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H. -W. Zhang

Publications and source records attributed to H. -W. Zhang.

At least 19 recordsLinked to original sources

Probing the Galactic Halo with RR Lyrae Stars. II. The Substructures of the Milky Way

We identify substructures of the Galactic halo using 3,003 type $ab$ RR Lyraes (RRab) with 6D position-velocity information from the SDSS, LAMOST, and Gaia EDR3. Based on the information, we define the separation of any two of the stars in the integrals of motion space and identify substructures by utilizing the friends-of-friends algorithm. We identify members belonging to several known substructures: the Sagittarius stream, the Gaia-Enceladus-Sausage (GES), the Sequoia, and the Helmi streams. In addition to these known substructures, there are three other substructures possibly associated with globular clusters NGC 5272, NGC 6656, and NGC 5024, respectively. Finally, we also find three remaining unknown substructures and one of them has large angular momentum and a mean metallicity $\rm -2.13\,dex$ which may be a new substructure. As for GES, we find that it accounts for a large part of substructures in the inner halo and the range of apocenter distance is from 10 to $34\,\rm kpc$, which suggests that the GES is mainly distributed in the inner halo. The near one-third proportion of the GES and the peak value $20\,\rm kpc$ of the apocenter distances suggest that GES could account for the break in the density profile of the Galactic halo at Galactocentric distance ${\sim}20-25\,\rm kpc$. The similarity of comparing the kinematic properties of Gaia-Enceladus-Sausage with the Hercules-Aquila Cloud and Virgo Overdensity suggests that the three substructures may have similar origins.

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Local Stellar Kinematics and Oort Constants from the LAMOST A-type Stars

We estimate the solar peculiar velocities and Oort constants using a sample of 5,627 A-type stars with $d<0.6\,\rm kpc$ and $|z|<0.1\,\rm kpc$, selected from the LAMOST surveys. The radial and tangential velocities of these A-type stars are fitted by using a non-axisymmetric model. The best-fitting result yields the solar peculiar velocities $(U_\odot,V_\odot,W_\odot)=(11.69\pm0.68, 10.16\pm0.51, 7.67\pm0.10)\,\rm km\,s^{-1}$ and Oort constants $A=16.31\pm0.89\,\rm km\,s^{-1}\,kpc^{-1}$, $B=-11.99\pm0.79\,\rm km\,s^{-1}\,kpc^{-1}$, $C=-3.10\pm0.48\,\rm km\,s^{-1}\,kpc^{-1}$, $K=-1.25\pm1.04\,\rm km\,s^{-1}\,kpc^{-1}$, respectively. $|K+C|>4\,\rm km\,s^{-1}\,kpc^{-1}$ means that there is a radial velocity gradient in the extended local disk, implying the local disk is in a non-asymmetric potential. Using the derived Oort constants, we derive the local angular velocity $Ω\,{\approx}\,A-B=28.30\pm1.19\,\rm km\,s^{-1}\,kpc^{-1}$. By using A-type star sample of different volumes, we further try to evaluate the impacts of the ridge pattern in $R$-$V_ϕ$ plane on constraining the solar motions and Oort constants. As the volume becomes larger toward the anti-center direction, the values of $A$ and $B$ become larger (implying a steeper slope of the local rotation curve) and the value of $V_\odot$ becomes smaller probably caused by the ridge structure and its signal increasing with distance.

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Diagonal Ridge pattern of different age populations found in Gaia DR2 with LAMOST Main-Sequence-Turn-Off and OB type Stars

We revisit the diagonal ridge feature (diagonal distributions in the $R, v_ϕ$ plane) found in $Gaia$ and present timing analysis for it between Galactocentric distances of $R=7.5$ and 12 \,kpc, using Main-Sequence-Turn-Off and OB stars selected from the LAMOST Galactic spectroscopic surveys. We recover the ridge pattern in the $R$--$v_ϕ$ plane color coded by mean radial velocity and find this feature is presented from very young (OB stars, few hundred \,Myr) to very old populations ($τ$ = 9$-$14 \,Gyr). Meanwhile, some ridge features are also revealed in the metallicity [Fe/H], [$α$/Fe] and $v_{z}$ distributions. In the $L_{Z}, v_ϕ$ plane, one of the ridge patterns, with constant angular momentum per unit mass, shows variations with different age populations compared. However, the remaining two ones are relatively stable, implying there might have two kinds of ridge patterns with different dynamical origins and evolution.

