arXiv subjects

Cuihua Du

Publications and source records attributed to Cuihua Du.

At least 19 recordsLinked to original sources

arXiv2026

Reconstructing the Stripping History of the Sagittarius Stream with Neural Networks

The Sagittarius (Sgr) Stream is produced by the ongoing disruption of the Sgr dwarf spheroidal (dSph) galaxy and is thought to contain multiple wraps that were stripped during different pericentric passages. In this study, we introduce a neural-network--based method trained on $N$-body simulations to infer the stripping time of Sgr Stream stars directly from their phase-space coordinates. We combine spectroscopic data from SEGUE, APOGEE DR17, and LAMOST DR7 LRS with \textit{Gaia} EDR3 astrometry and distance estimates from the latest \texttt{StarHorse} catalog to identify high-quality Sgr Stream members. Applying our method to these stars, we measure a clear metallicity gradient with stripping time, well described by a linear relation with slope $\sim 0.3~\mathrm{dex~Gyr^{-1}}$. We further predict the stripping times of globular clusters previously suggested to originate from the Sgr dSph. M 54, Terzan 7, Terzan 8, and Arp 2 exhibit stripping times consistent with being currently bound to the Sgr remnant. Pal 12, Whiting 1, and NGC 2419 are inferred to have been stripped $0.9 \pm 0.1$, $1.1 \pm 0.2$, and $2.1 \pm 0.2$ Gyr ago, respectively. For NGC 4147 and NGC 5634, whose membership in the Sgr system remains uncertain, our analysis suggests stripping times of $1.1 \pm 0.4$ and $1.1 \pm 0.1$ Gyr, respectively, if they are ultimately confirmed as genuine Sgr members. These results demonstrate that data-driven models of dynamical stripping histories offer a promising approach for reconstructing the formation and chemical evolution of the Sgr Stream.

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arXiv2026

Revisiting candidate high-velocity stars associated with the Sagittarius dwarf spheroidal galaxy

Hypervelocity stars (HVSs) are valuable tracers of extreme dynamical processes. The Sagittarius dwarf spheroidal galaxy (Sgr dSph), currently undergoing tidal disruption, offers a unique environment to search for such stars. We aim to identify candidate HVSs dynamically linked to the Sgr dSph and to assess their possible origins. Using Gaia DR3, DESI DR1, and LAMOST DR12, we selected stars with galactocentric velocities above 400 km\,s$^{-1}$ and traced their orbits in a realistic Galactic potential including the Sgr dSph and the Large Magellanic Cloud. We then tested three scenarios for their origin: the Hills mechanism, tidal disruption, and random halo star encounters. We identified 95 candidates passing within 2.5 half-mass radii of the Sgr dSph. Their kinematics are inconsistent with production by the Hills mechanism or tidal disruption but are well reproduced by halo stars that naturally cross the Sgr orbit. Furthermore, their metallicity distribution is consistent with that of the Milky Way halo rather than the Sgr stream or Sgr dSph. Our results suggest that our candidates and those in previous studies are most likely halo stars rather than genuine Sgr-origin HVSs. This highlights the need to account for the halo population when inferring stellar origins from orbital analysis and that chemical abundances will be a valuable constraint in the future. While we detect no unbound Sgr HVSs, such a discovery would directly imply extreme dynamical processes. Our results serve as a basis for future studies with upcoming surveys.

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arXiv2026

Chemical Properties and Sagittarius-induced Dynamical Perturbations of the GD-1 Stream

In this study, we investigate the chemical properties of the GD-1 stream using cross-matched, data-driven elemental abundances. The results reveal no clear $α$-knee in the [Mg/Fe]-[Fe/H] plane, and strong abundance consistency between the thin stream and cocoon, supporting a common origin. The absence of multiple-population signatures (e.g., C-N anti-correlation) suggests a low-mass progenitor. Using a test-particle simulation with the particle spray method and including perturbations from the Sagittarius (Sgr) dwarf galaxy, it shows that Sgr does not significantly heat the stream to form the cocoon, but modifies the intrinsic $ϕ_2$ distribution, in agreement with observations. The trailing arm narrowly distributed across the width of the stream, while the leading arm is more diffuse, indicating that major fraction of cocoon stars are present towards the leading arm. Sgr also drags more stream particles moving toward the Galactic center, producing an excess at $V_{\text{GSR}}<0$, consistent with data. Our study confirms the Sgr has a non-negligible dynamical influence on the GD-1 stream. Other heating mechanisms (e.g., dark matter sub-halo encounters and pre-stripping process inside the parent halo) remain to be considered, and higher-resolution spectroscopy is needed to further constrain chemical abundances.

