# Two Substructures in the nearby Stellar Halo Found in Gaia and RAVE

Hefan Li, Cuihua Du, Yanbin Yang, Heidi Jo Newberg, Jun Ma, Jianrong Shi, Yunsong Piao

► To cite this version:

Hefan Li, Cuihua Du, Yanbin Yang, Heidi Jo Newberg, Jun Ma, et al. Two Substructures in the nearby Stellar Halo Found in Gaia and RAVE. The Astrophysical Journal, 2020, 895 (1), pp.23. 10.3847/1538-4357/ab8733. hal-03228458

HAL Id: hal-03228458

https://hal.science/hal-03228458v1

Submitted on 6 Aug 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Two Substructures in the nearby Stellar Halo Found in Gaia and RAVE

Hefan Li¹, Cuihua Du², Yanbin Yang³, Heidi Jo Newberg⁴, Jun Ma²,⁵, Jianrong Shi²,⁵, and Yunsong Piao¹

¹School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China

²College of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China; ducuihua@ucas.ac.cn

³GEPI, Observatoire de Paris, PSL Research University, CNRS, Place Jules Janssen, F-92190 Meudon, France

⁴Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

⁵Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, People's Republic of China

Received 2019 July 17; revised 2020 March 30; accepted 2020 April 4; published 2020 May 20

## Abstract

We use the second Gaia data release (Gaia DR2), combined with Radial Velocity Experiment spectroscopic surveys, to identify the substructures in the nearby stellar halo. We select 3845 halo stars kinematically and chemically and determine their density distribution in energy and angular momentum space. To select the substructures from overdensities, we reshuffle the velocities and estimate their significance. Two statistically significant substructures, GR-1 and GR-2, are identified. GR-1 has a high binding energy and small z-angular momentum. GR-2 is metal-rich but retrograde. They are both new substructures, and may be accretion debris of dwarf galaxies.

*Unified Astronomy Thesaurus concepts: Galaxy kinematics (602); Galaxy stellar halos (598); Galaxy formation (595); Galaxy abundances (574); Galaxy dynamics (591); Solar neighborhood (1509)*

## 1. Introduction

According to the standard Lambda cold dark matter model, smaller scale objects could merge into larger galaxies because of gravity (White & Rees 1978). In this merging process, dwarf galaxies and their tidal debris are dispersed into a stellar halo (Searle & Zinn 1978; Freeman & Bland-Hawthorn 2002). These substructures arising from an accretion event provide important clues for the study of galaxy formation. Though losing their spatial correlation, they are still linked by their phase space properties (Helmi & White 1999a; Bullock & Johnston 2005). Grillmair & Carlin (2016) summarized the methods of how to identify halo streams and provided information on most streams and clouds discovered before 2015.

With the development of modern sky surveys, such as the Sloan Digital Sky Survey (SDSS; York et al. 2000), Hipparcos (van Leeuwen 2007), the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Cui et al. 2012; Deng et al. 2012; Zhao et al. 2012), the Radial Velocity Experiment (RAVE; Steinmetz et al. 2006), and the Gaia mission (Gaia Collaboration et al. 2018), more and more substructures are being discovered, such as the Sagittarius dwarf tidal stream (Ibata et al. 1994; Majewski et al. 2003; Belokurov et al. 2006), the Orphan Stream (Grillmair 2006; Belokurov et al. 2007; Newberg et al. 2010), and the Virgo Stellar Stream (Duffau et al. 2006; Newberg et al. 2007; Duffau et al. 2014).

Gaia DR2 (Gaia Collaboration et al. 2018) provides positions, proper motions, and parallaxes for more than one billion stars. The precision and accuracy of these astrometric and photometric properties are unprecedented. In particular, Gaia DR2 also provides radial velocities for over 7 million stars. This allows us to get the full 6D phase space information of the star. Using metal-rich halo stars with 7D measurements supplied by Gaia and SDSS, Belokurov et al. (2018) find an elongated structure in velocity space that they refer to as “Gaia Sausage.” They show that it could be deposited in a major accretion event by a massive satellite. Similarly, Helmi et al. (2018)

show that the inner halo is dominated by the streams with slightly retrograde and elongated trajectories. These streams originate from accretion debris of a massive object that they call “Gaia-Enceladus.” The stars of this structure have relatively low [α/Fe] and a large spread in [Fe/H]. This also suggests that they formed in a relatively massive system. According to Helmi et al. (2018), the accretion of “Gaia-Enceladus” heats the thick disk of the Galaxy.

Radial Velocity Experiment Data Release 5 (RAVE DR5) contains 520,781 spectra of 457,588 unique stars in the magnitude range $9 < I < 12$ (Kunder et al. 2017). The medium-resolution spectra ($R \sim 7500$) ensures the precision of radial velocity, atmospheric parameters and chemical abundances. Using Gaia DR2 and RAVE DR5, we can get kinematics and chemistry of stars. This can help us understand the early accumulation history of the Galaxy.

In this study we introduce the observational data from Gaia and RAVE in Section 2. Then we assemble a sample of halo stars selected from kinematic and chemical properties of stars. We discuss the method to identify substructures and estimate their significance in Section 3. Finally, we summarize our work in Section 4.

## 2. Data and Methods

Using quasars and validation solutions, Lindegren et al. (2018) determined the systematic error of Gaia DR2 parallaxes to be -0.029 mas. Huang et al. (2018) determined that the RV zero-points (RVZPs) of Gaia-RVS and RAVE DR5 are $0.36 \text{ km s}^{-1}$ and $0.17 \text{ km s}^{-1}$ based on APOGEE (Majewski et al. 2017) data. So we correct the values of radial velocity of our sample stars for RVZP using their determinations. We cross-match Gaia and RAVE catalogs and obtain 512,971 stars in common. If the radial velocity of a star is provided by both Gaia and RAVE, its radial velocity and error are given by:

$$rv = \frac{rv_G \sigma_R^2 + rv_R \sigma_G^2}{\sigma_G^2 + \sigma_R^2}, \quad \sigma_{rv}^2 = \frac{\sigma_R^2 \sigma_G^2}{\sigma_G^2 + \sigma_R^2},$$
where G and R represent Gaia and RAVE, respectively. We consider only stars with relative parallax error ≲20%, signal-to-noise ration of RAVE (S/N) ≳ 20 and radial velocity error $σ_{rv}$ ≲10 km s⁻¹. We also use the selection criterion $|rv_G - rv_R| \le \max(10, σ_R, σ_G)$ km s⁻¹ to ensure radial velocity reliability. Finally, the data set contains 372,321 stars.

We use the full Bayesian method to estimate distances and velocities (Luri et al. 2018):

$$P(\theta | \mathbf{x}) \propto \exp\left[-\frac{1}{2}(\mathbf{x} - \mathbf{m}(\theta))^\mathrm{T}\mathbf{C}_x^{-1}(\mathbf{x} - \mathbf{m}(\theta))\right] P(d | L), \quad (1)$$

where $\theta = (d, v_\alpha, v_\delta, v_r)^\mathrm{T}$, $\mathbf{x} = (\bar{\omega}, \mu_{\alpha^*}, \mu_\delta, rv)^\mathrm{T}$, $\mathbf{m} = (1/d, v_\alpha/kd, v_\delta/kd, v_r)^\mathrm{T}$, $k = 4.74047$, and $C_x$ is covariance matrix:

$$\left\{
\begin{array}{cccc}
\sigma_{\bar{\omega}}^2 & \rho_{\bar{\omega}}^{\mu_{\alpha^*}} \sigma_{\bar{\omega}} \sigma_{\mu_{\alpha^*}} & \rho_{\bar{\omega}}^{\mu_\delta} \sigma_{\bar{\omega}} \sigma_{\mu_\delta} & \rho_{\bar{\omega}}^{rv} \sigma_{\bar{\omega}} \sigma_{rv} \\
\rho_{\bar{\omega}}^{\mu_{\alpha^*}} \sigma_{\bar{\omega}} \sigma_{\mu_{\alpha^*}} & \sigma_{\mu_{\alpha^*}}^2 & \rho_{\mu_{\alpha^*}}^{\mu_\delta} \sigma_{\mu_{\alpha^*}} \sigma_{\mu_\delta} & \rho_{\mu_{\alpha^*}}^{rv} \sigma_{\mu_{\alpha^*}} \sigma_{rv} \\
\rho_{\bar{\omega}}^{\mu_\delta} \sigma_{\bar{\omega}} \sigma_{\mu_\delta} & \rho_{\mu_{\alpha^*}}^{\mu_\delta} \sigma_{\mu_{\alpha^*}} \sigma_{\mu_\delta} & \sigma_{\mu_\delta}^2 & \rho_{\mu_\delta}^{rv} \sigma_{\mu_\delta} \sigma_{rv} \\
\rho_{\bar{\omega}}^{rv} \sigma_{\bar{\omega}} \sigma_{rv} & \rho_{\mu_{\alpha^*}}^{rv} \sigma_{\mu_{\alpha^*}} \sigma_{rv} & \rho_{\mu_\delta}^{rv} \sigma_{\mu_\delta} \sigma_{rv} & \sigma_{rv}^2
\end{array}
\right\}.$$

The prior of distance is the exponentially decreasing space density prior introduced in Bailer-Jones et al. (2018):

$$P(d | L(l, b)) \propto d^2 \exp(-d/L(l, b)), \quad (2)$$

where L(l, b) is length scale, depending on Galactic longitude and latitude. We assume that the prior of $v_\alpha$, $v_\delta$, and $v_r$ are uniform and they are only nonzero between 0 and $v_{\max} = 750$ km s⁻¹, which is determined by experience. We choose the most probable value of d, $v_\alpha$, $v_\delta$, and $v_r$ as estimation of distances and velocities.

