The mass of the dark matter halo of the Milky Way can be estimated by fitting analytical models to the phase-space distribution of dynamical tracers. We test this approach using realistic mock stellar halos constructed from the Aquarius N-body simulations of dark matter halos in the $Λ$CDM cosmology. We extend the standard treatment to include a Navarro-Frenk-White (NFW) potential and use a maximum likelihood method to recover the parameters describing the simulated halos from the positions and velocities of their mock halo stars. We find that the estimate of halo mass is highly correlated with the estimate of halo concentration. The best-fit halo masses within the virial radius, $R_{200}$, are biased, ranging from a 40\% underestimate to a 5\% overestimate in the best case (when the tangential velocities of the tracers are included). There are several sources of bias. Deviations from dynamical equilibrium can potentially cause significant bias; deviations from spherical symmetry are relatively less important. Fits to stars at different galactocentric radii can give different mass estimates. By contrast, the model gives good constraints on the mass within the half-mass radius of tracers even when restricted to tracers within 60kpc. The recovered velocity anisotropies of tracers, $β$, are biased systematically, but this does not affect other parameters if tangential velocity data are used as constraints.
The inference of the Milky Way halo mass requires modelling the phase space structure of dynamical tracers, with different tracers following different models and having different levels of sensitivity to the halo mass. For steady-state models, phase correlations among tracer particles lead to an irreducible stochastic bias. This bias is small for satellite galaxies and dark matter particles, but as large as a factor of 2 for halo stars. This is consistent with the picture that satellite galaxies closely trace the underlying phase space distribution of dark matter particles, while halo stars ar…
Using realistic cosmological simulations of Milky Way sized haloes, we study their dynamical state and the accuracy of inferring their mass profiles with steady-state models of dynamical tracers. We use a new method that describes the phase-space distribution of a steady-state tracer population in a spherical potential without any assumption regarding the distribution of their orbits. Applying the method to five haloes from the Aquarius $Λ$CDM N-body simulation, we find that dark matter particles are an accurate tracer that enables the halo mass and concentration parameters to be recovered wit…
A method is proposed for constraining the Galactic gravitational potential from high precision observations of the phase space coordinates of a system of relaxed tracers. The method relies on an "ergodic" assumption that the observations are representative of the state of the system at any other time. The observed coordinates serve as initial conditions for moving the tracers forward in time in an assumed model for the gravitational field. The validity of the model is assessed by the statistical equivalence between the observations and the distribution of tracers at randomly selected times. Th…
We observe the density wave angular pattern speed OMEGA-p to be near 12 to 17 km / s / kpc, by the separation between a typical optical HII region (from the spiral arm dust lane) and using a HII evolution time model to yield its relative speed, and independently by the separation between a typical radio maser (from the spiral arm dust lane) with a maser model.
We use distant Blue Horizontal Branch stars with Galactocentric distances 16 < r/kpc < 48 as kinematic tracers of the Milky Way dark halo. We model the tracer density as an oblate, power-law embedded within a spherical power-law potential. Using a distribution function method, we estimate the overall power-law potential and the velocity anisotropy of the halo tracers. We measure the slope of the potential to be gamma ~ 0.4 and the overall mass within 50 kpc is ~ 4 x 10^11 M_sol. The tracer velocity anisotropy is radially biased with beta ~ 0.5, which is in good agreement with local solar neigh…
From the sun's location in the Galactic disk, one can use different arm tracers (CO, HII, thermal or ionized or relativistic electrons, masers, cold or hot dust, etc) to locate a tangent to each spiral arm in the disk of the Milky Way galaxy. We present a Master catalog of the astronomically observed tangents to the Galaxy's spiral arms, using different arm tracers from the literature. Some arm tracers can have slightly divergent results from several papers, so a mean is taken - see Appendix for CO, HII, and masers. The Master catalog of means currently consists of 63 mean tracer entries, spre…
The spiral structure of our Milky Way has not yet been well outlined. HII regions, giant molecular clouds (GMCs) and 6.7-GHz methanol masers are primary tracers for spiral arms. We collect and update the database of these tracers which has been used in Hou, Han & Shi (2009) for mapping the spiral structure.
