Applying Noether's theorem to matter in the Milky Way: evidence for external perturbations and non-steady-state effects from Gaia Data Release 2
Susan Gardner, Austin Hinkel, Brian Yanny
备注：
15 pages, 8 figure panels, AASTeX, accepted for publication in ApJ; sentence added to Table 1 in proofs; typos fixed; note companion paper Hinkel et al., arXiv:2003.08389, to appear in ApJ
We apply Noether's theorem to observations of main-sequence stars from the Gaia Data Release 2 archive to probe the matter distribution function of the Galaxy. That is, we examine the axial symmetry of stars at vertical heights $z$, $0.2 \le |z| \le 3$ kpc, to probe the quality of the angular momentum $L_z$ as an integral of motion. The failure of this symmetry test would speak to a Milky Way, in both its visible and dark matter, that is not isolated and/or not in steady state. The left-right symmetry-breaking pattern we have observed, north and south, reveals both effects, with a measured deviation from symmetry of typically 0.5%. We show that a prolate form of the gravitational distortion of the Milky Way by the Large Magellanic Cloud, determined from fits to the Orphan stream by Erkal et al., 2019, is compatible with the size and sign of the axial-symmetry-breaking effects we have discovered in our sample of up to 14.4 million main-sequence stars, speaking to a distortion of an emergent, rather than static, nature.
Angle/action based distribution function (DF) models can be optimised based on how well they reproduce observations thus revealing the current matter distribution in the Milky Way. Gaia data combined with data from other surveys, e.g. the RAVE/TGAS sample, and its full selection function will greatly improve their accuracy.
Measuring the escape velocity of the Milky Way is critical in obtaining the mass of the Milky Way, understanding the dark matter velocity distribution, and building the dark matter density profile. In Necib $\&$ Lin (2021), we introduced a strategy to robustly measure the escape velocity. Our approach takes into account the presence of kinematic substructures by modeling the tail of the stellar distribution with multiple components, including the stellar halo and the debris flow called the Gaia Sausage (Enceladus). In doing so, we can test the robustness of the escape velocity measurement for …
We summarise recent results from analysis of APOGEE/Gaia data for stellar populations in the Galactic halo, disk, and bulge, leading to constraints on the contribution of dwarf galaxies and globular clusters to the stellar content of the Milky Way halo. Interpretation of the extant data in light of cosmological numerical simulations suggests that the Milky Way has been subject to an unusually intense accretion history at z >~ 1.5.
We present a panoramic map of the stellar streams of the Milky Way based upon astrometric and photometric measurements from the Gaia DR2 catalogue. In this first contribution, we concentrate on the halo at heliocentric distances beyond 5 kpc, and at Galactic latitudes $|b|>30°$, using the STREAMFINDER algorithm to detect structures along plausible orbits that are consistent with the Gaia proper motion measurements. We find a rich network of criss-crossing streams in the halo. Some of these structures were previously-known, several are new discoveries, but others are potentially artefacts of th…
Gaia HyperVelocity Star (HVS) kinematic observations favor a local escape velocity of ~700 km/s, nearly forty-percent greater than conventional estimates. Combining HVS and dwarf galaxy satellite data reveal the global escape velocity profile for the Galaxy smoothly traces an unbroken Keplerian decline from the central bar to the most remote satellite galaxy. We reveal a robust upper bound in baryonic mass discrepancy (maximal relative accelerations) linked to the virial theorem and obtain a fundamental and universal mass discrepancy-acceleration relation for virialized compact cosmic objects.
The Gaia map of the Milky Way reveals a pair of triangular features at nearly symmetric locations on opposite sides of the Galactic Center. In this paper we explore the implications of these features assuming they are manifestations of a caustic ring in the dark matter distribution of the Milky Way halo. The existence of a series of such rings is predicted by the Caustic Ring Model. The model's phase-space distribution is that acquired by a rethermalizing Bose-Einstein condensate of axions or axion-like particles. We show that dust is gravitationally entrained by cold axion flows and propose t…
We present a proper-motion study on models of the dwarf spheroidal galaxy Sculptor, based on the predicted proper-motion accuracy of Gaia measurements. Gaia will measure proper motions of several hundreds of stars for a Sculptor-like system. Even with an uncertainty on the proper motion of order 1.5 times the size of an individual proper-motion value of ~10 mas/century, we find that it is possible to recover Sculptor's systemic proper motion at its distance of 79 kpc.
