The Substructures in the Anticenter Region of the Milky Way

We investigated the observational properties of Triangulum-Andromeda (TriAnd), Monoceros Ring (MRi), and Anti-Center Stream (ACS) in the anticenter region using K giants, M giants, and RGB stars from LAMOST and SDSS survey. The Friends of Friends algorithm was applied to select member stars of these structures. We found a new spur of TriAnd at l ∼ 133° based on member stars selected in this work and compiled from the literature. The distributions of radial velocity and proper motion of its member stars indicate that TriAnd is gradually moving away from the Sun. The comparisons of [Fe/H] and [α/Fe] between TriAnd and thick-disk/halo stars reveal that TriAnd is likely to originate from the thick disk. MRi and ACS are adjacent in space with a boundary around latitude 30°, and there is no significant difference between the two structures in velocity, proper motions, and orbits. We suggested that MRi and ACS probably have a common origin. We made projections of the four structures in three-dimensional space for the exploration of the movements between the Sagittarius (Sgr) stellar stream and MRi, and found that a new spur was formed by the Sgr stream members in the velocity distribution as it passed through the MRi region.


Introduction
The Milky Way (MW) is a galaxy with complex structures, and is worth exploring with updated observations. Previous studies predicted that the MW was born due to a series of complicated accretions and merger events (Searle & Zinn 1978;Blumenthal et al. 1984;Springel et al. 2006). In the past decades, with the improvement of the capabilities of observation instruments and the deepening of research, the comprehension and knowledge of the details of this enormous galaxy have gradually improved. The detection and identification of substructures contribute to the cognition of the MW. With the development of photometric and spectroscopic surveys, more and more substructures in the MW are gradually being discovered, These so-called stellar streams and overdensity populations are the basic units of this enormous and complex galaxy. They are related to the disruption of dwarf galaxies in the Galactic halo. In recent years, the detection of the Gaia-Sausage structure in velocity space is associated to the largest merge event of the Gaia-Sausage-Enceladus dwarf galaxy with the MW, which also brought a lot of debris stars into the Galactic disk. The LAMOST spectroscopic survey makes it possible to identify its metal-rich component after merging into the Galactic disk a long time ago (Yang et al. 2021;Zhao & Chen 2021). Recent merging of Sgr dwarf galaxy in the outer disk is reported, leaving many substructures in the anticenter region, which are interesting targets in many works.
Located in the south of the disk, there is a substructure called the Triangulum-Andromeda (TriAnd) overdensity. Rocha-Pinto et al. (2004) discover the TriAnd from Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) data, and Majewski et al. (2004) obtained the main-sequence and turnoff stars of TriAnd using the color-magnitude diagram (CMD). Subsequent researchers found that TriAnd has a spatial extension of approximately 100°< l < 150°, and − 40°< b < −15° Deason et al. 2014;Sheffield et al. 2014;Perottoni et al. 2018). Martin et al. (2007) detected two parts of TriAnd in the foreground of M31, TriAnd1, and TriAnd2. Sheffield et al. (2014) suggested that the TriAnd1 with the age of 6-10 Gyr (young) is nearer than the older TriAnd2 (10-12 Gyr) based on the 2MASS M giants data. Based on low-resolution spectroscopy, Deason et al. (2014) find that the Galactic standard of rest velocitiy (V gsr ) of TriAnd is about 50 km s −1 , and the heliocentric distance is about 20 kpc. Sales Silva et al. (2019) used highresolution spectroscopy and identified 13 candidates in the TriAnd overdensity region, among which seven stars were determined by kinematic analysis and the stellar orbits calculated by the orbital velocity of Gaia DR2. The origin of the TriAnd is controversial. Some authors believed that TriAnd is related to the disk (Xu et al. 2015;Li et al. 2017;Bergemann et al. 2018;Hayes et al. 2018;Sheffield et al. 2018), while the others thought that TriAnd is derived from the remains of dwarf galaxies (Chou et al. 2011;Deason et al. 2014;Sheffield et al. 2014).
