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We analyze four epochs of Hubble Space Telescope imaging over 18 yr for the Draco dwarf spheroidal galaxy. We measure precise proper motions for hundreds of stars and combine these with existing line-of-sight (LOS) velocities. This provides the first radially resolved 3D velocity dispersion profiles for any dwarf galaxy. These constrain the intrinsic velocity anisotropy and resolve the mass–anisotropy degeneracy. We solve the Jeans equations in oblate axisymmetric geometry to infer the mass profile. We find the velocity dispersion to be radially anisotropic along the symmetry axis and tangentially anisotropic in the equatorial plane, with a globally averaged value β B ¯ = − 0.20 − 0.53 + 0.28 , (where 1 – β B ≡ 〈 v tan 2 〉 / 〈 v rad 2 〉 in 3D). The logarithmic dark matter (DM) density slope over the observed radial range, Γdark, is − 0.83 − 0.37 + 0.32 , consistent with the inner cusp predicted in ΛCDM cosmology. As expected given Draco's low mass and ancient star formation history, it does not appear to have been dissolved by baryonic processes. We rule out cores larger than 487, 717, and 942 pc at 1 σ, 2 σ, and 3 σ confidence, respectively, thus imposing important constraints on the self-interacting DM cross section. Spherical models yield biased estimates for both the velocity anisotropy and the inferred slope. The circular velocity at our outermost data point (900 pc) is 24.19 − 2.97 + 6.31 km s − 1 . We infer a dynamical distance of 75.37 − 4.00 + 4.73 kpc and show that Draco has a modest LOS rotation, with v / σ = 0.22 ± 0.09 . Our results provide a new stringent test of the so-called "cusp–core" problem that can be readily extended to other dwarfs. [ABSTRACT FROM AUTHOR]

We estimate the mass of the Large Magellanic Cloud (LMC) using the kinematics of 30 LMC globular clusters (GCs). We combine proper motions measured with the Hubble Space Telescope, Gaia, or a combination of the two, from a recent study by Bennet et al. with literature line-of-sight velocities (LOSVs) to give three components of motion. With these, we derive a 3D velocity dispersion anisotropy β = − 0.72 − 1.07 + 0.62 , consistent with the GCs forming a flattened system with significant azimuthal motion. We then apply a tracer mass estimator and measure an enclosed mass M (< 13.2 kpc) = 2.66 − 0.36 + 0.42 × 10 10 M ⊙. This is broadly consistent with results from previous studies of the LOSVs of GCs and other luminous tracers. Assuming a cosmologically constrained Navarro–Frenk–White distribution for the dark matter, this implies a virial mass M virial = 1.80 − 0.54 + 1.05 × 10 11 M ⊙. Despite being an extrapolation by almost an order of magnitude in radius, this result is consistent with published estimates from other methods that are directly sensitive to the LMC's total mass. Our results support the conclusion that the LMC is approximately 17 − 6 + 10 % of the Milky Way's mass, making it a significant contributor to the Local Group potential. [ABSTRACT FROM AUTHOR]

We present the results of a spectroscopic survey of the outskirts of four globular – 1261, NGC 4590, NGC 1904, and NGC 1851 – covering targets within 1° from the cluster centres, with 2dF/AAOmega on the Anglo-Australian Telescope (AAT) and FLAMES on the very large telescope (VLT). We extracted chemo-dynamical information for individual stars, from which we estimated the velocity dispersion profile and the rotation of each cluster. The observations are compared to direct N -body simulations and appropriate limepy / spes models for each cluster to interpret the results. In NGC 1851, the detected internal rotation agrees with existing literature, and NGC  1261 shows some rotation signal beyond the truncation radius, likely coming from the escaped stars. We find that the dispersion profiles for both the observations and the simulations for NGC 1261, NGC 1851, and NGC 1904 do not decrease as the limepy / spes models predict beyond the truncation radius, where the N -body simulations show that escaped stars dominate; the dispersion profile of NGC 4590 follows the predictions of the limepy / spes models, though the data do not effectively extend beyond the truncation radius. The increasing/flat dispersion profiles in the outskirts of NGC 1261, NGC 1851, and NGC 1904, are reproduced by the simulations. Hence, the increasing/flat dispersion profiles of the clusters in question can be explained by the tidal interaction with the galaxy without introducing dark matter. [ABSTRACT FROM AUTHOR]

