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We present the results of a spectroscopic survey of the outskirts of 4 globular clusters -- NGC 1261, NGC 4590, NGC 1904, and NGC 1851 -- covering targets within 1 degree 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 {\sc limepy}/{\sc 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 {\sc limepy}/{\sc 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 {\sc limepy}/{\sc 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., Comment: 17 pages, 10 figures. Accepted by MNRAS. Comments are welcome

We have determined bulk proper motions (PMs) for 31 LMC GCs from Gaia eDR3 and Hubble Space Telescope data using multiple independent analysis techniques. Combined with literature values for distances, line-of-sight velocities and existing bulk PMs, we extract full 6D phase-space information for 32 clusters, allowing us to examine the kinematics of the LMC GC system in detail. Except for two GCs (NGC 2159 and NGC 2210) for which high velocities suggest they are not long-term members of the LMC system, the data are consistent with a flattened configuration that rotates like the stellar disk. The one-dimensional velocity dispersions are of order 30 km/s, similar to that of old stellar populations in the LMC disk. Similar to the case for Milky Way disk clusters, the velocity anisotropy is such that the dispersion is smallest in the azimuthal direction; however, alternative anisotropies cannot be ruled out due to distance uncertainties. The data are consistent with a single multi-dimensional Gaussian velocity distribution. Given the non-collisional nature of the LMC disk, this suggests that most, if not all, of the LMC GCs are formed by a single formation mechanism in the stellar disk, despite a significant spread in age and metallicity. Any accreted halo GC population is absent or far smaller in the LMC compared to the Milky Way., Comment: Accepted by ApJ, 19 pages, 5 figures, 4 tables

We present GaiaHub, a publicly available tool that combines $Gaia$ measurements with $Hubble$ $Space$ $Telescope$ ($HST$) archival images to derive proper motions (PMs). It increases the scientific impact of both observatories beyond their individual capabilities. $Gaia$ provides PMs across the whole sky, but the limited mirror size and time baseline restrict the best PM performance to relatively bright stars. $HST$ can measure accurate PMs for much fainter stars over a small field, but this requires two epochs of observation which are not always available. GaiaHub yields considerably improved PM accuracy compared to $Gaia$-only measurements, especially for faint sources $(G \gtrsim 18)$, requiring only a single epoch of $HST$ data observed more than $\sim 7$ years ago (before 2012). This provides considerable scientific value especially for dynamical studies of stellar systems or structures in and beyond the Milky Way (MW) halo, for which the member stars are generally faint. To illustrate the capabilities and demonstrate the accuracy of GaiaHub, we apply it to samples of MW globular clusters (GCs) and classical dwarf spheroidal (dSph) satellite galaxies. This allows us, e.g., to measure the velocity dispersions in the plane of the sky for objects out to and beyond $\sim 100$ kpc. We find, on average, mild radial velocity anisotropy in GCs, consistent with existing results for more nearby samples. We observe a correlation between the internal kinematics of the clusters and their ellipticity, with more isotropic clusters being, on average, more round. Our results also support previous findings that Draco and Sculptor dSph galaxies appear to be radially anisotropic systems., Comment: 24 pages, 18 figures. Accepted for publication in ApJ

We present comprehensive multi-component dynamical models of M54 (NGC6715), the nuclear star cluster of the Sagittarius dwarf galaxy (Sgr), which is undergoing a tidal disruption in the Milky Way halo. Previous papers in the series used a large MUSE mosaic data set to identify multiple stellar populations in the system and study their kinematic differences. Here we use Jeans-based dynamical models that fit the population properties (mean age and metallicity), spatial distributions, and kinematics simultaneously. They provide a solid physical explanation to our previous findings. The population-dynamical models deliver a comprehensive view of the whole system, and allow us to disentangle the different stellar populations. We explore their dynamical interplay and confirm our previous findings about the build-up of Sgr's nuclear cluster via contributions from globular cluster stars, Sgr inner field stars, and in-situ star formation. We explore various parameterisations of the gravitational potential and show the importance of a radially varying mass-to-light ratio for the proper treatment of the mass profile. We find a total dynamical mass within M54's tidal radius ($\sim75$ pc) of $1.60\pm0.07\times10^6$ Msun in excellent agreement with $N$-body simulations. The metal-poor globular cluster stars contribute about $65\%$ of the total mass or $1.04\pm0.05\times10^6$ Msun. The metal-rich stars can be further divided into young and intermediate age populations that contribute $0.32\pm0.02\times10^6$ Msun ($20\%$) and $0.24\pm0.02\times10^6$ Msun ($15\%$), respectively. Our population-dynamical models successfully distinguish the different stellar populations in Sgr's nucleus because of their different spatial distributions, ages, metallicities, and kinematic features., Comment: Accepted for publication in ApJ

Nuclear star clusters hosted by dwarf galaxies exhibit similar characteristics to high-mass, metal complex globular clusters. This type of globular clusters could, therefore, be former nuclei from accreted galaxies. M54 resides in the photometric center of the Sagittarius dwarf galaxy, at a distance where resolving stars is possible. M54 offers the opportunity to study a nucleus before the stripping of their host by the tidal field effects of the Milky Way. We use a MUSE data set to perform a detailed analysis of over 6600 stars. We characterize the stars by metallicity, age, and kinematics, identifying the presence of three stellar populations: a young metal-rich (YMR), an intermediate-age metal-rich (IMR), and an old metal-poor (OMP). The evidence suggests that the OMP population is the result of accretion of globular clusters in the center of the host, while the YMR population was born in-situ in the center of the OMP population.