We analyze recent observations of the spiral arm width in the Milky Way, as a function of the galactic radius, and we compare this relation with the prediction from the density wave theory. We use the following method: in each spiral arm, we concentrate on the separation (or offset) between the starforming region (radio masers) near the shock front of a density wave, and the aged star region (diffuse CO gas) near the potential minimum of a density wave; we take this separation between these two tracers as the arm width. New results: we find a typical separation (maser to diffuse CO gas) near 2…
The spiral structure of the Milky Way is not yet well determined. The keys to understanding this structure are to increase the number of reliable spiral tracers and to determine their distances as accurately as possible. HII regions, giant molecular clouds (GMCs), and 6.7-GHz methanol masers are closely related to high mass star formation, and hence they are excellent spiral tracers. We update the catalogs of Galactic HII regions, GMCs, and 6.7-GHz methanol masers, and then outline the spiral structure of the Milky Way. We collected data for more than 2500 known HII regions, 1300 GMCs, and 900…
The spiral structure of our Milky Way Galaxy is not yet known. HII regions and giant molecular clouds are the most prominent spiral tracers. We collected the spiral tracer data of our Milky Way from the literature, namely, HII regions and giant molecular clouds (GMCs). With weighting factors based on the excitation parameters of HII regions or the masses of GMCs, we fitted the distribution of these tracers with models of two, three, four spiral-arms or polynomial spiral arms. The distances of tracers, if not available from stellar or direct measurements, were estimated kinetically from the sta…
The ongoing interaction between the Milky Way (MW) and its largest satellite - the Large Magellanic Cloud (LMC) - creates a significant perturbation in the distribution and kinematics of distant halo stars, globular clusters and satellite galaxies, and leads to biases in MW mass estimates from these tracer populations. We present a method for compensating these perturbations for any choice of MW potential by computing the past trajectory of LMC and MW and then integrating the orbits of tracer objects back in time until the influence of the LMC is negligible, at which point the equilibrium appr…
We discuss a novel approach to "weighing" the Milky Way dark matter halo, one that combines the latest samples of halo stars selected from the Sloan Digital Sky Survey (SDSS) with state-of-the-art numerical simulations of Milky Way analogs. The fully cosmological runs employed in the present study include "Eris", one of the highest-resolution hydrodynamical simulations of the formation of a M_vir=8e11 M_sun late-type spiral, and the dark-matter only M_vir=1.7e12 M_sun "Via Lactea II" simulation. Eris provides an excellent laboratory for creating mock SDSS samples of tracer halo stars, and we s…
The Gaia era opens new possibilities for discovering the remnants of disrupted satellite galaxies in the Solar neighborhood. If the population of local accreted stars is correlated with the dark matter sourced by the same mergers, one can then map the dark matter distribution directly. Using two cosmological zoom-in hydrodynamic simulations of Milky Way-mass galaxies from the Latte suite of Fire-2 simulations, we find a strong correlation between the velocity distribution of stars and dark matter at the solar circle that were accreted from luminous satellites. This correspondence holds for dar…
Most of known RR Lyraes are type ab RR Lyraes (RRLab), and they are the excellent tool to map the Milky Way and its substructures. We find that 1148 RRLab stars determined by Drake et al.(2013) have been observed by spectroscopic surveys of SDSS and LAMOST. We derived radial velocity dispersion, circular velocity and mass profile from 860 halo tracers in our paper I. Here, we present the stellar densities and radial velocity distributions of thick disk and halo of the Milky Way. The 288 RRLab stars located in the thick disk have the mean metallicity of [Fe/H]$=-1.02$. Three thick disk tracers …
Context: The Faraday rotation measure (RM) is often used to study the magnetic field strength and orientation within the ionized medium of the Milky Way. Observations indicate a RM in the spiral arms that exceeds the commonly assumed range. This raises the question of under what conditions spiral arms create such strong RM. Aims: We investigate the effect of spiral arms on Galactic RMs through shock compression of the interstellar medium (ISM). It has recently been suggested that the Sagittarius spiral arm creates a strong peak in RM where the line of sight (LOS) is tangent to the arm, and tha…
We introduce a method to infer the vertical distribution of stars in the Milky Way using a Poisson likelihood function, with a view to applying our method to the Gaia catalogue. We show how to account for the sample selection function and for parallax measurement uncertainties. Our method is validated against a simulated sample drawn from a model with two exponential discs and a power-law halo profile. A mock Gaia sample is generated using the Gaia astrometry selection function, whilst realistic parallax uncertainties are drawn from the Gaia Astrometric Spread Function. The model is fit to the…
From the Sun, a look at the edge of each spiral arm in our Milky Way (seen tangentially, along the line of sight) can yield numerous insights. Using different arm tracers (dust, masers, synchrotron emission, CO gas, open star clusters), we observe here for the first time an age gradient (about 12 +/-2 Myrs/kpc), much as predicted by the density wave theory. This implies that the arm tracers are leaving the dust lane at a relative speed of about 81 +/-10 km/s. We then compare with recent optical data obtained from the Gaia satellite, pertaining to the spiral arms.