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arXiv2026

A Low-mass Model of The Milky Way: The Disk Warp Resulting from A Galaxy Merger

Previous studies have shown that disk warps can result from galaxy mergers. Recent research indicates a noticeable decline in the rotation curve (RC) of the Milky Way (MW), suggesting the need for a new low-mass model to describe its dynamical features. This study constructs a new Gaia-Sausage-Enceladus (GSE) merger model to characterize the RC features of our galaxy. We use the GIZMO code to simulate mergers with various orbital parameters to investigate how the disk warp evolves under different conditions. This simulation demonstrates the evolutionary mechanism of disk warp, which arises due to the asymmetric gravitational potential of the dark matter (DM) halo generated universally by galaxy mergers. The results indicate that the tilt angle of the DM halo partly reflects the gravitational strength at the $Z=0$ plane, while the gravitational strength on the disk plane reflects the amplitude of disk warp. We identify a dual-regime interaction mechanism driven by the asymmetric halo potential. On short timescales, we find a distinct anti-correlation between the halo's tilt angle and the disk's warp amplitude, indicating a `seesaw' mechanism of angular momentum exchange. On secular timescales, however, dynamical friction drives a global alignment, causing both the halo tilt and the warp amplitude to decay simultaneously. Furthermore, we demonstrate that high-inclination mergers can sustain long-lived prograde precession, where the persistent yet decaying gravitational torque maintains the prograde bending mode against differential wind-up.

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arXiv2025

Kinematic, Elemental and Structural Dependences on Metallicity in the Galactic Bulge

We selected Bulge stars from APOGEE DR17 cross-matched with astrometric data from \textit{Gaia} DR3. Bulge stars were divided into sub-samples with line-of-sight velocity dispersion analyzed and the peaks of MDF were detected by both Gaussian Mixture Models (GMM) and \texttt{scipy.signal.find\_peaks}. GMM is also conducted to kinematically distinguish the metal-poor and metal-rich populations. Analyses were put on the Bulge stars (including retrograde stars), their elemental abundances, and the [Mg/Mn]-[Al/Fe] plane to investigate potential accreted components. Finally, the shapes (X-shaped/boxy) of Bulge stars with different metallicities were analyzed through least-squares fitting based on the analytical Bulge models. By studying the kinematic, elemental and structural dependences on metallicity for Bulge stars, our findings are concluded as follows: 1. Six peaks are detected in the Bulge MDF, encompassing values reported in previous studies, suggesting a complex composition of Bulge populations. 2. An inversion relationship is well-observed in metal-rich sub-samples, while absent in metal-poor sub-samples. 3. Metal-poor populations exhibit larger dispersions than metal-rich stars (which is also revealed by GMM decomposition), suggesting that metal-rich stars are kinematically coherent. 4. Retrograde stars are confined to $\sim1$ kpc of the Galactic center, with their relative fraction decreasing at higher [Fe/H] -- a trend potentially linked to the ``spin-up'' process of Galactic disks. 5. Metal-rich Bulge stars with [Al/Fe] $<-0.15$ are likely associated with from disk accreted substructure, while all elemental planes exhibit bimodality but Na abundances rise monotonically with metallicity. 6. In general, stars with all metallicities support a boxy profile.

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arXiv2025

CNN-Derived Elemental Abundances of LAMOST DR10 Giants: Implications for Galactic Substructures

