The Galactic disc phase spirals at different Galactic positions revealed by Gaia and LAMOST data

TL;DR

This study maps and analyzes the phase spirals in stellar velocity distributions across the Milky Way disc using Gaia and LAMOST data, revealing their dependence on position and suggesting an external perturbation origin.

Contribution

It provides the first detailed mapping of phase spirals in the Galactic disc across multiple positions, highlighting their variation and supporting an external perturbation hypothesis.

Findings

Phase spirals vary strongly with Galactic position.

Spirals are most prominent near the Galactic center.

External perturbation, likely Sagittarius dwarf galaxy, caused the spirals.

Abstract

We have investigated the distributions of stellar azimuthal and radial velocity components $V_{\Phi}$ and $V_{R}$ in the vertical position-velocity plane $Z$-$V_{Z}$ across the Galactic disc of $6.34 \lesssim R \lesssim 12.34$\,kpc and $|\Phi| \lesssim 7.5^{\circ}$ using a Gaia and Gaia-LAMOST sample of stars. As found in previous works, the distributions exhibit significant spiral patterns. The $V_{R}$ distributions also show clear quadrupole patterns, which are the consequence of the well-known tilt of the velocity ellipsoid. The observed spiral and quadrupole patterns in the phase space plane vary strongly with radial and azimuthal positions. The phase spirals of $V_{\Phi}$ become more and more relaxed as $R$ increases. The spiral patterns of $V_{\Phi}$ and $V_{R}$ and the quadrupole patterns of $V_{R}$ are strongest at $-2^{\circ} < \Phi < 2^{\circ}$ but negligible at $4^{\circ} < \Phi < 6^{\circ}$ and $-6^{\circ} < \Phi < -4^{\circ}$. Our results suggest an external origin of the phase spirals. In this scenario, the intruder, most likely the previously well-known Sagittarius dwarf galaxy, passed through the Galactic plane in the direction towards either Galactic center or anti-center. The azimuthal variations of the phase spirals also help us constrain the passage duration of the intruder. A detailed model is required to reproduce the observed radial and azimuthal variations of the phase spirals of $V_{\Phi}$ and $V_{R}$.

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††slugcomment: 2018.9.19@altaffilmark{9}@altaffilmark{9}affiliationtext: LAMOST FELLOW

1. Introduction

It is recognized that the Milky Way is not steady and axisymmetric. The stellar populations of the Milky Way disc are perturbed by non-axisymmetric structures, including the Bar, the Spiral arms, the halo substructures and the satellite dwarf galaxies (Siebert et al., 2012; Gómez et al., 2013; Bovy et al., 2015), and therefore show significant phase spirals (Antoja et al., 2018; Bland-Hawthorn et al., 2018; Tian et al., 2018), as well as radial motions and vertical bulk motions (Sun et al., 2015; Williams et al., 2013; Carlin et al., 2013; Siebert et al., 2011; Huang et al., 2016; Carrillo et al., 2017; Wang et al., 2018). Studying those phase spirals and bulk motions can help us understand the perturbation history of the Milky Way (disc).

Antoja et al. (2018) first detect the remarkable phase spirals in the local stellar disc. They find that the distributions of stellar radial and azimuthal velocity components $V_{R}$ and $V_{\Phi}$ show significant spiral patterns in the vertical position-velocity plane $Z$-$V_{Z}$. Further works have studied the variations of the phase spirals with stellar age, action, chemistry and disc position using theLAMOST-Gaia (Tian et al., 2018) and GALAH-Gaia (Bland-Hawthorn et al., 2018) data. Their results not only confirm the original remarkable discovery of Antoja et al. (2018), but also resolve significant variations of the phase spirals with aforementioned parameters. Tian et al. (2018) find that the spirals are gradually apparent from $\tau<$ 0.5 Gyr, and then slowly disappearing until $\tau\,>$ 6.0 Gyr. Bland-Hawthorn et al. (2018) show that the phase spirals are easier discerned in the distributions of $\alpha$-poor stars than those of $\alpha$-rich stars. They also find that the spiral is clearest in stars with smaller action $J_{\rm r}$, and tighter in stars with smaller angular momentum $L_{\rm z}$. The radial and azimuthal variations of phase spirals are also found by Bland-Hawthorn et al. (2018). It’s worth noting that the sample of Bland-Hawthorn et al. (2018) only covers a small distance range of 1 kpc from the Sun, the spatial variations of the phase spirals need to be explored in a larger volume of the Galactic disc.