We use distances and Galactic coordinates (l, b) to obtain Galactocentric Cartesian coordinates (x, y, z) as follows (Jurić et al. 2008):

$$\begin{aligned}
x &= R_{\odot} - d \cos(b) \cos(l) \\
y &= -d \cos(b) \sin(l) \\
z &= d \sin(b) + z_{\odot},
\end{aligned}
\quad (3)$$

where $R_{\odot} = 8.2$ kpc is the Galactocentric distance of the Sun (Bland-Hawthorn & Gerhard 2016), $z_{\odot} = 25$ pc is the solar offset from local disk midplane (Jurić et al. 2008), d is distance, and (l, b) are the Galactic coordinates. Galactic space-velocity (U, V, W) can be calculated from d, $v_\alpha$, $v_\delta$, and $v_r$ (Johnson & Soderblom 1987). We correct the velocities based on the solar peculiar motion ($U_\odot$, $V_\odot$, $W_\odot$) = (10., 11., 7.) km s⁻¹ (Tian et al. 2015; Bland-Hawthorn & Gerhard 2016) and the LSR velocity $V_{\mathrm{LSR}} = 232.8$ km s⁻¹ (McMillan 2017). x and z are positive in the directions of the Sun, and the North Galactic Pole (NGP), respectively. The y axis is defined so as to keep the system right-handed. U, V, and W point toward the Galactic center, the Galactic rotation, and the NGP, respectively.

Halo stars are commonly selected based on metallicity or kinematics. They are considered to be more metal-poor than the disk, and typical metallicity of the inner halo is from [Fe/H] = −1.4 (e.g., An et al. 2015; Gu et al. 2015; Zuo et al. 2017; Gu et al. 2019) to [Fe/H] = −1.6 (e.g., Allende Prieto et al. 2006;

<figure><img src="image_2.png" /><figcaption>Figure 1. Distribution of ln(H/D) vs. ln(H/TD) for stars with H > D and H > TD. The black dashed line is the linear function for fitting ln(H/TD) and ln(H/D) using the least square method. Halo stars (blue dots) are defined as having ln(H/TD)*(ln(H/D)-b) > 110, and the dividing line is shown in solid black.</figcaption></figure>

Carollo et al. 2007, 2010). The criterion of kinematic selection is usually $|V - V_{\mathrm{LSR}}| > V_{\mathrm{cut}}$ in the Toomre diagram.

In addition, Posti et al. (2017) select halo stars based on the dynamic method. They compute the probability that a star belongs to a given component based on the star's actions and a self-consistent total gravitational potential. They also compare their method with two other methods: kinematic selection and metallicity selection. The former is based on the Toomre diagram we mentioned above. The latter first applied selection criteria [Fe/H] ≲ −1 dex and then used two Gaussian decomposition to further select in the velocity distribution. Only the kinematically selected halo shows a strong bias in the velocity distribution, and it is difficult to identify halo stars in the velocity space dominated by the disk stars. However, the sample selected by metallicity does not contain stars with [Fe/H] > −1 dex, so that halo stars with richer metallicity are discarded by the method. But in the dynamic and kinematic methods, the metallicity distribution is centered on [Fe/H] ~ −0.5 dex and extending out to [Fe/H] ~ 0.

For a given star, Bensby et al. (2003) calculate the probability that it belongs to the thin disk, the thick disk, and the stellar halo by assuming that the Galactic space velocities (U, V, W) of each population have Gaussian distributions.

On this basis, we use cylindrical velocities and spherical velocities instead of the Cartesian velocities and assume that the metallicity also has Gaussian distribution. There are many fewer halo stars than disk stars, so the probability that stars belong to the disk and the halo will be calculated separately.

In this work, we adopt the mean rotation of halo stars $\bar{v}_\phi = -38.8$ km s⁻¹ according to $\bar{v}_\phi = -(V_{\mathrm{LSR}} + V_\odot) + \Delta v_\phi$, $\Delta v_\phi$ is the difference between $\bar{v}_\phi$ of halo stars and $v_\phi$, $\Delta v_\phi = 205$ km s⁻¹ is derived from the study of Bond et al. (2010; $\bar{v}_\phi = -20$ km s⁻¹ for their adoption $V_{\mathrm{LSR}} = 220$ km s⁻¹ and $V_\odot = 5$ km s⁻¹). Here we adopt recent $V_{\mathrm{LSR}} = 232.8$ km s⁻¹ (McMillan 2017), $V_\odot = 11$ km s⁻¹ (Bland-Hawthorn & Gerhard 2016). The velocity ellipsoid in spherical coordinates is $(\sigma_r, \sigma_\theta, \sigma_\phi) = (141, 75, 85)$ km s⁻¹ (Bond et al. 2010). For the mean metallicity and dispersion of the halo stars, we use the recent results $[\mathrm{Fe/H}] = -1.43$ and $\sigma_{[\mathrm{Fe/H}]} = 0.36$ derived by Zuo et al. (2017). So the probability that stars belong to a halo (which we call H) can be given by a
<figure><img src="image_3.png" /><figcaption>Figure 2. Velocity distribution of our halo sample (black dots) and probability contours of two Gaussian components (thin and thick disk). The red (blue) lines show the 1σ, 2σ, and 3σ thin (thick) disk contours from inside to outside.</figcaption></figure>

four-dimensional Gaussian distribution:

$$f(v_r, v_\theta, v_\phi, [\text{Fe/H}]) = k \cdot \exp\left(-\frac{v_r^2}{2\sigma_r^2} - \frac{v_\theta^2}{2\sigma_\theta^2} - \frac{(v_\phi - \bar{v}_\phi)^2}{2\sigma_\phi^2} - \frac{([\text{Fe/H}] - \overline{[\text{Fe/H}]})^2}{2\sigma_{[\text{Fe/H}]}^2}\right), \quad (4)$$

where $k = \frac{1}{(2\pi)^2 \sigma_r \sigma_\theta \sigma_\phi \sigma_{[\text{Fe/H}]}}$. For those stars with no metallicity parameters, which is less than 10% of our sample, we set their [Fe/H] to -1 in Equation (4) to prevent the loss of halo stars.

Then we calculate the probability that stars belong to the thin disk and the thick disk (which we call D and TD). To minimize the influence of halo stars on the disk, we here remove stars with $v_\phi > -40 \text{ km s}^{-1}$ and $[\text{Fe/H}] < -1.4$. We use the SCI-KIT LEARN package in PYTHON (Pedregosa et al. 2012) to fit a two-component Gaussian Mixture Model to spherical velocities ($v_R$, $v_\phi$, and $v_z$) and stellar metallicity ([Fe/H]). In this fitting, each component has its own diagonal covariance matrix. The velocity dispersions of the thin and thick disks are $(\sigma_R, \sigma_\phi, \sigma_z) = (36, 24, 18) \text{ km s}^{-1}$ and $(\sigma_R, \sigma_\phi, \sigma_z) = (62, 45, 45) \text{ km s}^{-1}$, respectively. The mean $v_R$ and $v_z$ are close to $0 \text{ km s}^{-1}$ for both thin and thick disks. The mean of $v_\phi$ is $-224 \text{ km s}^{-1}$ for the thin disk and $-188 \text{ km s}^{-1}$ for the thick disk. The mean metallicity and dispersion are $-0.11, 0.28$ for the thin disk and $-0.47, 0.32$ for the thick disk.

We use the least square to fit the function:

$$\ln(\text{H/D}) = a * \ln(\text{H/TD}) + b \quad (5)$$

to stars with $H > D$ and $H > TD$. The optimal values for the parameters are $a = 4.14$ and $b = 15.14$. Then we select stars with $\ln(\text{H/TD}) * (\ln(\text{H/D}) - b) > 110$ and get a similar number of stars with $L_z > 0$ and stars with $L_z < 0$. We finally get 3845 sample halo stars. The result is shown in Figure 1. Figure 2 shows their velocity distribution and two Gaussian components (thin and thick disks) in the cylindrical coordinate system.

