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Ling Zhu

Publications and source records attributed to Ling Zhu.

At least 73 records · Page 4Linked to original sources
arXiv2020

A multi-objective optimization framework for on-line ridesharing systems

The ultimate goal of ridesharing systems is to matchtravelers who do not have a vehicle with those travelers whowant to share their vehicle. A good match can be found amongthose who have similar itineraries and time schedules. In thisway each rider can be served without any delay and also eachdriver can earn as much as possible without having too muchdeviation from their original route. We propose an algorithmthat leverages biogeography-based optimization to solve a multi-objective optimization problem for online ridesharing. It isnecessary to solve the ridesharing problem as a multi-objectiveproblem since there are some important objectives that must beconsidered simultaneously. We test our algorithm by evaluatingperformance on the Beijing ridesharing dataset. The simulationresults indicate that BBO provides competitive performancerelative to state-of-the-art ridesharing optimization algorithms.

math.OC↗
arXiv2020

A Universal fundamental plane and the $M_{dyn}-M_{\star}$ relation for galaxies with CALIFA and MaNGA

We use the stellar kinematics for $2458$ galaxies from the MaNGA survey to explore dynamical scaling relations between the stellar mass $M_{\star}$ and the total velocity parameter at the effective radius, $R_e$, defined as $S_{K}^{2}=KV_{R_e}^{2}+σ_{\star_e}^{2}$, which combines rotation velocity $V_{R_e}$, and velocity dispersion $σ_{\star_e}$. We confirm that spheroidal and spiral galaxies follow the same $M_{\star}-S_{0.5}$ scaling relation with lower scatter than the $M_{\star}-V_{R_e}$ and $M_{\star}-σ_{\star_e}$ ones. We also explore a more general Universal Fundamental Plane described by the equation $log(Υ_{e}) = log (S_{0.5}^{2}) - log (I_{e}) - log (R_{e}) + C$, which in addition to kinematics, $S_{0.5}$, and effective radius, $R_e$, it includes surface brightness, $I_e$, and dynamical mass-to-light ratio, $Υ_e$. We use sophisticated Schwarzschild dynamical models for a sub-sample of 300 galaxies from the CALIFA survey to calibrate the so called Universal Fundamental Plane. That calibration allows us to propose both: (i) a parametrization to estimate the difficult-to-measure dynamical mass-to-light ratio at the effective radius; and (ii) a new dynamical mass proxy consistent with dynamical models within $0.09\ dex$. We reproduce the relation between the dynamical mass and the stellar mass in the inner regions of galaxies. We use the estimated dynamical mass-to-light ratio from our analysis, $Υ_{e}^{fit}$, to explore the Universal Fundamental Plane with the MaNGA data set. We find that all classes of galaxies, from spheroids to disks, follow this Universal Fundamental Plane with a scatter significantly smaller $(0.05\ dex)$ than the one reported for the $M_{\star}-S_{0.5}$ relation $(0.1\ dex)$, the Fundamental Plane $(\sim 0.09\ dex)$ and comparable with Tully-Fisher studies $(\sim 0.05\ dex)$, but for a wider range of galaxy types.

astro-ph.GA↗
arXiv2020

A discrete chemo-dynamical model of M87's globular clusters: Kinematics extending to ~ 400 kpc

