arXiv subjects

Juntai Shen

Publications and source records attributed to Juntai Shen.

At least 55 records · Page 3Linked to original sources

arXiv2021

Constraints on the assembly history of the Milky Way's smooth, diffuse stellar halo from the metallicity-dependent, radially-dominated velocity anisotropy profiles probed with K giants and BHB stars using LAMOST, SDSS/SEGUE, and Gaia

We analyze the anisotropy profile of the Milky Way's smooth, diffuse stellar halo using SDSS/SEGUE blue horizontal branch stars and SDSS/SEGUE and LAMOST K giants. These intrinsically luminous stars allow us to probe the halo to approximately 100 kpc from the Galactic center. Line-of-sight velocities, distances, metallicities, and proper motions are available for all stars via SDSS/SEGUE, LAMOST, and Gaia, and we use these data to construct a full 7D set consisting of positions, space motions, and metallicity. We remove substructure from our samples using integrals of motion based on the method of Xue et al. We find radially dominated kinematic profiles with nearly constant anisotropy within 20 kpc, beyond which the anisotropy profile gently declines although remains radially dominated to the furthest extents of our sample. Independent of star type or substructure removal, the anisotropy depends on metallicity, such that the orbits of the stars become less radial with decreasing metallicity. For $-1.7<$ [Fe/H] $<-1$, the smooth, diffuse halo anisotropy profile begins to decline at Galactocentric distances $\sim20$ kpc, from $β\sim0.9$ to 0.7 for K giants and from $β\sim0.8$ to 0.1 for blue horizontal branch stars. For [Fe/H] $<-1.7$, the smooth, diffuse halo anisotropy remains constant along all distances with $0.2<β<0.7$ depending on the metallicity range probed, although independent on star type. These samples are ideal for estimating the total Galactic mass as they represent the virialized stellar halo system.

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arXiv2021

A LAMOST BHB Catalog and Kinematics Therein I: Catalog and Halo Properties

We collect a sample of stars observed both in LAMOST and Gaia which have colors implying a temperature hotter than 7000 K. We train a machine learning algorithm on LAMOST spectroscopic data which has been tagged with stellar classifications and metallicities, and use this machine to construct a catalog of Blue Horizontal Branch stars (BHBs) with metallicity information. Another machine is trained using Gaia parallaxes to predict absolute magnitudes for these stars. The final catalog of 13,693 BHBs is thought to be about 86\% pure, with $σ_{[Fe/H]}\sim$0.35 dex and $σ_{G}\sim$0.31 mag. These values are confirmed via comparison to globular clusters, although a covariance error seems to affect our magnitude and abundance estimates. We analyze a subset of this catalog in the Galactic Halo. We find that BHB populations in the outer halo appear redder, which could imply a younger population, and that the metallicity gradient is relatively flat around [Fe/H] = -1.9 dex over our sample footprint. We find that our metal rich BHB stars are on more radial velocity dispersion dominated orbits ($β\sim 0.70$) at all radii than our metal poor BHB stars ($β\sim 0.62$).

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arXiv2021

Unravelling stellar populations in the Andromeda Galaxy

To understand the history and formation mechanisms of galaxies it is crucial to determine their current multidimensional structure. Here we focus on stellar population properties, such as metallicity and [$α$/Fe] enhancement. We devise a new technique to recover the distribution of these parameters using spatially resolved, line-of-sight averaged data. Our chemodynamical method is based on the made-to-measure (M2M) framework and results in an $N$-body model for the abundance distribution. We test our method on a mock data set and find that the radial and azimuthal profiles are well-recovered, however only the overall shape of the vertical profile matches the true profile. We apply our procedure to spatially resolved maps of mean [Z/H] and [$α$/Fe] for the Andromeda Galaxy, using an earlier barred dynamical model of M31. We find that the metallicity is enhanced along the bar, with possible maxima at the ansae. In the edge-on view the [Z/H] distribution has an X shape due to the boxy/peanut bulge; the average vertical metallicity gradient is equal to $-0.133\pm0.006$ dex/kpc. We identify a metallicity-enhanced ring around the bar, which also has relatively lower [$α$/Fe]. The highest [$α$/Fe] is found in the centre, due to the classical bulge. Away from the centre, the $α$-overabundance in the bar region increases with height, which could be an indication of a thick disc. We argue that the galaxy assembly resulted in a sharp peak of metallicity in the central few hundred parsecs and a more gentle negative gradient in the remaining disc, but no [$α$/Fe] gradient. The formation of the bar lead to the re-arrangement of the [Z/H] distribution, causing a flat gradient along the bar. Subsequent star formation close to the bar ends may have produced the metallicity enhancements at the ansae and the [Z/H] enhanced lower-$α$ ring.