### 3. Analysis

Helmi et al. (2017) use the “Integrals of Motion” space, which consists of energy and two components of the angular momentum. They study the distribution of stars in this space and identify several substructures that could potentially be

<figure><img src="image_4.png" /><figcaption>Figure 3. Distribution of energy vs. $L_z$ (top panel), and $L_\perp$ vs. $L_z$ (bottom panel) for the halo sample that was selected in velocity and metallicity from the stars that were in common with both Gaia and RAVE. The green rectangle shows the range of Figure 4.</figcaption></figure>

related to merger events. Li et al. (2019) also identify halo substructures in this space and they improve the method of estimating statistical significance. Here, we use the latter method to find substructures from our sample stars.

First, we compute energy and angular momentum by adopting a Galaxy potential model (McMillan 2017) with four components: the cold gas disks near the Galactic plane, the thin and thick stellar disks, a bulge, and a dark matter halo. Figure 3 shows the distribution in energy versus z-angular momentum, $L_z$, in the upper panel, and $L_\perp = \sqrt{L_x^2 + L_y^2}$ versus $L_z$ in the lower panel for our sample stars. The green rectangle in this figure shows the populated region, $-2000 < L_z < 2000 \text{ km s}^{-1} \text{kpc}$, $-2.10 \times 10^5 < E < -0.9 \times 10^5 \text{ km s}^{-2}$, and $L_\perp < 2400 \text{ km s}^{-1} \text{kpc}$.

Then we scale the data to unit standard deviation and calculate the stellar density (which we call $kde_0$) in
<figure><img src="image_5.png" /><figcaption>Figure 4. Mean of three-dimensional (E, Lz, and L⊥) density kde<sub>real</sub> along the L<sub>⊥</sub> (left panel) and E (right panel). The black dots are the member stars of substructures.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 5. Similar to Figure 4, but now we use the average density of all 5000 randomized realizations of the data.</figcaption></figure>

E − L<sub>z</sub> − L<sub>⊥</sub> space using the kernel density estimator in SCI-KIT LEARN. We choose the “Tophat” kernel and the optimal bandwidth of the kernel is 0.28, which is determined by the cross-validation method (e.g., Weiss & Kulikowski 1991), also implemented in SCI-KIT LEARN. To show the three-dimensional density kde<sub>0</sub>(E, L<sub>z</sub>, L<sub>⊥</sub>) in the plane, we take the arithmetic mean value of kde<sub>0</sub>(E, L<sub>z</sub>, L<sub>⊥</sub>) along the specified axis as a two-dimensional density function. In Figure 4, the left panel shows the mean value along the L<sub>⊥</sub> and the right panel shows the mean value along the E. Because of the characteristics of the “Tophat” kernel, the number of stars in a spherical region with a radius of bandwidth can be derived from the density at the center of the sphere:

$$
N_0(E, L_z, L_\perp) = \frac{4}{3} \pi r^3 kde_0(E, L_z, L_\perp) \quad (6)
$$

where r = 0.28 is the bandwidth.

To identify the authentic overdensities instead of the relative
peaks of density, we reshuffle each velocity component (v<sub>R</sub>, v<sub>&theta;</sub>,
and v<sub>&phi;</sub>) to create 5000 randomized data sets. This scrambles the
correspondence between stars and their velocity components
and it means that each velocity component of a star may come
from different stars. We recompute their E, L<sub>z</sub>, L<sub>&perp;</sub> and use the

kernel density estimator with the same parameters to get the
densities, kde<sub>i</sub>(E, L<sub>z</sub>, L<sub>&perp;</sub>), and the numbers, N<sub>i</sub>(E, L<sub>z</sub>, L<sub>&perp;</sub>) just
like we did with real data. We have generated 5000 random
samples so i = 1, 2, 3, ..., 5000. We use the cumulative
distribution function of Poisson distribution:

$$
P(X < N_0) = \sum_{k=0}^{N_0-1} \frac{\lambda^k}{k!} e^{-\lambda} \quad (7)
$$

to estimate the significance. Parameter λ is the mean of N for
5000 randomized data sets:

$$
\lambda(E, L_z, L_{\perp}) = \frac{1}{5000} \sum_{i=1}^{5000} N_i(E, L_z, L_{\perp}). \quad (8)
$$

Figure 5 shows the average density of 5000 randomized data
sets. We can see a V-shaped envelope similar to the density
distribution of real data (Figure 4), but it is more smooth.
Figure 6 shows the difference between the kernel density of real
data and the average density of all 5000 randomized realizations
of the data. There are several clear overdensities. We divide the
E − Lz − L⊥ space into smaller cube pixels that are about 0.04
on a side. These pixels are used as probes to scan the “Integrals
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Similar to Figure 4, but now we use the difference between the kernel density of real data and the average density of all 5000 randomized realizations of the data.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Spherical velocity distribution for stars comprising the identified substructures.</figcaption></figure>

of Motion” space. We select pixels with significance >3.5σ and λ > 3. The clumps formed by adjacent pixels are part of one or more overdensities. We use SCI-KIT IMAGE (van der Walt et al. 2014) implementation to remove very small clumps and connect two clumps that are close but not adjacent. We only consider overdensities bigger than 230 pixels. When we use the above method to identify overdensity from random data, we only find one overdensity in 100 randomized data sets.

We identify two overdensities in “Integrals of Motion” space and the member stars are shown in Figure 4. The significance of the complete overdensity is also estimated. These overdensities are identified as substructures in this study, and we label them GR-1 and GR-2. The information of member stars is listed in Tables A1 and A2 in the Appendix. Velocity distribution of these member stars is shown in Figure 7. These stars are separated in spherical velocity space. GR-1 shows distinct separate clumps in $v_\phi - v_\theta$ space, and the velocity distribution characteristic is similar to VelHel-7 of Helmi et al. (2017) and GL-1, GL-2 of Li et al. (2019). Although VelHel-6 of Helmi et al. (2017) is closer to GR-1 in “Integrals of Motion” space, they have different characteristics in velocity space. Many more substructures have been reported by other authors (e.g., Klement et al. 2009; Zhao et al. 2015), but we have not found other substructures that are similar to ours. This may be due to different samples or methods.

<caption>**Table 1**</caption>

The Mean and Dispersion of Energy and Angular Momentum of Substructures

<table><thead><tr><th>Notation</th><th><i>E</i><br>(×10<sup>3</sup> km<sup>2</sup> s<sup>-2</sup>)</th><th><i>L</i><sub>z</sub><br>(km s<sup>-1</sup> kpc)</th><th><i>L</i><sub>⊥</sub><br>(km s<sup>-1</sup> kpc)</th></tr></thead><tbody><tr><td>GR-1</td><td>-185 ± 4</td><td>-237 ± 96</td><td>659 ± 70</td></tr><tr><td>GR-2</td><td>-186 ± 3</td><td>622 ± 87</td><td>375 ± 74</td></tr><tr><td>GL-1</td><td>-168 ± 3</td><td>-809 ± 161</td><td>978 ± 132</td></tr><tr><td>GL-2</td><td>-167 ± 1</td><td>-368 ± 87</td><td>1284 ± 57</td></tr><tr><td>VelHel-6</td><td>-176 ± 4</td><td>-542 ± 330</td><td>244 ± 117</td></tr><tr><td>VelHel-7</td><td>-174 ± 6</td><td>-919 ± 313</td><td>563 ± 162</td></tr></tbody></table>

Figure 8 shows metallicity distribution for the member stars, GR-1 is more similar to GL-1 of Li et al. (2019). We consider that this could be related to multiple accumulation from the same dwarf galaxy, which need further confirmation in the future. In addition, we can also see from Figure 9 that most member stars in GR-2 are metal-rich and slightly α-enriched, with a mean α-abundance of $[\alpha/Fe] = +0.1$ dex, the member stars in GR-1 are metal-poor and α-enriched with a mean α-abundance of $[\alpha/Fe] = +0.3$ dex. The mean and dispersion of energy and angular momentum of the above structures are listed in Table 1. The McMillan (2017) potential model was used to recomputed the substructure energy found by other authors.
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Metallicity distribution for the member stars comprising the identified substructures. The halo sample is shown as a gray histogram.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Chemical abundance distribution [α/Fe] vs. [Fe/H] for the member stars comprising the identified substructures. The orange dots represent “GR-1” and the green dots represent “GR-2.” Halo stars are shown in the background for comparison and the color coding corresponds to the number of halo stars in each pixel.</figcaption></figure>

## 4. Summary and Discussion

We cross-match Gaia DR2 and RAVE DR5 data to get a sample of stars with full phase space information. By combining kinematic and chemical properties of stars, we obtain 3845 halo sample stars. We determine the density field of the sample halo stars in “Integrals-of-Motion” space, defined by two components of the angular momentum, $L_⊥$ and $L_ζ$, and energy. In order to identify authentic substructures from several overdensities in this space, we estimate the statistical significance for these overdensities and identify two substructures, GR-1 and GR-2. The catalog of two substructures’ members are given in the Appendix.