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Mapping the Galactic disk with the LAMOST and Gaia Red clump sample. VI: An evidence for the long lived non-steady warp of non-gravitational scenarios

By combining LAMOST DR4 and Gaia DR2 common red clump stars with age and proper motion, we analyze the amplitude evolution of the stellar warp independently of any assumption with a simple model. The greatest height of the warp disk increases with Galactocentric distance in different populations and it is dependent on the age: the younger stellar populations exhibit stronger warp features than the old ones, accompanied with the warp amplitude $γ({\rm age})$ decreasing with age and its first derivative $\dotγ ({\rm age})$ is different from zero. The azimuth of line of nodes $ϕ_w$ is stable at $-$5 degree without clear time evolution, which perfectly confirms some of previous works. All these self-consistent evidences support that our Galactic warp should most likely be a long lived, but non-steady structure and not a transient one, which is supporting the warp is originated from gas infall onto the disk or other hypotheses that suppose that the warp mainly affects to the gas, and consequently younger populations tracing the gas are stronger than the older ones. In other words, the Galactic warp is induced by the non-gravitational interaction over the disk models.

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Probing the galactic halo with RR Lyrae stars I: The catalog

We present a catalog of 5,290 RR Lyrae stars (RRLs) with metallicities estimated from spectra of the LAMOST Experiment for Galactic Understanding and Exploration (LEGUE) and the Sloan Extension for Galactic Understanding and Exploration (SEGUE) surveys. Nearly 70 per cent of them (3,642 objects) also have systemic radial velocities measured. Given the pulsating nature of RRLs, metallicity estimates are based on spectra of individual exposures, by matching them with the synthetic templates. The systemic radial velocities are measured by fitting the observed velocity as a function of phase assuming an empirical pulsating velocity template curve. Various tests show that our analyses yield metallicities with a typical precision of 0.20\,dex and systemic radial velocities with uncertainties ranging from 5 to 21\,km\,s$^{-1}$ (depending on the number of radial velocity measurements available for a given star). Based on the well calibrated near-infrared $PM_{W1}Z$ or $PM_{K_{\rm s}}Z$, and $M_{V}$-[Fe/H] relations, precise distances are derived for these RRLs. Finally, we include Gaia DR2 proper motions in our catalog. The catalog should be very useful for various Galactic studies, especially of the Galactic halo.

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A catalogue of H$α$ emission-line point sources in the vicinity fields of M31 and M33 from the LAMOST survey

We present a catalogue of 3,305 H$α$ emission-line point sources observed with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) in the vicinity fields of M31 and M33 during September 2011 and January 2016. The catalogue contains 1,487 emission-line stars, 532 emission-line nebulae including 377 likely planetary nebulae (PNe), 83 H~{\textsc{ii}} regions candidates and 20 possible supernovae remnants (SNRs) and 1,286 unknown objects. Among them, 24 PN candidates, 19 H~{\sc ii} region candidates, 10 SNR candidates and 1 symbiotic star candidate are new discoveries. Radial velocities and fluxes estimated from the H$α$ line and those quantities of seven other major emission lines including H$β$, [O~{\textsc{iii}}]~$λ$4959, [O~{\textsc{iii}}]~$λ$5007, [N~{\textsc{ii}}]~$λ$6548, [N~{\textsc{ii}}]~$λ$6583, [S~{\textsc{ii}}]~$λ$6717 and [S~{\textsc{ii}}]~$λ$6731 lines of all the catalogued sources yielded from the LAMOST spectra are also presented in our catalogue. Our catalogue is an ideal starting point to study the chemistry properties and kinematics of M31 and M33.