Stellar parameters and abundances provide crucial insights into stellar and Galactic evolution studies. In this work, we developed a convolutional neural network (CNN) to estimate stellar parameters: effective temperature ($T_{\text{eff}}$), surface gravity (log $g$) and metallicity (both [Fe/H] and [M/H]) as well as six $α$-elements (C, N, O, Mg, Si, Ca) and [$α$/M]. We selected giant stars with $ 3500 \, \text{K} < T_{\text{eff}} < 5500 \, \text{K} $ and $ 0 \, \text{dex} < \log g < 3.6 \, \text{dex} $ from the LAMOST and APOGEE surveys, while requiring (S/N)$_g$ of the LAMOST low-resolution spectra $>$ 10, which leaves 1,100,858 giant stars. The spectral from LAMOST and the labels from APOGEE for 62,511 common stars were used as our training set. The corresponding test set yields scatters 50 K, 0.06 dex and 0.13 dex for $T_{\text{eff}}$, [Fe/H] and log $g$, respectively. For $α$ elements O, Mg, Si and Ca, the scatters are 0.05 dex, 0.04 dex, 0.03 and 0.04 dex, respectively. For C and N elements, the scatters are 0.07 dex and 0.05 dex. For [$α$/M] and [M/H], the scatters are 0.03 dex and 0.06 dex. The mean absolute error (MAE) of most elements are between 0.02 $-$ 0.04 dex. The predicted abundances were cross-matched with previously identified substructures PG1 and PG2, with their origins subsequently analyzed. Finally, the catalog is available at https://nadc.china-vo.org/res/r101529/.

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arXiv2025

Systematic search for blue hyper-velocity stars from LAMOST survey

Hypervelocity stars (HVSs) represent a unique class of objects capable of escaping the gravitational pull of the Milky Way due to extreme acceleration events, such as close encounters with the supermassive black hole at the Galactic center (GC), supernova explosions in binary systems, or multi-body dynamical interactions. Finding and studying HVSs are crucial to exploring these ejection mechanisms, characterizing central black holes, probing the GC environment, and revealing the distribution of dark matter in our galaxy. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectroscopic surveys have so far identified four B-type unbound HVSs. To expand this sample with the second-phase LAMOST survey that started in 2018, we conducted a systematic search for early-type HVSs using the LAMOST Data Release 10. We identified 125 early-type high-velocity candidates with total velocities exceeding 300 km\,s$^{-1}$. Among them, we report ten new unbound B- and A-type hypervelocity star (HVS) candidates (designated LAMOST-HVS5 through LAMOST-HVS14), tripling the number of unbound HVSs previously identified by LAMOST. Kinematic analyses suggest that these newly discovered HVS candidates likely originated either from the Galactic Center or via dynamical interactions. Future high-resolution follow-up observations promise to refine the stellar parameters, distances, and elemental abundances of these candidates, thereby providing deeper insights into their origins and broadening their potential applications across astrophysics.

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arXiv2025

Chemical Components in the Virgo Overdensity and Hercules-Aquila Cloud: hints of more than one merger event in GSE-like debris

Using elemental abundances for 1.26 million K giants in the LAMOST DR8 value-added catalog, we analyze the chemical abundances of the Virgo Overdensity (VOD) and Hercules-Aquila Cloud (HAC). We find two distinct chemical populations in both overdensities, which is in disagreement with the mainstream hypothesis that both overdensities are composed of materials from a single merger event, namely Gaia-Sausage-Enceladus (GSE). The two populations show different chemical trends: one exhibits low metallicities and high $α$ abundances, and the other shows high metallicities and low $α$ abundances, which is associated with the recently discovered Nereus and Virgo Radial Merger (VRM) components in the local stellar halo, respectively. The Nereus component in these overdensities uniquely exhibits a decreasing trend in the [Fe/H]-[Mn/Fe] plane. Out of all observed Milky Way dwarf galaxies, this trend is only found in the Sculptor dwarf galaxy, which provides clues for the properties of Nereus progenitor. We also find that the velocity ellipse with high aniostropy parameters that is usually considered to be part of GSE are actually a mix of the two components. Both overdensities are well-mixed in kinematic spaces, confirming recent claims that the debris of merger pairs are kinematically indistinguishable in a recent simulation. We find that the velocity ellipses of the VRM stars in these overdensities have large inclination angles, which may be an indication of the merger time in simulated merger events.

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arXiv2025

Investigate Substructures of the Inner Halo Using the StarGO Algorithm with APOGEE DR17