In this study, both substructures are new. The velocity distribution characteristic of GR-1 in our study is similar to VelHel-7 of Helmi et al. (2017) and GL-1, GL-2 of Li et al. (2019), but they are separated in “Integrals of Motion.” The metallicity of GR-2 is close to the thick disk, but GR-2 has retrograde trajectories. Their origin may be related to the

accretion events of the dwarf galaxy, which must be confirmed in the following studies. Bonaca et al. (2017) selected halo stars from Gaia, RAVE, and APOGEE data kinematically, and they showed that half of their halo sample stars have $[Fe/H] > -1$. The orbital directions of these metal-rich halo stars are preferentially prograde, which is different from the intrinsically isotropic orbital distribution of the metal-poor halo stars. At the same time, they also found similar properties in their Latte cosmological simulation and suggested that metal-rich halo stars in the solar neighborhood formed in situ within the Galactic disk. Other studies have also implied that some halo stars are preferentially on slight prograde orbits (e.g., Deason et al. 2017; Kafle et al. 2017; Bird et al. 2019), while the discovery that GR-2 has a retrograde orbit suggests that metal-rich stars may also originate from accretion. The history of the formation of the Galaxy may still remain in the dynamical and chemical properties of substructures. This can help us understand the early stages of the Galaxy.

We thank the referee and statistical editor for insightful comments and suggestions, which have improved the paper significantly. This work was supported by the National Natural Foundation of China (NSFC No. 11973042 and No. 11973052). H.J.N. acknowledges funding from NSF grant AST 16-15688. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for DPAC has been provided by national institutions, in particular, the institutions participating in the Gaia Multilateral Agreement.

Funding for RAVE has been provided by the Australian Astronomical Observatory; the Leibniz-Institut fuer Astrophysik Potsdam (AIP); the Australian National University; the Australian Research Council; the French National Research Agency; the German Research Foundation (SPP 1177 and SFB 881); the European Research Council (ERC-StG 240271 Galactica); the Istituto Nazionale di Astrofisica at Padova; The Johns Hopkins University; the National Science Foundation of the USA (AST-0908326); the W. M. Keck foundation; the Macquarie University; the Netherlands Research School for Astronomy; the Natural Sciences and Engineering Research Council of Canada; the Slovenian Research Agency; the Swiss National Science Foundation; the Science & Technology Facilities Council of the UK; Opticon; Strasbourg Observatory; and the Universities of Groningen, Heidelberg and Sydney. The RAVE website is at https://www.rave-survey.org.