The Gaia-ESO Survey (GES) is a large public spectroscopic survey that aims at observing with FLAMES@VLT the main stellar components of our Galaxy. The study of the population of open clusters is one of the main objectives of GES. We present some results from the first 18 months of observations, among them, a preliminary view of the radial metallicity gradient as traced by open cluster data and a comparison of the chemical patterns of clusters located in different parts of the Galactic disk.
We present orbits and their properties for 152 globular clusters of the Milky Way galaxy obtained using average Gaia DR2 proper motions and other astrometric data from the list of Vasiliev (2019). For orbit integrating we have used the axisymmetric model of the Galactic potential based on the Navarro-Frenk-White dark halo, and modified by Bajkova and Bobylev (2016) using circular velocities of Galactic objects in wide region of Galactocentric distances (up to 200 kpc) from Bhattacharjee et.al. (2014) catalog. Based on the analysis of the obtained orbits, we have modified the composition of the…
We have developed our original made-to-measure (M2M) algorithm, PRIMAL, with the aim of modelling the Galactic disc from upcoming Gaia data. From a Milky Way like N-body disc galaxy simulation, we have created mock Gaia data using M0III stars as tracers, taking into account extinction and the expected Gaia errors. In PRIMAL, observables calculated from the N-body model are compared with the target stars, at the position of the target stars. Using PRIMAL, the masses of the N-body model particles are changed to reproduce the target mock data, and the gravitational potential is automatically adju…
Machine learning can play a powerful role in inferring missing line-of-sight velocities from astrometry in surveys such as Gaia. In this paper, we apply a neural network to Gaia Early Data Release 3 (EDR3) and obtain line-of-sight velocities and associated uncertainties for ~92 million stars. The network, which takes as input a star's parallax, angular coordinates, and proper motions, is trained and validated on ~6.4 million stars in Gaia with complete phase-space information. The network's uncertainty on its velocity prediction is a key aspect of its design; by properly convolving these uncer…
We provide new values of the orbital parameters of 152 globular clusters, which are calculated using the new mean proper motions obtained from the Gaia EDR3 catalog data. The orbits were integrated 5 Gyr back in an axisymmetric three-component potential with a spherical bulge, disk component, and spherical dark halo in the Navarro-Frenk-White form, which we refined using the rotation curve of objects with large galactocentric distances up to 200 kpc. The obtained orbital parameters were compared with the orbital parameters of the same globular clusters calculated earlier in the same gravitatio…
We review the implications of the Gaia Data Release 2 catalogue for studying the dynamics of Milky Way globular clusters, focusing on two separate topics. The first one is the analysis of the full 6-dimensional phase-space distribution of the entire population of Milky Way globular clusters: their mean proper motions (PM) can be measured with an exquisite precision (down to 0.05 mas/yr, including systematic errors). Using these data, and a suitable ansatz for the steady-state distribution function (DF) of the cluster population, we then determine simultaneously the best-fit parameters of this …
The Milky Way (MW) is surrounded by a Vast Polar Structure (VPOS) of satellite galaxies, star clusters, and streams. Proper motion measurements for the brightest MW satellites indicate that they are predominantly co-orbiting along the VPOS. This is consistent with a dynamically stable structure. Assuming that all satellites that are aligned with the VPOS also co-orbit along this structure allows to empirically predict their systemic proper motions. Testing predictions for individual satellite galaxies at large distances requires high-accuracy proper motion measurements such as with the Hubble …
Multi-object spectrographs have opened a new window on the analyses of the chemo-dynamical properties of old Milky Way stars. These analyses allow us to trace back the internal mechanisms and the external factors that have influenced the evolution of our Galaxy, and therefore understand fundamental aspects of galaxy evolution in general. Here, we present recent results from the RAdial Velocity Experiment (RAVE) and the Gaia-ESO survey. These surveys explore the Milky Way properties in different ways, in terms of sample size and selection, magnitude range, and spectral resolution. We focus here…