Dynamical models allow us to connect the motion of a set of tracers to the underlying gravitational potential, and thus to the total (luminous and dark) matter distribution. They are particularly useful for understanding the mass and spatial distribution of dark matter (DM) in a galaxy. Globular clusters (GCs) are an ideal tracer population in dynamical models, since they are bright and can be found far out into the halo of galaxies. We aim to test how well Jeans-Anisotropic-MGE (JAM) models using GCs (positions and line-of-sight velocities) as tracers can constrain the mass and radial distrib…
We present the results of N-body models of the Milky Way and Large Magellanic Cloud system and study the kinematic reflex motion in the stellar halo owing to the barycentre displacement of the disc. In agreement with previous studies, we find that the Milky Way disc may be moving at 40 km/s relative to the barycentre prior to the Large Magellanic Cloud infall. The resulting reflex motion is visible in tangential velocities of the stellar halo as a simple dipole. The signal is strongest for stars with long dynamical times, identifiable in position-velocity data as stars with large apocentres, w…
We use Gaia photometry and astrometry to estimate the vertical spatial structure of the Milky Way at the Solar radius, formally accounting for sample incompleteness (the selection function) and parallax measurement uncertainty. Our results show impressive precision demonstrating the power of the Gaia data. However, systematic errors dominate the parameter value uncertainties. We thoroughly test and quantify the impacts of all systematic uncertainties. The vertical tracer density is modelled as a sum of two exponential profiles for the thin and thick discs, together with a spherically symmetric…
The Milky Way is a barred spiral galaxy, with physical properties inferred from various tracers informed by the extrapolation of structures seen in other galaxies. However, the distances of these tracers are measured indirectly and are model-dependent. We constructed a map of the Milky Way in three-dimensions based on the positions and distances of thousands of classical Cepheid variable stars. This map shows the structure of our Galaxy's young stellar population, and allows us to constrain the warped shape of the Milky Way's disk. A simple model of star formation in the spiral arms reproduces…
A family of spherical halo models with flat circular velocity curves is presented. This includes models in which the rotation curve has a finite central value but declines outwards (like the Jaffe model). It includes models in which the rotation curve is rising in the inner parts, but flattens asymptotically (like the Binney model). The family encompasses models with both finite and singular (cuspy) density profiles. The self-consistent distribution function depending on binding energy $E$ and angular momentum $L$ is derived and the kinematical properties of the models discussed. These really …
We present a family of robust tracer mass estimators to compute the enclosed mass of galaxy haloes from samples of discrete positional and kinematical data of tracers, such as halo stars, globular clusters and dwarf satellites. The data may be projected positions, distances, line of sight velocities or proper motions. Forms of the estimator tailored for the Milky Way galaxy and for M31 are given. Monte Carlo simulations are used to quantify the uncertainty as a function of sample size. For the Milky Way, the satellite sample consists of 26 galaxies with line-of-sight velocities. We find that t…
Identifying the structure of our Galaxy has always been fraught with difficulties, and while modern surveys continue to make progress building a map of the Milky Way, there is still much to understand. The arm and bar features are important drivers in shaping the interstellar medium, but their exact nature and influence still require attention. We present results of smoothed particle hydrodynamic simulations of gas in the Milky Way including star formation, stellar feedback, and ISM cooling, when exposed to different arm and bar features, with the aim of better understanding how well newly for…
We model the phase-space of the kinematic tracers using general, smooth distribution functions to derive a conservative lower bound on the total mass within 150-200 kpc. By approximating the potential as Keplerian, the phase-space distribution can be simplified to that of a smooth distribution of energies and eccentricities. Our approach naturally allows for calculating moments of the distribution function, such as the radial profile of the orbital anisotropy. We construct a family of phase-spaces with the resulting radial velocity dispersion overlapping with that of distant kinematic tracers,…