The Monoceros Ring (MRi; also known as GASS) is a ring structure discovered by Newberg et al. (2002) at low Galactic latitude near the anticenter by blue F turnoff stars. Yanny et al. (2003) inferred that the distance from the Galactic center to MRi is about 18 kpc by the faint turnoff stars of Sloan Digital Sky Survey (SDSS; York et al. 2000) and deemed that MRi surrounds the MW at low latitudes. In both Yanny et al. (2003) and Rocha-Pinto et al. (2003), evidence shows that the structure extends 5 kpc above and below the disk, and stars in the southern hemisphere are about 2 kpc further than those in the north. Simulations (Helmi et al. 2003;Martin et al. 2004: Peñarrubia et al. 2005). Li et al. (2012) show that MRi is likely to continue to move toward the low latitude, the distance from Galactic center is D gc ∼ 17.6 kpc. Based on the pan-STARRS survey, Slater et al. (2014) showed the most complete and continuous picture of the MRi, and Morganson et al. (2016) detected its three-dimensional structure and estimated the mass of MRi to be 4-6 × 10 7 M e . In Yang et al. (2019)ʼs work, the spectroscopic member stars of MRi in the northern and southern hemispheres were identified, and most of these member stars are located at 5-7 kpc above or below the Galactic disk. The origin of MRi is still a controversial issue at present. Some works suggested that MRi is the accretion debris of satellite galaxies (Yanny et al. 2003;Martin et al. 2004;Conn et al. 2005;Peñarrubia et al. 2005;Butler et al. 2007;de Jong et al. 2007), and the others thought MRi is parts of the warp or flare of the disk (Momany et al. 2006;Hammersley & López-Corredoira 2011;Xu et al. 2015;Sheffield et al. 2018;Laporte et al. 2020).
The Anti-Center Stream (ACS) is an interesting substructure detected in the direction of anticenter based on SDSS photometry by Grillmair (2006), and it was determined to be the result of massive dwarf galaxies destroyed by tides. The radial velocity and proper motion measurement of the ACS showed that ACS stars are in a prograde orbit. Grillmair et al. (2008) introduced an orbit model for these anticenter stellar streams. Based on the photometry and spectral data of SDSS DR8, Li et al. (2012) pointed out that the spatial position of the ACS is generally from b = 25°to 35°, and found that the mean metallicity of ACS is [Fe/H] = −0.96 dex. Carlin et al. (2010) measured the three-dimensional kinematics of stars in Kapteyns selected area 76 (SA 76), and obtained a total of 31 stars identified in the ACS. Using Gaia DR2 (Gaia Collaboration et al. 2018) data, Laporte et al. (2020) pointed out that most ACS stars have an old age (>10 Gyr) and ACS may be a part of the disk. Ramos et al. (2021) obtained high-purity giants samples for making a Mollweide projection map, which provides the precise characteristics of ACS.
In this work, we will use a percolation algorithm to filter the processed data, obtain samples of these substructures, and analyze the spatial and kinematic properties. This paper is organized as follows. In Section 2, the samples will be introduced, this section also show the application of a method to filter samples and obtain high-purity member stars. The properties of member stars will be analyzed in Section 3. Finally, there are discussion and summary in Section 4.

The Data
The spectral data used in this work comes from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Cui et al. 2012;Zhao et al. 2012) and Sloan Digital Sky Survey (SDSS). The LAMOST is a large-field telescope with a spectral survey covering a large area of the sky. Its coverage in dec. is from −10°to +90°, and the field of view is 5°. It has the capacity to provide low-resolution spectra (R ∼ 1800) (Cui et al. 2012). By providing different types of stars, LAMOST has improved the level of exploration of the structures and early evolution of the MW (Zhao et al. 2006;Deng et al. 2012;Li et al. 2015;Liu et al. 2015). SDSS present the photometry data of a large number of targets and a smaller but significant number of stellar spectra in the MW with the sky survey range covering both the southern and northern hemisphere (Brescia et al. 2014).