We applied Stars' Galactic Origin (StarGO) algorithm in 7D space (i.e., [Fe/H], [Mg/Fe], [Al/Fe], $L_{z}$, $J_{r}$, $J_{z}$, $E$) to analyze stars in the inner halo with APOGEE DR17. We identified some known substructures, including Gaia-Sausage-Enceladus (GSE), Sagittarius Stream (Sgr), LMS-1 (Wukong), Thamnos, Metal-Weak Thick Disk (MWTD) and Aleph. Additionally, we identified an undefined metal-poor group (UDG, with [Fe/H] $<-0.8$ dex) probably linked to known substructure like Aleph, as well as a high $α$-abundance substructure (HAS) associated with both the Nyx and Nyx-2 streams. Chemical abundance of the HAS supports the argument that Nyx and Nyx-2 share a common origin. We discovered three substructures, which we refer to as new-substructure candidate-1,2,3 (NSTC-1,2,3). Despite exhibiting disk-like dynamics, these NSTCs demonstrate notably low [Mg/Fe] ($<$ 0.2 dex) and [Al/Fe] ($<$ $-0.15$ dex), similar to the properties of dwarf galaxies. Their high orbital energy and low [$α$/Fe] indicate the association with recent accretion events.

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arXiv2024

Investigating the vertical distribution of the disk as a function of radial action: Results from simulations

Previous research has established a relationship between radial action and scale height in Galactic disks, unveiling a correlation between radial and vertical heating. This finding poses a challenge to our existing comprehension of heating theories and consequently encodes crucial insights into the formation and heating history of Galactic disks. In this study, we perform N-body simulations with the aim of verifying the existence of this correlation between radial action and scale height, thereby enhancing our comprehension of the heating history of Galactic disks. We find that the relationship between radial action and scale height in our simulations can be described by the same functional form observed in previous work. Furthermore, the relationships derived from our simulations align well with those of the Galactic thin disk. However, they do not coincide with the inner thick disk but exhibit a rough correspondence with the outer thick disk, suggesting the possibility that additional heating mechanisms may be required to explain the inner thick disk. We also find that the mean radial action and scale height undergo rapid increases during the initial stages of the simulation, yet remain relatively unchanged as the disk evolves further. By tracing example particles, we uncover a correlation between radial and vertical heating in our simulation: as a particle in the disk gains or loses radial action, its vertical motion tends to oscillate on a more or less extended orbit, accompanied by a tendency to migrate outward or inward, respectively. The massive, long-lasting particles in our simulation contribute to disk heating by solely enhancing the rate of increase in scale height with radial action, while maintaining the functional form that describes the relationship between these two variables.

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arXiv2024

Exploration of Halo Substructures in IoM Space with \textit{Gaia} DR3

Using kinematic data from the Gaia Data Release 3 catalog, along with metallicity estimates robustly derived from Gaia XP spectra, we have explored the Galactic stellar halo in search of both known and potentially new substructures. By applying the HDBSCAN clustering algorithm in IoM space (i.e. $E,L_{z}$ and $L_{\perp}$$ = \sqrt{L_{x}^2+L_{y}^2}$), we identified 5 previously known substructures: Gaia-Sausage-Enceladus (GSE), Helmi Streams, I'itoi + Sequoia and Hot Thick Disc. We additionally found NGC 3201 and NGC 5139 in this work, and NGC 3201 shares similar distributions in phase space and metallicties to Arjuna, which possibly implies that they have the same origin. Three newly discovered substructures are Prograde Substructure 1 (PG1), Prograde Substructure 2 (PG2) and the Low Energy Group. PG1, with a higher $V_ϕ$ than typical GSE member stars, is considered as either a low eccentricity and metal-rich part of GSE or part of the metal-poor disc. PG2, sharing kinematic similarities with Aleph, is thought to be its relatively highly eccentric component or the mixture of Aleph and disc. The Low Energy Group, whose metal-poor component of metallicity distribution function has a mean value [M/H] $\sim$ $-$1.29 (compared to that of Heracles [M/H] $\sim$ $-$1.26), may have associations with Heracles.

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arXiv2024

A high-velocity star recently ejected by an intermediate-mass black hole in M15

The existence of intermediate-mass black holes (IMBHs) is crucial for understanding various astrophysical phenomena, yet their existence remains elusive, except for the LIGO-Virgo detection. We report the discovery of a high-velocity star J0731+3717, whose backward trajectory about 21 Myr ago intersects that of globular cluster M15 within the cluster tidal radius. Both its metallicity [Fe/H] and its alpha-to-iron abundance ratio [$α$/Fe] are consistent with those of M15. Furthermore, its location falls right on the fiducial sequence of the cluster M15 on the color-absolute magnitude diagram, suggesting similar ages. These support that J0731+3717 is originally associated with M15 at a confidence level of "seven nines". We find that such a high-velocity star ($V_{\rm ej} = 548^{+6}_{-5}$ km s$^{-1}$) was most likely tidally ejected from as close as one astronomical unit to the center of M15, confirming an IMBH ($\ge 100 M_{\odot}$ with a credibility of 98%) as the exclusive nature of the central unseen mass proposed previously.

