arXiv subjects

Laura L. Watkins

Publications and source records attributed to Laura L. Watkins.

At least 37 records · Page 2Linked to original sources

arXiv2020

Disentangling the formation history of galaxies via population-orbit superposition: method validation

We present population-orbit superposition models for external galaxies based on Schwarzschild's orbit-superposition method, by tagging the orbits with age and metallicity. The models fit the density distributions, as well as kinematic, age and metallicity maps from Integral Field Unit (IFU) spectroscopy observations. We validate the method and demonstrate its power by applying it to mock data, similar to those obtained by the Multi-Unit Spectroscopic Explorer (MUSE) IFU on the Very Large Telescope (VLT). These mock data are created from Auriga galaxy simulations, viewed at three different inclination angles ($\vartheta=40^o, 60^o, 80^o$). Constrained by MUSE-like mock data, our model can recover the galaxy's stellar orbit distribution projected in orbital circularity $λ_z$ vs. radius $r$, the intrinsic stellar population distribution in age $t$ vs. metallicity $Z$, and the correlation between orbits' circularity $λ_z$ and stellar age $t$. A physically motivated age-metallicity relation improves recovering the intrinsic stellar population distributions. We decompose galaxies into cold, warm and hot + counter-rotating components based on their orbit circularity distribution, and find that the surface density, mean velocity, velocity dispersion, age and metallicity maps of each component from our models well reproduce those from simulation, especially for projections close to edge-on. These galaxies exhibit strong global age vs. $σ_z$ relation, which is well recovered by our model. The method has the power to reveal the detailed build-up of stellar structures in galaxies, and offers a complement to local resolved, and high-redshift studies of galaxy evolution.

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arXiv2020

A deep view into the nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. II. Kinematic characterization of the stellar populations

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).

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arXiv2019

The peculiar kinematics of the multiple populations in the globular cluster Messier 80 (NGC 6093)

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.

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arXiv2019

A deep view into the nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. I. Data and stellar population characterization

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.

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arXiv2019

Hunting for the Dark Matter Wake Induced by the Large Magellanic Cloud

Satellite galaxies are predicted to generate gravitational density wakes as they orbit within the dark matter (DM) halos of their hosts, causing their orbits to decay over time. The recent infall of the Milky Way's (MW) most massive satellite galaxy, the Large Magellanic Cloud (LMC), affords us the unique opportunity to study this process in action. In this work, we present high-resolution ($m_{dm} = 4 \times 10^4 M_{\odot}$ ) N-body simulations of the MW-LMC interaction over the past 2 Gyr. We quantify the impact of the LMC's passage on the density and kinematics of the MW's DM halo and the observability of these structures in the MW's stellar halo. The LMC is found to generate pronounced Local and Global wakes in both the DM and stellar halos, leads to both local overdensities and distinct kinematic patterns that should be observable with ongoing and future surveys. Specifically, the Global Wake will result in redshifted radial velocities of stars in the North and blueshifts in the South, at distances larger than 45 kpc. The Local Wake traces the orbital path of the LMC through the halo (50-200 kpc), resulting in a stellar overdensity with a distinct, tangential kinematic pattern that persists to the present day. The detection of the MW's halo response will constrain: the infall mass of the LMC and its orbital trajectory, the mass of the MW, and it may inform us about the nature of the dark matter particle itself.

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arXiv2019

Imprints of Evolution on the Internal Kinematics of Globular Clusters

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.

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arXiv2019

Evidence for an Intermediate-Mass Milky Way from Gaia DR2 Halo Globular Cluster Motions

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 $β= 0.46^{+0.15}_{-0.19}$, 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: $β= 0.52^{+0.11}_{-0.14}$, $M(< 39.5 \mathrm{kpc}) = 0.42^{+0.07}_{-0.06} 10^{12} \mathrm{M_\odot}$, 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.

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arXiv2019

First Gaia Dynamics of the Andromeda System: DR2 Proper Motions, Orbits, and Rotation of M31 and M33

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 $(μ_{α*},μ_δ)$ equals $(65 \pm 18 , -57 \pm 15)$ $μ$as yr$^{-1}$ for M31, and $(31 \pm 19 , -29 \pm 16)$ $μ$as yr$^{-1}$ for M33. In addition to the listed random errors, each component has an additional residual systematic error of 16 $μ$as yr$^{-1}$. These results are consistent at 0.8$σ$ and 1.0$σ$ 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.