Cold Dark Matter (CDM) theory, a pillar of modern cosmology and astrophysics, predicts the existence of a large number of starless dark matter halos surrounding the Milky Way (MW). However, clear observational evidence of these "dark" substructures remains elusive. Here, we present a detection method based on the small, but detectable, velocity changes that an orbiting substructure imposes on the stars in the MW disk. Using high-resolution numerical simulations we estimate that the new space telescope Gaia should detect the kinematic signatures of a few starless substructures provided the CDM …
We identify a simulated Milky Way analog in the EAGLE suite of cosmological hydrodynamical simulations. This galaxy not only shares similar global properties as the Milky Way, but was specifically selected because its merger history resembles that currently known for the Milky Way. In particular we find that this Milky Way analog has experienced its last significant merger (with a stellar mass ratio $\sim 0.2$) at $z\sim 1.2$. We show that this merger affected both the dynamical properties of the stars present at the time, contributing to the formation of a thick disk, and also leading to a si…
The Gaia-ESO Survey was designed to target all major Galactic components (i.e., bulge, thin and thick discs, halo and clusters), with the goal of constraining the chemical and dynamical evolution of the Milky Way. This paper presents the methodology and considerations that drive the selection of the targeted, allocated and successfully observed Milky Way field stars. The detailed understanding of the survey construction, specifically the influence of target selection criteria on observed Milky Way field stars is required in order to analyse and interpret the survey data correctly. We present t…
We present a search for "hyper-compact" star clusters in the Milky Way using a combination of Gaia and the Dark Energy Camera Legacy Survey (DECaLS). Such putative clusters, with sizes of ~1 pc and containing 500-5000 stars, are expected to remain bound to intermediate-mass black holes (Mbh~10^3-10^5 M-sun) that may be accreted into the Milky Way halo within dwarf satellites. Using the semi-analytic model SatGen we find an expected ~100 wandering intermediate-mass black holes with if every infalling satellite hosts a black hole. We do not find any such clusters in our search. Our upper limits …
The ratio of the first overtone (1O) / fundamental (F) periods of mixed-mode Cepheids that pulsate simultaneously in these two modes (F/1O) is metallicity-dependent. It can therefore be used to characterize the systems that host such variable stars. We want to take advantage of the F/1O double-mode Cepheids listed in the Gaia DR2 catalogue to derive the metallicity gradient in the Milky Way disk. The metallicity is derived from the ratio of the first overtone and fundamental periods provided by Gaia DR2 while the Gaia DR2 parallaxes are used to determine the Galactocentric distances of the sta…
The goal of this study is to present the development of a machine learning based approach that utilizes phase space alone to separate the Gaia DR2 stars into two categories: those accreted onto the Milky Way from those that are in situ. Traditional selection methods that have been used to identify accreted stars typically rely on full 3D velocity, metallicity information, or both, which significantly reduces the number of classifiable stars. The approach advocated here is applicable to a much larger portion of Gaia DR2. A method known as "transfer learning" is shown to be effective through ext…
Gaia's Radial Velocity Spectrometer (RVS) has been operating in routine phase for over one year since initial commissioning. RVS continues to work well but the higher than expected levels of straylight reduce the limiting magnitude. The end-of-mission radial-velocity (RV) performance requirement for G2V stars was 15 km/s at V = 16.5 mag. Instead, 15 km/s precision is achieved at 15 < V < 16 mag, consistent with simulations that predict a loss of 1.4 mag. Simulations also suggest that changes to Gaia's onboard software could recover ~0.14 mag of this loss. Consequently Gaia's onboard software w…
Using the data from Gaia (ESA) Data Release 2 we performed the orbital calculations of globular clusters (GCs) of the Milky Way. To explore possible close encounters (or collisions) between the GCs, using our own developed high-order phi-GRAPE code, we integrated backward and forward the orbits of 119 objects with reliable positions and proper motions. In calculations, we adopted a realistic axisymmetric Galactic potential (bulge + disk + halo). Using different impact conditions, we found four pairs of the six GCs that may have experienced an encounter within twice the sum of the half-mass rad…