In the theoretical view, several works have attempted to explain the observed phase space spiral patterns by either external (Antoja et al., 2018; Bland-Hawthorn et al., 2018; Binney & Schönrich, 2018) or internal (Khoperskov et al., 2018) perturbations. Both the two scenarios can reproduce the phase spirals of $V_{\Phi}$ and $V_{R}$ in the Solar neighborhood. Antoja et al. (2018), Binney & Schönrich (2018), and Bland-Hawthorn et al. (2018) suggest that the phase spirals are probably the consequence of the Sagittarius dwarf galaxy perturbation. Independent to the external perturbation scenario, Khoperskov et al. (2018) suggest that the observed phase space spirals can be produced naturally by vertical oscillations driven by the buckling of the stellar bar–no need of an external perturber (a massive satellite or a sub-halo). Whereas, simulations considering external or internal perturbations predict different spatial variations of the phase spirals. In the external scenario, Bland-Hawthorn et al. (2018) imply tighter phase space spirals in the inner disc due to faster vertical oscillations leaded by a stronger disc gravity in the inner disc. Khoperskov et al. (2018) have also predicted the properties of phase space spirals in different $R$ and $\Phi$ bins considering internal perturbations, but doesn’t find a tighter phase space spirals in the inner disc. Thus, studying the phase space spirals at different disc positions in a larger volume of the disc can no doubt distinguish the origins of the phase spirals. Unfortunately, hitherto all the observations focus on the Solar neighbourhood.

In the current work, we study the phase space spirals at different disc positions ($R$ and $\Phi$), in particular its radial variations to see whether the phase space spirals in the inner disc are tighter as predicted by the scenario of Bland-Hawthorn et al. (2018). Our work is based on the recently released Gaia DR2, which provides precise proper motions and distances for more than 1.3 billion stars, and precise line-of-sight velocities for more than 7 million stars. In addition, the LAMOST surveys have yielded precise line-of-sight velocities and metallicities for millions of stars. These data enable us to derive accurate three dimensional velocities for large samples of stars across the Galactic disc ranging from 6 kpc to 12 kpc, thus allowing us to examine the spatial variations of the phase space spirals across a wide range of the disc.

This paper is organised as follows. In Section 2, we briefly introduce the samples used. In Section 3, we present the main results. The discussions are presented in Section 4. Finally, we summary our work in Section  5.

2. Data

2.1. Coordinate systems

We use the Galactocentric cylindrical system ($R,\Phi,Z$) with $R$, the projected Galactocentric distance, increasing radially outwards, $\Phi$ in the direction of the Galactic rotation and $Z$ towards the North Galactic Pole. The Sun is assumed to be at the Galactic mid-plane (i.e. $Z_{0}$ $=$ 0 pc) and has a value of $R_{0}$ of 8.34 kpc (Reid et al., 2014). We adopt a local circular speed of rotation curve of $V_{c}(R_{0})$ $=$ $240\,\rm\,km\,s^{-1}$, and solar motions ($U_{\odot},V_{\odot},W_{\odot}$) $=$ ($11.1,12.24,7.25$) $\rm km\,s^{-1}$ relative to the Local Standard of Rest (Schönrich et al., 2010). The results presented in the current work are stable if we choose $Z_{0}$ $=$ 27 pc and other solar motions relative to the Local Standard of Rest (Huang et al., 2015).

2.2. The stellar samples

By June 2016, $\sim$ 6.5 million stellar spectra of signal-to-noise ratios (SNRs) higher than 10 for 4.4 million unique stars have been obtained with LAMOST (Xiang et al., 2017a) during the Pilot Surveys and the first four years of the five-year Phase I Regular Surveys of the LAMOST Galactic spectroscopic surveys (Zhao et al., 2012; Deng et al., 2012; Liu et al., 2014; Yuan et al., 2015). Stellar atmospheric parameters (effective temperature $T_{\mathrm{eff}}$,   surface gravity $\log\,g$, metallicity $\mathrm{\,[Fe/H]}$) and line-of-sight velocities $V_{l}$ with random error of 5 $\rm km\,s^{-1}$ derived from the spectra using LSP3 (Xiang et al., 2015, 2017b) are available.