Our work uses a sample of the combination of LAMOST DR5 and SDSS DR9 (Pâris et al. 2012). We first select the red giant branch (RGB) in the SDSS DR9. With the help of the fiducial-based distance algorithm of Tan et al. (2014), the distance information of the sample is improved. Then we adopted the LAMOST's fifth data release (DR5) to select K giants and M giants. M giants are very bright, with a temperature range of 2400-3700 K, and they can be applied to trace metal-rich structures, which is exactly what this work needs. To obtain the distances of the M giants, the method in Li et al. (2016) was applied. The absolute magnitude M J of the J band is obtained by using the color value (J-K 0 ) to calculate the distances in Li et al. (2016). Similarly, the data of K giants we adopted were derived from Zhang et al. (2020), and the data include distances. Finally, to get proper motion, we crossmatched the existing three types of stars with Gaia DR2 with a radius of 1¢¢. After the match, the sample data contains approximately ∼128,000 stars.

Spatial Velocity, Energy, and Angular Momentum
The radial velocity in the Galactic standard of rest frame (V gsr ) of each star was calculated from RV via the formula V gsr = RV + 10 cos l cos b + 225.2 sin l cos b + 7.2 sin b. Spatial velocities, V x , V y , and V z , are calculated by radial velocity (RV), distance, R.A., decl., and proper motions. According to the formula given by Li et al. (2019), we calculated the Energy and Angular Momentum of each star. We calculated as follows: Formulas are based on Galactocentric (X, Y, Z, V x , V y , V z ) with potential Φ tot (X, Y, Z). Since the data stemmed from different type stars in the LAMOST and SDSS, we adopted the method of Huang et al. (2019) to check them for consistency. With more than 20,000 stars in common, the metallicities of LAMOST stars are on average 0.06 dex higher than those of SDSS stars. The [α/Fe] of SDSS stars are on average 0.044 dex higher than those of LAMOST stars, consistent with the value of 0.04 dex by Xiang et al. (2017). The radial velocities of the two spectral data had been calibrated according to the measured values of the high-resolution spectra, and it shows no systematic deviation between the two data sets. Therefore, in this work, we took the sample data of LAMOST as the main source of metallicities and calibrated the SDSS data accordingly. We finally obtain the sample stars with spatial position, distance, metallicity, velocity, and proper motion.

FoF Algorithm
In order to obtain member stars of substructures, the Friends of Friends (FoF) algorithm is used for percolating stars. The FoF is an algorithm for group-finding. Initially, the selection of member stars is to combine 4Distance (galactic longitude, galactic latitude, radial velocity, and distance) with the FoF algorithm. This method is demonstrated in the work of Starkenburg et al. (2009) andJanesh et al. (2016). In Yang et al. (2019), the content of 4D has been expanded to 6D and its definition have been displayed in their work. The content of 6D contains two critical elements: position space and velocity space. The content of the location space includes the space coordinates of the stars, the galactic longitude and latitude, and the heliocentric distance, the content of the velocity space includes line-of-sight velocity and tangential velocity along Galactic longitude and tangential velocity along Galactic latitude. In this work, based on the content of 6D, we used velocity space and position space to identify structures. The restrictions imposed by the FoF method are as follows: where 1 and 2 represent any two stars, our limit commences with the position and velocity in the space of each star. Meanwhile, we use a link restriction to control the structures sample quantity contained within a certain distance. The restriction on the amount of sample is related to the size of the detected structure, so the different structures require different limiting extents. In order to accurately detect different structures, the restricted parameters need amendments repeatedly.