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arXiv2024

A Potential Dynamical Origin of The Galactic Disk Warp: The Gaia-Sausage-Enceladus Major Merger

Previous studies have revealed that the Galactic warp is a long-lived, nonsteady, and asymmetric structure. There is a need for a model that accounts for the warp's long-term evolution. Given that this structure has persisted for over 5 Gyrs, its timeline may coincide with the completion of Gaia-Sausage-Enceladus (GSE) merger. Recent studies indicate that the GSE, the significant merger of our Galaxy, was likely a gas-rich merger and the large amount of gas introduced could have created a profound impact on the Galactic morphology. This study utilizes GIZMO simulation code to construct a gas-rich GSE merger. By reconstructing the observed characteristics of the GSE, we successfully reproduce the disk warp and capture nearly all of its documented features that aligns closely with observational data from both stellar and gas disks. This simulation demonstrates the possibility that the single major merger could generate the Galactic warp amplitude and precession. Furthermore, the analysis of the warp's long-term evolution may offer more clues into the formation history of the Milky Way.

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arXiv2024

Compositions of the Hercules-Aquila Cloud and Virgo Over-density

Based on a sample of K giant from Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) Data Release 8 and a sample of RR Lyrae (RRL) from \textit{Gaia} Data Release 3, we investigate the compositions of the Hercules-Aquila Cloud (HAC) and Virgo Over-density (VOD) and their collective contribution to the tilt and triaxiality of the stellar halo ($r\,\textless\,40\,{\rm kpc}$) as well as two breaks at $\approx15\,{\rm kpc}$ and 30\,kpc. We apply the Gaussian mixture model (GMM) to divide the stellar halo into the isotropic component and the radially biased anisotropic component, namely Gaia-Sausage-Enceladus (GSE), and find that both HAC and VOD are dominated by the GSE debris stars with weights of $0.67^{+0.09}_{-0.07}$ and $0.57^{+0.07}_{-0.06}$, respectively. In addition, using the K giants with orbital parameters, we identify the member stars of known substructures, including GSE, Sagittarius (Sgr), Helmi Streams, Sequoia, Thamnos, Pontus, Wukong, and Metal-weak Thick Disk (MWTD), to probe the compositions of low-eccentricity stars in the HAC and VOD regions. In density fittings of the RRL sample, we note that the absence of HAC and VOD has a weak effect on the shape of halo. Finally, we find that the radially biased anisotropic halo contributes majorly to the stellar halo that can be modelled with a tilted triaxial ellipsoid and a doubly broken power law with breaking radii at $18.08^{+2.04}_{-3.22}\,{\rm kpc}$ and $33.03^{+1.30}_{-1.21}\,{\rm kpc}$. This has important significance for understanding the status of large diffuse over-densities in the Milky Way.

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arXiv2024

The origin of High-velocity stars considering the impact of the Large Magellanic Cloud

Utilizing astrometric parameters sourced from \textit{Gaia} Data Release 3 and radial velocities obtained from various spectroscopic surveys, we identify 519 high-velocity stars (HiVels) with a total velocity in the Galactocentric restframe greater than 70\% of their local escape velocity under the {\tt\string Gala} {\tt\string MilkyWayPotential}. Our analysis reveals that the majority of these HiVels are metal-poor late-type giants, and we show 9 HiVels that are unbound candidates to the Galaxy with escape probabilities of 50\%. To investigate the origins of these HiVels, we classify them into four categories and consider the impact of the Large Magellanic Cloud (LMC) potential on their backward-integration trajectories. Specifically, we find that one of the HiVels can track back to the Galactic Center, and three HiVels may originate from the Sagittarius dwarf spheroidal galaxy (Sgr dSph). Furthermore, some HiVels appear to be ejected from the Galactic disk, while others formed within the Milky Way or have an extragalactic origin. Given that the LMC has a significant impact on the orbits of Sgr dSph, we examine the reported HiVels that originate from the Sgr dSph, with a few of them passing within the half-light radius of the Sgr dSph.