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arXiv2020

The Bar and Spiral Arms in the Milky Way: Structure and Kinematics

The Milky Way is a spiral galaxy with the Schechter characteristic luminosity $L_*$, thus an important anchor point of the Hubble sequence of all spiral galaxies. Yet the true appearance of the Milky Way has remained elusive for centuries. We review the current best understanding of the structure and kinematics of our home galaxy, and present an updated scientifically accurate visualization of the Milky Way structure with almost all components of the spiral arms, along with the COBE image in the solar perspective. The Milky Way contains a strong bar, four major spiral arms, and an additional arm segment (the Local arm) that may be longer than previously thought. The Galactic boxy bulge that we observe is mostly the peanut-shaped central bar viewed nearly end-on with a bar angle of 25-30 degrees from the Sun-Galactic center line. The bar transitions smoothly from a central peanut-shaped structure to an extended thin part that ends around R ~ 5 kpc. The Galactic bulge/bar contains ~ 30-40% of the total stellar mass in the Galaxy. Dynamical modelling of both the stellar and gas kinematics yields a bar pattern rotation speed of ~ 35-40 km/s/kpc, corresponding to a bar rotation period of ~ 160-180 Myr. From a galaxy formation point of view, our Milky Way is probably a pure-disk galaxy with little room for a significant merger-made, "classical" spheroidal bulge, and we give a number of reasons why this is the case.

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arXiv2020

Understanding the velocity distribution of the Galactic Bulge with APOGEE and Gaia

We revisit the stellar velocity distribution in the Galactic bulge/bar region with APOGEE DR16 and {\it Gaia} DR2, focusing in particular on the possible high-velocity (HV) peaks and their physical origin. We fit the velocity distributions with two different models, namely with Gauss-Hermite polynomial and Gaussian mixture model (GMM). The result of the fit using Gauss-Hermite polynomials reveals a positive correlation between the mean velocity ($\bar{V}$) and the "skewness" ($h_{3}$) of the velocity distribution, possibly caused by the Galactic bar. The $n=2$ GMM fitting reveals a symmetric longitudinal trend of $|μ_{2}|$ and $σ_{2}$ (the mean velocity and the standard deviation of the secondary component), which is inconsistent to the $x_{2}$ orbital family predictions. Cold secondary peaks could be seen at $|l|\sim6^\circ$. However, with the additional tangential information from {\it Gaia}, we find that the HV stars in the bulge show similar patterns in the radial-tangential velocity distribution ($V_{\rm R}-V_{\rm T}$), regardless of the existence of a distinct cold HV peak. The observed $V_{\rm R}-V_{\rm T}$ (or $V_{\rm GSR}-μ_{l}$) distributions are consistent with the predictions of a simple MW bar model. The chemical abundances and ages inferred from ASPCAP and CANNON suggest that the HV stars in the bulge/bar are generally as old as, if not older than, the other stars in the bulge/bar region.

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arXiv2020

Mapping the tilt of the Milky Way bulge velocity ellipsoids with ARGOS and $Gaia$ DR2

Until the recent advent of $Gaia$ Data Release 2 (DR2) and deep multi-object spectroscopy, it has been difficult to obtain 6-D phase space information for large numbers of stars beyond 4 kpc, in particular towards the Galactic centre, where dust and crowding effects are significant. In this study we combine line-of-sight velocities from the Abundances and Radial velocity Galactic Origins Survey (ARGOS) spectroscopic survey with proper motions from $Gaia$ DR2, to obtain a sample of $\sim$ 7,000 red clump stars with 3-D velocities. We perform a large scale stellar kinematics study of the Milky Way (MW) bulge to characterize the bulge velocity ellipsoids. We measure the tilt $l_{v}$ of the major-axis of the velocity ellipsoid in the radial-longitudinal velocity plane in 20 fields across the bulge. The tilt or vertex deviation, is characteristic of non-axisymmetric systems and a significant tilt is a robust indicator of non-axisymmetry or bar presence. We compare the observations to the predicted kinematics of an N-body boxy-bulge model formed from dynamical instabilities. In the model, the $l_{v}$ values are strongly correlated with the angle ($α$) between the bulge major-axis and the Sun-Galactic centre line-of-sight. We use a maximum likelihood method to obtain an independent measurement of $α$, from bulge stellar kinematics alone. The most likely value of $α$ given our model is $α= (29 \pm 3)^{\circ}$. In the Baade's window, the metal-rich stars display a larger vertex deviation ($l_{v} = -40^{\circ}$) than the metal-poor stars ($l_{v} = 10^{\circ}$) but we do not detect significant $l_{v}-$metallicity trends in the other fields.