In the percolation of member stars, the first step is to properly limit the ranges of structures in the position space and velocity space, so as to reduce redundant stars and find target member stars. We then set the number of member stars connections to limit the range, denoted by "link-limit." For any two member stars in space, their distance in the position space is expressed as , which is less than the adaptive threshold of position space. The threshold is affected by the original data density in-unit position space.
in the velocity space, which is less than the adaptive threshold, and affected by the data density of unit velocity space within the threshold range in the position space. The higher the density, the lower the threshold in velocity space. For the position space, its threshold is affected by the value of link-limit. Because of the data density of the structure, we set the threshold within a suitable interval instead of a fixed value. The threshold of velocity space is influenced by the distance and velocity of stars. In the space, we connected the two stars with a straight line to get the distance in the case of determining the position of any two adjacent stars (A, B) and took star A as the origin, and then did a projection from the star B at the end of the straight line to the motion direction of star A. The purpose of this step is to make star B on the line of the motion direction of Star A, which is conducive to limiting the motion direction of star B. As the velocities of any two adjacent stars in a stellar stream are similar, so we set the threshold value as the projection value of star B on star A multiplied by the coefficient K 1 and plus a coefficient K 2 . K 2 is the maximum coefficient when the velocities of two stars are in the same direction, and K 2 is the possible difference value between the velocities of two stars. The value of K 1 and K 2 depends on the property of the structure. The choice of stellar velocities is within this threshold in the velocity space.
The application of thresholds follows the next explanation: is the threshold set after sorting the distance of stars in link-limit. It is not a fixed value and can be adjusted according to the original density of the structure.

=´+
The above steps are applied to the selection of target stars. The position and velocity limitations of the TriAnd, MRi and ACS are based on previous literature on them, including galactic longitude, galactic latitude, scale height, Galactocentric distance and velocity. Thus we have a preliminary distribution of stars in the region of the three structures. After that, the data are filtered by the algorithm many times to obtain the final result.

Results of FoF
The selection of structure groups not only depends on the position relationship among member stars but also on the velocity direction of each member star being in an appropriate range. The stars in a region are likely to be a group if both their positions and velocities satisfied the above criteria.
The final results are different according to the filter criteria for each structure. The parameters of the TriAnd, MRi, ACS, and Sgr in the selection are shown in Table 1. Parameters are limited in the table about the structures' position, scale height, velocity, and other factors. If the ranges of these parameters were expanded, the number of structures' member stars would increase. This would result in the inclusion of irrelevant stars. In particular, parameters such as link-limit, K 1 , and K 2 are set according to the density of the structures.
Note. The contents from columns 2 to 6 are based on the basic properties, and the contents of 7columns to 9 show the components of the threshold value in the position and velocity space.
Finally, we identified and percolated the member stars of MRi, ACS, and TriAnd. In the identification of TriAnd, 128 member stars (2 RGB stars, 111 K giants, and 15 M giants) were gained, as shown in Table 2 (see Appendix). The size of ACS is much smaller than that of TriAnd, ACS has only 32 member stars (10 RGB stars, 22 K giants), which are listed in Table 3 (see Appendix). Due to the deviation of metallicity, several stars have been removed from the initial member stars of MRi. Table 4 (see Appendix) shows the final filtered result of MRi, including 132 member stars (9 M giants, 123 K giants).

Analysis of Three Substructures
Although there is a discrepancy in the number of selected member stars, we have investigated the characteristics and properties of these structures that are shared by all the stars, and the final samples can be used to investigate and analyze features of these structures.

The Properties of TriAnd
As a substructure located in the southern part of the disk, the TriAnd has 128 member stars. The spatial distribution of the  Sheffield et al. (2014). There is an extended spur in 125°< l < 140°, which is clearly present in space and is marked with black rectangles on the left and right panels. stars can give us an intuitional introduction. The left panel of Figure 1 shows the spatial distribution and heliocentric distance distribution. The right panel presents the comparison of the TriAnd stars obtained in this work and the results of other works. In the left panel, TriAnd is distributed in 115°< l < 165°, − 35°< b < − 13°. The Galactic longitude increases, its Galactic latitude gradually decreases, and TriAnd looks like a slightly inclined stripe. The heliocentric distance distribution ranges from 10 kpc to 25 kpc, and the distribution of member stars at 15 kpc to 20 kpc is relatively dense. The comparison in the right panel shows a detail: in the range of 125°< l < 140°, which contains a large number of member stars, mainly from Rocha-Pinto et al. (2004); Sheffield et al. (2014) and this work. These stars form a spur and extend to the south as shown in a black rectangle. We tentatively regard it as a substructure of TriAnd, and it may be related to the accretion of dwarf galaxies.