# Appendix

## Appendix A
Member Stars of the New Identified Substructures

Unique source identifiers in Gaia, positions, metallicities, space velocities and z-angular momentum for the member stars are provided in Tables A1 and A2.
<table><caption>Table A1
GR-1, 4.57 σ, 99 Stars</caption><thead><tr><th>Source-id</th><th>l<br>(deg)</th><th>b<br>(deg)</th><th>[Fe/H]<br>(dex)</th><th>x<br>(kpc)</th><th>y<br>(kpc)</th><th>z<br>(kpc)</th><th>U<br>(km s<sup>-1</sup>)</th><th>V<br>(km s<sup>-1</sup>)</th><th>W<br>(km s<sup>-1</sup>)</th><th>L<sub>z</sub><br>(km s<sup>-1</sup> kpc)</th></tr></thead><tbody><tr><td>6098916889620300672</td><td>323.15</td><td>14.25</td><td>-1.37</td><td>5.8</td><td>1.8</td><td>0.8</td><td>-4.0</td><td>11.3</td><td>102.6</td><td>-72.8</td></tr><tr><td>4715376531932531200</td><td>296.65</td><td>-54.22</td><td>...</td><td>7.6</td><td>1.1</td><td>-1.7</td><td>44.2</td><td>39.7</td><td>-84.7</td><td>-254.8</td></tr><tr><td>6360190882785741952</td><td>314.12</td><td>-29.00</td><td>-1.31</td><td>6.9</td><td>1.3</td><td>-1.0</td><td>-34.7</td><td>45.7</td><td>-83.7</td><td>-361.7</td></tr><tr><td>6822643716784658560</td><td>39.70</td><td>-54.34</td><td>-1.34</td><td>7.1</td><td>-0.9</td><td>-1.9</td><td>-10.7</td><td>41.5</td><td>105.5</td><td>-286.8</td></tr><tr><td>6273670931270685184</td><td>323.42</td><td>33.63</td><td>-0.99</td><td>7.0</td><td>0.9</td><td>1.0</td><td>59.2</td><td>31.6</td><td>84.7</td><td>-167.9</td></tr><tr><td>6333120597271443456</td><td>351.45</td><td>43.27</td><td>-0.99</td><td>6.6</td><td>0.2</td><td>1.5</td><td>11.8</td><td>21.8</td><td>-120.0</td><td>-141.6</td></tr><tr><td>4705104619428366720</td><td>297.60</td><td>-51.35</td><td>-1.24</td><td>7.7</td><td>1.0</td><td>-1.4</td><td>-86.2</td><td>26.0</td><td>72.5</td><td>-284.4</td></tr><tr><td>6697060904572244352</td><td>4.08</td><td>-30.38</td><td>-0.85</td><td>6.1</td><td>-0.1</td><td>-1.2</td><td>-39.3</td><td>20.0</td><td>-117.5</td><td>-116.3</td></tr><tr><td>6419114462535500160</td><td>321.46</td><td>-22.26</td><td>-0.78</td><td>6.8</td><td>1.1</td><td>-0.7</td><td>-17.2</td><td>16.6</td><td>-78.7</td><td>-132.1</td></tr><tr><td>6194053026560559488</td><td>309.59</td><td>38.58</td><td>-1.0</td><td>7.0</td><td>1.4</td><td>1.5</td><td>-43.7</td><td>21.3</td><td>87.4</td><td>-210.9</td></tr><tr><td>6718953383671971584</td><td>359.73</td><td>-19.67</td><td>...</td><td>5.5</td><td>0.0</td><td>-0.9</td><td>63.7</td><td>71.0</td><td>117.3</td><td>-392.7</td></tr><tr><td>6806331572732029568</td><td>21.09</td><td>-35.16</td><td>-1.23</td><td>6.0</td><td>-0.9</td><td>-1.7</td><td>11.6</td><td>26.5</td><td>-100.3</td><td>-168.3</td></tr><tr><td>6467385187658987904</td><td>337.95</td><td>-35.23</td><td>-1.32</td><td>7.0</td><td>0.5</td><td>-0.9</td><td>-79.6</td><td>34.2</td><td>81.8</td><td>-278.0</td></tr><tr><td>4353736643479056384</td><td>13.12</td><td>25.24</td><td>-1.84</td><td>3.9</td><td>-1.0</td><td>2.1</td><td>-138.2</td><td>79.2</td><td>-89.7</td><td>-169.2</td></tr><tr><td>4195113433837448064</td><td>31.42</td><td>-17.88</td><td>-1.48</td><td>6.0</td><td>-1.3</td><td>-0.8</td><td>-61.6</td><td>77.2</td><td>83.9</td><td>-380.7</td></tr><tr><td>4905172506836913920</td><td>306.76</td><td>-56.55</td><td>-1.71</td><td>7.4</td><td>1.1</td><td>-2.1</td><td>27.3</td><td>48.6</td><td>103.4</td><td>-328.3</td></tr><tr><td>6469232749446813824</td><td>342.02</td><td>-34.68</td><td>-1.92</td><td>7.3</td><td>0.3</td><td>-0.6</td><td>28.4</td><td>43.6</td><td>90.0</td><td>-310.4</td></tr><tr><td>6846461582481204096</td><td>15.92</td><td>-30.53</td><td>-2.18</td><td>6.9</td><td>-0.4</td><td>-0.7</td><td>113.9</td><td>26.2</td><td>116.6</td><td>-222.9</td></tr><tr><td>6674640385011413120</td><td>352.97</td><td>-36.08</td><td>-1.21</td><td>3.9</td><td>0.5</td><td>-3.2</td><td>-138.8</td><td>27.3</td><td>65.7</td><td>-179.7</td></tr><tr><td>4342588209752172160</td><td>1.94</td><td>27.96</td><td>...</td><td>4.1</td><td>-0.1</td><td>2.2</td><td>39.5</td><td>78.2</td><td>-168.0</td><td>-329.7</td></tr><tr><td>6740456223339677312</td><td>4.82</td><td>-26.64</td><td>-0.92</td><td>4.5</td><td>-0.3</td><td>-1.9</td><td>88.1</td><td>23.0</td><td>171.4</td><td>-130.6</td></tr><tr><td>6446375551973492992</td><td>336.94</td><td>-28.45</td><td>-2.25</td><td>6.3</td><td>0.8</td><td>-1.1</td><td>3.0</td><td>44.7</td><td>106.9</td><td>-278.2</td></tr><tr><td>6415779334530809728</td><td>321.53</td><td>-27.67</td><td>-1.76</td><td>6.3</td><td>1.5</td><td>-1.2</td><td>111.1</td><td>52.1</td><td>-92.1</td><td>-161.5</td></tr><tr><td>6450293932239999744</td><td>330.69</td><td>-36.96</td><td>...</td><td>6.8</td><td>0.8</td><td>-1.2</td><td>-98.0</td><td>32.1</td><td>59.7</td><td>-295.9</td></tr><tr><td>5813464395238590976</td><td>325.97</td><td>-16.33</td><td>-0.89</td><td>4.6</td><td>2.5</td><td>-1.3</td><td>-50.5</td><td>31.8</td><td>-168.5</td><td>-269.1</td></tr><tr><td>6407668963103576064</td><td>329.03</td><td>-48.49</td><td>...</td><td>6.6</td><td>1.0</td><td>-2.1</td><td>2.5</td><td>50.7</td><td>-101.4</td><td>-329.6</td></tr><tr><td>4414394741476513536</td><td>0.09</td><td>42.57</td><td>-0.92</td><td>6.1</td><td>-0.0</td><td>1.9</td><td>32.8</td><td>44.4</td><td>-106.1</td><td>-271.8</td></tr><tr><td>6253774890413942912</td><td>346.87</td><td>28.95</td><td>-1.0</td><td>5.8</td><td>0.6</td><td>1.4</td><td>-140.6</td><td>34.9</td><td>-74.2</td><td>-281.0</td></tr><tr><td>6580544764022363520</td><td>359.77</td><td>-44.69</td><td>...</td><td>5.6</td><td>0.0</td><td>-2.6</td><td>-29.1</td><td>51.3</td><td>-121.3</td><td>-285.8</td></tr><tr><td>6278779051839299328</td><td>335.20</td><td>33.52</td><td>-1.76</td><td>5.4</td><td>1.3</td><td>2.1</td><td>89.5</td><td>99.6</td><td>97.5</td><td>-415.5</td></tr><tr><td>4181613110374697344</td><td>23.20</td><td>-18.28</td><td>-1.36</td><td>4.7</td><td>-1.5</td><td>-1.2</td><td>-81.7</td><td>114.7</td><td>101.1</td><td>-410.0</td></tr><tr><td>5795111411562833152</td><td>312.90</td><td>-12.76</td><td>...</td><td>6.3</td><td>2.0</td><td>-0.6</td><td>14.7</td><td>48.0</td><td>114.5</td><td>-273.0</td></tr><tr><td>6446682796754391936</td><td>338.27</td><td>-28.03</td><td>-0.86</td><td>6.6</td><td>0.7</td><td>-0.9</td><td>83.1</td><td>42.8</td><td>124.0</td><td>-225.7</td></tr><tr><td>6189105151220002816</td><td>311.71</td><td>34.25</td><td>-1.75</td><td>6.7</td><td>1.7</td><td>1.6</td><td>-56.3</td><td>34.0</td><td>-68.7</td><td>-323.6</td></tr><tr><td>6482200419648454144</td><td>351.91</td><td>-37.26</td><td>-1.06</td><td>6.1</td><td>0.3</td><td>-1.6</td><td>68.6</td><td>54.7</td><td>-94.1</td><td>-315.0</td></tr><tr><td>6793672002009076864</td><td>13.51</td><td>-35.00</td><td>...</td><td>4.6</td><td>-0.9</td><td>-2.6</td><td>-126.2</td><td>57.2</td><td>63.3</td><td>-153.6</td></tr><tr><td>6662369212476955136</td><td>348.99</td><td>-20.38</td><td>-1.25</td><td>6.3</td><td>0.4</td><td>-0.7</td><td>69.6</td><td>55.7</td><td>-81.0</td><td>-325.2</td></tr><tr><td>4354802482560690048</td><td>12.75</td><td>27.77</td><td>-2.03</td><td>5.9</td><td>-0.5</td><td>1.3</td><td>-41.8</td><td>15.1</td><td>-111.0</td><td>-67.1</td></tr><tr><td>6855988919456460928</td><td>22.31</td><td>-30.34</td><td>-0.9</td><td>4.8</td><td>-1.4</td><td>-2.1</td><td>-95.6</td><td>51.8</td><td>73.9</td><td>-114.2</td></tr><tr><td>5807722092676009600</td><td>319.95</td><td>-16.37</td><td>-0.98</td><td>7.1</td><td>0.9</td><td>-0.4</td><td>79.2</td><td>37.2</td><td>92.3</td><td>-193.9</td></tr><tr><td>6617500174464520832</td><td>18.51</td><td>-51.33</td><td>...