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arXiv2020

Kinematics of RR Lyrae stars in the Galactic bulge with OGLE-IV and Gaia DR2

We analyze the kinematics and spatial distribution of 15,599 fundamental-mode RR Lyrae (RRL) stars in the Milky Way bulge by combining OGLE-IV photometric data and Gaia DR2 proper motions. We show that the longitudinal proper motions and the line-of-sight velocities can give similar results for the rotation in the Galactic central regions. The angular velocity of bulge RRLs is found to be around $35$ km s$^{-1}$ kpc$^{-1}$, significantly smaller than that for the majority of bulge stars ($50-60$ km s$^{-1}$ kpc$^{-1}$); bulge RRLs have larger velocity dispersion (120$-$140 km s$^{-1}$) than younger stars. The dependence of the kinematics of the bulge RRLs on their metallicities is shown by their rotation curves and spatial distributions. Metal-poor RRLs ([Fe/H]<$-1$) show a smaller bar angle than metal-rich ones. We also find clues suggesting that RRLs in the bulge are not dominated by halo stars. These results might explain some previous conflicting results over bulge RRLs and help understand the chemodynamical evolution of the Galactic bulge.

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arXiv2020

The Blanco DECam Bulge Survey. I. The Survey Description and Early Results

The Blanco Dark Energy Camera (DECam) Bulge survey is a Vera Rubin Observatory (LSST) pathfinder imaging survey, spanning $\sim 200$ sq. deg. of the Southern Galactic bulge, $-2^\circ <$b$< -13^\circ$ and $-11^\circ <$l$ < +11^\circ$. We have employed the CTIO-4m telescope and the Dark Energy Camera (DECam) to image a contiguous $\sim 200$ sq. deg. region of the relatively less reddened Southern Galactic bulge, in SDSS $u$ + Pan-STARRS$grizy$. Optical photometry with its large colour baseline will be used to investigate the age and metallicity distributions of the major structures of the bulge. Included in the survey footprint are 26 globular clusters imaged in all passbands. Over much of the bulge, we have Gaia DR2 matching astrometry to $i\sim 18$, deep enough to reach the faint end of the red clump. This paper provides the background, scientific case, and description of the survey. We present an array of new reddening-corrected colour-magnitude diagrams that span the extent of Southern Galactic bulge. We argue that a population of massive stars in the blue loop evolutionary phase, proposed to lie in the bulge, are instead at $\sim 2$ kpc from the Sun and likely red clump giants in the old disk. A bright red clump near $(l,b)=(+8^\circ,-4^\circ)$ may be a feature in the foreground disk, or related to the long bar reported in earlier work. We also report the first map of the blue horizontal branch population spanning the BDBS field of regard, and our data does not confirm the reality of a number of proposed globular clusters in the bulge.

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arXiv2020

Anisotropy of the Milky Way's stellar halo using K giants from LAMOST and $Gaia$

The anisotropy parameter $β$ characterizes the extent to which orbits in stellar systems are predominantly radial or tangential, and is likely to constrain, for the stellar halo of the Milky Way, scenarios for its formation and evolution. We have measured the anisotropy $β$ as a function of Galactocentric radius from $5-100$ kpc for over 8600 metal poor ([Fe/H] $<-1.3$) halo K giants from the LAMOST catalog with line-of-sight velocities and distances, matched to proper motions from the second $Gaia$ data release. We construct full 6-D positions and velocities for the K giants to directly measure the 3 components of the velocity dispersion $(σ_r, σ_θ, σ_ϕ)$ (in spherical coordinates). We find that the orbits in the halo are radial over our full Galactocentric distance range reaching over 100 kpc. The anisotropy remains remarkably unchanged with Galactocentric radius from approximately 5 to 25 kpc, with an amplitude that depends on the metallicity of the stars, dropping from $β\approx 0.9$ for $-1.8 \leq$ [Fe/H] $< -1.3$ (for the bulk of the stars) to $β\approx 0.6$ for the lowest metallicities ([Fe/H] $< -1.8$). Considering our sample as a whole, $β\approx0.8$ and, beyond 25 kpc, the orbits gradually become less radial and anisotropy decreases to $β<0.3$ past 100 kpc. Within 8 kpc, $β<0.8$. The measurement of anisotropy is affected by substructure and streams, particularly beyond a Galactocentric distance of approximately 25 kpc, where the Sagittarius stream is prominent in the data. These results are complimentary to recent analysis of simulations by Loebman et al. and of SDSS/$Gaia$ DR1 data by Belokurov et al.