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arXiv2023

Dynamical substructures of local metal-poor halo

Based on 4,\,098 very metal-poor (VMP) stars with 6D phase-space and chemical information from \textit{Gaia} DR3 and LAMOST DR9 as tracers, we apply an unsupervised machine learning algorithm, Shared Nearest Neighbor (SNN), to identify stellar groups in the action-energy (\textbf{\textit{J}}-$E$) space. We detect seven previously known mergers in local samples, including Helmi Stream, Gaia-Sausage-Enceladus (GSE), Metal-weak Thick Disk (MWTD), Pontus, Wukong, Thamnos, and I'itoi+Sequoia+Arjuna. According to energy, we further divide GSE and Wukong into smaller parts to explore the orbital characteristics of individual fragments. Similarly, the division of Thamnos is based on action. It can be found that the apocentric distances of GSE parts of high and medium energy levels are located at $29.5\pm3.6\,{\rm kpc}$ and $13.0\pm2.7\,{\rm kpc}$, respectively, which suggests that GSE could account for breaks in the density profile of the Galactic halo at both $\approx30$\,kpc and $15\text{-}18$\,kpc. The VMP stars of MWTD move along prograde orbits with larger eccentricities than those of its more metal-rich stars, which indicates that the VMP part of MWTD may be formed by accreting with dwarf galaxies. Finally, we summarize all substructures discovered in our local VMP samples. Our results provide a reference for the formation and evolution of the inner halo of the Milky Way (MW).

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arXiv2023

Discovery of the shell structure via break radii in the outer halo of the Milky Way

Based on the \textit{Gaia} DR3 RR Lyrae catalog, we use two methods to fit the density profiles with an improved broken power law, and find that there are two break radii coinciding with the two apocenter pile-ups of high-eccentricity Gaia-Sausage-Enceladus (GSE) merger. Also, there is a break caused by the Sagittarius (Sgr) stream. Combining the positions of all breaks, we briefly analyze the metallicity and its dispersion as a function of $r$ as well as its distribution in cylindrical coordinates. For the clean sample, the $z\text{-to-}x$ ellipsoid axial ratio $q$ in $36\,{\rm kpc}\,\textless\,r\,\textless\,96\,{\rm kpc}$ becomes much smaller than that of the inner halo $(r\,\textless\,36\,{\rm kpc})$, while the major axis has a large uncertainty in the region of $36-66\,{\rm kpc}$ and the one in the region of $66-96\,{\rm kpc}$ is obviously different from that dominated by the Hercules-Aquila Cloud (HAC) and the Virgo Overdensity (VOD) in the inner halo, which indicates that there is an over-density structure distributed at low zenithal angles. Finally, we found that the over-density structure in the outer halo ($r\,\textgreater\,50\,{\rm kpc}$) is shell-shaped and relatively metal-rich compared to the outer background halo. We conclude that the shells could be the apocenter pile-ups of the high-eccentricity GSE merger, which is supported by previous numerical simulations.

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arXiv2022

Investigating the vertical distribution of the disk as a function of radial action

As heating processes can broaden the distributions of radial actions and the vertical distributions of the Galactic disks, we investigate the vertical distribution of the Galactic disks as a function of radial action based on Apache Point Observatory Galactic Evolution Experiment(APOGEE) and Gaia data in order to deepen our understanding of the formation and heating history of the Galactic disks. We find that the distributions of radial action for both the thin and thick disks can be approximately described by pseudo-isothermal distributions, which give a statistical measurement for the temperature of the disk as indicated by the mean radial action of the star sample. Estimations of the scale heights in different radial action ranges for these pseudo-isothermal distributions of the disks seem to show fixed relationships between radial action $J_R$ and scale height $h$. We describe these relationships with a two-parameter function of $h = \sqrt{J_R /a} + b$, where $a$ and $b$ are free parameters. When testing with a three-parameter function of $h=\sqrt[α]{J_R/a}+b$, we find that this two-parameter function describes the thin disk well, but we note the function should be used with care for the thick disk. When comparing the best-fit relationships between the inner and outer disk for both of the thin and thick disks, we find that the relationships are nearly the same for the thin disks but are different for the thick disks. The inner thick disk shows a nearly flattened relationship, while the outer thick disk presents a gradually increasing relationship. This work highlights an alternative way to unveil the heating history of the disks by investigating the relationship between scale height and radial action, as these relationships encode the formation and heating history of the Galactic disks.

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