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Yang Huang

Publications and source records attributed to Yang Huang.

At least 181 records · Page 10Linked to original sources
arXiv2023

An update of the catalog of radial velocity standard stars from the APOGEE DR17

We present an updated catalog of 46,753 radial velocity (RV) standard stars selected from the APOGEE DR17. These stars cover the Northern and Southern Hemispheres almost evenly, with 62% being red giants and 38% being main-sequence stars. These RV standard stars are stable on a baseline longer than 200 days (54% longer than one year and 10% longer than five years) with a median stability better than 215 m s$^{-1}$. The average observation number of those stars are 5 and each observation is required to have spectral-to-noise-ratio (SNR) greater than 50 and RV measurement error smaller than 500 m s$^{-1}$. Based on the new APOGEE RV standard star catalog, we have checked the RV zero points (RVZPs) for current large-scale stellar spectroscopic surveys including RAVE, LAMOST, GALAH and Gaia. By carefully analysis, we estimate their mean RVZP to be $+0.149$ km s$^{-1}$, $+4.574$ km s$^{-1}$ (for LRS), $-0.031$ km s$^{-1}$ and $+0.014$ km s$^{-1}$, respectively, for the four surveys. In the RAVE, LAMOST (for MRS), GALAH and Gaia surveys, RVZP exhibits systematic trend with stellar parameters (mainly [Fe/H], $T_{\rm{eff}}$, log $g$, $G_{\rm{BP}}-G_{\rm{RP}}$ and $G_{\rm{RVS}}$). The corrections of those small but clear RVZPs are of vital importances for these massive spectroscopic surveys in various studies that require extremely high radial velocity accuracies.

astro-ph.SR↗
arXiv2023

Beyond spectroscopy. II. Stellar parameters for over twenty million stars in the northern sky from SAGES DR1 and Gaia DR3

We present precise photometric estimates of stellar parameters, including effective temperature, metallicity, luminosity classification, distance, and stellar age, for nearly 26 million stars using the methodology developed in the first paper of this series, based on the stellar colors from the Stellar Abundances and Galactic Evolution Survey (SAGES) DR1 and Gaia EDR3. The optimal design of stellar-parameter sensitive $uv$ filters by SAGES has enabled us to determine photometric-metallicity estimates down to $-3.5$, similar to our previous results with the SkyMapper Southern Survey (SMSS), yielding a large sample of over five million metal-poor (MP; [Fe/H]$\le -1.0$) stars and nearly one million very metal-poor (VMP; [Fe/H]$\le -2.0$) stars. The typical precision is around $0.1$ dex for both dwarf and giant stars with [Fe/H]$>-1.0$, and 0.15-0.25/0.3-0.4 dex for dwarf/giant stars with [Fe/H]$<-1.0$. Using the precise parallax measurements and stellar colors from Gaia, effective temperature, luminosity classification, distance and stellar age are further derived for our sample stars. This huge data set in the Northern sky from SAGES, together with similar data in the Southern sky from SMSS, will greatly advance our understanding of the Milky Way, in particular its formation and evolution.

astro-ph.GA↗
arXiv2023

The Stellar Abundances and Galactic Evolution Survey (SAGES) -- -- I. General Description and the First Data Release (DR1)

The Stellar Abundances and Galactic Evolution Survey (SAGES) of the northern sky is a specifically-designed multi-band photometric survey aiming to provide reliable stellar parameters with accuracy comparable to those from low-resolution optical spectra. It was carried out with the 2.3-m Bok telescope of Steward Observatory and three other telescopes. The observations in the $u_s$ and $v_s$ passband produced over 36,092 frames of images in total, covering a sky area of $\sim9960$ degree$^2$. The median survey completeness of all observing fields for the two bands are of $u_{\rm s}=20.4$ mag and $v_s=20.3$ mag, respectively, while the limiting magnitudes with signal-to-noise ratio (S/N) of 100 are $u_s\sim17$ mag and $v_s\sim18$ mag, correspondingly. We combined our catalog with the data release 1 (DR1) of the first of Panoramic Survey Telescope And Rapid Response System (Pan-STARRS1, PS1) catalog, and obtained a total of 48,553,987 sources which have at least one photometric measurement in each of the SAGES $u_s$ and $v_s$ and PS1 $grizy$ passbands, which is the DR1 of SAGES and it will be released in our paper. We compare our $gri$ point-source photometry with those of PS1 and found an RMS scatter of $\sim2$% in difference of PS1 and SAGES for the same band. We estimated an internal photometric precision of SAGES to be on the order of $\sim1$%. Astrometric precision is better than $0^{\prime\prime}.2$ based on comparison with the DR1 of Gaia mission. In this paper, we also describe the final end-user database, and provide some science applications.

astro-ph.GA↗
arXiv2023

The outer low-$α$ disc of the Milky Way -- I: evidence for the first pericentric passage of Sagittarius?