We examine the degree of energy equipartition in 9 Galactic globular clusters using proper motions measured with the Hubble Space Telescope. For most clusters in the sample, this is the first energy equipartition study ever performed. This study is also the largest of its kind, albeit with only 9 clusters. We begin by rigorously cleaning the catalogues to remove poor-quality measurements and to ensure high signal-to-noise for the study. Using the cleaned catalogues, we investigate how velocity dispersion $\sigma$ changes with stellar mass $m$. We fit two functional forms: the first, a classic power-law of the form $\sigma \propto m^{-\eta}$ where $\eta$ is the degree of energy equipartition, and the second from Bianchini et al. (2016) parameterised by an equipartition mass $m_{eq}$ where $\eta$ changes with stellar mass. We find that both functions fit well but cannot distinguish with statistical significance which function provides the best fit. All clusters exhibit varying degrees of partial equipartition; no cluster is at or near full equipartition. We search for correlations of $\eta$ and $m_{eq}$ with various cluster properties. The most significant correlation is observed with the number of core or median relaxation times ($N_{core}$ or $N_{half}$) the cluster has experienced. Finally, we determine the radial equipartition profile for each cluster, that is, how the degree of equipartition changes with projected distance from the cluster centre. We do not detect statistically significant trends in the degree of equipartition with radius. Overall, our observational findings are in broad agreement with theoretical predictions from N-body models published in recent years., Comment: 26 pages, 16 figures, 2 tables, accepted for publication in ApJ

We present an astrometric study of the proper motions (PMs) in the core of the globular cluster NGC 6441. The core of this cluster has a high density and observations with current instrumentation are very challenging. We combine ground-based, high-angular-resolution NACO@VLT images with Hubble Space Telescope ACS/HRC data and measure PMs with a temporal baseline of 15 yr for about 1400 stars in the centermost 15 arcseconds of the cluster. We reach a PM precision of $\sim$30 $��$as yr$^{-1}$ for bright, well-measured stars. Our results for the velocity dispersion are in good agreement with other studies and extend already-existing analyses of the stellar kinematics of NGC 6441 to its centermost region never probed before. In the innermost arcsecond of the cluster, we measure a velocity dispersion of (19.1 $\pm$ 2.0) km s$^{-1}$ for evolved stars. Because of its high mass, NGC 6441 is a promising candidate for harbouring an intermediate-mass black hole (IMBH). We combine our measurements with additional data from the literature and compute dynamical models of the cluster. We find an upper limit of $M_{\rm IMBH} < 1.32 \times 10^4\,\textrm{M}_\odot$ but we can neither confirm nor rule out its presence. We also refine the dynamical distance of the cluster to $12.74^{+0.16}_{-0.15}$ kpc. Although the hunt for an IMBH in NGC 6441 is not yet concluded, our results show how future observations with extremely-large telescopes will benefit from the long temporal baseline offered by existing high-angular-resolution data., 16 pages, 12 figures, 2 tables. Accepted for publication in MNRAS

We apply four different mass modelling methods to a suite of publicly available mock data for spherical stellar systems. We focus on the recovery of the density and velocity anisotropy as a function of radius, using either line-of-sight velocity data only, or adding proper motion data. All methods perform well on isotropic and tangentially anisotropic mock data, recovering the density and velocity anisotropy within their 95% confidence intervals over the radial range 0.25 < R/Rhalf < 4, where Rhalf is the half light radius. However, radially-anisotropic mocks are more challenging. For line-of-sight data alone, only methods that use information about the shape of the velocity distribution function are able to break the degeneracy between the density profile and the velocity anisotropy to obtain an unbiased estimate of both. This shape information can be obtained through directly fitting a global phase space distribution function, by using higher order 'Virial Shape Parameters', or by assuming a Gaussian velocity distribution function locally, but projecting it self-consistently along the line of sight. Including proper motion data yields further improvements, and in this case, all methods give a good recovery of both the radial density and velocity anisotropy profiles., 17 pages, 8 figures. Accepted for publication in MNRAS

The authors would like to thank the researchers and engineers who are not coauthors of this paper but who have taken part and have brought their contribution to the proposed missions to ESA successive calls: NEAT (M3), micro-NEAT (S1), and Theia (M4 and M5). An extensive list of supporters for the science objectives is given in [17]. We thank also Arianna Gallo for her contribution in our investigation of the shape of the MilkyWay dark matter halo and Krzysztof A. Rybicki who generated the plots from Fig. 14. We are grateful to the anonymous referee who helped to improve the quality of the paper with his/her remarks. Concerning the funding of our work, we would like to acknowledge the support of many agencies or programs. R.B. acknowledges support from NASA’s Virtual Planetary Laboratory lead team under cooperative agreements NNA13AA93A. A.C.M.C. acknowledges support from CFisUC strategic project (UID/FIS/04564/2019). F.C. acknowledges support by the Swiss National Science Foundation (SNSF) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (COSMICLENS: grant agreement No. 787886). M.F. received support from Polish National Science Centre (NCN) under Grant No. 2017/26/D/ST9/00591. M.F. gratefully acknowledge the support of the Swedish National Space Agency (DNR 65/19, 174/18). D.H. thanks the Swedish National Space Agency (SNSA/Rymdstyrelsen) for their support. A.M. thanks the Portugese Fundac¸ ˜ao para a Ciˆencia e a Tecnologia (FCT) through the Strategic Programme UID/FIS/00099/2019 for CENTRA. P.S. acknowledges support from the Australian Research Council under grant FT190100814. L.W. acknowledges support from the Polish NCN grants: Harmonia No. 2018/06M/ST9/00311 and Daina No. 2017/27/L/ST9/03221. The OATo team acknowledges partial funding by the Italian Space Agency (ASI) under contracts 2014-025-R.1.2015 and 2018-24-HH.0, and by a grant from the Italian Ministry of Foreign Affairs and International Cooperation (ASTRA). A.C. and F.M. acknowledge support by the LabEx FOCUS ANR-11-LABX-0013. The work of C.J., X.L. and J.P. was supported by the Spanish Ministry of Science, Innovation and University (MICIU/FEDER, UE) through grants RTI2018-095076-B-C21, ESP2016-80079-C2-1-R, and the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia ’Mar´ıa de Maeztu’) through grants MDM-2014-0369 and CEX2019-000918-M. A.K.-M., A.A., V.C., P.G., P.G., A.M.A., A.M., M.S. were supported by Fundac¸ ˜ao para a Ciˆencia e a Tecnologia, with grants reference UIDB/00099/ 2020 and SFRH/BSAB/142940/2018 (P.G. only). A.D. and L.O. also acknowledge partial support from the Italian Ministry of Education, University and Research (MIUR) under the Departments of Excellence grant L.232/2016, and from the INFN grant InDark. G.J.W. gratefully acknowledges support of an Emeritus Fellowship from The Leverhulme Trust. EV is supported by Spanish grant PGC2018-101950-B-100. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. Open access funding provided by Istituto Nazionale di Astrofisica within the CRUI-CARE Agreement., Sky survey telescopes and powerful targeted telescopes play complementary roles in astronomy. In order to investigate the nature and characteristics of the motions of very faint objects, a flexibly-pointed instrument capable of high astrometric accuracy is an ideal complement to current astrometric surveys and a unique tool for precision astrophysics. Such a space-based mission will push the frontier of precision astrometry from evidence of Earth-mass habitable worlds around the nearest stars, to distant Milky Way objects, and out to the Local Group of galaxies. As we enter the era of the JamesWebb Space Telescope and the new ground-based, adaptive-optics-enabled giant telescopes, by obtaining these high precision measurements on key objects that Gaia could not reach, a mission that focuses on high precision astrometry science can consolidate our theoretical understanding of the local Universe, enable extrapolation of physical processes to remote redshifts, and derive a much more consistent picture of cosmological evolution and the likely fate of our cosmos. Already several missions have been proposed to address the science case of faint objects in motion using high precision astrometry missions: NEAT proposed for the ESA M3 opportunity, micro-NEAT for the S1 opportunity, and Theia for the M4 and M5 opportunities. Additional new mission configurations adapted with technological innovations could be envisioned to pursue accurate measurements of these extremely small motions. The goal of this White Paper is to address the fundamental science questions that are at stake when we focus on the motions of faint sky objects and to briefly review instrumentation and mission profiles., NASA’s Virtual Planetary Laboratory NNA13AA93A, CFisUC strategic project (UID/FIS/04564/2019), Swiss National Science Foundation (SNSF), European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (COSMICLENS: grant agreement No. 787886), Polish National Science Centre (NCN) under Grant No. 2017/26/D/ST9/00591, Swedish National Space Agency (DNR 65/19, 174/18), Swedish National Space Agency (SNSA/Rymdstyrelsen), Portugese Fundacão para a Ciência e a Tecnologia (FCT) through the Strategic Programme UID/FIS/00099/2019 for CENTRA, Australian Research Council under grant FT190100814, Polish NCN grants: Harmonia No. 2018/06M/ST9/00311 and Daina No. 2017/27/L/ST9/03221, Italian Space Agency (ASI) under contracts 2014-025-R.1.2015 and 2018-24-HH.0, Italian Ministry of Foreign Affairs and International Cooperation (ASTRA), LabEx FOCUS ANR-11-LABX-0013, Spanish Ministry of Science, Innovation and University (MICIU/FEDER, UE) through grants RTI2018-095076-B-C21, ESP2016-80079-C2-1-R, Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia ’Mar´ıa de Maeztu’) through grants MDM-2014-0369 and CEX2019-000918-M, Fundacão para a Ciência e a Tecnologia, with grants reference UIDB/00099/ 2020 and SFRH/BSAB/142940/2018 (P.G. only), Italian Ministry of Education, University and Research (MIUR) under the Departments of Excellence grant L.232/2016, and from the INFN grant InDark, Emeritus Fellowship from The Leverhulme Trust, Spanish grant PGC2018-101950-B-100, Istituto Nazionale di Astrofisica within the CRUI-CARE Agreement