In order to have a deeper comprehension of TriAnd, we conducted a kinematic analysis of TriAnd stars. The number of our sample is large, which can better demonstrate the nature of TriAnd. We also cross-matched the member stars from the literature with Gaia DR2 to obtain the corresponding proper motions. The literature includes Rocha-Pinto et al.   Figure 2. The best-fit curve is shown by a magenta curve. The V gsr of most member stars is greater than 0 km s −1 (indicated by the black dashed line), which indicates that the TriAnd is gradually moving away from the Sun. . Spatial distribution of this work in the X-Y plane. The red dots represent the member stars of this work, and the red arrows represent the velocity direction of each star. The black dot represents Galactic center, the black triangle represents the Sun, and the red curve is the calculated average orbit of TriAnd in this work. The velocity direction of the TriAnd is roughly in line with the red orbit, and it moves clockwise in the X-Y plane.  the proper motion of TriAnd stars in Figure 2. The left panel represents proper motion along longitude, which is mainly located between −1 and +1 mas yr −1 . The proper motion along longitude is 0 mas yr −1 for the stars who mostly concentrate in the range of l from 130°to 140°. The proper motion along longitude conforms to a linear functional relationship. We made a linear fitting to the data of this work, shown by the magenta line on the left panel. The right panel represents the total proper motion ( While most velocity values are greater than 0 km s −1 , the positive velocity values can be considered as TriAnd structure is moving away from the Sun. Almost all velocity values are in the range from 0 to 150 km s −1 , the fitting curve shows that the peak velocity value is around 135°in Galactic longitude. Figure 4 shows the spatial distribution and the motion of the  TriAnd structure. Red dots represent the TriAnd member stars and red arrows show moving direction. We calculated the TriAnd's orbit using member stars in this work by the Galpy program (Bovy 2015), and the gravitational potential of the MW is adopted from McMillan (2017). The orbit of TriAnd is shown with the red curve in Figure 4. TriAnd moves in a clockwise direction in the X-Y plane and moves away gradually from the Sun (black triangle) in the anticenter region. This is also consistent with the result in Figure 3. That is, the dynamic analysis gives consistent results. Kinematic features provide us with an intuitive comprehension of the properties of structures, and metallicity analysis gives the composition of structures. To study the metallicity of the TriAnd stream, a linear relationship is shown between metallicity and longitude in Figure 5, which shows the l-[Fe/H] diagram of TriAnd stars in the range from 115°to 165°in the Galactic longitude. The metallicity ranges from −1.0 to −0.5 dex. The upper panel shows the individual points of the stars, the lower panel presents the median (circle) of the individual point with a bin size of ∼10 degrees in longitude. We made box plots of TriAnd stars on the lower panel, the upper/lower quartiles of the stars are shown with blue lines/orange lines. The red dashed line is the result of linear fitting to the median of each bin, and the slope of the fitting line is 0.0021 ± 0.0016 dex/deg, which is nearly flat. The linear fitting shows that the metallicity of TriAnd has a small gradient.
The TriAnd samples have three types of stars: RGB (2 stars), K giants (111 stars), and M giants (15 stars). Since the RGB sample has only two stars, it is ignored. We show the histograms of metallicity between K and M giants in Figure 6. They are not much different: the metallicity peaks are concentrated at −0.6 dex and −0.45 dex for K giants and M giants, respectively. In view of the larger star number and narrower distribution, we suggested that the metallicity distribution from K giants may be more reliable.