Phase-space data, chemistry, and ages together reveal a complex structure in the outer low-$α$ disc of the Milky Way. The age-vertical velocity dispersion profiles beyond the Solar Neighbourhood show a significant jump at 6 Gyr for stars beyond the Galactic plane. Stars older than 6 Gyr are significantly hotter than younger stars. The chemistry and age histograms reveal a bump at [Fe/H] = -0.5, [$α$/Fe] = 0.1, and an age of 7.2 Gyr in the outer disc. Finally, viewing the stars beyond 13.5 kpc in the age-metallicity plane reveals a faint streak just below this bump, towards lower metallicities at the same age. Given the uncertainty in age, we believe these features are linked and suggest a pericentric passage of a massive satellite 6 Gyr ago that heated pre-existing stars, led to a starburst in existing gas. New stars also formed from the metal-poorer infalling gas. The impulse approximation was used to characterise the interaction with a satellite, finding a mass of ~1e11 M$_{\odot}$, and a pericentric position between 12 and 16 kpc. The evidence points to an interaction with the Sagittarius dwarf galaxy, likely its first pericentric passage.

astro-ph.GA↗
arXiv2023

Precise Masses, Ages of ~1.0 million RGB and RC stars observed by the LAMOST

We construct a catalogue of stellar masses and ages for 696,680 red giant branch (RGB) stars, 180,436 primary red clump (RC) stars, and 120,907 secondary RC stars selected from the LAMOST\,DR8. The RGBs, primary RCs, and secondary RCs are identified with the large frequency spacing ($Δν$) and period spacing ($ΔP$), estimated from the LAMOST spectra with spectral SNRs $> 10$ by the neural network method supervised with the seismologic information from LAMOST-Kepler sample stars. The purity and completeness of both RGB and RC samples are better than 95\% and 90\%, respectively. The mass and age of RGBs and RCs are determined again with the neural network method by taking the LAMOST-Kepler giant stars as the training set. The typical uncertainties of stellar mass and age are, respectively, 10\% and 30\% for the RGB stellar sample. For RCs, the typical uncertainties of stellar mass and age are 9\% and 24\%, respectively. The RGB and RC stellar samples cover a large volume of the Milky Way (5 $< R < 20$\,kpc and $|Z| <$\,5\,kpc), which are valuable data sets for various Galactic studies.

astro-ph.GA↗
arXiv2023

On the origins of extreme velocity stars as revealed by large-scale Galactic surveys

We assemble a large sample of 12,784 high-velocity stars with total velocity $\it{V}_{\rm{GSR}}\ge {\rm 300}$ km s$^{-1}$, selected from RAVE DR5, SDSS DR12, LAMOST DR8, APOGEE DR16, GALAH DR2, and $Gaia$ EDR3. In this sample, 52 are marginally hypervelocity star (HVS) candidates that have $\it{V}_{\rm{GSR}}$ exceeding their local escape velocities within $2σ$ confidence levels, 40 of which are discovered for the first time. All candidates are metal-poor, late-type halo stars, significantly different from the previous identified HVSs, which are largely massive early-type stars, discovered by extreme radial velocity. This finding suggests that our newly identified HVS candidates are ejected by different mechanisms from the previous population. To investigate their origins, for 547 extreme velocity stars with ${V}_{\rm{GSR}}\ge0.8V_{\rm{esc}}$, we reconstruct their backward-integrated trajectories in the Galactic potential. According to the orbital analysis, no candidates are found to be definitely ejected from the Galactic-center (GC), while 8 metal-poor extreme velocity stars are found to have a closest distance to the GC within 1kpc. Intriguingly, 15 extreme velocity stars (including 2 HVS candidates) are found to have experienced close encounters with the Sagittarius dSph, suggesting that they originated from this dSph. This hypothesis is supported by an analysis of the [$α$/Fe]--[Fe/H] diagram. From a preliminary analysis of all the 547 extreme velocity stars, we propose a general picture: Star ejection from Galactic subsystems such as dwarf galaxies and globular clusters can be an important channel to produce extreme velocity stars or even HVSs, particularly the metal-poor late-type halo population.

