the DTGs as well, with past work mostly confirming our substructure identification. Each of these associations allow insights into the dynamical and chemical properties of the parent substructures.
The implications of past group and stellar associations were explored with emphasis placed on the structure associations. Chemically peculiar stellar associations and previously identified Chemo-Dynamically Tagged Groups (CDTGs) were addressed as being good candidates for high-resolution follow-up spectroscopy targets, due to the statistical likelihood of the other members being chemically peculiar as well, mostly focused on rprocess-enhanced stars.
The methods presented here will be used on larger samples of field stars that we are in the process of assembling -the HK/HES/HKII surveys (Beers et al. 1985(Beers et al. , 1992Christlieb et al. 2008;Rhee 2001) (a subset of which were analyzed by Limberg et al. 2021a), as well as SDSS/LAMOST and APOGEE. These data sets will also be supplemented with photometric estimates of effective temperature and metallicity from Huang et al. (2021b), which allows stars from the HK/HES/HKII surveys with no previous spectroscopic follow-up to be explored, expanding the data set used by Limberg et al. (2021a).

APPENDIX
Here we present the tables for the Initial (Table 8) and Final (Table 9) Samples of the RAVE DR6 survey. We also present Table 10 which describes the identified CEMP stars and their associated morphological groups, according to the regions defined by Yoon et al. (2016).  The surface gravity of the star as given by the n-SSPP Table 8 continued   The surface gravity of the star as given by the n-SSPP Table 9 continued  Parameter Procedure − The procedure used to determine the adopted stellar parameters (T eff , log g, The orbital energy of the star as given by AGAMA Table 9 continued