We present an analysis of the kinematics of 14 satellites of the Milky Way (MW). We use proper motions (PMs) from the $Gaia$ Early Data Release 3 (EDR3) and line-of-sight velocities ($v_{\mathrm{los}}$) available in the literature to derive the systemic 3D motion of these systems. For six of them, namely the Carina, Draco, Fornax, Sculptor, Sextans, and Ursa Minor dwarf spheroidal galaxies (dSph), we study the internal kinematics projecting the stellar PMs into radial, $V_R$ (expansion/contraction), and tangential, $V_T$ (rotation), velocity components with respect to the centre of mass. We find significant rotation in the Carina ($|V_T| = 9.6 \pm 4.5 \ {\rm{km \ s^{-1}}}\>$), Fornax ($|V_T| = 2.8 \pm 1.3 \ {\rm{km \ s^{-1}}}\>$), and Sculptor ($|V_T| = 3.0 \pm 1.0 \ {\rm{km \ s^{-1}}}\>$) dSphs. Besides the Sagittarius dSph, these are the first measurements of internal rotation in the plane of the sky in the MW's classical dSphs. All galaxies except Carina show $|V_T| / ��_v < 1$. We find that slower rotators tend to show, on average, larger sky-projected ellipticity (as expected for a sample with random viewing angles) and are located at smaller Galactocentric distances (as expected for tidal stirring scenarios in which rotation is transformed into random motions as satellites sink into the parent halo). However, these trends are small and not statistically significant, indicating that rotation has not played a dominant role in shaping the 3D structure of these galaxies. Either tidal stirring had a weak impact on the evolution of these systems or it perturbed them with similar efficiency regardless of their current Galactocentric distance., 12 pages, 5 figures, 3 tables. Accepted for publication in MNRAS

The Sagittarius dwarf spheroidal galaxy (Sgr dSph) is in an advanced stage of disruption but still hosts its nuclear star cluster (NSC), M54, at its center. In this paper, we present a detailed kinematic characterization of the three stellar populations present in M54: young metal-rich (YMR); intermediate-age metal-rich (IMR); and old metal-poor (OMP), based on the spectra of $\sim6500$ individual M54 member stars extracted from a large MUSE/VLT dataset. We find that the OMP population is slightly flattened with a low amount of rotation ($\sim0.8$ km s$^{-1}$) and with a velocity dispersion that follows a Plummer profile. The YMR population displays a high amount of rotation ($\sim5$ km s$^{-1}$) and a high degree of flattening, with a lower and flat velocity dispersion profile. The IMR population shows a high but flat velocity dispersion profile, with some degree of rotation ($\sim2$ km s$^{-1}$). We complement our MUSE data with information from \textit{Gaia DR2} and confirm that the stars from the OMP and YMR populations are comoving in 3D space, suggesting that they are dynamically bound. While dynamical evolutionary effects (e.g. energy equipartition) are able to explain the differences in velocity dispersion between the stellar populations, the strong differences in rotation indicate different formation paths for the populations, as supported by an $N$-body simulation tailored to emulate the YMR-OMP system. This study provides additional evidence for the M54 formation scenario proposed in our previous work, where this NSC formed via GC accretion (OMP) and in situ formation from gas accretion in a rotationally supported disc (YMR)., 21 Pages, 10 figures. Accepted for publication by ApJ