Precise parallaxes and proper motions of 1.3 billion stars in the Milky Way are now provided by the Gaia DR2 (Gaia Collaboration et al., 2018). Distances and asymmetric uncertainties are also available for those 1.3 billion stars in Gaia DR2 provided by Bailer-Jones et al. (2018), who derive the distances and uncertainties with a Bayesian method. In the current work, we adopt their distances. Line-of-sight velocities $V_{l}$ for 7 million stars are also provided with an accuracy of $\sim$ 1 $\rm km\,s^{-1}$. Combining the distances, proper motions and the line-of-sight velocities $V_{l}$ of millions of stars provided by the Gaia DR2, we derive accurate three-dimensional velocities of 7,224,631 (hereafter named the ”Gaia sample”) stars. Three-dimensional velocities of 3,600,275 (hereafter named the ”Gaia-LAMOST sample”) stars are also derived using the distances, proper motions from Gaia DR2 and $V_{l}$ from the LAMOST surveys.

We estimate three-dimensional velocities ($U,V,W$) and associated uncertainties of the individual stars using the method of Johnson et al. (1987). When we derive the errors of ($U,V,W$), the errors of distances, proper motions and line-of-sight velocities are considered based on the the principle of uncertainty propagation. Then we transform ($U,V,W$) to ($V_{\rm R},V_{\Phi},V_{\rm Z}$). Errors of ($V_{\rm R},V_{\Phi},V_{\rm Z}$) are also estimated based on the principle of uncertainty propagation.

In order to obtain reliable results, we have removed stars with $V_{\rm R},V_{\Phi}$ and $V_{\rm Z}$ uncertainties larger than 50 $\rm\,km^{-1}$, stars of distance uncertainties larger than 25 per cent, and stars of $|V_{\rm R}|\,>\,400\,\rm\,km\,s^{-1}$, or $|V_{\Phi}-240|\,>\,400\,\rm\,km\,s^{-1}$, or $|V_{\rm Z}|\,>\,400\,\rm\,km\,s^{-1}$. Finally, the Gaia sample contains 6,150,394 stars, and the Gaia-LAMOST sample contains 3,344,860 stars.

3. Results

In this Section, we examine the spatial variations of the phase spirals of $V_{\Phi}$ and $V_{R}$ using the two samples. Firstly, we divide the Gaia sample into 6 radial bins of $R$ from 6.34 kpc to 11.34 kpc and 6 azimuthal bins of $\Phi$ from $-6^{\circ}$ to $6^{\circ}$ to investigate the phase spirals of $V_{\Phi}$ and $V_{R}$ in the different bins of $R$ and $\Phi$. Stars in the Gaia-LAMOST sample are also divided into 6 radial bins of $R$ from 7.34 kpc to 12.34 kpc to investigate the phase spirals of $V_{\Phi}$ and $V_{R}$ at different $R$. The distribution of the Gaia-LAMOST sample stars in the $Z$-$\Phi$ plane is not symmetric, which is the consequence of the LAMOST sampling strategy, limiting magnitudes and so on. Above the Galactic plane, most of the stars have negative values of $\Phi$, whereas below the Galactic plane, most of the stars have positive $\Phi$. Thus, we do not study the azimuthal variations of the phase spirals with the Gaia-LAMOST sample. When we explore the radial and azimuthal variations of the phase spirals, we adopt an azimuthal range $\Phi$ of [$-7.5^{\circ},7.5^{\circ}$] and a radial range $R$ of [7.84, 8.84] kpc, respectively. Likewise, when we examine the distributions of $V_{\Phi}$ and $V_{R}$ in the $Z$-$V_{Z}$ plane, we adopt bin sizes of $\Delta Z=0.01\,$kpc and $\Delta V_{Z}=1.0\,\rm{km\,s^{-1}}$.

3.1. The phase spirals at different Galactic positions as revealed by the Gaia sample

3.1.1 Slicing by $R$

We firstly investigate the radial variations of the phase space spirals using the Gaia sample. Fig. 1 shows the distributions of $V_{\Phi}-228\,\rm{kms^{-1}}$ (left panels) and $V_{R}$ (right panels) of the Gaia sample stars in the $Z$-$V_{Z}$ plane and in the different radial bins. The radial range and number of stars in each bin are labeled in the Figure.