astro-ph.GA↗
arXiv2023

FAN: Fatigue-Aware Network for Click-Through Rate Prediction in E-commerce Recommendation

Since clicks usually contain heavy noise, increasing research efforts have been devoted to modeling implicit negative user behaviors (i.e., non-clicks). However, they either rely on explicit negative user behaviors (e.g., dislikes) or simply treat non-clicks as negative feedback, failing to learn negative user interests comprehensively. In such situations, users may experience fatigue because of seeing too many similar recommendations. In this paper, we propose Fatigue-Aware Network (FAN), a novel CTR model that directly perceives user fatigue from non-clicks. Specifically, we first apply Fourier Transformation to the time series generated from non-clicks, obtaining its frequency spectrum which contains comprehensive information about user fatigue. Then the frequency spectrum is modulated by category information of the target item to model the bias that both the upper bound of fatigue and users' patience is different for different categories. Moreover, a gating network is adopted to model the confidence of user fatigue and an auxiliary task is designed to guide the learning of user fatigue, so we can obtain a well-learned fatigue representation and combine it with user interests for the final CTR prediction. Experimental results on real-world datasets validate the superiority of FAN and online A/B tests also show FAN outperforms representative CTR models significantly.

cs.IR↗
arXiv2023

Spatial metallicity variations of mono-temperature stellar populations revealed by early-type stars in LAMOST

We investigate the radial metallicity gradients and azimuthal metallicity distributions on the Galactocentric $X$--$Y$ plane using mono-temperature stellar populations selected from LAMOST MRS young stellar sample. The estimated radial metallicity gradient ranges from $-$0.015\,dex/kpc to $-$0.07\,dex/kpc, which decreases as effective temperature decreases (or stellar age increases) at $7500 < T_{\rm eff} < 12500$\,K ($τ< $1.5 Gyr). The azimuthal metallicity excess (metallicity after subtracting radial metallicity gradient, $Δ$\,[M/H]) distributions exhibit inhomogeneities with dispersions of 0.04\,dex to 0.07\,dex, which decrease as effective temperature decreases. We also identify five potential metal-poor substructures with large metallicity excess dispersions. The metallicity excess distributions of these five metal-poor substructures suggest that they contain a larger fraction of metal-poor stars compared to other control samples. These metal-poor substructures may be associated with high-velocity clouds that infall into the Galactic disk from the Galactic halo, which are not quickly well-mixed with the pre-existing ISM of the Galactic disk. As a result, these high-velocity clouds produce some metal-poor stars and the observed metal-poor substructures. The variations of metallicity inhomogeneities with different stellar populations indicate that high-velocity clouds are not well mixed with the pre-existing Galactic disk ISM within 0.3\,Gyr.

astro-ph.GA↗
arXiv2023

MOEF: Modeling Occasion Evolution in Frequency Domain for Promotion-Aware Click-Through Rate Prediction

Promotions are becoming more important and prevalent in e-commerce to attract customers and boost sales, leading to frequent changes of occasions, which drives users to behave differently. In such situations, most existing Click-Through Rate (CTR) models can't generalize well to online serving due to distribution uncertainty of the upcoming occasion. In this paper, we propose a novel CTR model named MOEF for recommendations under frequent changes of occasions. Firstly, we design a time series that consists of occasion signals generated from the online business scenario. Since occasion signals are more discriminative in the frequency domain, we apply Fourier Transformation to sliding time windows upon the time series, obtaining a sequence of frequency spectrum which is then processed by Occasion Evolution Layer (OEL). In this way, a high-order occasion representation can be learned to handle the online distribution uncertainty. Moreover, we adopt multiple experts to learn feature representations from multiple aspects, which are guided by the occasion representation via an attention mechanism. Accordingly, a mixture of feature representations is obtained adaptively for different occasions to predict the final CTR. Experimental results on real-world datasets validate the superiority of MOEF and online A/B tests also show MOEF outperforms representative CTR models significantly.

cs.LG↗
arXiv2023

Sparse Bayesian Learning-Based 3D Spectrum Environment Map Construction-Sampling Optimization, Scenario-Dependent Dictionary Construction and Sparse Recovery