We study the mass distribution and kinematics of the giant elliptical galaxy M87 (NGC 4486) using discrete chemo-dynamical, axisymmetric Jeans equation modelling. Our catalogue comprises 894 globular clusters (GCs) extending to a projected radius of $\sim 430$ kpc with line-of-sight velocities and colours, and Multi Unit Spectroscopic Explorer (MUSE) integral field unit data within the central $2.4$ kpc of the main galaxy. The gravitational potential for our models is a combination of a luminous matter potential with a varying mass-to-light ratio for the main galaxy, a supermassive black hole and a dark matter (DM) potential with a cusped or cored DM halo. The best-fitting models with either a cusped or a cored DM halo show no significant differences and both are acceptable. We obtain a total mass of $(2.16 \pm 0.38) \times 10^{13} M_{\odot}$ within $\sim$ 400 kpc. By including the stellar mass-to-light ratio gradient, the DM fraction increases from $\sim$ 26 percent (with no gradient) to $\sim$ 73 percent within $1\,R_e^{\rm maj}$ (major axis of half-light isophote, 14.2 kpc), and from $\sim$ 84 percent to $\sim$ 94 percent within $5\,R_e^{\rm maj}$ (71.2 kpc). Red GCs have moderate rotation with $V_{\rm max}/σ\sim$ 0.4, and blue GCs have weak rotation with $V_{\rm max}/σ\sim$ 0.1. Red GCs have tangential velocity dispersion anisotropy, while blue GCs are consistent with being nearly isotropic. Our results suggest that red GCs are more likely to be born in-situ, while blue GCs are more likely to be accreted.

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arXiv2020

Disentangling the formation history of galaxies via population-orbit superposition: method validation

We present population-orbit superposition models for external galaxies based on Schwarzschild's orbit-superposition method, by tagging the orbits with age and metallicity. The models fit the density distributions, as well as kinematic, age and metallicity maps from Integral Field Unit (IFU) spectroscopy observations. We validate the method and demonstrate its power by applying it to mock data, similar to those obtained by the Multi-Unit Spectroscopic Explorer (MUSE) IFU on the Very Large Telescope (VLT). These mock data are created from Auriga galaxy simulations, viewed at three different inclination angles ($\vartheta=40^o, 60^o, 80^o$). Constrained by MUSE-like mock data, our model can recover the galaxy's stellar orbit distribution projected in orbital circularity $λ_z$ vs. radius $r$, the intrinsic stellar population distribution in age $t$ vs. metallicity $Z$, and the correlation between orbits' circularity $λ_z$ and stellar age $t$. A physically motivated age-metallicity relation improves recovering the intrinsic stellar population distributions. We decompose galaxies into cold, warm and hot + counter-rotating components based on their orbit circularity distribution, and find that the surface density, mean velocity, velocity dispersion, age and metallicity maps of each component from our models well reproduce those from simulation, especially for projections close to edge-on. These galaxies exhibit strong global age vs. $σ_z$ relation, which is well recovered by our model. The method has the power to reveal the detailed build-up of stellar structures in galaxies, and offers a complement to local resolved, and high-redshift studies of galaxy evolution.

astro-ph.GA↗
arXiv2020

Some estimates of precision of the Huygens approximation

In this paper are given some estimates of precision of the Huygens approximation $x \approx \frac{2}{3} \sin x + \frac{1}{3} \tan x,$ for right neighbourhood of zero, by determining some boundaries for the Huygens function $f(x) = \frac{2}{3} \sin x + \frac{1}{3} \tan x,$ for $x \in \left(0, \fracπ{2} \right)$, in forms of some polynomial and some rational functions.

math.GM↗
arXiv2019

SDSS-IV MaNGA: Internal mass distributions and orbital structures of early-type galaxies and their dependence on environment

In our earlier 2019 paper, we evaluated the reliability of Schwarzschild's orbit-superposition dynamical modelling method in estimating the internal mass distribution, intrinsic stellar shapes and orbit distributions of early-type galaxies (ETGs) taken from the Illustris cosmological simulation. We now apply the same techniques to galaxies taken from the integral-field survey Mapping Nearby Galaxies with APO (MaNGA), using a sample of 149 ETGs in the mass range of $10^{9.90}\sim10^{11.80} M_{\odot}$ and made up of 105 central and 44 satellite galaxies. We find that low-mass ETGs with $\log(M_*/M_{\odot})<11.1$ have an average dark matter fraction of $\sim0.2$ within one effective radius $R_{\rm e}$, tend to be oblate-like, and are dominated by rotation about their minor axis. High-mass ETGs with $\log(M_*/M_{\odot})>11.1$ have an average dark matter fraction of $\sim0.4$ within one effective radius $R_{\rm e}$, tend to be prolate-like, and are dominated by rotation about their major axis and by centrophilic orbits. The changes of internal structures within one $R_{\rm e}$ are dominated by the total stellar mass of the individual galaxies. We find no differences of internal structures between central and satellite ETGs for the same stellar masses. However, for similar stellar mass and colour distributions, we find that ETGs more prolate-like, or with more hot orbits, tend to have higher close neighbour counts at $r_p\sim40$ kpc.