The distributions of $V_{\Phi}$ show significant phase spirals. Our results confirm the previous finding of Antoja et al. (2018), Bland-Hawthorn et al. (2018) and Tian et al. (2018) for the Solar neighbourhood. The phase spirals are apparent in all the radial bins, especially in the bin of $6.34\,\rm{kpc}<$ $R$ $<10.34\,\rm{kpc}$. The results strongly support the idea that the phase spirals are a disc-wide phenomenon (Bland-Hawthorn et al., 2018).

Besides, the phase spirals of $V_{\Phi}$ vary strongly with Galactic radius $R$ as Fig. 1 shows. The larger the $R$, the more relaxed of the phase spirals. In Fig. 1, the inner spirals become more and more relaxed as $R$ increases, and essentially disappear at $R>$ 9.34 kpc. The outer spirals are stronger in the outer disc than in the inner disc. One can find 3 spirals at $R<$ 9.34 kpc, 2 spirals at $9.34<R<10.34$ kpc and only 1 spiral at $10.34<R<11.34$ kpc in the phase space plane of $-1<Z<1$ kpc and $-50<V_{Z}<50\,\rm{km\,s^{-1}}$. The observed results presented here are consistent with the N-body simulation predictions of Bland-Hawthorn et al. (2018) (see their Fig. 22), who suggest that the stronger disc gravity in the inner disc leads to faster vertical oscillations and tighter phase spirals. In this scenario, one can see more spirals in the inner disc than in the outer disc in the same phase space region, which is indeed what one sees in Fig. 1.

The distributions of $V_{R}$ in the phase space plane at different Galactic radii are also presented in Fig. 1. They show clear quadrupole patterns at all Galactic radii except that of $R>10.34$ kpc, values of $V_{R}$ are relatively small in the top left and bottom right parts of each right panels compared to those in the top right and bottom left corners. The quadrupole patterns, first mentioned by Bland-Hawthorn et al. (2018) (see their Fig. 16), are the consequence of the well-known tilt of the velocity ellipsoid (Siebert et al., 2008; Binney et al., 2014; Bland-Hawthorn et al., 2018). The quadrupole patterns are the clearest at 8.34 kpc $<R<$ 9.34 kpc with the smallest $V_{R}$ in the top left and the bottom right region, consistent with the previously observed radial velocity dip in the Solar neighborhood (Siebert et al., 2011; Huang et al., 2016; Tian et al., 2017; Carrillo et al., 2017).

At $7.34<R<$ 10.34 kpc, the phase spirals are also found in the distributions of $V_{R}$, which are broadly similar to those of $V_{\Phi}$. However, the phase spirals are less tightly wound compared to those of $V_{\Phi}$, again consistent with the numerical simulation results of Bland-Hawthorn et al. (2018). In the innermost ($R<$ 7.34 kpc) and the outermost ($R>$ 10.34 kpc) parts of the disc, the phase spirals are barely visible.

3.1.2 Slicing by $\Phi$

We now investigate the distributions of $V_{\Phi}$ and $V_{R}$ of the Gaia sample stars in phase space plane in different azimuthal bins. Fig. 2 shows the main results. The azimuthal range and the number of stars in each bin are labeled in the Figure.

The phase spirals of $V_{\Phi}$ are apparent in all azimuthal bins. Three spirals are clearly seen, with shapes quite similar. The phase spirals become stronger as $\Phi$ increases, and are the strongest at $-2^{\circ}<\Phi<2^{\circ}$, and then fade away as $\Phi$ further increases. Interestingly, the mean values of $V_{\Phi}$ at $-2^{\circ}<\Phi<2^{\circ}$ are the smallest.

The distributions of $V_{R}$ in the phase space plane in the different $\Phi$ bins are also presented in Fig. 1. Similarly, the phase spirals are found in all the $\Phi$ bins, and are the strongest at $-2^{\circ}<\Phi<2^{\circ}$. Besides, quadrupole patterns are found in all the bins, and are also the strongest at $-2^{\circ}<\Phi<2^{\circ}$.

3.2. The phase spirals at different Galactic positions as revealed by the Gaia-LAMOST sample

In order to verify the robustness of our detections of the phase spirals at different Galactic positions, we show in Fig. 3 the $V_{\Phi}$ and $V_{R}$ distributions of the Gaia-LAMOST sample in the $Z$-$V_{Z}$ plane at different Galactic radii. What Fig. 3 reveals are broadly similar to those by Fig. 1.