The metallicity of the structure can be used to explore its evolutionary history. In Figure 7, the comparisons of metallicities of the TriAnd and the disk/halo are shown. The mean metallicity of TriAnd is −0.64 dex, which is similar to the metallicity of stars with |Z| < 2 kpc in the disk region. We present the metallicity distribution of stars with 5 kpc < |Z| < 7 kpc in the halo region on the lower right panel. Meanwhile, TriAnd is located below the disk from −7 kpc to −5 kpc (Hayes et al. 2018). Here the 0 < |Z| < 2 region represents the thick disk, while the 5 < |Z| < 7 region corresponds to the in situ halo. As shown in the right panel of Figure 7, the metallicity of TriAnd is more metal rich than the metallicity of stars in the in situ halo (−1.45 dex). In Figure

Relationship Between MRi and ACS
Besides the TriAnd structure, MRi and ACS are also notable structures in the anticenter region. The MRi is a ringlike  structure, its Galactic longitude is generally 100°< l < 240°, and its Galactic latitude is roughly 15°< b < 40° (Slater et al. 2014;Li et al. 2017;Sheffield et al. 2018). The ACS is a structure located slightly higher than MRi, and it is very close to the MRi in space. Previous works show that the member stars of ACS are distributed in the Galactic latitude b ∼25°-40° ( Li et al. 2012;Laporte et al. 2020;Ramos et al. 2021). Due to the close proximity between the two structures in space, we will explore MRi and ACS together in this section.
We have obtained the selected sample of the MRi and ACS in Section 2.4. The member stars of the two structures are shown with different color symbols in Figure 9 where the distributions of space, velocity, and heliocentric distance are compared between MRi and ACS. The Galactic longitude l of the MRi is between 150°and 220°, and the Galactic latitude b is from +15°to +32°. The ACS is attached to the top of MRi, and its spatial distribution (160°< l < 180°, 28°< b < 40°) is smaller than that of MRi. There is an overlap between the two structures in the distribution of Galactic latitude. The distribution of V gsr of the MRi and ACS is from −70 to +70 km s −1 . It can be seen that velocity distribution presents a linear characteristic. As for distance, the MRi stars are more diffuse in the distance range of 10-20 kpc, but most stars are concentrated in the range of 10-15 kpc. The mean heliocentric distance of the MRi is 13.4 kpc, which is greater than that (10.5 kpc) of ACS. The average Galactic orbits of MRi and ACS are shown in Figure 10. The orbits are calculated by the Galpy python module, the gravitational potential of the MW is adopted from McMillan (2017). We can see that the average Galactic orbits of MRi and ACS are similar.
In order to comprehend the two structures, the radial velocities of the two structures are shown in the left panel of Figure 11. The velocity histograms show the distribution of each velocity segment of the two structures, and the curvefitting results show that the mean radial velocity of the ACS is greater than that of MRi. The V gsr of MRi is distributed on both sides of 0 km s −1 and the peak is nearly at 0 km s −1 . The V gsr of most ACS stars are greater than 0 km s −1 , ACS's velocities are concentrated around 30 km s −1 . The right panel shows that the l-proper motion of member stars of the ACS and MRi, and the proper motions of the stars of MRi and ACS, are mainly concentrated in 0.5-1.0 mas yr −1 . The proper motion distributions of ACS and MRi are mixed, and the mean proper motion of ACS (0.714 mas yr −1 ) is greater than that of MRi (0.262 mas yr −1 ).
The energy versus angular momentum diagram can be used to understand the physical properties of structures ). In Figure 12, the MRi has larger angular momentum than that of ACS. The MRi and ACS member stars form a linear distribution, which reflects that the ACS is likely related to the MRi.