We present intermediate-resolution (R$\sim$1000) spectra in the $\sim$3500-10,000 A range of 14 globular clusters in the magellanic irregular galaxy NGC 4449 acquired with the Multi Object Double Spectrograph on the Large Binocular Telescope. We derived Lick indices in the optical and the CaII-triplet index in the near-infrared in order to infer the clusters' stellar population properties. The inferred cluster ages are typically older than $\sim$9 Gyr, although ages are derived with large uncertainties. The clusters exhibit intermediate metallicities, in the range $-1.2\lesssim$[Fe/H]$\lesssim-0.7$, and typically sub-solar [$\alpha/Fe$] ratios, with a peak at $\sim-0.4$. These properties suggest that i) during the first few Gyrs NGC 4449 formed stars slowly and inefficiently, with galactic winds having possibly contributed to the expulsion of the $\alpha$-elements, and ii) globular clusters in NGC 4449 formed relatively "late", from a medium already enriched in the products of type Ia supernovae. The majority of clusters appear also under-abundant in CN compared to Milky Way halo globular clusters, perhaps because of the lack of a conspicuous N-enriched, second-generation of stars like that observed in Galactic globular clusters. Using the cluster velocities, we infer the dynamical mass of NGC 4449 inside 2.88 kpc to be M($, Comment: Accepted for publication in MNRAS; corrected typo in author list

The globular cluster (GC) system of the Milky Way (MW) provides important information on the MW’s present structure and past evolution. Full 3d motions, accessed through proper motions (PMs), are required to calculate accurate orbits of GCs in the MW halo. We present our HST program to create a PM database for 20 halo GCs. We demonstrate how the observed PMs of individual GCs can be used to study their origins, and we also describe how the PM measurements of our entire targets can be used to constrain the anisotropy profile. Finally, we describe how our PM results can be used for Gaia as an external check, and discuss prospects of PM measurements with HST and Gaia in the coming years.

We combine MUSE spectroscopy and Hubble Space Telescope ultraviolet (UV) photometry to perform a study of the chemistry and dynamics of the Galactic globular cluster Messier 80 (M80, NGC 6093). Previous studies have revealed three stellar populations that not only vary in their light-element abundances, but also in their radial distributions, with concentration decreasing with increasing nitrogen enrichment. This remarkable trend, which sets M80 apart from the other Galactic globular clusters, points towards a complex formation and evolutionary history. To better understand how M80 formed and evolved, revealing its internal kinematics is key. We find that the most N-enriched population rotates faster than the other two populations at a 2 sigma confidence level. While our data further suggest that the intermediate population shows the least amount of rotation, this trend is rather marginal (1 - 2 sigma). Using axisymmetric Jeans models, we show that these findings can be explained from the radial distributions of the populations if they possess different angular momenta. Our findings suggest that the populations formed with primordial kinematical differences., Comment: Accepted for publication in MNRAS, 13 pages, 7 figures

Using data from Gaia DR2, we study the radial number density profiles of the Galactic globular cluster sample. Proper motions are used for accurate membership selection, especially crucial in the cluster outskirts. Due to the severe crowding in the centres, the Gaia data is supplemented by literature data from HST and surface brightness measurements, where available. This results in 81 clusters with a complete density profile covering the full tidal radius (and beyond) for each cluster. We model the density profiles using a set of single-mass models ranging from King and Wilson models to generalised lowered isothermal limepy models and the recently introduced spes models, which allow for the inclusion of potential escapers. We find that both King and Wilson models are too simple to fully reproduce the density profiles, with King (Wilson) models on average underestimating(overestimating) the radial extent of the clusters. The truncation radii derived from the limepy models are similar to estimates for the Jacobi radii based on the cluster masses and their orbits. We show clear correlations between structural and environmental parameters, as a function of Galactocentric radius and integrated luminosity. Notably, the recovered fraction of potential escapers correlates with cluster pericentre radius, luminosity and cluster concentration. The ratio of half mass over Jacobi radius also correlates with both truncation parameter and PE fraction, showing the effect of Roche lobe filling., 23 pages, 23 figures. Accepted in MNRAS

Globular clusters are collisional systems, meaning that the stars inside them interact on timescales much shorter than the age of the Universe. These frequent interactions transfer energy between stars and set up observable trends that tell the story of a cluster's evolution. This contribution focuses on what we can learn by studying velocity anisotropy and energy equipartition in globular clusters with Hubble Space Telescope proper motions., Comment: 4 pages, 3 figures. To appear in Proceedings IAU Symposium No. 351 "Star Clusters: From the Milky Way to the Early Universe", 2019

As we enter a golden age for studies of internal kinematics and dynamics of Galactic globular clusters (GCs), it is timely to assess the performance of modelling techniques in recovering the mass, mass profile, and other dynamical properties of GCs. Here, we compare different mass-modelling techniques (distribution-function (DF)-based models, Jeans models, and a grid of N-body models) by applying them to mock observations from a star-by-star N-body simulation of the GC M 4 by Heggie. The mocks mimic existing and anticipated data for GCs: surface brightness or number density profiles, local stellar mass functions, line-of-sight velocities, and Hubble Space Telescope- and Gaia-like proper motions. We discuss the successes and limitations of the methods. We find that multimass DF-based models, Jeans, and N-body models provide more accurate mass profiles compared to single-mass DF-based models. We highlight complications in fitting the kinematics in the outskirts due to energetically unbound stars associated with the cluster ("potential escapers", not captured by truncated DF models nor by N-body models of clusters in isolation), which can be avoided with DF-based models including potential escapers, or with Jeans models. We discuss ways to account for mass segregation. For example, three-component DF-based models with freedom in their mass function are a simple alternative to avoid the biases of single-mass models (which systematically underestimate the total mass, half-mass radius, and central density), while more realistic multimass DF-based models with freedom in the remnant content represent a promising avenue to infer the total mass and the mass function of remnants., Comment: 27 pages, 12 figures, MNRAS accepted

We present a catalog of relative proper motions for 368,787 stars in the 30 Doradus region of the Large Magellanic Cloud (LMC), based on a dedicated two-epoch survey with the Hubble Space Telescope (HST) and supplemented with proper motions from our pilot archival study. We demonstrate that a relatively short epoch difference of 3 years is sufficient to reach a $\sim$0.1 mas yr$^{-1}$ level of precision or better. A number of stars have relative proper motions exceeding a 3-sigma error threshold, representing a mixture of Milky Way denizens and 17 potential LMC runaway stars. Based upon 183 VFTS OB-stars with the best proper motions, we conclude that none of them move faster than $\sim$0.3 mas yr$^{-1}$ in each coordinate -- equivalent to $\sim$70 km s$^{-1}$. Among the remaining 351 VFTS stars with less accurate proper motions, only one candidate OB runaway can be identified. We rule out any OB star in our sample moving at a tangential velocity exceeding $\sim$120 km s$^{-1}$. The most significant result of this study is finding 10 stars over wide range of masses, which appear to be ejected from the massive star cluster R136 in the tangential plane to angular distances from $35^{\prime\prime}$ out to $407^{\prime\prime}$, equivalent to 8-98 pc. The tangential velocities of these runaways appear to be correlated with apparent magnitude, indicating a possible dependence on the stellar mass., 45 pages (in referee format), 12 figures, 3 tables. Submitted to AJ. Comments are welcome