Compared to Fig. 1, the spiral patterns of $V_{\Phi}$ are less well resolved by the Gaia-LAMOST sample stars, especially for the inner spirals in the inner disc ($7.34<R<9.34$ kpc). As mentioned in Section 2, line-of-sight velocities of the Gaia-LAMOST sample stars are much less accurate than those of the Gaia sample. This is responsible for the aforementioned difference. In Fig. 3, the phase spirals in outer disc ($R>9.34$ kpc) are much stronger than those seen in Fig. 1. This may be partly due to the fact that stars in the Gaia-LAMOST sample have smaller mean values of the absolute azimuthal angle compared to those of the Gaia sample stars at $R>9.34$ kpc, consistent with the results of Section 3.1.2.

In Fig. 3, the distributions of $V_{R}$ in the phase space plane are broadly consistent with what seen in Fig. 1, but less clearly. The quadrupole patterns are also similar to those uncovered by the Gaia sample. In Fig. 3, the quadrupole patterns are seen even at $R>10.34$ kpc. This is not the case when using Gaia sample. The reason is that stars in the Gaia-LAMOST sample have smaller mean values of $|\Phi|$ than those of the Gaia sample, considering that the spiral and quadrupole patterns of stars of smaller $|\Phi|$ are stronger than those of larger $|\Phi|$. Moreover, there is a clear break of $V_{R}$ from south side ($Z<0$ kpc) to north ($Z\,>\,0$ kpc), especially in the range of $7.84<R<9.84$ kpc. We suggest that it might be caused by the quadrupole patterns of the spirals, the bright limiting magnitudes and very low sampling rates of the LAMOST surveys in the solar neighbourhood after careful check.

4. Discussion

4.1. The effects of three dimensional velocity errors on the phase spirals

As discussed in Section 3.1.1, there are 3 phase spirals of $V_{\Phi}$ in the inner disc ($R<9.34$ kpc) but only 1 or 2 phase spirals in the outer disc ($R>9.34$ kpc). Meanwhile, the errors of the three dimensional velocities of stars at $R>9.34$ kpc are larger than those of stars at $R<9.34$ kpc. In order to check the relationship between spiral numbers and velocity errors, we use Monte Carlo method to check if the spirals in the range of [7.84,8.84] kpc are still robust. We firstly increase the errors of three dimensional velocities of each star at $7.84<R<8.84$ kpc by scaling with a factor, which is estimated as the ratio of the mean random velocity errors of stars at $9.34<R<10.34$ kpc and those of stars at $7.84<R<8.84$ kpc. The final velocities of the star are derived by adding the errors, which are randomly generated assuming Gaussian distributions, with the increased errors as the dispersions. We then examine the resultant $V_{\Phi}$ and $V_{R}$ distributions in the phase plane. The process is repeated 1000 times, and the resultant 1000 distributions of $V_{\Phi}$ and $V_{R}$ are quite similar one to the other.

Fig. 4 shows one of the resultant $V_{\Phi}$ and $V_{R}$ distributions in the phase space plane before and after increasing the velocity errors for stars at $7.84<R<8.84$ kpc. The phase spirals of $V_{\Phi}$ and $V_{R}$ seen show negligible differences before and after increasing the velocity errors. We therefore conclude that the results of more relaxed phase spirals of $V_{\Phi}$ in the outer disc are authentic.

4.2. Origins of phase spirals

Our results as revealed by both the Gaia and the Gaia-LAMOST samples suggest that the phase space spirals of $V_{\Phi}$ become more relaxed as $R$ increases. The phenomenon is exactly predicted by the N-body simulations of Bland-Hawthorn et al. (2018), who suggest that the passage of the Sagittarius through the Galactic plane, a scenario of an external origin, produces the vertical phase-mixing and phase spirals. The predicted radial variations of the phase spirals of $V_{\Phi}$ as driven by buckling of the stellar bar (internal origin; Khoperskov et al., 2018) are on the other hand not so consistent with what observed here. Our results suggest instead an origin of the phase spirals that are developed from an external perturbation.