We construct a suite of discrete chemo-dynamical models of the giant elliptical galaxy NGC 5846. These models are a powerful tool to constrain both the mass distribution and internal dynamics of multiple tracer populations. We use Jeans models to simultaneously fit stellar kinematics within the effective radius Re, planetary nebula (PN) radial velocities out to 3 Re, and globular cluster (GC) radial velocities and colours out to 6 Re. The best-fitting model is a cored dark matter halo which contributes ∼10 per cent of the total mass within 1 Re, and 67 per cent ± 10 per cent within 6 Re, although a cusped dark matter halo is also acceptable. The red GCs exhibit mild rotation with vmax/σ0 ∼ 0.3 in the region R > Re, aligned with but counter-rotating to the stars in the inner parts, while the blue GCs and PNe kinematics are consistent with no rotation. The red GCs are tangentially anisotropic, the blue GCs are mildly radially anisotropic, and the PNe vary from radially to tangentially anisotropic from the inner to the outer region. This is confirmed by general made-to-measure models. The tangential anisotropy of the red GCs in the inner regions could stem from the preferential destruction of red GCs on more radial orbits, while their outer tangential anisotropy – similar to the PNe in this region – has no good explanation. The mild radial anisotropy of the blue GCs is consistent with an accretion scenario. [ABSTRACT FROM AUTHOR]

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 characterized correctly. Here, we present a kinematic study of 16,276 SDSS/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 [α/Fe] abundances and infer the local velocity distribution independently for each sub-sample using a maximum-likelihood method that accounts for possible contaminants. We show by constructing vertical Jeans models that the different sub-samples yield consistent results only when we allow the velocity ellipsoid in the disc to be tilted, demonstrating that the common assumption of decoupled radial and vertical motions in the disc is incorrect. Further, we obtain that the tilt of the velocity ellipsoid is consistent among the different sub-samples. We find that increase in the tilt with height is well described by the relation αtilt = (-0.90 ± 0.04) arctan(|z|/R⊙) - (0.01 ± 0.005), which is close to alignment with the spherical coordinate system and hence a velocity ellipsoid pointing to the Galactic Centre. We also confirm earlier findings that the sub-samples behave almost isothermally with both radial and vertical velocity dispersion approximately constant with height. We conclude that the coupling between radial and vertical motion captured in the velocity ellipsoid tilt cannot be ignored when considering dynamical models of the solar neighbourhood. In a subsequent paper, we will develop a new modelling scheme informed by these results and make an improved determination of the local dark matter density. [ABSTRACT FROM AUTHOR]

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. The estimators all assume that the tracer population has a scale-free density and moves in a scale-free potential in the region of interest. The circumstances under which the boundary terms can be discarded and the estimator converges are derived. 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 Galaxy, the satellite sample consists of 26 galaxies with line-of-sight velocities. We find that the mass of the Milky Way within 300 kpc is assuming velocity isotropy. However, the mass estimate is sensitive to the assumed anisotropy and could plausibly lie between and , if anisotropies implied by simulations or by the observations are used. Incorporating the proper motions of six Milky Way satellites into the data set, we find . The range here if plausible anisotropies are used is still broader, from to . Note that our error bars only incorporate the statistical uncertainty. There are much greater uncertainties induced by velocity anisotropy and by selection of satellite members. For M31, there are 23 satellite galaxies with measured line-of-sight velocities, but only M33 and IC 10 have proper motions. We use the line-of-sight velocities and distances of the satellite galaxies to estimate the mass of M31 within 300 kpc as assuming isotropy. There is only a modest dependence on anisotropy, with the mass varying between and . Incorporating the proper motion data set does not change the results significantly. Given the uncertainties, we conclude that the satellite data by themselves yield no reliable insights into which of the two galaxies is actually the more massive. Leo I has long been known to dominate mass estimates for the Milky Way due to its substantial distance and line-of-sight velocity. We find that And XII and And XIV similarly dominate the estimated mass of M31. As such, we repeat the calculations without these galaxies, in case they are not bound – although on the balance of the evidence, we favour their inclusion in mass calculations. [ABSTRACT FROM AUTHOR]