We present an improved data-reduction technique to obtain high-precision proper motions (PMs) of globular clusters using Hubble Space Telescope data. The new reduction is superior to the one presented in the first paper of this series for the faintest sources in very crowded fields. We choose the globular cluster NGC 362 as a benchmark to test our new procedures. We measure PMs of 117 450 sources in the field, showing that we are able to obtain a PM precision better than 10 $\mu$as yr$^{-1}$ for bright stars. We make use of this new PM catalog of NGC 362 to study the cluster's internal kinematics. We investigate the velocity-dispersion profiles of the multiple stellar populations hosted by NGC 362 and find new pieces of information on the kinematics of first- and second-generation stars. We analyze the level of energy equipartition of the cluster and find direct evidence for its post-core-collapsed state from kinematic arguments alone. We refine the dynamical mass of the blue stragglers and study possible kinematic differences between blue stragglers formed by collisions and mass transfer. We also measure no significant cluster rotation in the plane of the sky. Finally, we measure the absolute PM of NGC 362 and of the background stars belonging to the Small Magellanic Cloud, finding a good agreement with previous estimates in the literature. We make the PM catalog publicly available., Comment: 27 pages, 19 figures, 4 tables, accepted for publication in ApJ

STScI grants [GO-14118, 14662]; Chilean BASAL Centro de Excelencia en Astrofisica y Tecnologias Afines (CATA) grant [PFB-06/2007]; Centre national d'etudes spatiale (CNES) [0101973]; UTINAM Institute of the Universite de Franche-Comte - Region de Franche-Comte and Institut des Sciences de l'Univers (INSU); European Research Council through the ERC-StG project [716082]; NASA [NAS 5-26555]

We estimate the mass of the Milky Way (MW) within 21.1 kpc using the kinematics of halo globular clusters (GCs) determined by Gaia. The second Gaia data release (DR2) contained a catalogue of absolute proper motions (PMs) for a set of Galactic GCs and satellite galaxies measured using Gaia DR2 data. We select from the catalogue only halo GCs, identifying a total of 34 GCs spanning $2.0 < r < 21.1$ kpc, and use their 3D kinematics to estimate the anisotropy over this range to be $��= 0.46^{+0.15}_{-0.19}$, in good agreement, though slightly lower than, a recent estimate for a sample of halo GCs using HST PM measurements further out in the halo. We then use the Gaia kinematics to estimate the mass of the MW inside the outermost GC to be $M(< 21.1 \mathrm{kpc}) = 0.21^{+0.04}_{-0.03} 10^{12} \mathrm{M_\odot}$, which corresponds to a circular velocity of $v_\mathrm{circ}(21.1 \mathrm{kpc}) = 206^{+19}_{-16}$ km/s. The implied virial mass is $M_\mathrm{virial} = 1.28^{+0.97}_{-0.48} 10^{12} \mathrm{M_\odot}$. The error bars encompass the uncertainties on the anisotropy and on the density profile of the MW dark halo, and the scatter inherent in the mass estimator we use. We get improved estimates when we combine the Gaia and HST samples to provide kinematics for 46 GCs out to 39.5 kpc: $��= 0.52^{+0.11}_{-0.14}$, $M(< 39.5 \mathrm{kpc}) = 0.42^{+0.07}_{-0.06} 10^{12} \mathrm{M_\odot}$, and $M_\mathrm{virial} = 1.54^{+0.75}_{-0.44} 10^{12} \mathrm{M_\odot}$. We show that these results are robust to potential substructure in the halo GC distribution. While a wide range of MW virial masses have been advocated in the literature, from below $10^{12} \mathrm{M_\odot}$ to above $2 \times 10^{12}\mathrm{M_\odot}$, these new data imply that an intermediate mass is most likely., 16 pages, 9 figures, 3 tables, accepted for publication in ApJ (updated to match accepted version)

Line-of-sight kinematic studies indicate that many Galactic globular clusters have a significant degree of internal rotation. However, three-dimensional kinematics from a combination of proper motions and line-of-sight velocities are needed to unveil the role of angular momentum in the formation and evolution of these old stellar systems. Here we present the first quantitative study of internal rotation on the plane-of-the-sky for a large sample of globular clusters using proper motions from Gaia DR2. We detect signatures of rotation in the tangential component of proper motions for 11 out of 51 clusters at a $>$3-sigma confidence level, confirming the detection reported in Gaia collaboration et al. (2018) for 8 clusters, and additionally identify 11 GCs with a 2-sigma rotation detection. For the clusters with a detected global rotation, we construct the two-dimensional rotation maps and proper motion rotation curves, and we assess the relevance of rotation with respect to random motions ($V/\sigma\sim0.08-0.51$). We find evidence of a correlation between the degree of internal rotation and relaxation time, highlighting the importance of long-term dynamical evolution in shaping the clusters current properties. This is a strong indication that angular momentum must have played a fundamental role in the earliest phases of cluster formation. Finally, exploiting the spatial information of the rotation maps and a comparison with line-of-sight data, we provide an estimate of the inclination of the rotation axis for a subset of 8 clusters. Our work demonstrates the potential of Gaia data for internal kinematic studies of globular clusters and provides the first step to reconstruct their intrinsic three-dimensional structure., Comment: Accepted for publication in MNRAS

The center of the Sagittarius dwarf spheroidal galaxy (Sgr dSph) hosts a nuclear star cluster, M54, which is the only galaxy nucleus that can be resolved into individual stars at optical wavelengths. It is thus a key target for understanding the formation of nuclear star clusters and their relation to globular clusters. We present a large Multi-Unit Spectroscopic Explorer (MUSE) data set that covers M54 out to $\sim$2.5 half-light radius, from which we extracted the spectra of $\sim$6600 cluster member stars. We use these data in combination with HST photometry to derive age and metallicity for each star. The stellar populations show a well defined age-metallicity relation, implying an extended formation history for the central region of Sgr dSph. We classify these populations into three groups, all with the same systemic velocity: young metal-rich (YMR; 2.2\,Gyr, \mbox{[Fe/H]$=-0.04$}); intermediate-age metal-rich (IMR; 4.3\,Gyr, \mbox{[Fe/H]$=-0.29$}); and old metal-poor (OMP; 12.2\,Gyr, \mbox{[Fe/H]$=-1.41$}). The YMR and OMP populations are more centrally concentrated than the IMR population, which are likely stars of the Sgr dSph. We suggest the OMP population is the result of accretion and merging of two or more old and metal-poor globular clusters dragged to the center by dynamical friction. The YMR is consistent with being formed by in situ star formation in the nucleus. The ages of the YMR population suggest that it may have been triggered into forming when the Sgr dSph began losing its gas during the most recent interaction with the Milky Way, $\sim$3\,Gyr ago., 24 pages, 13 figures. Accepted for publication in ApJ