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A large catalogue of molecular clouds with accurate distances within 4 kpc of the Galactic disk

We present a large, homogeneous catalogue of molecular clouds within 4 kpc from the Sun at low Galactic latitudes ($|b|$ $<$ 10\degr) with unprecedented accurate distance determinations. Based on the three-dimensional dust reddening map and estimates of colour excesses and distances of over 32 million stars presented in Chen et al, we have identified 567 dust/molecular clouds with a hierarchical structure identification method and obtained their distance estimates by a dust model fitting algorithm. The typical distance uncertainty is less than 5 per cent. As far as we know, this is the first large catalogue of molecular clouds in the Galactic plane with distances derived in a direct manner. The clouds are seen to lie along the Sagittarius, Local and Perseus Arms. In addition to the known structures, we propose the existence of a possible {\it spur}, with a pitch angle of about 34\degr, connecting the Local and the Sagittarius Arms in the fourth quadrant. We have also derived the physical properties of those molecular clouds. The distribution of cloud properties in different parameter spaces agrees grossly with the previous results. Our cloud sample is an ideal starting point to study the concentration of dust and gas in the solar vicinity and their star formation activities.

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Mapping the Galactic disk with the LAMOST and Gaia Red clump sample. II. 3D asymmetrical kinematics of mono-age populations in the disk between 6$-14$ \,kpc

We perform analysis of the three-dimensional kinematics of Milky Way disk stars in mono-age populations. We focus on stars between Galactocentric distances of $R=6$ and 14 \,kpc, selected from the combined LAMOST DR4 red clump giant stars and Gaia DR2 proper motion catalogue. We confirm the 3D asymmetrical motions of recent works and provide time tagging of the Galactic outer disk asymmetrical motions near the anticenter direction out to Galactocentric distances of 14\,kpc. Radial Galactocentric motions reach values up to 10 km s$^{-1}$, depending on the age of the population, and present a north-south asymmetry in the region corresponding to density and velocity substructures that were sensitive to the perturbations in the early 6 \,Gyr. After that time, the disk stars in this asymmetrical structure have become kinematically hotter, and are thus not sensitive to perturbations, and we find the structure is a relatively younger population. With quantitative analysis, we find stars both above and below the plane at $R\gtrsim 9$ kpc that exhibit bending mode motions of which the sensitive duration is around 8 \,Gyr. We speculate that the in-plane asymmetries might not be mainly caused by a fast rotating bar, intrinsically elliptical outer disk, secular expansion of the disk, or streams. Spiral arm dynamics, out-of-equilibrium models, minor mergers or others are important contributors. Vertical motions might be dominated by bending and breathing modes induced by complicated inner or external perturbers. It is likely that many of these mechanisms are coupled together.

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Mapping the Galactic disk with the LAMOST and Gaia Red clump sample: III: A new velocity substructure and time stamps of the Galactic disk asymmetry in the disk between 12$-$15 \,kpc

We investigate the three-dimensional asymmetrical kinematics and present time stamps of the Milky Way disk between Galactocentric distances of $R=12$ and 15 \,kpc, using red clump stars selected from the LAMOST Galactic survey, also with proper motion measurements provided by the Gaia DR2. We discover velocity substructure above the Galactic plane corresponding to a density dip found recently ("south-middle opposite" density structure[R $\sim$ 12-15 \,kpc, Z $\sim$ 1.5 \,kpc] discovered in \citet{Wang2018b, Wang2018c}) in the radial and azimuthal velocity. For the vertical velocity, we detect clear vertical bulk motions or bending mode motions, which has no clear north-south asymmetry corresponding to the in-plane asymmetrical features. In the subsample of stars with different ages, we find that there is little temporal evolution of the in-plane asymmetry from 0$-$14 \,Gyr, which means the structure is sensitive to the perturbations in almost cosmic time possibly. We propose that the possible scenario of this asymmetric velocity structure is caused by the mechanisms generated in-plane, rather than vertical perturbations.