If this scenario of an external origin is true, the location of the intruder passing through the Galactic plane and the mass and passage duration of the intruder become important issues. An intruder will attract stars to it changing their three dimensional velocities as the intruder pass through the Galaxy (Binney & Schönrich, 2018, see their Figs. 1 and 2). Meanwhile, the phase spirals at different Galactic positions especially its radial and azimuthal variations are no doubt strongly affected by the aforementioned parameters of the intruder. In other words, one can study the intruding passage location and duration through the radial and azimuthal variations of the phase spirals of $V_{\Phi}$ and $V_{R}$.

When an intruder pass through the Galactic plane, the effect of the intruder on the star in the line of the Galactic center and the intruder is largest, and the phase spiral in this direction is clearest. In Fig. 2, we find that the phase spirals of $V_{\Phi}$ and $V_{R}$ are clearest at $-2^{\circ}<\Phi<2^{\circ}$, become weaker as $|\Phi|\,>\,2^{\circ}$. It suggests that the external intruder passes through the Galactic plane in the direction of the Galactic center or anti-center.

The phase spirals of $V_{\Phi}$ and $V_{R}$ at $4^{\circ}<\Phi<6^{\circ}$ and $-6^{\circ}<\Phi<-4^{\circ}$ are significantly weaker, almost invisible, suggesting that the speed of the intruder is quite fast such that it mainly affects stars within an azimuthal angle range of $8^{\circ}$, or about 2 per cent of the rotation period of a star at a Galactic radius $R\approx R_{0}$. The volume that the intruder can affect also directly linked to its mass, more massive intruder can affect larger volume.

As discussed in the previous works, the most probably perturbation source is the Sagittarius dwarf, which has a ”trefoil” orbit over the past 2.3 Gyr. It crossed the disc about 420 Myr ago at $R=13$ kpc and transited again about 50 Myr ago (Bland-Hawthorn et al., 2018; Law et al., 2005; Tepper-García & Bland-Hawthorn, 2018). If the Sagittarius dwarf is responsible for the phase spirals, the results presented here can help constrain its orbit and mass, even the shape of the Galactic halo. Detailed modeling is required to reproduce the observed spatial variations of the phase spirals of $V_{\Phi}$ and $V_{R}$.

5. Summary

In this Letter, we study the phase space spirals of $V_{\Phi}$ and $V_{R}$ using the Gaia and LAMOST data, and investigate the radial and azimuthal variations of the spiral and quadrupole patterns in the phase space plane. The main results are the following:

• •

The distributions of $V_{\Phi}$ in the $Z$-$V_{Z}$ plane show strong spiral patterns at $6.34<R<12.34$ kpc.

• •

The phase spirals of $V_{\Phi}$ become more relaxed as $R$ increases.

• •

The distributions of $V_{R}$ in the $Z$-$V_{Z}$ plane show strong quadrupole patterns in all $R$ and $\Phi$ bins. They also show spiral patterns but not so tightly wound as those of $V_{\Phi}$. In the innermost ($R<$ 7.34 kpc) and outermost disc ($R>$ 10.34 kpc), the spiral patterns are barely visible.

• •

The spiral patterns of $V_{\Phi}$ and the quadrupole and spiral patterns of $V_{R}$ in the $Z$-$V_{Z}$ plane are the strongest at $-2^{\circ}<\Phi<2^{\circ}$, but almost invisible at $4^{\circ}<\Phi<6^{\circ}$ and $-6^{\circ}<\Phi<-4^{\circ}$.

The radial variations of the phase spirals of $V_{\Phi}$ is consistent with the predictions of perturbation by an external intruder as suggested by Bland-Hawthorn et al. (2018), but inconsistent with an internal origin as suggested by Khoperskov et al. (2018). The azimuthal variations of the phase spirals of $V_{\Phi}$ and $V_{R}$ suggest that the intruder passes through the Galactic plane in the direction of either the Galactic center or the anti-center. The azimuthal variations of the phase spirals of $V_{\Phi}$ and $V_{R}$ also tell us something about the mass and the passage duration of the intruder. A detailed model is required to reproduce the results presented here.

6. ACKNOWLEDGEMENTS

This work is supported by the National Natural Science Foundation of China 11833006, U1531244 and 11473001. Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. The LAMOST FELLOWSHIP is supported by Special Funding for Advanced Users, budgeted and administrated by Center for Astronomical Mega-Science, Chinese Academy of Sciences (CAMS).