We present a new framework for modelling discrete kinematic data. Current techniques typically involve binning. Our approach works directly with the discrete data and uses maximum-likelihood methods to assess the probability of the dataset given model predictions. We avoid making hard cuts on the datasets by allowing for a contaminating population in our models. We apply our models to discrete proper-motion and line-of-sight-velocity data of Galactic globular cluster omega Centauri and find a mildly radial velocity anisotropy beta = 0.10 +/- 0.02, an inclination angle i = 50 +/- 1 deg, a V-band mass-to-light ratio Upsilon = 2.71 +/- 0.05 Msun/Lsun and a distance d = 4.59 +/- 0.08 kpc. All parameters are in agreement with previous studies, demonstrating the feasibility of our methods. We find that the models return lower distances and higher mass-to-light ratios than expected when we include proper motion stars with high errors or for which there is some blending. We believe this not a fault of our models but is instead due to underestimates or missing systematic uncertainties in the provided errors.

High-precision proper motions of the globular cluster 47 Tuc have allowed us to measure for the first time the cluster rotation in the plane of the sky and the velocity anisotropy profile from the cluster core out to about 13'. These profiles are coupled with prior measurements along the line of sight and the surface-brightness profile, and fit all together with self-consistent models specifically constructed to describe quasi-relaxed stellar systems with realistic differential rotation, axisymmetry and pressure anisotropy. The best-fit model provides an inclination angle i between the rotation axis and the line-of-sight direction of 30 deg, and is able to simultaneously reproduce the full three-dimensional kinematics and structure of the cluster, while preserving a good agreement with the projected morphology. Literature models based solely on line-of-sight measurements imply a significantly different inclination angle (i=45 deg), demonstrating that proper motions play a key role in constraining the intrinsic structure of 47 Tuc. Our best-fit global dynamical model implies an internal rotation higher than previous studies have shown, and suggests a peak of the intrinsic V/sigma ratio of ~0.9 at around two half-light radii, with a non-monotonic intrinsic ellipticity profile reaching values up to 0.45. Our study unveils a new degree of dynamical complexity in 47 Tuc, which may be leveraged to provide new insights into the formation and evolution of globular clusters., Comment: 15 pages, 14 figures, 8 tables, accepted for publication in ApJ

Sub-subgiants are stars observed to be redder than normal main-sequence stars and fainter than normal subgiant (and giant) stars in an optical color-magnitude diagram. The red straggler stars, which lie redward of the red giant branch, may be related and are often grouped together with the sub-subgiants in the literature. These stars defy our standard theory of single-star evolution, and are important tests for binary evolution and stellar collision models. In total, we identify 65 sub-subgiants and red stragglers in 16 open and globular star clusters from the literature; 50 of these, including 43 sub-subgiants, pass our strict membership selection criteria (though the remaining sources may also be cluster members). In addition to their unique location on the color-magnitude diagram, we find that at least 58% (25/43) of sub-subgiants in this sample are X-ray sources with typical 0.5-2.5 keV luminosities of order 10^30 - 10^31 erg/s. Their X-ray luminosities and optical-to-X-ray flux ratios are similar to those of RS CVn active binaries. At least 65% (28/43) of the sub-subgiants in our sample are variables, 21 of which are known to be radial-velocity binaries. Typical variability periods are, 21 pages, 7 figures, 4 tables, accepted for publication in ApJ

We present a pilot study of Galactic globular cluster (GC) proper motion (PM) determinations using Gaia data. We search for GC stars in the Tycho-Gaia Astrometric Solution (TGAS) catalogue from Gaia Data Release 1 (DR1), and identify five members of NGC104 (47 Tucanae), one member of NGC5272 (M3), five members of NGC6121 (M4), seven members of NGC6397, and two members of NGC6656 (M22). By taking a weighted average of member stars, fully accounting for the correlations between parameters, we estimate the parallax (and, hence, distance) and PM of the GCs. This provides a homogeneous PM study of multiple GCs based on an astrometric catalog with small and well-controlled systematic errors, and yields random PM errors similar to existing measurements. Detailed comparison to the available Hubble Space Telescope (HST) measurements generally shows excellent agreement, validating the astrometric quality of both TGAS and HST. By contrast, comparison to ground-based measurements shows that some of those must have systematic errors exceeding the random errors. Our parallax estimates have uncertainties an order of magnitude larger than previous studies, but nevertheless imply distances consistent with previous estimates. By combining our PM measurements with literature positions, distances, and radial velocities, we measure Galactocentric space motions for the clusters and find that these also agree well with previous analyses. Our analysis provides a framework for determining more accurate distances and PMs of Galactic GCs using future Gaia data releases. This will provide crucial constraints on the near end of the cosmic distance ladder and provide accurate GC orbital histories., 15 pages, 11 figures, 4 tables. Published in ApJ. Revised to match published version

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 $R_{\rm e}$, planetary nebula (PN) radial velocities out to $3\, R_{\rm e}$, and globular cluster (GC) radial velocities and colours out to $6\,R_{\rm e}$. The best-fitting model is a cored DM halo which contributes $\sim 10\%$ of the total mass within $1\,R_{\rm e}$, and $67\% \pm 10\%$ within $6\,R_{\rm e}$, although a cusped DM halo is also acceptable. The red GCs exhibit mild rotation with $v_{\rm max}/\sigma_0 \sim 0.3$ in the region $R > \,R_{\rm e}$, 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., Comment: Accepted by MNRAS