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arXiv2020

Dissecting the Phase Space Snail Shell

The on-going vertical phase mixing, manifesting itself as a snail shell in the $Z-V_{Z}$ phase space, has been discovered with the Gaia DR2 data. To better understand the origin and properties of the phase mixing process, we study the vertical phase-mixing signatures in arches (including the classical ``moving groups'') of the $V_{R}-V_ϕ$ phase space near the Solar circle. Interestingly, the phase space snail shell exists only in the arches with $|V_ϕ - V_{\rm LSR}| \lesssim 30$ km/s, i.e., stars on dynamically ``colder'' orbits. The snail shell becomes much weaker and eventually disappears for increasingly larger radial action ($J_{R}$), quantifying the ``hotness'' of orbits. Thus one should pay closer attention to the colder orbits in future phase mixing studies. We also confirm that the Hercules stream has two branches (at fast and slow $V_ϕ$), which may not be explained by a single mechanism, since only the fast branch shows the prominent snail shell feature. The hotter orbits may have phase-wrapped away already due to the much larger dynamical range in radial variation to facilitate faster phase mixing. To explain the lack of a well-defined snail shell in the hotter orbits, the disk should have been perturbed at least $500$ Myr ago. Our results offer more support to the recent satellite-disk encounter scenario than the internal bar buckling perturbation scenario as the origin of the phase space mixing. Origin of the more prominent snail shell in the $V_ϕ$ color-coded phase space is also discussed.

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arXiv2020

Testing the Prediction of Fuzzy Dark Matter Theory in the Milky Way Center

The fuzzy dark matter model (FDM, also known as quantum wave dark matter model) argues that light bosons with a mass of $\sim10^{-22}{\;{\rm eV}}$ are a possible candidate for dark matter in the Universe. One of the most important predictions of FDM is the formation of a soliton core instead of a density cusp at the center of galaxies. If FDM is the correct theory of dark matter, then the predicted soliton core can help to form the Central Molecular Zone (CMZ) in the Milky Way. We present high-resolution hydrodynamical simulations of gas flow patterns to constrain the properties of the soliton core based on a realistic Milky Way potential. We find that a dense center is required to form a reasonable CMZ. The size and kinematics of the CMZ offer a relatively strong constraint on the inner enclosed mass profile of the Galaxy. If a soliton core is not considered, a compact nuclear bulge alone with a radially varying mass-to-light ratio can match the observed size and kinematics of the CMZ. A soliton core model with a mass of $\approx4.0\times10^8{\; {\rm M}_{\odot}}$ and a core radius of $\approx0.05{\;{\rm kpc}}$, together with a less massive nuclear bulge with a constant mass-to-light ratio, also agrees nicely with the current data. Such a FDM soliton core corresponds to a boson mass of $\sim2-7\times10^{-22}{\;{\rm eV}}$, which could be further constrained by the improved determination of the mass-to-light ratio in the Galactic center.

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arXiv2019

Testing the Tremaine-Weinberg Method Applied to Integral-field Spectroscopic Data Using a Simulated Barred Galaxy

Tremaine and Weinberg (TW) proposed a conceptually simple procedure relying on long-slit spectroscopy to measure the pattern speeds of bars ($Ω_{\rm p}$) in disk galaxies. Using a simulated galaxy, we investigate the potential biases and uncertainties of TW measurements using increasingly popular integral-field spectrographs (IFSs), for which multiple pseudo-slits (and thus independent measurements) can be constructed with a single observation. Most important, to establish the spatial coverage required and ensure the validity of the measurements, the inferred $Ω_{\rm p}$ must asymptotically converge as the (half-)length of each pseudo-slit used is increased. The requirement for our simulation is to reach $\approx1.3$ times the half-light radius, but this may vary from galaxy to galaxy. Only those slits located within the bar region yield accurate measurements. We confirm that the position angle of the disk is the dominant source of systematic error in TW $Ω_{\rm p}$ measurements, leading to under/overestimates of tens of percents for inaccuracies of even a few degrees. Recasting the data so that the data grid aligns with the disk major axis leads to slightly reduced uncertainties. Accurate measurements are obtained only for well-defined ranges of the bar angle (relative to the galaxy major axis) $ϕ_{\rm bar}$ and the inclination angle $i$, here $10\lesssimϕ_{\rm bar}\lesssim75^{\circ}$ and $105\lesssimϕ_{\rm bar}\lesssim170^{\circ}$ and $15\lesssim i\lesssim70^{\circ}$. The adopted (pseudo-)slit widths, spatial resolution, and (unless extremely aggressive) spatial binning of IFS data have no significant impact on the measurements. Our results thus provide useful guidelines for reliable and accurate direct $Ω_{\rm p}$ measurements with IFS observations.

