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.
We define new potential-density pairs and examine the impact of the potential flattening on the vertical velocity ellipsoid tilt, $δ$. By means of numerical integrations and analytical calculations, we estimate $δ$ in a variety of galactic potentials. We show that at 1 kpc above the Galactic plane at the solar radius, $δ$ can differ by 5 degrees, depending on whether the dark matter halo is flat or spherical. This result excludes the possibility of an extremely flattened Galactic dark halo.
Accurate determination of the local dark matter density is important for understanding the nature and distribution of dark matter in the universe. This requires that the local velocity distribution is characterised correctly. Here, we present a kinematic study of 16,276 SEGUE G-type dwarf stars in the solar neighbourhood, with which we determine the shape of the velocity ellipsoid in the meridional plane. We separate our G-dwarf stars based on their [Fe/H] and [alpha/Fe] abundances and infer the local velocity distribution independently for each sub-sample using a maximum-likelihood method tha…
The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7,224,631 stars with full six-dimensional phase space information. Bayesian distances of these stars are available from the catalogue of Schönrich et al. (2019). We exploit this to map out the behaviour of the velocity ellipsoid within 5 kpc of the Sun. We find that the tilt of the disc-dominated RVS sample is accurately described by the relation $α= (0.952 \pm 0.007)\arctan (|z|/R)$, where ($R,z$) are cylindrical polar coordinates. This corresponds to velocity ellipsoids close to spherical alignment (for which the normalising co…
The structure and evolution of the stellar velocity ellipsoid plays an important role in shaping galaxies undergoing bar driven secular evolution and the eventual formation of a boxy/peanut bulge such as present in the Milky Way. Using collisionless N-body simulations, we show that during the formation of such a boxy/peanut bulge, the meridional shear stress of stars, which can be measured by the meridional tilt of the velocity ellipsoid, reaches a characteristic peak in its time evolution. It is shown that the onset of a bar buckling instability is closely connected to the maximum meridional …
A sample of roughly 1,800 halo subdwarf stars with radial velocities and proper motions is assembled, using the repeated multi-band Sloan Digital Sky Survey photometric measurements in Stripe 82. Our sample of halo subdwarfs is extracted via a reduced proper motion diagram and distances are obtained using photometric parallaxes, thus giving full phase space information. The tilt of the velocity ellipsoid with respect to the spherical polar coordinate system is computed and found to be consistent with zero for two of the three tilt angles, and very small for the third. We prove that if the inne…
We study the dynamical properties of halo stars located in the Solar Neighbourhood. Our goal is to explore how the properties of the halo depend on the selection criteria used for defining a sample of halo stars. Once this is understood we proceed to measure the shape and orientation of the halo's velocity ellipsoid and we use this information to put constraints on the gravitational potential of the Galaxy. We use the recently released Gaia DR1 catalogue cross-matched to the RAVE dataset for our analysis. We develop a dynamical criterion based on the distribution function of stars in various G…
The velocity distribution of stars is a sensitive probe of the gravitational potential of the Galaxy, and hence of its dark matter distribution. In particular, the shape of the dark halo (e.g. spherical, oblate, or prolate) determines velocity correlations, and different halo geometries are expected to result in measurable differences. Here we explore and interpret the correlations in the $(v_R, v_z)$-velocity distribution as a function of position in the Milky Way. We selected a high-quality sample of stars from the Gaia DR2 catalogue and characterised the orientation of the velocity distribu…
The stellar velocity ellipsoid of the solar neighbour is re-examined using intermediate-old mono-abundances stellar groups with high quality chemistry data together with parallaxes and proper motions from Gaia DR1. We find the average velocity dispersion values for the three space velocity components for the thin and thick disc of (σ_{U},σ_{V},σ_{W})_{thin} = (33 \pm 4, 28 \pm 2, 23 \pm 2) and (σ_{U},σ_{V},σ_{W})_{thick} = (57 \pm 6, 38 \pm 5, 37 \pm 4) km s^{-1}, respectively. The mean values of the ratio between the semi-axes of the velocity ellipsoid for the thin disc are found to be, σ_{V}…