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Milky Way tomography with the SkyMapper Southern Survey: I: Atmospheric parameters and distances of one million red giants

Accurate determinations of atmospheric parameters (effective temperature $T_{\rm eff}$, surface gravity log $g$ and metallicity [Fe/H]) and distances for large complete samples are of vital importance for various Galactic studies. We have developed a photometric method to select red giant stars and estimate their atmospheric parameters from the photometric colors provided by the SkyMapper Southern Survey (SMSS) data release (DR) 1.1, using stars in common with the LAMOST Galactic spectroscopic surveys as a training set. Distances are estimated with two different approaches: one based on the Gaia DR2 parallaxes for nearby ($d \leq 4.5$ kpc) bright stars and another based on the absolute magnitudes predicted by intrinsic color $(g-i)_0$ and photometric metallicity [Fe/H] for distant ($d > 4.5$ kpc) faint stars. Various tests show that our method is capable of delivering atmospheric parameters with a precision of $\sim$80 K for $T_{\rm eff}$, $\sim$0.18 dex for [Fe/H] and $\sim$0.35 dex for log $g$, but with a significant systematic error at log $g \sim$ 2.3. For distances delivered from $(g-i)_0$ and photometric [Fe/H], our test with the member stars of globular clusters show a median uncertainty of 16 per cent with a negligible zero-point offset. Using this method, atmospheric parameters and distances of nearly one million red giant stars are derived from SMSS DR1.1. Proper motion measurements from Gaia DR2 are available for almost all of the red giant stars, and radial velocity measurements from several large spectroscopic surveys are available for 44 per cent of these. This sample will be accessible online at https://yanghuang0.wixsite.com/yangh/research .

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

We have investigated the distributions of stellar azimuthal and radial velocity components $V_Φ$ 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 $|Φ| \lesssim 7.5^{\circ}$ 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 $V_Φ$ become more and more relaxed as $R$ increases. The spiral patterns of $V_Φ$ and $V_{R}$ and the quadrupole patterns of $V_{R}$ are strongest at $-2^{\circ} < Φ< 2^{\circ}$ but negligible at $4^{\circ} < Φ< 6^{\circ}$ and $-6^{\circ} < Φ< -4^{\circ}$. 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 $V_Φ$ and $V_{R}$.

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Three-dimensional interstellar dust reddening maps of the Galactic plane

We present new three-dimensional (3D) interstellar dust reddening maps of the Galactic plane in three colours, E(G-Ks), E(Bp-Rp) and E(H-Ks). The maps have a spatial angular resolution of 6 arcmin and covers over 7000 deg$^2$ of the Galactic plane for Galactic longitude 0 deg $<$ $l$ $<$ 360 deg and latitude $|b|$ $<$ $10$ deg. The maps are constructed from robust parallax estimates from the Gaia Data Release 2 (Gaia DR2) combined with the high-quality optical photometry from the Gaia DR2 and the infrared photometry from the 2MASS and WISE surveys. We estimate the colour excesses, E(G-Ks), E(Bp-Rp) and E(H-Ks), of over 56 million stars with the machine learning algorithm Random Forest regression, using a training data set constructed from the large-scale spectroscopic surveys LAMOST, SEGUE and APOGEE. The results reveal the large-scale dust distribution in the Galactic disk, showing a number of features consistent with the earlier studies. The Galactic dust disk is clearly warped and show complex structures possibly spatially associated with the Sagittarius, Local and Perseus arms. We also provide the empirical extinction coefficients for the Gaia photometry that can be used to convert the colour excesses presented here to the line-of-sight extinction values in the Gaia photometric bands.

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Metallicity distributions of mono-age stellar populations of the Galactic disc from the LAMOST Galactic spectroscopic surveys