</td><td>6.1</td><td>-0.7</td><td>-2.7</td><td>25.8</td><td>21.0</td><td>-79.7</td><td>-147.0</td></tr><tr><td>6390694633874538496</td><td>316.76</td><td>-45.53</td><td>-2.11</td><td>7.6</td><td>0.5</td><td>-0.8</td><td>-56.5</td><td>42.9</td><td>-94.2</td><td>-357.2</td></tr><tr><td>6593804217121507968</td><td>1.38</td><td>-58.28</td><td>-1.08</td><td>6.4</td><td>-0.0</td><td>-2.9</td><td>12.5</td><td>26.9</td><td>-85.4</td><td>-171.7</td></tr><tr><td>6511387028823212544</td><td>342.42</td><td>-51.60</td><td>-2.28</td><td>7.0</td><td>0.4</td><td>-1.5</td><td>33.0</td><td>53.7</td><td>-82.2</td><td>-365.9</td></tr><tr><td>6777598718260083584</td><td>10.49</td><td>-42.97</td><td>-1.1</td><td>5.9</td><td>-0.4</td><td>-2.2</td><td>12.2</td><td>55.5</td><td>94.3</td><td>-330.7</td></tr><tr><td>6667233009535349888</td><td>349.07</td><td>-32.38</td><td>-2.27</td><td>4.6</td><td>0.7</td><td>-2.3</td><td>-158.1</td><td>-6.4</td><td>49.9</td><td>-82.0</td></tr><tr><td>6082279178445547520</td><td>309.20</td><td>12.41</td><td>-0.62</td><td>6.3</td><td>2.4</td><td>0.7</td><td>116.5</td><td>91.5</td><td>92.2</td><td>-297.2</td></tr><tr><td>6305435577383801472</td><td>340.62</td><td>35.43</td><td>-0.63</td><td>6.2</td><td>0.7</td><td>1.5</td><td>-63.9</td><td>17.1</td><td>129.9</td><td>-150.9</td></tr><tr><td>4381400665271860480</td><td>19.62</td><td>25.70</td><td>-0.86</td><td>4.6</td><td>-1.3</td><td>1.9</td><td>124.8</td><td>30.3</td><td>120.1</td><td>-300.1</td></tr><tr><td>6497164021283998976</td><td>318.68</td><td>-60.57</td><td>-1.06</td><td>7.7</td><td>0.5</td><td>-1.2</td><td>-11.1</td><td>19.7</td><td>72.8</td><td>-156.6</td></tr><tr><td>6317919780298422272</td><td>354.53</td><td>37.65</td><td>-1.42</td><td>5.5</td><td>0.3</td><td>2.1</td><td>-68.2</td><td>72.9</td><td>-102.1</td><td>-421.0</td></tr><tr><td>6443381955472092160</td><td>337.29</td><td>-33.10</td><td>-1.56</td><td>5.0</td><td>1.4</td><td>-2.3</td><td>81.2</td><td>58.4</td><td>-68.8</td><td>-180.5</td></tr><tr><td>6415791880133409920</td><td>321.64</td><td>-27.75</td><td>...</td><td>6.9</td><td>1.1</td><td>-0.9</td><td>71.3</td><td>40.3</td><td>-90.3</td><td>-201.0</td></tr><tr><td>5531106613768555648</td><td>259.73</td><td>-9.26</td><td>...</td><td>8.3</td><td>0.4</td><td>-0.0</td><td>46.6</td><td>38.5</td><td>-79.3</td><td>-300.5</td></tr><tr><td>6003500922668306944</td><td>328.93</td><td>12.10</td><td>-0.65</td><td>4.9</td><td>2.0</td><td>0.9</td><td>76.8</td><td>88.4</td><td>-147.6</td><td>-274.7</td></tr><tr><td>2597932671179367936</td><td>48.94</td><td>-55.83</td><td>...</td><td>8.0</td><td>-0.2</td><td>-0.3</td><td>-29.1</td><td>36.4</td><td>83.3</td><td>-287.2</td></tr><tr><td>6753447365539976448</td><td>11.45</td><td>-24.54</td><td>...</td><td>4.4</td><td>-0.8</td><td>-1.7</td><td>-2.0</td><td>27.7</td><td>168.0</td><td>-121.1</td></tr><tr><td>6259344638358421504</td><td>346.72</td><td>33.62</td><td>-1.39</td><td>5.5</td><td>0.6</td><td>1.9</td><td>-105.6</td><td>23.1</td><td>-93.0</td><td>-194.2</td></tr><tr><td>6267173332950478336</td><td>354.53</td><td>32.41</td><td>...</td><td>5.5</td><td>0.3</td><td>1.7</td><td>21.4</td><td>73.8</td><td>-145.6</td><td>-402.6</td></tr><tr><td>6858853692704665856</td><td>28.81</td><td>-33.91</td><td>...</td><td>6.4</td><td>-1.0</td><td>-1.4</td><td>38.5</td><td>44.4</td><td>112.4</td><td>-321.5</td></tr><tr><td>6575958662367490816</td><td>354.95</td><td>-46.37</td><td>-1.86</td><td>6.5</td><td>0.1</td><td>-1.7</td><td>14.1</td><td>29.2</td><td>92.3</td><td>-189.0</td></tr><tr><td>6649706450595363712</td><td>339.06</td><td>-20.93</td><td>-1.45</td><td>5.5</td><td>1.1</td><td>-1.1</td><td>-170.2</td><td>21.2</td><td>66.2</td><td>-294.3</td></tr><tr><td>5796181476896205696</td><td>309.48</td><td>-13.05</td><td>-1.15</td><td>4.8</td><td>4.1</td><td>-1.2</td><td>19.7</td><td>51.8</td><td>-100.1</td><td>-168.0</td></tr></tbody></table>
<table><caption>Table A1
(Continued)</caption><thead><tr><th>Source-id</th><th><i>l</i><br>(deg)</th><th><i>b</i><br>(deg)</th><th>[Fe/H]<br>(dex)</th><th><i>x</i><br>(kpc)</th><th><i>y</i><br>(kpc)</th><th><i>z</i><br>(kpc)</th><th><i>U</i><br>(km s<sup>-1</sup>)</th><th><i>V</i><br>(km s<sup>-1</sup>)</th><th><i>W</i><br>(km s<sup>-1</sup>)</th><th><i>L</i><sub>z</sub><br>(km s<sup>-1</sup> kpc)</th></tr></thead><tbody><tr><td>6262591290040852096</td><td>354.40</td><td>28.33</td><td>-1.66</td><td>5.8</td><td>0.2</td><td>1.3</td><td>17.1</td><td>59.3</td><td>88.7</td><td>-340.8</td></tr><tr><td>6491444052558679424</td><td>325.39</td><td>-52.77</td><td>...</td><td>7.9</td><td>0.2</td><td>-0.5</td><td>32.5</td><td>15.4</td><td>-76.8</td><td>-113.3</td></tr><tr><td>6835943340714822016</td><td>34.27</td><td>-40.98</td><td>...</td><td>6.3</td><td>-1.3</td><td>-1.9</td><td>74.2</td><td>17.0</td><td>135.5</td><td>-202.2</td></tr><tr><td>6695050172681806080</td><td>5.27</td><td>-34.07</td><td>...</td><td>6.8</td><td>-0.1</td><td>-1.0</td><td>66.5</td><td>38.8</td><td>-66.1</td><td>-271.2</td></tr><tr><td>6484804307998121600</td><td>357.52</td><td>-41.88</td><td>-1.81</td><td>5.2</td><td>0.1</td><td>-2.7</td><td>104.5</td><td>89.2</td><td>-63.5</td><td>-451.4</td></tr><tr><td>6426826888067362944</td><td>327.79</td><td>-31.15</td><td>...</td><td>4.7</td><td>2.2</td><td>-2.5</td><td>55.2</td><td>44.4</td><td>-103.0</td><td>-85.6</td></tr><tr><td>6135575638078558080</td><td>303.84</td><td>18.99</td><td>-0.86</td><td>7.0</td><td>1.7</td><td>0.7</td><td>97.8</td><td>65.1</td><td>90.2</td><td>-286.9</td></tr><tr><td>6849425139977703040</td><td>19.65</td><td>-31.12</td><td>-1.44</td><td>4.3</td><td>-1.4</td><td>-2.5</td><td>63.0</td><td>31.0</td><td>-101.8</td><td>-220.8</td></tr><tr><td>6676827996537504896</td><td>357.93</td><td>-39.33</td><td>-0.54</td><td>5.0</td><td>0.1</td><td>-2.6</td><td>48.8</td><td>12.5</td><td>-92.9</td><td>-56.5</td></tr><tr><td>3637344787222734592</td><td>323.91</td><td>58.37</td><td>-0.92</td><td>7.0</td><td>0.8</td><td>2.4</td><td>-36.7</td><td>29.1</td><td>102.9</td><td>-235.6</td></tr><tr><td>6531487956804986752</td><td>333.30</td><td>-67.53</td><td>-0.8</td><td>7.2</td><td>0.5</td><td>-2.7</td><td>-43.0</td><td>22.4</td><td>89.1</td><td>-182.9</td></tr><tr><td>6658598265547671936</td><td>346.95</td><td>-25.55</td><td>...</td><td>5.3</td><td>0.7</td><td>-1.4</td><td>103.8</td><td>36.5</td><td>-86.6</td><td>-121.4</td></tr><tr><td>6848010210249401856</td><td>16.83</td><td>-30.86</td><td>-0.61</td><td>5.7</td><td>-0.8</td><td>-1.5</td><td>-79.5</td><td>71.6</td><td>-141.5</td><td>-347.8</td></tr><tr><td>5819645609098141824</td><td>318.78</td><td>-12.46</td><td>-1.43</td><td>5.6</td><td>2.3</td><td>-0.7</td><td>24.9</td><td>61.4</td><td>-101.9</td><td>-289.4</td></tr><tr><td>6478853059576336768</td><td>349.20</td><td>-43.11</td><td>-1.67</td><td>7.2</td><td>0.2</td><td>-0.9</td><td>53.5</td><td>19.4</td><td>109.4</td><td>-130.5</td></tr><tr><td>6582323258440558848</td><td>1.65</td><td>-44.70</td><td>-2.34</td><td>6.1</td><td>-0.1</td><td>-2.1</td><td>68.3</td><td>36.9</td><td>-69.0</td><td>-228.5</td></tr><tr><td>6260477753814244608</td><td>351.60</td><td>28.36</td><td>...</td><td>6.6</td><td>0.2</td><td>0.9</td><td>-45.9</td><td>36.4</td><td>-99.3</td><td>-251.9</td></tr><tr><td>6814677347020224000</td><td>24.96</td><td>-47.69</td><td>-1.38</td><td>7.3</td><td>-0.4</td><td>-1.1</td><td>-14.0</td><td>49.7</td><td>-102.2</td><td>-355.3</td></tr><tr><td>6704697528226119552</td><td>348.94</td><td>-18.76</td><td>...</td><td>4.8</td><td>0.7</td><td>-1.1</td><td>122.8</td><td>76.9</td><td>154.0</td><td>-290.2</td></tr><tr><td>6269052359662541440</td><td>324.22</td><td>29.93</td><td>...</td><td>5.6</td><td>1.8</td><td>1.8</td><td>-149.4</td><td>2.8</td><td>-76.4</td><td>-290.8</td></tr><tr><td>6463190104122275968</td><td>342.04</td><td>-42.00</td><td>...</td><td>6.0</td><td>0.7</td><td>-2.1</td><td>-4.8</td><td>17.8</td><td>-95.5</td><td>-110.4</td></tr><tr><td>5786628095241089408</td><td>308.11</td><td>-15.41</td><td>-1.67</td><td>7.7</td><td>0.6</td><td>-0.2</td><td>-17.8</td><td>39.5</td><td>-99.2</td><td>-315.7</td></tr><tr><td>5913106227764290176</td><td>333.24</td><td>-13.38</td><td>...</td><td>6.1</td><td>1.0</td><td>-0.5</td><td>24.0</td><td>34.1</td><td>-108.8</td><td>-184.3</td></tr><tr><td>6278040695420767104</td><td>331.57</td><td>32.66</td><td>...