The spectrum environment map (SEM), which can visualize the information of invisible electromagnetic spectrum, is vital for monitoring, management, and security of spectrum resources in cognitive radio (CR) networks. In view of a limited number of spectrum sensors and constrained sampling time, this paper presents a new three-dimensional (3D) SEM construction scheme based on sparse Bayesian learning (SBL). Firstly, we construct a scenario-dependent channel dictionary matrix by considering the propagation characteristic of the interested scenario. To improve sampling efficiency, a maximum mutual information (MMI)-based optimization algorithm is developed for the layout of sampling sensors. Then, a maximum and minimum distance (MMD) clustering-based SBL algorithm is proposed to recover the spectrum data at the unsampled positions and construct the whole 3D SEM. We finally use the simulation data of the campus scenario to construct the 3D SEMs and compare the proposed method with the state-of-the-art. The recovery performance and the impact of different sparsity on the constructed SEMs are also analyzed. Numerical results show that the proposed scheme can reduce the required spectrum sensor number and has higher accuracy under the low sampling rate.

eess.SP↗
arXiv2023

Novel black holes in higher derivative gravity

We find a class of novel black holes in higher derivative theory. The novel black holes follow behavior of~\sch\ ones at large mass limit, while dramatically differentiate from ~\sch\ ones for little holes because of the effects which may root in quantum gravity. The temperature of the hole takes maximum for a specific mass, which is related to the new sale introduced in the higher derivative theory, and goes to zero at little mass limit. This property leads to a significant observation that the novel black hole may be a candidate for dark matters evading constraint from $γ$-ray burst.

gr-qc↗
arXiv2022

Photometric metallicity and distance estimates for $\sim$ 136,000 RR Lyrae stars from Gaia DR3

We present a sample of 135,873 RR Lyrae stars (RRLs) with precise photometric-metallicity and distance estimates from our newly calibrated $P-ϕ_{31}-R_{21}-$[Fe/H]/$P-R_{21}-$[Fe/H] and $G$ band absolute magnitude-metallicity relations. The $P-ϕ_{31}-R_{21}-$[Fe/H] and $P-R_{21}-$[Fe/H] relations for type RRab and type RRc stars are obtained from nearly 2700 Gaia-identified RRLs with precise $ϕ_{31}$ and $R_{21}$ measurements from the light curves and metallicity estimates from spectroscopy. Using 236 nearby RRLs with accurate distances estimated from parallax measurements with Gaia EDR3, new $G$ band absolute magnitude-metallicity relations and near-infrared period-absolute magnitude-metallicity relations are constructed. External checks, using other high-resolution spectroscopic sample of field RRLs and RRL members of globular clusters (GCs), show that the typical uncertainties in our photometric-metallicity estimates are about 0.24 and 0.16 dex for type RRab/c stars, respectively, without significant systematic bias with respect to high-resolution spectroscopic metallicity measurements. The accuracies of these metallicity estimates are much improved, especially for RRab stars, when compared to those provided by the Gaia DR3 release. Validations of our distance estimates, again by using members of GCs, show that the typical distance errors are only 3-4%. The distance modulus $μ_0=18.503\pm0.001(stat)\pm0.040(syst)$ mag for the LMC and $μ_0=19.030\pm0.003(stat)\pm0.043(syst)$ mag for the SMC are estimated from our RRab sample, respectively, and are in excellent agreement with previous measurements. The mean metallicities of the LMC and SMC derived in this work are also consistent with the previous determinations. Using our sample, a steep metallicity gradient of $-0.024\pm0.001$ dex/kpc is found for the LMC, while a negligible metallicity gradient is obtained for the SMC.

astro-ph.SR↗
arXiv2022

The Circular Velocity Curve of the Milky Way from 5 to 25 kpc using luminous red giant branch star