We have investigated the metallicity distributions of mono-age stellar populations across the disc of $6 \lesssim R \lesssim 12$\,kpc and $|Z| \lesssim 2$\,kpc using samples selected from the main-sequence turn-off and sub-giant (MSTO-SG) stars targeted by the LAMOST Galactic Spectroscopic surveys. Both the mean values and the profiles of the distributions exhibit significant variations with age and position. We confirm that the oldest ($>11$\,Gyr) stars have nearly flat radial [Fe/H] gradients at all heights above the disc but show negative vertical [Fe/H] gradients. For stars younger than 11\,Gyr, the radial [Fe/H] gradients flatten with $|Z|$, while the vertical [Fe/H] gradients flatten with $R$. Stars of 4--6\,Gyr exhibit steeper negative radial [Fe/H] gradients than those of either younger or older ages. Values of [$α$/Fe] of mono-age stellar populations also show significant radial and vertical gradients, with patterns varying with age. The [Fe/H] distribution profiles of old ($>8$\,Gyr) stars vary little with $R$, while those of younger stars exhibit strong radial variations, probably a consequence of significant radial migration. The [$α$/Fe] radial distribution profiles show opposite patterns of variations with age compared to those of [Fe/H]. We have also explored the impacts of stellar mixing by epicycle motions (blurring) on the [Fe/H] and [$α$/Fe] distributions, and found that blurring mainly change the widths of the distribution profiles. Our results suggest that the disc may have experienced a complex assemblage history, in which both the "inside-out" and "upside-down" formation processes may have played an important role.

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A holistic perspective on the dynamics of G035.39-00.33: the interplay between gas and magnetic fields

Magnetic field is one of the key agents that play a crucial role in shaping molecular clouds and regulating star formation, yet the complete information on the magnetic field is not well constrained due to the limitations in observations. We study the magnetic field in the massive infrared dark cloud G035.39-00.33 from dust continuum polarization observations at 850 $\micron$ with SCUBA-2/POL-2 at JCMT. The magnetic field tends to be perpendicular to the densest part of the main filament (F$_{M}$), whereas it has a less defined relative orientation in the rest of the structure, where it tends to be parallel to some diffuse regions. A mean plane-of-the-sky magnetic field strength of $\sim$50 $μ$G for F$_{M}$ is obtained using Davis-Chandrasekhar-Fermi method. Based on $^{13}$CO (1-0) line observations, we suggest a formation scenario of F$_{M}$ due to large-scale ($\sim$10 pc) cloud-cloud collision. Using additional NH$_3$ line data, we estimate that F$_{M}$ will be gravitationally unstable if it is only supported by thermal pressure and turbulence. The northern part of F$_{M}$, however, can be stabilized by a modest additional support from the local magnetic field. The middle and southern parts of F$_{M}$ are likely unstable even if the magnetic field support is taken into account. We claim that the clumps in F$_{M}$ may be supported by turbulence and magnetic fields against gravitational collapse. Finally, we identified for the first time a massive ($\sim$200 M$_{\sun}$), collapsing starless clump candidate, "c8", in G035.39-00.33. The magnetic field surrounding "c8" is likely pinched, hinting at an accretion flow along the filament.

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The selection function of the LAMOST Spectroscopic Survey of the Galactic Anticentre

We present a detailed analysis of the selection function of the LAMOST Spectroscopic Survey of the Galactic Anti-centre (LSS-GAC). LSS-GAC was designed to obtain low resolution optical spectra for a sample of more than 3 million stars in the Galactic anti-centre. The second release of value-added catalogues of the LSS-GAC (LSS-GAC DR2) contains stellar parameters, including radial velocity, atmospheric parameters, elemental abundances and absolute magnitudes deduced from 1.8 million spectra of 1.4 million unique stars targeted by the LSS-GAC between 2011 and 2014. For many studies using this database, such as those investigating the chemodynamical structure of the Milky Way, a detailed understanding of the selection function of the survey is indispensable. In this paper, we describe how the selection function of the LSS-GAC can be evaluated to sufficient detail and provide selection function corrections for all spectroscopic measurements with reliable parameters released in LSS-GAC DR2. The results, to be released as new entries in the LSS-GAC value-added catalogues, can be used to correct the selection effects of the catalogue for scientific studies of various purposes.

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Mapping the three-dimensional dust extinction toward the supernova remnant S147 - the S147 dust cloud

We present a three dimensional (3D) extinction analysis in the region toward the supernova remnant (SNR) S147 (G180.0-1.7) using multi-band photometric data from the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anticentre (XSTPS-GAC), 2MASS and WISE. We isolate a previously unrecognised dust structure likely to be associated with SNR S147. The structure, which we term as "S147 dust cloud", is estimated to have a distance $d$ = 1.22 $\pm$ 0.21 kpc, consistent with the conjecture that S147 is associated with pulsar PSR J0538 + 2817. The cloud includes several dense clumps of relatively high extinction that locate on the radio shell of S147 and coincide spatially with the CO and gamma-ray emission features. We conclude that the usage of CO measurements to trace the SNR associated MCs is unavoidably limited by the detection threshold, dust depletion, and the difficulty of distance estimates in the outer Galaxy. 3D dust extinction mapping may provide a better way to identify and study SNR-MC interactions.