We perform a test of John Moffat's Modified Gravity theory (MOG) within the Milky Way, adopting the well known "Rotation Curve" method. We use the dynamics of observed tracers within the disk to determine the gravitational potential as a function of galactocentric distance, and compare that with the potential that is expected to be generated by the visible component only (stars and gas) under different "flavors" of the MOG theory, making use of a state-of-the-art setup for both the observed tracers and baryonic morphology. Our analysis shows that in both the original and the modified version (…
An updated catalog of 205 observed tangents to the spiral arms (in Galactic longitudes) since 1980 is presented. This represents an addition of 80 arm tangents in 6 years (since 2016). Most arm tangents are observed at telescopes in the radio regime. In this study, the separation of each arm tracer from the dust lane is analyzed to obtain the relative speed away from the dust lane (an age gradient). Each arm tracer is observed to be separated from the dust lane, showing an age gradient of about 11.3 +/- 2 Myr/kpc across the spiral arm; this gives a relative speed away from the dust lane of abo…
Recent spectroscopic observations of the outer halo globular cluster (GC) NGC 2419 show that it is unique among GCs, in terms of chemical abundance patterns, and some suggest that it was originated in the nucleus of a dwarf galaxy. Here we show, from the Subaru narrow-band photometry employing a calcium filter, that the red giant-branch (RGB) of this GC is split into two distinct subpopulations. Comparison with spectroscopy has confirmed that the redder RGB stars in the $hk$[=(Ca$-b)-(b-y)$] index are enhanced in [Ca/H] by $\sim$0.2 dex compared to the bluer RGB stars. Our population model fur…
A large fraction of Galactic very-high energy (VHE; E$\gtrsim$100 GeV) $γ$-ray sources is cataloged as unidentified. In this work we explore the possibility that these unidentified sources are located in ambients particularly rich in material content unaccounted by traditional tracers. In a scenario where the VHE emission is due to the interaction of the accelerated particles with a target mass, a large mass of untraced material could be substantially contributing to the VHE emission from these regions. Here, we use three tracers for the commonly explored components: intensity of the $^\textrm…
Modified Newtonian dynamics (MOND) is an empirical theory originally proposed to explain the rotation curves of spiral galaxies by modifying the gravitational acceleration, rather than by invoking dark matter. Here,we set constraints on MOND using an up-to-date compilation of kinematic tracers of the Milky Way and a comprehensive collection of morphologies of the baryonic component in the Galaxy. In particular, we find that the so-called "standard" interpolating function cannot explain at the same time the rotation curve of the Milky Way and that of external galaxies for any of the baryonic mo…
We perform an extensive review of the numerous studies and methods used to determine the total mass of the Milky Way. We group the various methods into seven broad classes, including: i) estimating Galactic escape velocity using high velocity objects; ii) measuring the rotation curve through terminal and circular velocities; iii) modeling halo stars, globular clusters and satellite galaxies with the Spherical Jeans equation and iv) with phase-space distribution functions; v) simulating and modeling the dynamics of stellar streams and their progenitors; vi) modeling the motion of the Milky Way,…
We use the method of statistical parallax to constrain the distance-scale zero points and analyze the kinematics of extensive samples of Galactic classical Cepheids, RR Lyrae type variables, and blue horizontal branch stars, which serve as standard candles/kinematic tracers of various Galactic populations. We obtain three consistent estimates for the local circular velocity based on the mean velocities of halo RR Lyrae variables, BHB stars, and Galactic rotation curve inferred from Cepheid data with an average value of 210+/-6 km/s, which is close to the average circular velocity in the 5-40 k…
Some important predictions from 4 main models of spiral arm formation are tested here, using observational data acquired for the Milky Way galaxy. Many spiral arm models (density wave, tidal wave, nuclear Lyapunov tube, or dynamic transient wave) have some consistencies with some of the observations, and some inconsistencies. Our 4 tests consist of the relative locations and relative speeds of different arm tracers away from the dust lane, and the global arm pitch angle as obtained over two Galactic quadrants and several Galactic radii, as well as the arm's continuity of shape from Galactic qu…