The metallicity comparison of member stars in ACS and MRi is shown in Figure 13. For ACS, RGB stars are slightly more metal poor than K giants, while M giants are more metal  In sum, we obtained similar characteristics between ACS and MRi member stars. MRi and ACS are close neighbors in space, and they are separated around b ∼30°. The distributions of velocity, angular momentum, and heliocentric distance are similar, and the proper motions of the two structures are mixed. In Figure 10, their Galactic orbits are also similar. In Figures 11  and 14, ACS (the green shadow) is a part of MRi (the blue shadow) in velocity and metallicity distributions. We thus suggested that MRi and ACS may have a common origin, and ACS is a part of MRi.

MRi and Sagittarius Stream
The Sagittarius (Sgr) stream is prominent in the MW. It was discovered in 1994 and its scale is very large, passing through the entire MW. The Sagittarius dwarf galaxy is elongated in the direction of the galactic plane, indicating that it was torn by the tidal force of the MW and formed the Sgr stream (Ibata et al. 1994). The Sagittarius stellar stream is divided into the leading arm and the trailing arm. Both have a wide distribution of metallicity, and the trailing arm is more metal rich than the leading arm (Shi et al. 2012).
Due to the scale and kinematic features of the Sgr stream, when it passes through the outer disk of the MW, it will have an impact on the structures of the disk. Purcell et al. (2011) believed that the impact of the Sgr stream is likely to be the reason for the construction of the MRi near the disk. Under the premise of the interaction between the Sagittarius dwarf galaxy and the MW, the Sgr stream passes through the disk many times, and some substructures on the disk will be formed, such as the MRi and ACS (Laporte et al. 2020). In addition, these merging processes of Sgr with the MW also excited many disequilibrium features in the disk in the R versus V f plane coded by V R as shown in Figure 13 of Laporte et al. (2019), where the presence of ridges of Hercules, Arcturus, Sirius, and many other moving groups in the solar neighborhood (Zhao et al. 2009) can be clearly seen.
In this selection, we selected the members of the Sgr stream, which is located near the MRi region. The selection method is the same as that being used in the selection of the MRi member stars. The kinematic features of the selected Sgr member stars correspond with the leading arm in the model of Law & Majewski (2010). In the context of the interaction between the Sgr stream and MW, we will analyze the Sgr stream and MRi. The spatial distribution of structures can provide clues to finding the correlation between each other, as shown in Figure 15. Figure 15 shows the three-dimensional spatial projections of all structures mentioned above. The X gc , Y gc , and Z gc represent the three-dimensional space of the MW, and the arrows represent the projections of the velocity direction and the velocity size of the member stars in the corresponding plane. Blue dots (MRi), green dots(ACS), red dots (TriAnd),  orange dots (Sgr stream), and the colorful arrows represent their respective structures. In the X-Y plane, the movements of the four structures can be clearly shown. The TriAnd, MRi, and ACS all move around the Galactic center in a clockwise direction, the Sgr stream moves along the negative direction of X-axis. In the X-Z plane, the movement direction of ACS is upturned contrasting that of MRi. In the Y-Z plane, the Sgr stream members form a spur in the velocity distribution in the black circle when the Sgr stream passes through the MRi region. Therefore, the spur can be regarded as the deflection of these stars in the velocity distribution. The reason for the construction of the spur may be the interaction of the Sgr stream and the disk, which is similar to the prediction by the Purcell et al. (2011) and Laporte et al. (2020).
In order to verify the membership of the spur stars, the relationship between the Sgr stream and MRi in the angular momentum-energy plane is shown in Figure 16. The left panel clearly shows two linear distributions formed by the member stars of the two structures. At the same angular momentum, the Sgr stream has higher energy than the MRi. In the right panel, the stars in the velocity spur are represented by red dots, and the red dots locate in the distribution sequence of the Sgr stream, which means that these stars belong to Sgr stream rather than MRi. We tentatively speculate that this spur of velocity distribution was formed in the Sgr stream due to the disk's response to the Sgr merge event.