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Systematic NLTE study of the -2.6 < [Fe/H] < 0.2 F and G dwarfs in the solar neighbourhood. I. Stellar atmosphere parameters

We present atmospheric parameters for 51 nearby FG dwarfs uniformly distributed over the -2.60 < [Fe/H] < +0.20 metallicity range that is suitable for the Galactic chemical evolution research. Lines of iron, Fe I and Fe II, were used to derive a homogeneous set of effective temperatures, surface gravities, iron abundances, and microturbulence velocities. We used high-resolution (R>60000) Shane/Hamilton and CFHT/ESPaDOnS observed spectra and non-local thermodynamic equilibrium (NLTE) line formation for Fe I and Fe II in the classical 1D model atmospheres. The spectroscopic method was tested with the 20 benchmark stars, for which there are multiple measurements of the infrared flux method (IRFM) Teff and their Hipparcos parallax error is < 10%. We found NLTE abundances from lines of Fe I and Fe II to be consistent within 0.06 dex for every benchmark star, when applying a scaling factor of S_H = 0.5 to the Drawinian rates of inelastic Fe+H collisions. The obtained atmospheric parameters were checked for each program star by comparing its position in the log g-Teff plane with the theoretical evolutionary track in the Yi et al. (2004) grid. Our final effective temperatures lie in between the T_IRFM scales of Alonso et al. (1996) and Casagrande et al. (2011), with a mean difference of +46 K and -51 K, respectively. NLTE leads to higher surface gravity compared with that for LTE. The shift in log g is smaller than 0.1 dex for stars with either [Fe/H] > -0.75, or Teff < 5750 K, or log g > 4.20. NLTE analysis is crucial for the VMP turn-off and subgiant stars, for which the shift in log g between NLTE and LTE can be up to 0.5 dex. The obtained atmospheric parameters will be used in the forthcoming papers to determine NLTE abundances of important astrophysical elements from lithium to europium and to improve observational constraints on the chemo-dynamical models of the Galaxy evolution.

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The evolution of stellar metallicity gradients of the Milky Way disk from LSS-GAC main sequence turn-off stars: a two-phase disk formation history?

We use 297 042 main sequence turn-off stars selected from the LSS-GAC to determine the radial and vertical gradients of stellar metallicity of the Galactic disk in the anti-center direction. We determine ages of those turn-off stars by isochrone fitting and measure the temporal variations of metallicity gradients. Our results show that the gradients, both in the radial and vertical directions, exhibit significant spatial and temporal variations. The radial gradients yielded by stars of oldest ages (>11 Gyr) are essentially zero at all heights from the disk midplane, while those given by younger stars are always negative. The vertical gradients deduced from stars of oldest ages (>11Gyr) are negative and show only very weak variations with the Galactocentric distance in the disk plane, $R$, while those yielded by younger stars show strong variations with $R$. After being essentially flat at the earliest epochs of disk formation, the radial gradients steepen as age decreases, reaching a maxima (steepest) at age 7-8 Gyr, and then they flatten again. Similar temporal trends are also found for the vertical gradients. We infer that the assemblage of the Milky Way disk may have experienced at least two distinct phases. The earlier phase is probably related to a slow, pressure-supported collapse of gas, when the gas settles down to the disk mainly in the vertical direction. In the later phase, there are significant radial flows of gas in the disk, and the rate of gas inflow near the solar neighborhood reaches a maximum around a lookback time of 7-8 Gyr. The transition of the two phases occurs around a lookback time between 8 and 11 Gyr. The two phases may be responsible for the formation of the Milky Way thick and thin disks, respectively. And, as a consequence, we recommend that stellar age is a natural, physical criterion to distinguish thin and thick disk stars. ... (abridged)

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