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arXiv2019

Fast Inflow Directly Feeding Black Hole Accretion Disk in Quasars

Quasars are high-luminosity active galactic nuclei believed to be powered by accretion of interstellar matter onto a super-massive black hole (SMBH) therein. Most of the observed energy is released in an accretion disk of inspiralling gas surrounding the SMBH. An enormous amount of fueling material is expected to be transported inwards. However, basic questions remain unanswered as to whether and how the accretion disks are supplied with external gas, since no disk-feeding inflow has hitherto been observed clearly. Here we report the discovery of highly redshifted broad absorption lines arising from neutral hydrogen and helium atoms in a small sample of quasars. Their absorption troughs show a broad range of Doppler velocities from zero extending continuously inward up to as high as $\sim 5,000$ km s$^{-1}$. We thus see through streams of cold gas moving with a radially inward velocity component that spans an immense gradient---a result of gravitational acceleration by the central SMBH. Extensive photo-ionization modeling for the archetypical object SDSS J103516.20+142200.6 indicates the inflowing gas to be dense, thick and moderately ionized, with a characteristic distance to the SMBH of $\sim 1,000$ gravitational radii, possibly overlapping or close to the outer accretion disk. Our results present the first compelling evidence for the long-sought inflow directly feeding quasars' accretion disks with external materials, likely originating from the dusty torus at a parsec scale. Our approach provides a new tool to probe the bulk of the so far elusive fueling inflows in quasars. Their studies may help address some of the fundamental questions concerning accretion physics, the onset and sustainment of quasar activity, and the SMBH growth at centers of most galaxies.

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arXiv2019

The global stability of M33: still a puzzle

The inner disc of the local group galaxy M33 appears to be in settled rotational balance, and near IR images reveal a mild, large-scale, two-arm spiral pattern with no strong bar. We have constructed N-body models that match all the extensive observational data on the kinematics and surface density of stars and gas in the inner part of M33. We find that currently favoured models are unstable to the formation of a strong bar of semi-major axis 2 < a_B < 3 kpc within 1 Gyr, which changes the dynamical properties of the models to become inconsistent with the current, apparently well-settled, state. The formation of a bar is unaffected by how the gas component is modelled, by increasing the mass of the nuclear star cluster, or by making the dark matter halo counter-rotate, but it can be prevented by either reducing the mass-to-light ratio of the stars to Upsilon_V ~ 0.6 or Upsilon_K ~ 0.23 in solar units or by increasing the random motions of the stars. Also a shorter and weaker bar results when the halo is rigid and unresponsive. However, all three near-stable models support multi-arm spirals, and not the observed large-scale bi-symmetric spiral. A two-arm spiral pattern could perhaps be tidally induced, but such a model would require an implausibly low mass disc to avoid a bar and there is no visible culprit. Thus the survival of the current state of this exceptionally well-studied galaxy is not yet understood. We also suspect that many other unbarred galaxies present a similar puzzle.