Discussion and Conclusions
TriAnd, MRi, and ACS are significant structures in the anticenter region. The member stars of the structures are selected from LAMOST and SDSS, including K giants, M giants, and RGB stars. The sample data were cross-matched with Gaia DR2 to obtain the proper motion, and the methods to derive the distances are taken from the literature (Tan et al. 2014;Li et al. 2016;Zhang et al. 2020). Angular momentum, energy, and kinematic parameters were calculated. Finally, based on the FoF algorithm in Yang et al. (2019), we selected member stars of TriAnd, MRi, and ACS.
(1) TriAnd is a structure in the anticenter region (115°< l < 165°, − 35°< b < − 13°), and the mean heliocentric distance is 17.3 kpc. In Galactic longitude 125°< l < 140°, a new spur is found in TriAnd, which is also manifested in the data from the literature Sheffield et al. 2014). With a larger number of member stars, the TriAnd in this work has a better performance in the distribution of proper motion and radial velocity along Galactic longitude, which indicates that TriAnd is gradually moving away from the Sun.
(2) TriAnd's metallicity gradually increases along Galactic longitude. The mean [Fe/H] of TriAnd is −0.64 dex, which is similar to the metallicity of stars in the thick disk and more metal rich than that of stars in the in situ halo, which is the current place where TriAnd located. The [α/Fe] of TriAnd is consistent with [α/Fe] of stars in the thick disk, indicating that TriAnd likely originated from the thick disk, and reached the halo after continuous movement.
(3) MRi and ACS are two adjacent structures in space. In the spatial distribution, the ACS is above the MRi, and the boundary between the two structures is the line of b ∼ 30°. The mean heliocentric distance of the MRi is larger than that of Figure 15. Three-dimensional space distribution of TriAnd, ACS, MRi, and Sgr stream. The top, middle, and bottom panels correspond to the X-Y plane, Y-Z plane, and X-Z plane, respectively. Dots and arrows indicate the member stars: MRi (blue), ACS (green), TriAnd (red), and Sgr (orange). The big black dot represents the Galactic center. Top panel: except for Sgr stream, the other three structures are moving clockwise around the Galactic center. Middle panel: except for TriAnd, the other three structures locate above the disk. When the Sgr stream passed through the MRi region, some Sgr member stars' velocities formed a spur which was marked with a black circle in the picture. Bottom panel: based on the projection of the spatial distribution, it is obvious that the velocity direction of ACS is upwardly tilted compared to that of MRi, and ACS is at the edge of MRi region.
ACS. The mean velocity V gsr of the ACS is greater than that of MRi, and the velocity of the overall ACS is greater than 0 km s −1 , and the velocity of MRi is distributed on both sides of the zero. It can be seen from velocity and proper motion that ACS and MRi move in the same direction in space. The member stars of ACS and MRi together form a linear relationship in the angular momentum-energy distribution map, which shows that the two structures have a high correlation. The mean metallicity of MRi in this work is [Fe/ H] = −0.58 dex, which is similar to the results of Li et al. (2021). The difference in the metallicity of ACS and MRi is not large. Therefore, we infer that MRi and ACS are likely to have a common origin, or ACS is a part of MRi.
(4) In order to explore the relationship between the Sgr stream and the anticenter structures, we show their threedimensional distributions. In the middle panel of Figure 15, it can be seen that when the Sgr stream moves from the high latitude to the low latitude along Z gc , it passes through the MRi region, and the velocity distributions of some Sgr member stars form a spur in the space. This phenomenon may be the result of the disk's response to the Sgr merge event. Finally, in order to confirm the attribution of the deflected stars, we show the angular momentum-energy diagram of the Sgr stream and MRi, and stars from the spur are in the sequence of the Sgr stream, but not in the MRi sequence, which indicates that the deflection of Sgr stars is robust.

Appendix
We list the member stars of TriAnd, ACS, and MRi in Table 2, Table 3, and Table 4 respectively as follows.