We present a sample of 254,882 luminous red giant branch (LRGB) stars selected from the APOGEE and LAMOST surveys. By combining photometric and astrometric information from the 2MASS and Gaia surveys, the precise distances of the sample stars are determined by a supervised machine learning algorithm: the gradient boosted decision trees. To test the accuracy of the derived distances, member stars of globular clusters (GCs) and open clusters (OCs) are used. The tests by cluster member stars show a precision of about 10 per cent with negligible zero-point offsets, for the derived distances of our sample stars. The final sample covers a large volume of the Galactic disk(s) and halo of $0<R<30$ kpc and $|Z|\leqslant15$ kpc. The rotation curve (RC) of the Milky Way across radius of $5\lesssim R\lesssim25$ kpc have been accurately measured with $\sim$ 54,000 stars of the thin disk population selected from the LRGB sample. The derived RC shows a weak decline along $R$ with a gradient of $-1.83\pm0.02$ $({\rm stat.}) \pm 0.07$ $({\rm sys.})$ km s$^{-1}$ kpc$^{-1}$, in excellent agreement with the results measured by previous studies. The circular velocity at the solar position, yielded by our RC, is $234.04\pm0.08$ $({\rm stat.}) \pm 1.36$ $({\rm sys.})$ km s$^{-1}$, again in great consistent with other independent determinations. From the newly constructed RC, as well as constraints from other data, we have constructed a mass model for our Galaxy, yielding a mass of the dark matter halo of $M_{\rm{200}}$ = ($8.05\pm1.15$)$\times$10$^{11} \rm{M_\odot}$ with a corresponding radius of $R_{\rm{200}}$ = $192.37\pm9.24$ kpc and a local dark matter density of $0.39\pm0.03$ GeV cm$^{-3}$.

astro-ph.GA↗
arXiv2022

Deep Learning-Based Rate-Splitting Multiple Access for Reconfigurable Intelligent Surface-Aided Tera-Hertz Massive MIMO

Reconfigurable intelligent surface (RIS) can significantly enhance the service coverage of Tera-Hertz massive multiple-input multiple-output (MIMO) communication systems. However, obtaining accurate high-dimensional channel state information (CSI) with limited pilot and feedback signaling overhead is challenging, severely degrading the performance of conventional spatial division multiple access. To improve the robustness against CSI imperfection, this paper proposes a deep learning (DL)-based rate-splitting multiple access (RSMA) scheme for RIS-aided Tera-Hertz multi-user MIMO systems. Specifically, we first propose a hybrid data-model driven DL-based RSMA precoding scheme, including the passive precoding at the RIS as well as the analog active precoding and the RSMA digital active precoding at the base station (BS). To realize the passive precoding at the RIS, we propose a Transformer-based data-driven RIS reflecting network (RRN). As for the analog active precoding at the BS, we propose a match-filter based analog precoding scheme considering that the BS and RIS adopt the LoS-MIMO antenna array architecture. As for the RSMA digital active precoding at the BS, we propose a low-complexity approximate weighted minimum mean square error (AWMMSE) digital precoding scheme. Furthermore, for better precoding performance as well as lower computational complexity, a model-driven deep unfolding active precoding network (DFAPN) is also designed by combining the proposed AWMMSE scheme with DL. Then, to acquire accurate CSI at the BS for the investigated RSMA precoding scheme to achieve higher spectral efficiency, we propose a CSI acquisition network (CAN) with low pilot and feedback signaling overhead, where the downlink pilot transmission, CSI feedback at the user equipments (UEs), and CSI reconstruction at the BS are modeled as an end-to-end neural network based on Transformer.

eess.SP↗
arXiv2022

How Close Dark Matter Halos and MOND Are to Each Other: Three-Dimensional Tests Based on Gaia DR2

Aiming at discriminating different gravitational potential models of the Milky Way, we perform tests based on the kinematic data powered by the Gaia DR2 astrometry, over a large range of $(R,z)$ locations. Invoking the complete form of Jeans equations that admit three integrals of motion, we use the independent $R$- and $z$-directional equations as two discriminators ($T_R$ and $T_z$). We apply the formula for spatial distributions of radial and vertical velocity dispersions proposed by Binney et al., and successfully extend it to azimuthal components, $σ_θ(R,z)$ and $V_θ(R,z)$; the analytic form avoids the numerical artifacts caused by numerical differentiation in Jeans-equations calculation given the limited spatial resolutions of observations, and more importantly reduces the impact of kinematic substructures in the Galactic disk. It turns out that whereas the current kinematic data are able to reject Moffat's Modified Gravity (let alone the Newtonian baryon-only model), Milgrom's MOND is still not rejected. In fact, both the carefully calibrated fiducial model invoking a spherical dark matter (DM) halo and MOND are equally consistent with the data at almost all spatial locations (except that probably both have respective problems at low-$|z|$ locations), no matter which a tracer population or which a meaningful density profile is used. Because there is no free parameter at all in the quasi-linear MOND model we use, and the baryonic parameters are actually fine-tuned in the DM context, such an effective equivalence is surprising, and might be calling forth a transcending synthesis of the two paradigms.