astro-ph.GA↗
arXiv2019

Mapping the dark matter halo of early-type galaxy NGC 2974 through orbit-based models with combined stellar and cold gas kinematics

We present an orbit-based method of combining stellar and cold gas kinematics to constrain the dark matter profile of early-type galaxies. We apply this method to early-type galaxy NGC 2974, using Pan-STARRS imaging and SAURON stellar kinematics to model the stellar orbits, and introducing HI kinematics from VLA observation as a tracer of the gravitational potential. The introduction of the cold gas kinematics shows a significant effect on the confidence limits of especially the dark halo properties: we exclude more than $95\%$ of models within the $1-σ$ confidence level of Schwarzschild modelling with only stellar kinematics, and reduce the relative uncertainty of the dark matter fraction significantly to $10\%$ within $5 R_\mathrm{e}$. Adopting a generalized-NFW dark matter profile, we measure a shallow cuspy inner slope of $0.6^{+0.2}_{-0.3}$ when including the cold gas kinematics in our model. We cannot constrain the inner slope with the stellar kinematics alone.

astro-ph.GA↗
arXiv2019

NGC 7457: Evidence for merger-driven cylindrical rotation in disc galaxies

We construct Schwarzschild orbit-based models of NGC 7457, known as a peculiar low-mass lenticular galaxy. Our best-fitting model successfully retrieves most of the unusual kinematics behaviours of this galaxy, in which, the orbital distribution of stars is dominated by warm and hot orbits. The reconstructed surface brightness of the hot component matches fairly well the photometric bulge and the reconstructed LOSVD map of this component shows clear rotation around the major photometric axis of the galaxy. In the absence of a dominant cold component, the outer part of our model is dominated by warm orbits, representing an exponential thick disc. Our orbital analysis also confirm the existence of a counter-rotating orbital substructure in the very centre, reported in previous observational studies. By comparing our model with a variety of simulation studies, and considering the stellar kinematics and populations properties of this galaxy, we suggest that the thick disc is most likely a dynamically heated structure, formed through the interactions and accretion of satellite(s) with near-polar initial inclination. We also suggest a merger-driven process as the most plausible scenario to explain the observed and dynamically-modelled properties of the bulge of NGC 7457. We conclude that both the high level of cylindrical rotation and unusually low velocity dispersion reported for the NGC 7457 have most-likely external origins. Therefore, NGC 7457 could be considered as a candidate for merger-driven cylindrical rotation in the absence of a strong bar in disc galaxies.

astro-ph.GA↗
arXiv2019

Constraining nuclear star cluster formation using MUSE-AO observations of the early-type galaxy FCC47

Nuclear star clusters (NSCs) are found in at least 70% of all galaxies, but their formation path is still unclear. In the most common scenarios, NSCs form in-situ from the galaxy's central gas reservoir, through merging of globular clusters (GCs), or through a combination of the two. As the scenarios pose different expectations for angular momentum and stellar population properties of the NSC in comparison to the host galaxy and the GC system, it is necessary to characterise the stellar light, NSC and GCs simultaneously. The large NSC (r$_\rm{eff} = 66$ pc) and rich GC system of the early-type Fornax cluster galaxy FCC47 (NGC1336) render this galaxy an ideal laboratory to constrain NSC formation. Using MUSE science verification data assisted by adaptive optics, we obtained maps for the stellar kinematics and for stellar-population properties of FCC47. We extracted the spectra of the central NSC and determined line-of-sight velocities of 24 GCs and metallicities of five. FCC47 shows two decoupled components (KDCs): a rotating disk and the NSC. Our orbit-based dynamical Schwarzschild model revealed that the NSC is a distinct kinematic feature and it constitutes the peak of metallicity and old ages in the galaxy. The main body consists of two counter-rotating populations and is dominated by a more metal-poor population. The GC system is bimodal with a dominant metal-poor population and the total GC system mass is $\sim 17\%$ of the NSC mass ($\sim$ 7 $\times$ $10^8 M_\odot$). The rotation, high metallicity and high mass of the NSC cannot be uniquely explained by GC-inspiral and most likely requires additional, but quickly quenched, in-situ formation. The presence of two KDCs most probably are evidence of a major merger that has altered the structure of FCC47 significantly, indicating the important role of galaxy mergers in forming the complex kinematics in the galaxy-NSC system.