We employ Gaia DR2 proper motions for 151 Milky Way globular clusters from Vasiliev (2019) in tandem with distances and line-of-sight velocities to derive their kinematical properties. To assign clusters to the Milky Way thick disk, bulge, and halo we follow the approach of Posti et al. (2018) who distinguished among different Galactic stellar components using stars's orbits. In particular, we use the ratio $L_{z}/e$, the $Z$ projection of the angular momentum to the eccentricity, as population tracer, which we complement with chemical abundances extracted from the literature and Monte-Carlo s…
This contribution to the Stellar Clusters & Associations: A RIA Workshop on Gaia deals with surveys of stars, in particular spectroscopic surveys, with attention to their impact on cluster studies, and their connectionwith Gaia. I review some of the scientific reasons why we want large spectroscopic surveys, what requirements these put on the instrumentation. Then I turn to a review of the current and future instrumentation that will enable us to complement Gaia's excellent distances and proper motions with the desired ground-based spectroscopy to obtain additional radial velocities and elemen…
The second data release from the Gaia mission (DR2) provides a comprehensive and unprecedented picture of the motions of astronomical sources in the plane of the sky, extending from the solar neighborhood to the outer reaches of the Milky Way. I present proper motion measurements based on Gaia DR2 for 17 ultra-faint dwarf galaxies within 100 kpc of the Milky Way. I compile the spectroscopically-confirmed member stars in each dwarf bright enough for Gaia astrometry from the literature, producing member samples ranging from 2 stars in Triangulum II to 68 stars in Bootes I. From the spectroscopic…
In this paper we introduce a new method for analysing Milky Way phase-space which allows us to reveal the imprint left by the Milky Way bar and spiral arms on the stars with full phase-space data in Gaia Data Release 2. The unprecedented quality and extended spatial coverage of these data enable us to discover six prominent stellar density structures in the disc to a distance of 5 kpc from the Sun. Four of these structures correspond to the spiral arms detected previously in the gas and young stars (Scutum-Centaurus, Sagittarius, Local and Perseus). The remaining two are associated with the ma…
We confirm the reality of the recently discovered Milky Way stellar cluster $\textit{Gaia}$ 1 using spectra acquired with the HERMES and AAOmega spectrographs of the Anglo-Australian Telescope. This cluster had been previously undiscovered due to its close angular proximity to Sirius, the brightest star in the sky at visual wavelengths. Our observations identified 41 cluster members, and yielded an overall metallicity of [Fe/H]$=-0.13\pm0.13$ and barycentric radial velocity of $v_r=58.30\pm0.22$ km/s. These kinematics provide a dynamical mass estimate of $12.9^{+4.6}_{-3.9}\times10^3$ M$_{\odo…
While the precise relationship between the Milky Way disk and the symmetry planes of the dark matter halo remains somewhat uncertain, a time-varying disk orientation with respect to an inertial reference frame seems probable. Hierarchical structure formation models predict that the dark matter halo is triaxial and tumbles with a characteristic rate of ~2 rad/Hubble time (~30 muas/yr). These models also predict a time-dependent accretion of gas, such that the angular momentum vector of the disk should be misaligned with that of the halo. These effects, as well as tidal effects of the LMC, will …
With Gaia Data Release 2, the astronomical community is entering a new era of multidimensional surveys of the Milky Way. This new phase-space view of our Galaxy demands new tools for comparing observations to simulations of Milky-Way-mass galaxies in a cosmological context, to test the physics of both dark matter and galaxy formation. We present ananke, a framework for generating synthetic phase-space surveys from high-resolution baryonic simulations, and use it to generate a suite of synthetic surveys resembling Gaia DR2 in data structure, magnitude limits, and observational errors. We use th…
We have established a mixture model approach to derive the parallax of the Milky Way globular clusters. It avoids the problem of cluster membership determination and provides a completely independent astrometrical solution by purely using the parallax data. This method is validated with simulated clusters of \cite{2017MNRAS.467..412P}. We have resolved 120 real globular clusters by the mixture model using parallaxes of the second data release of \gaia. They construct the largest direct parallax sample up to now. In comparing with other direct parallax results based on cluster members, includin…