We make use of the Hubble Space Telescope proper-motion catalogs derived by Bellini et al. (2014) to produce the first radial velocity-dispersion profiles sigma(R) for blue straggler stars (BSSs) in Galactic globular clusters (GCs), as well as the first dynamical estimates for the average mass of the entire BSS population. We show that BSSs typically have lower velocity dispersions than stars with mass equal to the main-sequence turnoff mass, as one would expect for a more massive population of stars. Since GCs are expected to experience some degree of energy equipartition, we use the relation sigma~M^-eta, where eta is related to the degree of energy equipartition, along with our velocity-dispersion profiles to estimate BSS masses. We estimate eta as a function of cluster relaxation from recent Monte Carlo cluster simulations by Bianchini et al. (2016b) and then derive an average mass ratio M_BSS /M_MSTO=1.50+/-0.14 and an average mass M_BSS=1.22+/-0.12 M_Sun from 598 BSSs across 19 GCs. The final error bars include any systematic errors that are random between different clusters, but not any potential biases inherent to our methodology. Our results are in good agreement with the average mass of M_BSS=1.22+/-0.06 M_Sun for the 35 BSSs in Galactic GCs in the literature with properties that have allowed individual mass determination., 12 pages, 8 figures, 3 tables. Accepted for publication in ApJ

High-precision kinematic studies of globular clusters require an accurate knowledge of all possible sources of contamination. Amongst other sources, binary stars can introduce systematic biases in the kinematics. Using a set of Monte Carlo cluster simulations with different concentrations and binary fractions, we investigate the effect of unresolved binaries on proper-motion dispersion profiles, treating the simulations like HST proper-motion samples. Since globular clusters evolve towards a state of partial energy equipartition, more massive stars lose energy and decrease their velocity dispersion. As a consequence, on average, binaries have a lower velocity dispersion, since they are more massive kinematic tracers. We show that, in the case of clusters with high binary fraction (initial binary fraction of 50%) and high concentration (i.e., closer to energy equipartition), unresolved binaries introduce a color-dependent bias in the velocity dispersion of main-sequence stars of the order of 0.1-0.3 km s$^{-1}$ (corresponding to $1-6$% of the velocity dispersion), with the reddest stars having a lower velocity dispersion, due to the higher fraction of contaminating binaries. This bias depends on the ability to distinguish binaries from single stars, on the details of the color-magnitude diagram and the photometric errors. We apply our analysis to the HSTPROMO data set of NGC 7078 (M15) and show that no effect ascribable to binaries is observed, consistent with the low binary fraction of the cluster. Our work indicates that binaries do not significantly bias proper-motion velocity-dispersion profiles, but should be taken into account in the error budget of kinematic analyses., 7 pages, 3 figure, 2 tables. Accepted for publication in ApJ Letters

We present VLT/FORS2 spectroscopy of candidate blue horizontal branch (BHB) stars in the vicinity of the Hercules ultrafaint dwarf galaxy. We identify eight convincing Hercules BHB members, and a further five stars with similar systemic velocities to that of Hercules, but ~ 0.5 kpc from the centre of the galaxy along its major axis. It is likely that these stars once belonged to Hercules, but have been tidally stripped and are now unbound. We emphasise the usefulness of looking for any gradient in the systemic velocity of this stretched system, which would further support our interpretation of the origin of its elongated and distended morphology.

Proper motions (PMs) are required to calculate accurate orbits of globular clusters (GCs) in the Milky Way (MW) halo. We present our HST program to create a PM database for 20 GCs at distances of RGC = 10–100 kpc. Targets are discussed along with PM measurement methods. We also describe how our PM results can be used for Gaia as an external check, and discuss the synergy between HST and Gaia as astrometric instruments in the coming years.

The 3D velocities of M31 and M33 are important for understanding the evolution and cosmological context of the Local Group. Their most massive stars are detected by Gaia, and we use Data Release 2 (DR2) to determine the galaxy proper motions (PMs). We select galaxy members based on, e.g., parallax, PM, color-magnitude-diagram location, and local stellar density. The PM rotation of both galaxies is confidently detected, consistent with the known line-of-sight rotation curves: $V_{\rm rot} = -206\pm86$ km s$^{-1}$ (counter-clockwise) for M31, and $V_{\rm rot} = 80\pm52$ km s$^{-1}$ (clockwise) for M33. We measure the center-of-mass PM of each galaxy relative to surrounding background quasars in DR2. This yields that $({\mu}_{\alpha*},{\mu}_{\delta})$ equals $(65 \pm 18 , -57 \pm 15)$ $\mu$as yr$^{-1}$ for M31, and $(31 \pm 19 , -29 \pm 16)$ $\mu$as yr$^{-1}$ for M33. In addition to the listed random errors, each component has an additional residual systematic error of 16 $\mu$as yr$^{-1}$. These results are consistent at 0.8$\sigma$ and 1.0$\sigma$ with the (2 and 3 times higher-accuracy) measurements already available from Hubble Space Telescope (HST) optical imaging and VLBA water maser observations, respectively. This lends confidence that all these measurements are robust. The new results imply that the M31 orbit towards the Milky Way is somewhat less radial than previously inferred, $V_{\rm tan, DR2+HST} = 57^{+35}_{-31}$ km s$^{-1}$, and strengthen arguments that M33 may be on its first infall into M31. The results highlight the future potential of Gaia for PM studies beyond the Milky Way satellite system., Comment: 15 pages, 7 figures, ApJ, in press

We present Hubble Space Telescope (HST) absolute proper motion (PM) measurements for 20 globular clusters (GCs) in the Milky Way (MW) halo at Galactocentric distances $R_{\rm GC} \approx 10-100$ kpc, with median per-coordinate PM uncertainty 0.06 mas yr$^{-1}$. Young and old halo GCs do not show systematic differences in their 3D Galactocentric velocities, derived from combination with existing line-of-sight velocities. We confirm the association of Arp 2, Pal 12, Terzan 7, and Terzan 8 with the Sagittarius (Sgr) stream. These clusters and NGC 6101 have tangential velocity $V_{\rm tan} > 290$ km s$^{-1}$, whereas all other clusters have $V_{\rm tan} < 200$ km s$^{-1}$. NGC 2419, the most distant GC in our sample, is also likely associated with the Sgr stream, whereas NGC 4147, NGC 5024, and NGC 5053 definitely are not. We use the distribution of orbital parameters derived using the 3D velocities to separate halo GCs that either formed within the MW or were accreted. We also assess the specific formation history of e.g. Pyxis and Terzan 8. We constrain the MW mass via an estimator that considers the full 6D phase-space information for 16 of the GCs from $R_{\rm GC} = 10$ to 40 kpc. The velocity dispersion anisotropy parameter $\beta = 0.609^{+0.130}_{-0.229}$. The enclosed mass $M (

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 the mass of the Milky Way within 300 kpc is ~ 0.9 x 10^12 solar masses assuming velocity isotropy. However, the mass estimate is sensitive to the anisotropy and could plausibly lie between 0.7 - 3.4 x 10^12 solar masses. Incorporating the proper motions of 6 Milky Way satellites into the dataset, we find ~ 1.4 x 10^12 solar masses. The range here if plausible anisotropies are used is still broader, from 1.2 - 2.7 x 10^12 solar masses. 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 ~ 1.4 x 10^12 solar masses assuming isotropy. There is only a modest dependence on anisotropy, with the mass varying between 1.3 -1.6 x 10^12 solar masses. 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.