We examine the vertical structure of Galactic disk kinematics over a Galactocentric radial distance range of $R=5-15$ $\rm{kpc}$ and up to $3$ $\rm{kpc}$ away from the Galactic plane, using the K-type giants surveyed by LAMOST. Based on robust measurements of three-dimensional velocity moments, a wobbly disk is detected in a phenomenological sense. An outflow dominates the radial motion of the inner disk, while in the outer disk there exist alternate outward and inward flows. The vertical bulk velocities is a combination of breathing and bending modes. A contraction-like breathing mode with am…
We analyse high spatial resolution near infra-red (NIR) imaging of NGC6384, a Milky Way like galaxy, using ARGOS commissioning data at the Large Binocular Telescope (LBT). ARGOS provides a stable PSF$_{\rm FWHM}\!=\!0.2"\!-\!0.3"$ AO correction of the ground layer across the LUCI2 NIR camera $4'\!\times4'$ field by using six laser guide stars (three per telescope) and a natural guide star for tip-tilt sensing and guiding. Enabled by this high spatial resolution we analyse the structure of the nuclear star cluster (NSC) and the central kiloparsec of NGC6384. We find via 2D modelling that the NS…
We look for observational signatures that could discriminate between Newtonian and modified Newtonian (MOND) dynamics in the Milky Way, in view of the advent of large astrometric and spectroscopic surveys. Indeed, a typical signature of MOND is an apparent disk of "phantom" dark matter, which is uniquely correlated with the visible disk-density distribution. Due to this phantom dark disk, Newtonian models with a spherical halo have different signatures from MOND models close to the Galactic plane. The models can thus be differentiated by measuring dynamically (within Newtonian dynamics) the di…
From a sample of 15651 RR Lyrae with accurate proper motions in Gaia DR2, we measure the azimuthally averaged kinematics of the inner stellar halo between 1.5 kpc and 20 kpc from the Galactic centre. We find that their kinematics are strongly radially anisotropic, and their velocity ellipsoid nearly spherically aligned over this volume. Only in the inner regions $\lesssim$ 5 kpc does the anisotropy significantly fall (but still with $β>$ 0.25) and the velocity ellipsoid tilt towards cylindrical alignment. In the inner regions, our sample of halo stars rotates at up to 50 km s$^{-1}$, which may…
We study Milky Way kinematics using a sample of 18.8 million main-sequence stars with r<20 and proper-motion measurements derived from SDSS and POSS astrometry, including ~170,000 stars with radial-velocity measurements from the SDSS spectroscopic survey. Distances to stars are determined using a photometric parallax relation, covering a distance range from ~100 pc to 10 kpc over a quarter of the sky at high Galactic latitudes (|b|>20 degrees). We find that in the region defined by 1 kpc <Z< 5 kpc and 3 kpc <R< 13 kpc, the rotational velocity for disk stars smoothly decreases, and all three co…
The variation of the kinematical properties of the Galactic thick disk with Galactic height Z are studied by means of 412 red giants observed in the direction of the south Galactic pole up to 4.5 kpc from the plane. We confirm the non-null mean radial motion toward the Galactic anticenter found by other authors, but we find that it changes sign at |Z|=3 kpc, and the proposed inward motion of the LSR alone cannot explain these observations. The rotational velocity decreases with |Z| by -30 km/s/kpc, but the data are better represented by a power-law with index 1.25, similar to that proposed fro…
We exploit the first \gaia data release to study the properties of the Galactic stellar halo as traced by RR Lyrae. We demonstrate that it is possible to select a pure sample of RR Lyrae using only photometric information available in the Gaia+2MASS catalogue. The final sample contains about 21600 RR Lyrae covering an unprecedented fraction ($\sim60\%$) of the volume of the Galactic inner halo ($\text{R}<28$ kpc). We study the morphology of the stellar halo by analysing the RR Lyrae distribution with parametric and non-parametric techniques. Taking advantage of the uniform all-sky coverage, we…
We study the velocity distribution of Milky Way disk stars in a kiloparsec-sized region around the Sun, based on ~ 2 million M-type stars from DR7 of SDSS, which have newly re-calibrated absolute proper motions from combining SDSS positions with the USNO-B catalogue. We estimate photometric distances to all stars, accurate to ~ 20 %, and combine them with the proper motions to derive tangential velocities for this kinematically unbiased sample of stars. Based on a statistical de-projection method we then derive the vertical profiles (to heights of Z = 800 pc above the disk plane) for the first…