We present a detailed analysis of kinematics of the Milky Way disk in solar neighborhood using GAIA DR3 catalog. To determine the local kinematics of the stellar disks of the Milky Way galaxy we use a complete sample of 278,228 red giant branch (RGB) stars distributed in a cylinder, centered at the Sun with a 1 kpc radius and half-height of 0.5 kpc. We determine separately the kinematical properties of RGB stars for each Galactic hemisphere in search for possible asymmetries. The kinematical properties of the RGB stars reveal the existence of two kinematically distinct components: the thin dis…
According to our current cosmological model, galaxies like the Milky Way are expected to experience many mergers over their lifetimes. The most massive of the merging galaxies will be dragged towards the disc-plane, depositing stars and dark matter into an accreted disc structure. In this work, we utilize the chemo-dynamical template developed in Ruchti et al. to hunt for accreted stars. We apply the template to a sample of 4,675 stars in the third internal data release from the Gaia-ESO Spectroscopic Survey. We find a significant component of accreted halo stars, but find no evidence of an ac…
The Milky Way galaxy is a typical spiral galaxy which consists of a black hole in its centre, a barred bulge and a disk which contains spiral arms. The complex structure of the Galaxy makes it extremely difficult and challenging to model its mass distribution, particularly for the Galactic disk which plays the most important role in the dynamics and evolution of the Galaxy. Conventionally an axisymmetric disk model with an exponential brightness distribution and a constant mass-to-light ratio is assumed for the Galactic disk. In order to generate a flat rotation curve, a dark halo has also to …
We characterize the Gaia-Enceladus-Sausage kinematic structure recently discovered in the Galactic halo using photometric metallicities from the SkyMapper survey, and kinematics from Gaia radial velocities measurements. By examining the metallicity distribution functions (MDFs) of stars binned in kinematic/action spaces, we find that the $\sqrt{J_R}$ vs $L_z$ space allows for the cleanest selection of Gaia-Enceladus-Sausage stars with minimal contamination from disc or halo stars formed in situ or in other past mergers. Stars with $30 \leq \sqrt{J_R} \leq 50$ (kpc km s$^{-1})^{1/2}$ and $-500 …
We live in an age where an enormous amount of astrometric, photometric, asteroseismic, and spectroscopic data of Milky Way stars are being acquired, many orders of magnitude larger than about a decade ago. Thanks to the Gaia astrometric mission and followup ground-based spectroscopic surveys in the next 5-10 years about 10-20 Million stars will have accurate 6D kinematics and chemical composition measurements. KEPLER-2, PLATO, and TESS will provide asteroseismic ages for a good fraction of those. In this article we outline some outstanding problems concerning the formation and evolution of the…
We investigate the vertical metallicity gradients of five mono-age stellar populations between 0 and 11 Gyr for a sample of 18 435 dwarf stars selected from the cross-matched Tycho-Gaia Astrometric Solution (TGAS) and RAdial Velocity Experiment (RAVE) Data Release 5. We find a correlation between the vertical metallicity gradients and age, with no vertical metallicity gradient in the youngest population and an increasingly steeper negative vertical metallicity gradient for the older stellar populations. The metallicity at disc plane remains almost constant between 2 and 8 Gyr, and it becomes s…
Parallaxes measured by the Gaia mission have huge significance for astronomy, but parallaxes in Gaia DR2 are known to have systematic errors that depend on the source position and other quantities. We use the abundant information in faint Milky Way stars, along with the GOG simulation of the Gaia catalog, to probe the spatial dependence of Gaia DR2 parallax systematic errors in an empirical way. The parallax signal, concentrated in thick disk turnoff stars with magnitude G ~ 17, is sufficient to construct maps of the parallax systematic error over the majority of the sky. These maps show a loc…
Evidence for multiple crossings and stripping of Gaia-Enceladus/Sausage across the Milky Way
INAF - Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所阿切尔西天文台）；Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze（佛罗伦萨大学物理与天文学系）；Alma Mater Studiorum, Università di Bologna（博洛尼亚大学）；INAF, Osservatorio di Astrofisica e Scienza dello Spazio（意大利国家天体物理研究所空间科学天文台）；INAF - Padova Observatory（意大利国家天体物理研究所帕多瓦天文台）