astro-ph.GA↗
arXiv2019

NIHAO XVI: The properties and evolution of kinematically selected discs, bulges and stellar haloes

We use 25 simulated galaxies from the NIHAO project to define and characterize a variety of kinematic stellar structures: thin and thick discs, large scale single discs, classical and pseudo bulges, spheroids, inner discs, and stellar haloes. These structures have masses, spins, shapes and rotational support in good agreement with theoretical expectations and observational data. Above a dark matter halo mass of $2.5\times10^{\rm~11}M_{\rm\odot}$, all galaxies have a classical bulge and 70\% have a thin and thick disc. The kinematic (thin) discs follow a power-law relation between angular momentum and stellar mass $J_{\rm *}=3.4M_{\rm *}^{\rm1.26\pm0.06}$, in very good agreement with the prediction based on the empirical stellar-to-halo mass relation in the same mass range, and show a strong correlation between maximum `observed' rotation velocity and dark matter halo circular velocity $v_{\rm c}=6.4v_{\rm max}^{0.64\pm0.04}$. Tracing back in time these structures' progenitors, we find all to lose a fraction $1-f_j$ of their maximum angular momentum. Thin discs are significantly better at retaining their high-redshift spins ($f_j\sim0.70$) than thick ones ($f_j\sim0.40$). Stellar haloes have their progenitor baryons assembled the latest ($z_{\rm~1/2}\sim1.1$) and over the longest timescales ($τ\sim6.2$~Gyr), and have the smallest fraction of stars born in-situ ($f_{\rm in-situ}=0.35\pm0.14$). All other structures have $1.5\lesssim z_{\rm1/2}\lesssim3$, $τ=4\pm2$~Gyr and $f_{\rm in-situ}\gtrsim0.9$.

astro-ph.GA↗
arXiv2019

A study of stellar orbit fractions: simulated IllustrisTNG galaxies compared to CALIFA observations

Motivated by the recently discovered kinematic "Hubble sequence" shown by the stellar orbit-circularity distribution of 260 CALIFA galaxies, we make use of a comparable galaxy sample at z = 0 with a stellar mass range from 5E9 to 5E11 solar masses, selected from the IllustrisTNG simulation and study their stellar orbit compositions in relation to a number of other fundamental galaxy properties.We find that the TNG100 simulation broadly reproduces the observed fractions of different orbital components and their stellar mass dependencies. In particular, the mean mass dependencies of the luminosity fractions for the kinematically warm and hot orbits are well reproduced within model uncertainties of the observed galaxies. The simulation also largely reproduces the observed peak and trough features at a stellar mass of 1-2E10 solar masses, in the mean distributions of the cold- and hot-orbit fractions, respectively, indicating fewer cooler orbits and more hotter orbits in both more- and less-massive galaxies beyond such a mass range. Several marginal disagreements are seen between the simulation and observations: the average cold-orbit (counter-rotating) fractions of the simulated galaxies below (above) a stellar mass of 6E10 solar masses, are systematically higher than the observational data by < 10% (absolute orbital fraction); the simulation also seems to produce more scatter for the cold-orbit fraction and less so for the non-cold orbits at any given galaxy mass. Possible causes that stem from the adopted heating mechanisms are discussed.