We examine the dynamical effects on disk stars of a "long bar" in the Milky Way by inserting a triaxial rotating bar into an axisymmetric disk+bulge+dark halo potential and integrating 3-D orbits of 104 tracer stars over a period of 2 Gyr. The long bar has been detected via "clump giants" in the IR by Lopez-Corredoira et al. (2007), and is estimated to have semi-major axes of (3.9 : 0.6 : 0.1) kpc and a mass of 6 10^9 Msun. We find such a structure has a slight impact on the inner disk-system, moving tracers near to the bar into the bar-region, as well as into the bulge. These effects are unde…
The Fornax dwarf spheroidal galaxy is the most massive satellites of the Milky Way, claimed to be embedded in a huge dark matter halo, and the only among the Milky Way satellites hosting five globular clusters. Interestingly, their estimated masses, ages and positions seem hardly compatible with the presence of a significant dark matter component, as expected in the $Λ$ CDM scheme. Indeed, if Fornax would have a CDM halo with a standard density profile, all its globular clusters should have sunk to the galactic centre many Gyr ago due to dynamical friction. Due to this, some authors proposed t…
A Self-Consistent Jeans Analysis of the Milky Way Rotation Curve
Tsinghua University（清华大学）；LIRA, Observatoire de Paris, Université PSL, CNRS（巴黎天文台 LIRA 实验室，巴黎大学，法国国家科学研究中心）；Center for Astronomy, Space Science and Astrophysics, Independent University, Bangladesh（孟加拉独立大学天体物理学、空间科学与天文学中心）；Local Universe and Time-Domain Astronomy Laboratory, Department of Astronomy, China West Normal University（西华师范大学天文学院本地宇宙与时域天文实验室）
Fully cosmological, high resolution N-Body + SPH simulations are used to investigate the chemical abundance trends of stars in simulated stellar halos as a function of their origin. These simulations employ a physically motivated supernova feedback recipe, as well as metal enrichment, metal cooling and metal diffusion. As presented in an earlier paper, the simulated galaxies in this study are surrounded by stellar halos whose inner regions contain both stars accreted from satellite galaxies and stars formed in situ in the central regions of the main galaxies and later displaced by mergers into…
We build a sample of distant (D > 80 kpc) stellar halo stars with measured radial velocities. Faint ($20 < g <22$) candidate blue horizontal branch (BHB) stars were selected using the deep, but wide, multi-epoch Sloan Digital Sky Survey photometry. Follow-up spectroscopy for these A-type stars was performed using the VLT-FORS2 instrument. We classify stars according to their Balmer line profiles, and find 7 are bona fide BHB stars and 31 are blue stragglers (BS). Owing to the magnitude range of our sample, even the intrinsically fainter BS stars can reach out to D ~ 90 kpc. We complement this …
The stellar density distribution of the bulge is analyzed through one of its tracers. We use oxygen-rich Miras variables from the Catchpole et al. (2016) survey and OGLE-III survey as standard candles. The average age of these stars is around 9 Gyr. The population traced by Mira variables matches a boxy bulge prediction, not an X-shaped one, because only one peak is observed in the density along the analyzed lines of sight, whereas the prediction of an X-shape gives two clear peaks.
The dwarf galaxy companions to the Milky Way are unique cosmological laboratories. With luminosities as low as 10^-7 L_MW, they inhabit the lowest mass dark matter halos known to host stars and are presently the most direct tracers of the distribution, mass spectrum, and clustering scale of dark matter. Their resolved stellar populations also facilitate detailed studies of their history and mass content. To fully exploit this potential requires a well-defined census of virtually invisible galaxies to the faintest possible limits and to the largest possible distances. I review the past and pres…
Using hydrodynamical simulations, we study how well the underlying gravitational potential of a galaxy cluster can be modelled dynamically with different types of tracers. In order to segregate different systematics and the effects of varying estimator performances, we first focus on applying a generic minimal assumption method (oPDF) to model the simulated haloes using the full 6-D phasespace information. We show that the halo mass and concentration can be recovered in an ensemble unbiased way, with a stochastic bias that varies from halo to halo, mostly reflecting deviations from steady stat…
We derive the mass model of the Milky Way (MW) using a cored dark matter (DM) halo profile and recent data. The method used consists in fitting a spherically symmetric model of the Galaxy with a Burkert DM halo profile to available data: MW terminal velocities in the region inside the solar circle, circular velocity as recently estimated from maser star forming regions at intermediate radii, and velocity dispersions of stellar halo tracers for the outermost Galactic region. The latter are reproduced by integrating the Jeans equation for every modeled mass distribution, and by allowing for diff…