We apply a statistical deconvolution of the parallax errors based on Lucy's inversion method (LIM) to the Gaia-DR3 sources to measure their three dimensional velocity components in the range of Galactocentric distances $R$ between 8 kpc and 30 kpc with their corresponding errors and root mean square values. We find results that are consistent with those obtained by applying LIM to the Gaia-DR2 sources, and we conclude that the method gives convergent and more accurate results by improving the statistics of the data-set and lowering observational errors. The kinematic maps reconstructed with LI…
Open clusters are convenient probes of the structure and history of the Galactic disk. They are also fundamental to stellar evolution studies. The second Gaia data release contains precise astrometry at the sub-milliarcsecond level and homogeneous photometry at the mmag level, that can be used to characterise a large number of clusters over the entire sky. In this study we aim to a establish list of members and derive mean parameters, in particular distances, for as many clusters as possible, making use of Gaia data alone. We compile a list of thousands of known or putative clusters from the l…
The length and pattern speed of the Milky Way bar are still controversial. Photometric and spectroscopic surveys of the inner Galaxy, as well as gas kinematics, favour a long and slowly rotating bar, with corotation around a Galactocentric radius of 6 kpc. On the other hand, the existence of the Hercules stream in local velocity space favours a short and fast bar with corotation around 4 kpc. This follows from the fact that the Hercules stream looks like a typical signature of the outer Lindblad resonance of the bar. As we showed recently, reconciling this local stream with a slow bar would ne…
From Gaia to GaiaNIR: II. A new view of the Milky Way bar
Lund University（隆德大学）；Universitat de Barcelona (UB)（巴塞罗那大学）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；INAF – Osservatorio Astrofisico di Torino（意大利国家天体物理研究所都灵天文台）；Observatoire Astronomique de Strasbourg, Université de Strasbourg/CNRS（斯特拉斯堡天文台，斯特拉斯堡大学/法国国家科学研究中心）；University of Surrey（萨里大学）
Using action-based distribution function for the dynamical model of the Milky Way we have estimated its total mass and its density profile. Constraints are coming from the globular cluster proper motions from Gaia EDR3, from the rotation curve based on Gaia DR2 data, and from the vertical force data. We use Bayesian Markov chain Monte Carlo method to explore the parameters, for which the globular cluster distribution function and the Galactic potential are fully constrained. Numerical simulations are used to study the uncertainties on the potential constraint if considering a possible massive …
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…
We present the results of the kinematic investigations carried out with the use of spatial velocities of red giants and sub-giants containing in the $Gaia$~EDR3 catalogue. The twelve kinematic parameters of the Ogorodnikov--Milne model have been derived for stellar systems with radii 0.5 and 1.0 kpc, located along the direction the Galactic center -- the Sun -- the Galactic anticenter within the range of Galactocentric distances $R$ 0--8--16~kpc. By combining some of the local parameters the information related to the Galaxy as a whole has been received in the distance range 4--12~kpc, in part…
Based on Gaia Early Data Release 3 (EDR3), we estimate the proper motions for 46 dwarf spheroidal galaxies (dSphs) of the Milky Way. The uncertainties in proper motions, determined by combining both statistical and systematic errors, are smaller by a factor 2.5, when compared with Gaia Data Release 2. We have derived orbits in four Milky Way potential models that are consistent with the MW rotation curve, with total mass ranging from $2.8\times10^{11}$ $M_{\odot}$ to $15\times10^{11}$ $M_{\odot}$. Although the type of orbit (ellipse or hyperbola) are very dependent on the potential model, the …
We construct the first comprehensive dynamical model for the high-quality subset of stellar kinematics of the Milky Way disc, with full 6D phase-space coordinates, provided by the Gaia Data Release 2. We adopt an axisymmetric approximation and use an updated Jeans Anisotropic Modelling (JAM) method, which allows for a generic shape and radial orientation of the velocity ellipsoid, as indicated by the Gaia data, to fit the mean velocities and all three components of the intrinsic velocity dispersion tensor. The Milky Way is the first galaxy for which all intrinsic phase space coordinates are av…