astro-ph.GA↗
arXiv2019

Combining Stellar Populations with Orbit-Superposition Dynamical Modelling - the Formation History of the Lenticular Galaxy NGC 3115

We present a combination of the Schwarzschild orbit-superposition dynamical modelling technique with the spatially-resolved mean stellar age and metallicity maps to uncover the formation history of galaxies. We apply this new approach to a remarkable 5-pointing mosaic of VLT/MUSE observations obtained by Guérou et al. (2016) extending to a maximum galactocentric distance of $120''$ ($\sim 5.6\ {\rm kpc}$) along the major axis, corresponding to $\sim 2.5\ {\rm R}_e$. Our method first identifies `families' of orbits from the dynamical model that represent dynamically-distinct structures of the galaxy. Individual ages and metallicities of these components are then fit for using the stellar-population information. Our results highlight components of the galaxy that are distinct in the combined stellar dynamics/populations space, which implies distinct formation paths. We find evidence for a dynamically-cold, metal-rich disk, consistent with a gradual in-situ formation. This disk is embedded in a generally-old population of stars, with kinematics ranging from dispersion-dominated in the centre to an old, diffuse, metal-poor stellar halo at the extremities. We find also a direct correlation between the dominant dynamical support of these components, and their associated age, akin to the relation observed in the Milky Way. This approach not only provides a powerful model for inferring the formation history of external galaxies, but also paves the way to a complete population-dynamical model.

astro-ph.GA↗
arXiv2019

Evaluating the ability of triaxial Schwarzschild modelling to estimate properties of galaxies from the Illustris simulation

We evaluate the capabilities of Schwarzschild's orbit-superposition method by applying it to galaxies from the large scale, high resolution Illustris simulation. Nine early-type galaxies with a range of triaxiality are selected, and we create mock integral field unit data for five line-of-sight projections of each galaxy. Each of the 45 mock data sets is taken as an independent observed galaxy. Using van den Bosch's 2008 triaxial Schwarzschild implementation, we assess model estimates of various galaxy properties, covering mass profiles, intrinsic shapes, stellar orbit distributions and velocity anisotropies. Total mass within $\overline{R_{\rm e}}$ is recovered well with average deviations within $\pm15$ percent. Stellar mass is underestimated by $\sim24$ percent and dark matter overestimated by $\sim38$ percent (assuming an NFW dark matter profile and allowing for degeneracy between stellar mass and dark matter mass). Using a gNFW profile, these values improve to $\sim13$ percent for stellar mass and $\sim18$ percent for dark matter. Axis ratio estimates show a moderate bias of $Δ(b/a)=0.07$ and $Δ(c/a)=0.14$ ($a\ge b\ge c$). Distributions of the orbit circularities $λ_z$ and $λ_x$, representing rotation about the minor and major axes, are well reconstructed. Separating orbits into thermal categories, our models match the average fractions of these categories to within $10$ percent. Velocity anisotropy is well estimated with values matching in the inner regions but becoming slightly radially biased in the outer regions. Overall, the galaxy property estimates we obtained using Schwarzschild modelling are not implausible and are representative of the simulated galaxies we modelled.

astro-ph.GA↗
arXiv2018

A dynamical view on stellar metallicity gradient diversity across the Hubble sequence with CALIFA

We analyze radial stellar metallicity and kinematic profiles out to 1Re in 244 CALIFA galaxies ranging from morphological type E to Sd, to study the evolutionary mechanisms of stellar population gradients. We find that linear metallicity gradients exhibit a clear correlation with galaxy morphological type - with early type galaxies showing the steepest gradients. We show that the metallicity gradients simply reflect the local mass-metallicity relation within a galaxy. This suggests that the radial stellar population distribution within a galaxys effective radius is primarily a result of the \emph{in-situ} local star formation history. In this simple picture, the dynamically derived stellar surface mass density gradient directly predicts the metallicity gradient of a galaxy. We show that this correlation and its scatter can be reproduced entirely by using independent empirical galaxy structural and chemical scaling relations. Using Schwarzschild dynamical models, we also explore the link between a galaxys local stellar populations and their orbital structures. We find that galaxies angular momentum and metallicity gradients show no obvious causal link. This suggests that metallicity gradients in the inner disk are not strongly shaped by radial migration, which is confirmed by the lack of correlation between the metallicity gradients and observable probes of radial migration in the galaxies, such as bars and spiral arms. Finally, we find that galaxies with positive metallicity gradients become increasingly common towards low mass and late morphological types - consistent with stellar feedback more efficiently modifying the baryon cycle in the central regions of these galaxies.