astro-ph.GA↗
arXiv2022

Stellar Loci VI: An Updated Catalog of the Best and Brightest Metal-poor Stars

We employ Gaia, 2MASS, and ALLWISE photometry, as well as astrometric data from Gaia, to search for relatively bright very metal-poor ([Fe/H] $< -2.0$; VMP) giant star candidates using three different criteria: 1) our derived Gaia photometric metallicities, 2) the lack of stellar molecular absorption near 4.6 microns, and 3) their high tangential velocities. With different combinations of these criteria, we have identified six samples of candidates with $G <$ 15: the Gold sample (24,304 candidates), the Silver GW sample (40,157 candidates), the Silver GK sample (120,452 candidates), the Bronze G sample (291,690 candidates), the Bronze WK sample (68,526 candidates), and the Low $b$ sample (4,645 candidates). The Low $b$ sample applies to sources with low Galactic latitude, $|b| < 10^\circ$, while the others are for sources with $|b| > 10^\circ$. By cross-matching with results derived from medium-resolution ($R \sim$ 1800) from LAMOST DR8, we establish that the success rate for identifying VMP stars is 60.1$\%$ for the Gold sample, 39.2$\%$ for the Silver GW sample, 41.3$\%$ for the Silver GK sample, 15.4$\%$ for the Bronze G sample, 31.7$\%$ for the Bronze WK sample, and 16.6$\%$ for the Low $b$ sample, respectively. An additional strict cut on the quality parameter $RUWE < 1.1$ can further increase the success rate of the Silver GW, Silver GK, and Bronze G samples to 46.9$\%$, 51.6$\%$, and 29.3$\%$, respectively. Our samples provide valuable targets for high-resolution follow-up spectroscopic observations, and are made publicly available.

astro-ph.SR↗
arXiv2022

A dynamically discovered and characterized non-accreting neutron star -- M dwarf binary candidate

Optical time-domain surveys can unveil and characterize exciting but less-explored non-accreting and/or non-beaming neutron stars (NS) in binaries. Here we report the discovery of such a NS candidate using the LAMOST spectroscopic survey. The candidate, designated LAMOST J112306.9+400736 (hereafter J1123), is in a single-lined spectroscopic binary containing an optically visible M star. The star's large radial velocity variation and ellipsoidal variations indicate a relatively massive unseen companion. Utilizing follow-up spectroscopy from the Palomar 200-inch telescope and high-precision photometry from TESS, we measure a companion mass of $1.24_{-0.03}^{+0.03}~M_{\odot}$. Main-sequence stars with this mass are ruled out, leaving a NS or a massive white dwarf (WD). Although a massive WD cannot be ruled out, the lack of UV excess radiation from the companion supports the NS hypothesis. Deep radio observations with FAST yielded no detections of either pulsed or persistent emission. J1123 is not detected in numerous X-ray and gamma-ray surveys. These non-detections suggest that the NS candidate is not presently accreting and pulsing. Our work exemplifies the capability of discovering compact objects in non-accreting close binaries by synergizing the optical time-domain spectroscopy and high-cadence photometry.

astro-ph.SR↗
arXiv2022

Probing the Galactic halo with RR Lyrae stars $-$ III. The chemical and kinematic properties of the stellar halo

Based on a large spectroscopic sample of $\sim$ 4,300 RR Lyrae stars with metallicity, systemic radial velocity and distance measurements, we present a detailed analysis of the chemical and kinematic properties of the Galactic halo. Using this sample, the metallicity distribution function (MDF) as a function of $r$ and the velocity anisotropy parameter $β$ profiles (for different metallicity populations) are derived for the stellar halo. Both the chemical and kinematic results suggest that the Galactic halo is composed of two distinct parts, the inner halo and outer halo. The cutoff radius ($\sim$ 30 kpc) is similar to the previous break radius found in the density distribution of the stellar halo. We find that the inner part is dominated by a metal-rich population with extremely radial anisotropy ($β\sim 0.9$). These features are in accordance with those of ``{\it Gaia}-Enceladus-Sausage'' (GES) and we attribute this inner halo component as being dominantly composed of stars deposited from this ancient merged satellite. We find that GES probably has a slightly negative metallicity gradient. The metal-poor populations in the inner halo are characterized as a long-tail in MDF with an anisotropy of $β\sim 0.5$, which is similar to that of the outer part. The MDF for the outer halo is very broad with several weak peaks and the value of $β$ is around 0.5 for all metallicities.

astro-ph.GA↗