</td><td>5.2</td><td>1.6</td><td>2.2</td><td>-12.0</td><td>54.6</td><td>118.7</td><td>-302.3</td></tr><tr><td>4378858147711990400</td><td>15.26</td><td>26.08</td><td>-1.19</td><td>4.3</td><td>-1.1</td><td>2.0</td><td>-109.2</td><td>69.4</td><td>-85.7</td><td>-186.8</td></tr><tr><td>6512412907532485376</td><td>334.55</td><td>-57.07</td><td>-2.37</td><td>7.4</td><td>0.4</td><td>-1.3</td><td>17.5</td><td>32.0</td><td>-81.7</td><td>-230.8</td></tr><tr><td>4403212776946445696</td><td>5.26</td><td>38.55</td><td>-1.91</td><td>6.1</td><td>-0.2</td><td>1.7</td><td>-102.8</td><td>30.7</td><td>-101.4</td><td>-165.6</td></tr><tr><td>5912911678614539264</td><td>333.42</td><td>-14.12</td><td>-0.97</td><td>4.9</td><td>1.7</td><td>-0.9</td><td>-54.1</td><td>32.9</td><td>-127.7</td><td>-250.1</td></tr><tr><td>6768555926615706624</td><td>17.19</td><td>-21.63</td><td>-0.66</td><td>6.2</td><td>-0.6</td><td>-0.8</td><td>103.7</td><td>24.0</td><td>-98.7</td><td>-213.1</td></tr><tr><td>5915043425508255488</td><td>330.27</td><td>-10.37</td><td>...</td><td>5.5</td><td>1.6</td><td>-0.6</td><td>-67.7</td><td>3.1</td><td>-125.0</td><td>-122.8</td></tr><tr><td>6421895681498235008</td><td>327.66</td><td>-27.84</td><td>-1.57</td><td>3.5</td><td>3.0</td><td>-2.9</td><td>17.7</td><td>20.6</td><td>-117.6</td><td>-19.0</td></tr><tr><td>6558374658235864960</td><td>343.17</td><td>-47.90</td><td>...</td><td>7.1</td><td>0.3</td><td>-1.2</td><td>-93.7</td><td>42.1</td><td>67.8</td><td>-330.7</td></tr><tr><td>5789859839093874048</td><td>306.39</td><td>-13.48</td><td>...</td><td>6.2</td><td>2.7</td><td>-0.8</td><td>44.4</td><td>31.6</td><td>108.5</td><td>-74.6</td></tr><tr><td>6147829420291613312</td><td>293.98</td><td>19.21</td><td>-1.66</td><td>7.2</td><td>2.3</td><td>0.9</td><td>-40.7</td><td>7.0</td><td>-85.0</td><td>-145.6</td></tr><tr><td>5809476294773601408</td><td>321.46</td><td>-12.93</td><td>...</td><td>5.3</td><td>2.3</td><td>-0.8</td><td>-114.4</td><td>-13.2</td><td>86.2</td><td>-190.0</td></tr><tr><td>6473910342493757824</td><td>347.11</td><td>-34.07</td><td>-0.54</td><td>7.2</td><td>0.2</td><td>-0.7</td><td>-77.4</td><td>25.4</td><td>-110.9</td><td>-200.1</td></tr></tbody></table>
<table><caption>Table A2
GR-2, 3.62 σ, 34 Stars</caption><thead><tr><th>Source-id</th><th>l<br>(deg)</th><th>b<br>(deg)</th><th>[Fe/H]<br>(dex)</th><th>x<br>(kpc)</th><th>y<br>(kpc)</th><th>z<br>(kpc)</th><th>U<br>(km s<sup>-1</sup>)</th><th>V<br>(km s<sup>-1</sup>)</th><th>W<br>(km s<sup>-1</sup>)</th><th>L<sub>z</sub><br>(km s<sup>-1</sup> kpc)</th></tr></thead><tbody><tr><td>6449845198355290240</td><td>330.85</td><td>-39.03</td><td>-1.31</td><td>7.2</td><td>0.5</td><td>-0.9</td><td>-43.8</td><td>-107.5</td><td>-41.7</td><td>754.9</td></tr><tr><td>6258852675626795392</td><td>349.00</td><td>32.38</td><td>-1.25</td><td>5.4</td><td>0.5</td><td>1.8</td><td>132.6</td><td>-113.8</td><td>-88.8</td><td>690.0</td></tr><tr><td>6317052506146717312</td><td>357.69</td><td>34.39</td><td>-1.07</td><td>6.2</td><td>0.1</td><td>1.4</td><td>17.4</td><td>-74.9</td><td>43.9</td><td>469.4</td></tr><tr><td>6004194645781493888</td><td>329.88</td><td>13.49</td><td>-0.99</td><td>5.1</td><td>1.8</td><td>0.9</td><td>137.6</td><td>-78.2</td><td>63.5</td><td>646.3</td></tr><tr><td>5789526515270303872</td><td>306.13</td><td>-14.70</td><td>-0.81</td><td>7.7</td><td>0.7</td><td>-0.2</td><td>10.3</td><td>-66.6</td><td>-57.1</td><td>520.3</td></tr><tr><td>4348288219771571200</td><td>2.98</td><td>30.15</td><td>-0.84</td><td>5.6</td><td>-0.1</td><td>1.5</td><td>-41.9</td><td>-124.0</td><td>-46.4</td><td>702.6</td></tr><tr><td>6158877588002891648</td><td>302.54</td><td>28.80</td><td>-1.28</td><td>6.4</td><td>2.8</td><td>1.8</td><td>35.2</td><td>-77.7</td><td>37.2</td><td>597.4</td></tr><tr><td>5790486663802736896</td><td>308.13</td><td>-12.20</td><td>-1.0</td><td>5.6</td><td>3.3</td><td>-0.9</td><td>91.8</td><td>-72.6</td><td>56.7</td><td>711.0</td></tr><tr><td>6218157791784797184</td><td>331.26</td><td>26.34</td><td>-0.73</td><td>6.3</td><td>1.1</td><td>1.1</td><td>119.1</td><td>-75.2</td><td>32.8</td><td>597.6</td></tr><tr><td>6114741713797552384</td><td>317.33</td><td>23.45</td><td>-1.25</td><td>5.1</td><td>2.9</td><td>1.9</td><td>47.9</td><td>-70.9</td><td>70.7</td><td>498.4</td></tr><tr><td>6665690974540896640</td><td>345.53</td><td>-31.25</td><td>...</td><td>5.3</td><td>0.8</td><td>-1.8</td><td>-55.8</td><td>-109.9</td><td>56.7</td><td>535.9</td></tr><tr><td>6251112216848937984</td><td>342.22</td><td>27.38</td><td>-0.67</td><td>5.3</td><td>0.9</td><td>1.6</td><td>94.3</td><td>-73.4</td><td>45.3</td><td>474.8</td></tr><tr><td>4404899977538537856</td><td>7.05</td><td>34.56</td><td>-0.76</td><td>4.7</td><td>-0.4</td><td>2.5</td><td>-46.1</td><td>-128.3</td><td>-53.8</td><td>617.9</td></tr><tr><td>6074173720472593152</td><td>303.28</td><td>9.29</td><td>-0.62</td><td>6.7</td><td>2.3</td><td>0.5</td><td>-25.3</td><td>-97.7</td><td>-64.1</td><td>597.7</td></tr><tr><td>6511309066576795136</td><td>342.42</td><td>-52.23</td><td>-2.11</td><td>6.1</td><td>0.7</td><td>-2.8</td><td>38.8</td><td>-90.6</td><td>25.3</td><td>580.4</td></tr><tr><td>4342924973847237760</td><td>358.88</td><td>29.57</td><td>-1.23</td><td>4.9</td><td>0.1</td><td>1.9</td><td>101.9</td><td>-144.6</td><td>0.7</td><td>710.4</td></tr><tr><td>3506830356119273728</td><td>314.08</td><td>42.52</td><td>...</td><td>6.3</td><td>2.0</td><td>2.6</td><td>12.1</td><td>-104.7</td><td>10.2</td><td>680.0</td></tr><tr><td>6788387646043341824</td><td>15.38</td><td>-40.50</td><td>-0.63</td><td>6.4</td><td>-0.5</td><td>-1.6</td><td>-10.6</td><td>-91.0</td><td>-39.8</td><td>587.8</td></tr><tr><td>6435386925388937472</td><td>330.59</td><td>-25.94</td><td>...</td><td>4.1</td><td>2.3</td><td>-2.3</td><td>-27.2</td><td>-130.3</td><td>-115.4</td><td>465.8</td></tr><tr><td>6313449367881650688</td><td>344.81</td><td>41.32</td><td>...</td><td>5.1</td><td>0.8</td><td>2.8</td><td>71.2</td><td>-94.0</td><td>-3.8</td><td>540.1</td></tr><tr><td>6646407636533587712</td><td>346.56</td><td>-27.10</td><td>-1.02</td><td>7.2</td><td>0.2</td><td>-0.5</td><td>-47.5</td><td>-74.1</td><td>49.9</td><td>518.8</td></tr><tr><td>6309259232147407616</td><td>348.38</td><td>37.29</td><td>...</td><td>6.3</td><td>0.4</td><td>1.5</td><td>16.7</td><td>-109.8</td><td>-56.2</td><td>697.6</td></tr><tr><td>6589763718048296064</td><td>9.28</td><td>-48.73</td><td>...</td><td>6.5</td><td>-0.3</td><td>-2.0</td><td>4.3</td><td>-76.4</td><td>-39.1</td><td>492.9</td></tr><tr><td>5810135417625152128</td><td>323.29</td><td>-19.57</td><td>-0.51</td><td>6.9</td><td>0.9</td><td>-0.5</td><td>38.3</td><td>-93.2</td><td>50.4</td><td>683.5</td></tr><tr><td>5818135185049009664</td><td>327.52</td><td>-12.48</td><td>...</td><td>5.5</td><td>1.7</td><td>-0.7</td><td>150.8</td><td>-72.6</td><td>-74.1</td><td>657.8</td></tr><tr><td>6480211231315277056</td><td>352.33</td><td>-42.67</td><td>-0.67</td><td>6.0</td><td>0.3</td><td>-2.0</td><td>-82.2</td><td>-98.0</td><td>25.0</td><td>567.5</td></tr><tr><td>4357650217678900736</td><td>11.60</td><td>29.84</td><td>...</td><td>6.2</td><td>-0.4</td><td>1.2</td><td>98.1</td><td>-97.7</td><td>11.8</td><td>568.9</td></tr><tr><td>6428120360420225024</td><td>329.39</td><td>-28.65</td><td>-1.15</td><td>4.5</td><td>2.2</td><td>-2.4</td><td>-54.0</td><td>-152.4</td><td>-72.1</td><td>558.7</td></tr><tr><td>6240366689710897408</td><td>348.61</td><td>23.95</td><td>-0.19</td><td>4.3</td><td>0.8</td><td>1.8</td><td>-37.1</td><td>-162.6</td><td>-36.1</td><td>668.5</td></tr><tr><td>6632745826600895232</td><td>334.74</td><td>-22.72</td><td>...</td><td>7.3</td><td>0.4</td><td>-0.4</td><td>-74.9</td><td>-83.6</td><td>46.0</td><td>578.8</td></tr><tr><td>6713848351184784640</td><td>355.03</td><td>-21.46</td><td>-0.55</td><td>5.3</td><td>0.2</td><td>-1.1</td><td>124.8</td><td>-105.3</td><td>113.3</td><td>591.8</td></tr><tr><td>5768695992600783744</td><td>309.10</td><td>-23.19</td><td>-1.03</td><td>5.5</td><td>3.3</td><td>-1.8</td><td>116.5</td><td>-28.2</td><td>-24.2</td><td>539.5</td></tr><tr><td>5819460581907006976</td><td>318.99</td><td>-12.95</td><td>-0.54</td><td>4.0</td><td>3.7</td><td>-1.3</td><td>118.0</td><td>-91.8</td><td>-86.3</td><td>798.3</td></tr><tr><td>6260416898417038336</td><td>350.39</td><td>28.86</td><td>-0.53</td><td>4.9</td><td>0.6</td><td>1.9</td><td>-30.0</td><td>-172.5</td><td>18.5</td><td>828.0</td></tr></tbody></table>