We analyse the density profiles of the stellar halo populations in eight Milky-Way mass galaxies, simulated within the $Λ$-Cold Dark Matter scenario. We find that accreted stars can be well-fitted by an Einasto profile, as well as any subsample defined according to metallicity. We detect a clear correlation between the Einasto fitting parameters of the low-metallicity stellar populations and those of the dark matter haloes. The correlations for stars with [Fe/H]$<-3$ allow us to predict the shape of the dark matter profiles within residuals of $\sim 10 $ per cent, in case the contribution from…
In an effort to improve our understanding of the spiral arm structure of the Milky Way, we use Classical Cepheids (CCs) to increase the number of young tracers on the far side of the Galactic disk with accurately determined distances. We use a sample of 30 CCs, discovered using near-infrared photometry from the VISTA Variables in the Vía Láctea survey (VVV) and classified based on their radial velocities and metallicities. We combine them with another 20 CCs from the literature for which VVV photometry is available. The compiled sample of CCs with homogeneously computed distances based on VVV …
Recent measurements suggest that the Large Magellanic Cloud (LMC) may weigh as much as 25\% of the Milky Way. In this work we explore how such a large satellite affects mass estimates of the Milky Way based on equilibrium modelling of the stellar halo or other tracers. In particular, we show that if the LMC is ignored, the Milky Way mass is overestimated by as much as 50\%. This bias is due to the bulk motion in the outskirts of the Galaxy's halo and can be, at least in part, accounted for with a simple modification to the equilibrium modelling. Finally, we show that the LMC has a substantial …
Dynamical mirages: how bar-induced resonant trapping can mimic substructure clustering in dynamical parameter spaces
Università degli Studi di Bologna（博洛尼亚大学）；Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, INAF（意大利国家天体物理研究所博洛尼亚天文与空间科学观测站）；Instituto de Astrofísica, Pontificia Universidad Católica de Chile（智利天主教公立大学天体物理研究所）；Instituto Milenio de Astrofísica MAS（MAS天体物理千年研究所）
We calculate the expected imprint of the ionized gas in the Milky-Way halo on the Cosmic Microwave Background (CMB) through the kinetic Sunyaev-Zel'dovich (kSZ) effect. Unlike other Galactic foregrounds, the halo kSZ signature covers the full sky, generates anisotropies on large angular scales, is not accompanied by spectral distortions, and could therefore be confused with primordial CMB anisotropies. We construct theoretical models for various halo components, including smooth diffuse gas, filaments of cold inflowing gas and high velocity clouds. We find that the kSZ effect for all component…
We compare the observed radial velocity of different arm tracers, taken near the tangent to a spiral arm. A slight difference is predicted by the density wave theory, given the shock predicted at the entrance to the inner spiral arm. In many of these spiral arms, the observed velocity offset confirms the prediction of the density wave theory (with a separation between the maser velocity and the CO gas peak velocity, of about 20 km/s) - when the observed offset is bigger than the error estimates. The time to reach the next spiral arm is given.
We investigate the temperature distribution of CO-dark molecular hydrogen (H2) in a series of disk galaxies simulated using the AREPO moving-mesh code. In conditions similar to those in the Milky Way, we find that H2 has a flat temperature distribution ranging from 10 - 100 K. At $T < 30$ K the gas is almost fully molecular and has a high CO content, whereas at $T > 30$ K, the H2 fraction spans a broader range and the CO content is small, allowing us to classify gas in these two regimes as CO-bright and CO-dark, respectively. The mean sound speed in the CO-dark H2 is 0.64 km/s, significantly l…
We test a Yukawa correction to the Newtonian potential, making use of our own Galaxy - the Milky Way - as a testbed. We include as free parameter the Yukawa strength and range and the dark matter profile parameters, and compare several morphologies for the bulge, gas, and disk components, also using Bayesian model selection criteria. We employ up-to-date datasets for both the visible (baryonic) component of the Milky Way, and for the tracers of the gravitational potential (the Rotation Curve). We find that the data are consistent with the Newtonian potential, and constrain the Yukawa coupling …
Estimating accretion times of halo substructures in the Milky Way
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Astronomical Institute, Tohoku University（东北大学天文学研究所）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究所）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