The self-consistent vertical density distribution in a thin, isothermal disc is typically given by a sech^2 law, as shown in the classic work by Spitzer (1942). This is obtained assuming that the radial and vertical motions are decoupled and only the vertical term is used in the Poisson equation. We argue that in the region of low density as in the outer disc this treatment is no longer valid. We develop a general, complete model that includes both radial and vertical terms in the Poisson equation and write these in terms of the full radial and vertical Jeans equations which take account of th…
We have investigated the distributions of stellar azimuthal and radial velocity components $V_Φ$ and $V_{R}$ in the vertical position-velocity plane $Z$-$V_{Z}$ across the Galactic disc of $6.34 \lesssim R \lesssim 12.34$\,kpc and $|Φ| \lesssim 7.5^{\circ}$ using a Gaia and Gaia-LAMOST sample of stars. As found in previous works, the distributions exhibit significant spiral patterns. The $V_{R}$ distributions also show clear quadrupole patterns, which are the consequence of the well-known tilt of the velocity ellipsoid. The observed spiral and quadrupole patterns in the phase space plane vary …
We present the age-velocity dispersion relation (AVR) in three dimensions in the solar neighbourhood using 3,564 commonly observed sub-giant/red-giant branch stars selected from LAMOST, which gives the age and radial velocity, and \emph{Gaia}, which measures the distance and proper motion. The stars are separated into metal-poor (${\rm [Fe/H]<-0.2}$\,dex and metal-rich (${\rm [Fe/H]>-0.2}$\,dex) groups, so that the metal-rich stars are mostly $α$-poor, while the metal-poor group are mostly contributed by $α$-enhanced stars. Thus, the old and metal-poor stars likely belong to the chemically def…
We analyze the 3D kinematics of a sample of $\sim 4400$ red clump stars ranging between 5 and 10 kpc from the Galactic center and up to 3 kpc from the Galactic plane. This sample is representative for the metal-rich ([Fe/H] = -0.6 to 0.5) thick disk. Absolute proper motions are from the fourth release of the Southern Proper Motion Program, and radial velocities from the second release of the Radial Velocity Experiment. The derived kinematical properties of the thick disk include: the rotational velocity gradient $\partial V_θ / \partial z = -25.2 \pm 2.1$ km s$^{-1}$ kpc$^{-1}$, velocity dispe…
We use the Stripe 82 proper motion catalogue of Bramich et al. (2008) to study the kinematics of Galactic disk stars in the solar neighborhood. We select samples of dwarf stars with reliable spectra and proper motions. They have cylindrical polar radius between 7 < R < 9 kpc, heights from the Galactic plane satisfying z < 2 kpc and span a range of metallicities -1.5 < [Fe/H] < 0. We develop a method for calculating and correcting for the halo contamination in our sample using the distribution of rotational velocities. Two Gaussians representing disk and halo populations are used to fit the rad…
The precision of the Gaia data offers a unique opportunity to study the internal velocity field of star clusters. We develop and validate a forward-modelling method for the internal motions of stars in a cluster. The model allows an anisotropic velocity dispersion matrix and linear velocity gradient describing rotation and shear, combines radial velocities available for a subset of stars, and accounts for contamination from background sources via a mixture model. We apply the method to Gaia DR2 data of the Hyades cluster and its tidal tails, dividing and comparing the kinematics of stars withi…
We use the second data releases of the ESA Gaia astrometric survey and the high-resolution GALAH spectroscopic survey to analyse the structure of our Galaxy's disc components. With GALAH, we separate the alpha-rich and alpha-poor discs (with respect to Fe), which are superposed in both position and velocity space, and examine their distributions in action space. We study the distribution of stars in the zV_z phase plane, for both V_phi and V_R, and recover the remarkable "phase spiral" discovered by Gaia. We identify the anticipated quadrupole signature in zV_z of a tilted velocity ellipsoid f…
This paper shows how a self-consistent dynamical model can be obtained by fitting the gravitational potential of the Milky Way to the stellar kinematics and densities from Gaia data. Using the Besancon Galaxy Model we derive a potential and the disc stellar distribution functions are computed based on three integrals of motion to model stationary stellar discs. The gravitational potential and the stellar distribution functions are built self-consistently, and then adjusted to be in agreement with the kinematics and the density distributions obtained from Gaia observations. A Markov chain Monte…