ORCID iDs

Cuihua Du https://orcid.org/0000-0002-3954-617X

Heidi Jo Newberg https://orcid.org/0000-0001-8348-0983

Jun Ma https://orcid.org/0000-0001-6329-6644

Jianrong Shi https://orcid.org/0000-0002-0349-7839

References

Allende Prieto, C., Beers, T. C., Wilhelm, R., et al. 2006, ApJ, 636, 804

An, D., Beers, T. C., Santucci, R. M., et al. 2015, ApJL, 813, L28

Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., et al. 2018, AJ, 156, 58

Belokurov, V., Erkal, D., Evans, N. W., et al. 2018, MNRAS, 478, 611

Belokurov, V., Evans, N. W., Irwin, M. J., et al. 2007, ApJ, 658, 337

Belokurov, V., Zucker, D. B., Evans, N. W., et al. 2006, ApJL, 642, L137

Bensby, T., Feltzing, S., & Lundström, I. 2003, A&A, 410, 527

Bird, S. A., Xue, X.-X., Liu, C., et al. 2019, AJ, 157, 104

Bland-Hawthorn, J., & Gerhard, O. 2016, ARA&A, 54, 529

Bonaca, A., Conroy, C., Wetzel, A., et al. 2017, ApJ, 845, 101

Bond, N. A., Ivezić, Ž., Sesar, B., et al. 2010, ApJ, 716, 1

Bullock, J. S., & Johnston, K. V. 2005, ApJ, 635, 931

Carollo, D., Beers, T. C., Chiba, M., et al. 2010, ApJ, 712, 692

Carollo, D., Beers, T. C., Lee, Y. S., et al. 2007, Natur, 450, 1020

Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, RAA, 12, 1197

Deason, A. J., Belokurov, V., Koposov, S. E., et al. 2017, MNRAS, 470, 1259

Deng, L.-C., Newberg, H. J., Liu, C., et al. 2012, RAA, 12, 735

Duffau, S., Vivas, A. K., Zinn, R., et al. 2014, A&A, 566, A118

Duffau, S., Zinn, R., Vivas, A. K., et al. 2006, ApJL, 636, L97

Freeman, K., & Bland-Hawthorn, J. 2002, ARA&A, 40, 487

Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1

Grillmair, C. J. 2006, ApJL, 645, L37

Grillmair, C. J., & Carlin, J. L. 2016, in Tidal Streams in the Local Group and Beyond, ed. H. Newberg & J. Carlin (Cham: Springer), 87

Gu, J.-Y., Du, C.-H., Jia, Y.-P., et al. 2015, MNRAS, 452, 3092

Gu, J.-Y., Du, C.-H., & Zuo, W.-B., 2019, ApJ, 877, 83

Helmi, A., Babusiaux, C., Koppelman, H. H., et al. 2018, Natur, 563, 85

Helmi, A., Veljanoski, J., Breddels, M. A., et al. 2017, A&A, 598, A58

Helmi, A., & White, S. D. M. 1999a, MNRAS, 307, 495

Huang, Y., Liu, X.-W., Chen, B.-Q., et al. 2018, AJ, 156, 90

Ibata, R. A., Gilmore, G., & Irwin, M. J. 1994, Natur, 370, 194

Johnson, D. R. H., & Soderblom, D. R. 1987, AJ, 93, 864

Jurić, M., Ivezić, Ž., Brooks, A., et al. 2008, ApJ, 673, 864

Kafle, P. R., Sharma, S., Robotham, A. S. G., et al. 2017, MNRAS, 470, 2959

Klement, R., Rix, H. W., Flynn, C., et al. 2009, ApJ, 698, 865

Kunder, A., Kordopatis, G., Steinmetz, M., et al. 2017, AJ, 153, 75

Li, H.-F., Du, C.-H., Liu, S., Donlon, T., & Newberg, H. J., 2019, ApJ, 874, 84

Lindegren, L., Hernández, J., Bombrun, A., et al. 2018, A&A, 616, A2

Luri, X., Brown, A. G. A., Sarro, L. M., et al. 2018, A&A, 616, A9

Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94

Majewski, S. R., Skrutskie, M. F., Weinberg, M. D., et al. 2003, ApJ, 599, 1082

McMillan, P. J. 2017, MNRAS, 465, 76

Newberg, H. J., Willett, B. A., Yanny, B., & Xu, Y. 2010, ApJ, 711, 32

Newberg, H. J., Yanny, B., Cole, N., et al. 2007, ApJ, 668, 221

Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2012, arXiv:1201.0490

Posti, L., Helmi, A., Veljanoski, J., & Breddels, M. 2017, A&A, 615, 70

Searle, L., & Zinn, R. 1978, ApJ, 225, 357

Steinmetz, M., Zwitter, T., Siebert, A., et al. 2006, AJ, 132, 1645

Tian, H.-J., Liu, C., Carlin, J. L., et al. 2015, ApJ, 809, 145

van der Walt, S., Schönberger, J. L., Nunez-Iglesias, J., et al. 2014, PeerJ, 2, 453
van Leeuwen, F. 2007, Hipparcos, the New Reduction of the Raw Data (Berlin: Springer)

Weiss, S. M., & Kulikowski, C. A. 1991, Computer Systems that Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems (San Francisco, CA: Morgan Kaufman)

White, S. D. M., & Rees, M. J. 1978, MNRAS, 183, 341

York, D. G., Adelman, J., Anderson, J. E., Jr., et al. 2000, AJ, 120, 1579

Zhao, G., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, RAA, 12, 723

Zhao, J.-K., Zhao, G., Chen, Y.-Q., et al. 2015, RAA, 15, 1378

Zuo, W.-B., Du, C.-H., Jing, Y.-J., et al. 2017, ApJ, 841, 59