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arXiv2018

Shape of LOSVD\lowercase{s} in barred disks: Implications for future IFU surveys

The shape of LOSVDs (line-of-sight velocity distributions) carries important information about the internal dynamics of galaxies. The skewness of LOSVDs represents their asymmetric deviation from a Gaussian profile. Correlations between the skewness parameter ($h_3$) and the mean velocity (\vm) of a Gauss-Hermite series reflect the underlying stellar orbital configurations of different morphological components. Using two self-consistent $N$-body simulations of disk galaxies with different bar strengths, we investigate \hv\ correlations at different inclination angles. Similar to previous studies, we find anticorrelations in the disk area, and positive correlations in the bar area when viewed edge-on. However, at intermediate inclinations, the outer parts of bars exhibit anticorrelations, while the core areas dominated by the boxy/peanut-shaped (B/PS) bulges still maintain weak positive correlations. When viewed edge-on, particles in the foreground/background disk (the wing region) in the bar area constitute the main velocity peak, whereas the particles in the bar contribute to the high-velocity tail, generating the \hv\ correlation. If we remove the wing particles, the LOSVDs of the particles in the outer part of the bar only exhibit a low-velocity tail, resulting in a negative \hv\ correlation, whereas the core areas in the central region still show weakly positive correlations. We discuss implications for IFU observations on bars, and show that the variation of the \hv\ correlation in the disk galaxy may be used as a kinematic indicator of the bar and the B/PS bulge.

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arXiv2017

Rapid formation of black holes in galaxies: a self-limiting growth mechanism

We present high-quality fluid dynamical simulations of isothermal gas flows in a rotating barred potential. We show that a large quantity of gas is driven right into the nucleus of a model galaxy when the potential lacks a central mass concentration, but the inflow stalls at a nuclear ring in comparison simulations that include a central massive object. The radius of the nuclear gas ring increases linearly with the mass of the central object. We argue that bars drive gas right into the nucleus in the early stages of disk galaxy formation, where a nuclear star cluster and perhaps a massive black hole could be created. The process is self-limiting, however, because inflow stalls at a nuclear ring once the mass of gas and stars in the nucleus exceeds ~1% of the disk mass, which shuts off rapid growth of the black hole. We briefly discuss the relevance of these results to the seeding of massive black holes in galaxies, the merger model for quasar evolution, and the existence of massive black holes in disk galaxies that lack a significant classical bulge.

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arXiv2017

Chemical abundances and ages of the bulge stars in APOGEE high-velocity peaks

A cold high-velocity (HV, $\sim$ 200 km/s) peak was first reported in several Galactic bulge fields based on the APOGEE commissioning observations. Both the existence and the nature of the high-velocity peak are still under debate. Here we revisit this feature with the latest APOGEE DR13 data. We find that most of the low latitude bulge fields display a skewed Gaussian distribution with a HV shoulder. However, only 3 out of 53 fields show distinct high-velocity peaks around 200 km/s. The velocity distribution can be well described by Gauss-Hermite polynomials, except the three fields showing clear HV peaks. We find that the correlation between the skewness parameter ($h_{3}$) and the mean velocity ($\bar{v}$), instead of a distinctive HV peak, is a strong indicator of the bar. It was recently suggested that the HV peak is composed of preferentially young stars. We choose three fields showing clear HV peaks to test this hypothesis using the metallicity, [$α$/M] and [C/N] as age proxies. We find that both young and old stars show HV features. The similarity between the chemical abundances of stars in the HV peaks and the main component indicates that they are not systematically different in terms of chemical abundance or age. In contrast, there are clear differences in chemical space between stars in the Sagittarius dwarf and the bulge stars. The strong HV peaks off-plane are still to be explained properly, and could be different in nature.

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arXiv2017

Orbital decomposition of CALIFA spiral galaxies

Schwarzschild orbit-based dynamical models are widely used to uncover the internal dynamics of early-type galaxies and globular clusters. Here we present for the first time the Schwarzschild models of late-type galaxies: an SBb galaxy NGC 4210 and an S0 galaxy NGC 6278 from the CALIFA survey. The mass profiles within $2\,R_e$ are constrained well with $1σ$ statistical error of $\sim 10\%$. The luminous and dark mass can be disentangled with uncertainties of $\sim 20\%$ and $\sim 50\%$ respectively. From $R_e$ to $2\,R_e$, the dark matter fraction increases from $14\pm10\%$ to $18\pm10\%$ for NGC 4210 and from $15\pm10\%$ to $30\pm20\%$ for NGC 6278. The velocity anisotropy profiles of both $σ_r/σ_t$ and $σ_z/σ_R$ are well constrained. The inferred internal orbital distributions reveal clear substructures. The orbits are naturally separated into three components: a cold component with near circular orbits, a hot component with near radial orbits, and a warm component in between. The photometrically-identified exponential disks are predominantly made up of cold orbits only beyond $\sim 1\,R_e$, while they are constructed mainly with the warm orbits inside. Our dynamical hot components are concentrated in the inner regions, similar to the photometrically-identified bulges. The reliability of the results, especially the orbit distribution, are verified by applying the model to mock data.

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