We present an analysis of the substructure revealed by 407 RR Lyraes in Sloan Digital Sky Survey (SDSS) Stripe 82. Period estimates are determined to high accuracy using a string-length method. A subset of 178 RR Lyraes with spectrally derived metallicities are employed to derive metallicity-period-amplitude relations, which are then used to find metallicities and distances for the entire sample. The RR Lyraes lie between 5 and 115 kpc from the Galactic center. They are divided into subsets of 316 RRab types and 91 RRc types based on their period, colour and metallicity. The density distribution is not smooth, but dominated by clumps and substructure. Samples of 55 and 237 RR Lyraes associated with the Sagittarius Stream and the Hercules-Aquila Cloud respectively are identified. Hence, ~ 70 % of the RR Lyraes in Stripe 82 belong to known substructure. There is a sharp break in the density distribution at Galactocentric radii of 40 kpc, reflecting the fact that the dominant substructure in Stripe 82 - the Hercules-Aquila Cloud and the Sagittarius Stream - lies within 40 kpc. In fact, almost 60 % of all the RR Lyraes in Stripe 82 are associated with the Hercules-Aquila Cloud alone, which emphasises its pre-eminence. Additionally, evidence of a new and distant substructure - the Pisces Overdensity - is found, consisting of 28 faint RR Lyraes centered on Galactic coordinates (80 deg, -55 deg) and with distances of ~ 80 kpc. The total stellar mass in the Pisces Overdensity is ~10000 solar masses and its metallicity is [Fe/H] ~ -1.5., Comment: 15 pages, submitted to MNRAS

We present a new discrete chemo-dynamical axisymmetric modeling technique, which we apply to the dwarf spheroidal galaxy Sculptor. The major improvement over previous Jeans models is that realistic chemical distributions are included directly in the dynamical modelling of the discrete data. This avoids loss of information due to spatial binning and eliminates the need for hard cuts to remove contaminants and to separate stars based on their chemical properties. Using a combined likelihood in position, metallicity and kinematics, we find that our models naturally separate Sculptor stars into a metal-rich and a metal-poor population. Allowing for non-spherical symmetry, our approach provides a central slope of the dark matter density of $\gamma = 0.5 \pm 0.3$. The metal-rich population is nearly isotropic (with $\beta_r^{red} = 0.0\pm0.1$) while the metal-poor population is tangentially anisotropic (with $\beta_r^{blue} = -0.2\pm0.1$) around the half light radius of $0.26$ kpc. A weak internal rotation of the metal-rich population is revealed with $v_{max}/\sigma_0 = 0.15 \pm 0.15$. We run tests using mock data to show that a discrete dataset with $\sim 6000$ stars is required to distinguish between a core ($\gamma = 0$) and cusp ($\gamma = 1$), and to constrain the possible internal rotation to better than $1\,\sigma$ confidence with our model. We conclude that our discrete chemo-dynamical modelling technique provides a flexible and powerful tool to robustly constrain the internal dynamics of multiple populations, and the total mass distribution in a stellar system., Comment: Accepted by MNRAS

We present the first study of high-precision internal proper motions (PMs) in a large sample of globular clusters, based on Hubble Space Telescope (HST) data obtained over the past decade with the ACS/WFC, ACS/HRC, and WFC3/UVIS instruments. We determine PMs for over 1.3 million stars in the central regions of 22 clusters, with a median number of ~60,000 stars per cluster. These PMs have the potential to significantly advance our understanding of the internal kinematics of globular clusters by extending past line-of-sight (LOS) velocity measurements to two- or three-dimensional velocities, lower stellar masses, and larger sample sizes. We describe the reduction pipeline that we developed to derive homogeneous PMs from the very heterogeneous archival data. We demonstrate the quality of the measurements through extensive Monte-Carlo simulations. We also discuss the PM errors introduced by various systematic effects, and the techniques that we have developed to correct or remove them to the extent possible. We provide in electronic form the catalog for NGC 7078 (M 15), which consists of 77,837 stars in the central 2.4 arcmin. We validate the catalog by comparison with existing PM measurements and LOS velocities, and use it to study the dependence of the velocity dispersion on radius, stellar magnitude (or mass) along the main sequence, and direction in the plane of the sky (radial/tangential). Subsequent papers in this series will explore a range of applications in globular-cluster science, and will also present the PM catalogs for the other sample clusters., 34 pages, 22 figures (3 in low res), 30 tables, accepted for publication in ApJ on October 20, 2014

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 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 disk to be tilted, demonstrating that the common assumption of decoupled radial and vertical motions in the disk 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 alpha_tilt = (-0.90 +- 0.04) arctan(|z|/R_sun) - (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., Comment: accepted by MNRAS; 14 pages

We analyze line-of-sight velocity and proper motion data of stars in the Galactic globular cluster M15 using a new method to fit dynamical models to discrete kinematic data. Our fitting method maximizes the likelihood for individual stars and, as such, does not suffer the same loss of spatial and velocity information incurred when spatially binning data or measuring velocity moments. In this paper, we show that the radial variation in M15 of the mass-to-light ratio is consistent with previous estimates and theoretical predictions, which verifies our method. Our best-fitting axisymmetric Jeans models do include a central dark mass of $\sim2 \pm 1\cdot 10^3M_\odot$, which can be explained by a high concentration of stellar remnants at the cluster center. This paper shows that, from a technical point of view and with current computing power, spatial binning of data is no longer necessary. This not only leads to more accurate fits, but also avoids biased mass estimates due to the loss of resolution. Furthermore, we find that the mass concentration in M15 is significantly higher than previously measured, and is in close agreement with theoretical predictions for core-collapsed globular clusters without a central intermediate-mass black hole., Accepted by MNRAS; 8 pages, 7 figures