astro-ph.GA↗
arXiv2018

Morphology and kinematics of orbital components in CALIFA galaxies across the Hubble sequence

Based on the stellar orbit distribution derived from orbit-superposition Schwarzschild models, we decompose each of 250 representative present-day galaxies into four orbital components: cold with strong rotation, warm with weak rotation, hot with dominant random motion and counter-rotating (CR). We rebuild the surface brightness ($Σ$) of each orbital component and we present in figures and tables a quantification of their morphologies using the Sersic index \textit{n}, concentration $C = \log{(Σ_{0.1R_e}/Σ_{R_e})}$ and intrinsic flattening $q_{\mathrm{Re}}$ and $q_{\mathrm{Rmax}}$, with $R_e$ the half-light-radius and $R_{\mathrm{max}}$ the CALIFA data coverage. We find that: (1) kinematic hotter components are generally more concentrated and rounder than colder components, and (2) all components become more concentrated and thicker/rounder in more massive galaxies; they change from disk-like in low mass late-type galaxies to bulge-like in high-mass early type galaxies. Our findings suggest that Sersic \textit{n} is not a good discriminator between rotating bulges and non-rotating bulges. The luminosity fraction of cold orbits $f_{\rm cold}$ is well correlated with the photometrically-decomposed disk fraction $f_{\rm disk}$ as $f_{\mathrm{cold}} = 0.14 + 0.23f_{\mathrm{\mathrm{disk}}}$. Similarly, the hot orbit fraction $f_{\rm hot}$ is correlated with the bulge fraction $f_{\rm bulge}$ as $f_{\mathrm{hot}} = 0.19 + 0.31f_{\mathrm{\mathrm{bulge}}}$. The warm orbits mainly contribute to disks in low-mass late-type galaxies, and to bulges in high-mass early-type galaxies. The cold, warm, and hot components generally follow the same morphology ($ε= 1-q_{\rm Rmax}$) versus kinematics ($σ_z^2/\overline{V_{\mathrm{tot}}^2}$) relation as the thin disk, thick disk/pseudo bulge, and classical bulge identified from cosmological simulations.

astro-ph.GA↗
arXiv2018

The EDGE-CALIFA survey: validating stellar dynamical mass models with CO kinematics

Deriving circular velocities of galaxies from stellar kinematics can provide an estimate of their total dynamical mass, provided a contribution from the velocity dispersion of the stars is taken into account. Molecular gas (e.g., CO) on the other hand, is a dynamically cold tracer and hence acts as an independent circular velocity estimate without needing such a correction. In this paper we test the underlying assumptions of three commonly used dynamical models, deriving circular velocities from stellar kinematics of 54 galaxies (S0-Sd) that have observations of both stellar kinematics from the CALIFA survey, and CO kinematics from the EDGE survey. We test the Asymmetric Drift Correction (ADC) method, as well as Jeans, and Schwarzschild models. The three methods each reproduce the CO circular velocity at 1Re to within 10%. All three methods show larger scatter (up to 20%) in the inner regions (R < 0.4Re) which may be due to an increasingly spherical mass distribution (which is not captured by the thin disk assumption in ADC), or non-constant stellar M/L ratios (for both the JAM and Schwarzschild models). This homogeneous analysis of stellar and gaseous kinematics validates that all three models can recover Mdyn at 1Re to better than 20%, but users should be mindful of scatter in the inner regions where some assumptions may break down.

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