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arXiv2018

Mass modelling globular clusters in the Gaia era: a method comparison using mock data from an $N$-body simulation of M4

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.

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arXiv2018

Absolute HST Proper Motion (HSTPROMO) of Distant Milky Way Globular Clusters: Galactocentric Space Velocities and the Milky Way Mass

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 $β= 0.609^{+0.130}_{-0.229}$. The enclosed mass $M (<39.5 \rm{kpc}) = 0.61^{+0.18}_{-0.12} \times 10^{12}$ M$_{\odot}$, and the virial mass $M_\rm{vir} = 2.05^{+0.97}_{-0.79} \times 10^{12}$ M$_{\odot}$, are consistent with, but on the high side among recent mass estimates in the literature.

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arXiv2017

Tycho-Gaia Astrometric Solution Parallaxes and Proper Motions for Five Galactic Globular Clusters

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.

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arXiv2017

On the Origin of Sub-subgiant Stars. I. Demographics

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 <15 days. At least 33% (14/43) of the sub-subgiants are H-alpha emitters. These observational demographics provide strong evidence that binarity is important for sub-subgiant formation. Finally, we find that the number of sub-subgiants per unit mass increases toward lower-mass clusters, such that the open clusters in our sample have the highest specific frequencies of sub-subgiants.

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arXiv2017

HST proper motions in Galactic globular clusters

Proper motions (PMs) are crucial to fully understand the internal dynamics of globular clusters (GCs). To that end, the Hubble Space Telescope (HST) Proper Motion (HSTPROMO) collaboration has constructed large, high-quality PM catalogues for 22 Galactic GCs. We highlight some of our exciting recent results: the first directly-measured radial anisotropy profiles for a large sample of GCs; the first dynamical distance and mass-to-light (M/L) ratio estimates for a large sample of GCs; and the first dynamically-determined masses for hundreds of blue-straggler stars (BSSs) across a large GC sample.

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arXiv2016

A discrete chemo-dynamical model of the giant elliptical galaxy NGC 5846: dark matter fraction, internal rotation and velocity anisotropy out to six effective radii

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 $v_{\rm max}/σ_0 \sim 0.3$ 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.

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arXiv2016

A discrete chemo-dynamical model of the dwarf spheroidal galaxy Sculptor: mass profile, velocity anisotropy and internal rotation

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 $γ= 0.5 \pm 0.3$. The metal-rich population is nearly isotropic (with $β_r^{red} = 0.0\pm0.1$) while the metal-poor population is tangentially anisotropic (with $β_r^{blue} = -0.2\pm0.1$) around the half light radius of $0.26$ kpc. A weak internal rotation of the metal-rich population is revealed with $v_{max}/σ_0 = 0.15 \pm 0.15$. We run tests using mock data to show that a discrete dataset with $\sim 6000$ stars is required to distinguish between a core ($γ= 0$) and cusp ($γ= 1$), and to constrain the possible internal rotation to better than $1\,σ$ 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.

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arXiv2015

Hubble Space Telescope proper motion (HSTPROMO) catalogs of Galactic globular clusters. III. Dynamical distances and mass-to-light ratios

We present dynamical distance estimates for 15 Galactic globular clusters and use these to check the consistency of dynamical and photometric distance estimates. For most of the clusters, this is the first dynamical distance estimate ever determined. We extract proper-motion dispersion profiles using cleaned samples of bright stars from the Hubble Space Telescope proper-motion catalogs recently presented in Bellini et al. (2014) and compile a set of line-of-sight velocity-dispersion profiles from a variety of literature sources. Distances are then estimated by fitting spherical, non-rotating, isotropic, constant mass-to-light (M/L) dynamical models to the proper-motion and line-of-sight dispersion profiles together. We compare our dynamical distance estimates with literature photometric estimates from the Harris (1996, 2010 edition) globular cluster catalog and find that the mean fractional difference between the two types is consistent with zero at just $-1.9 \pm 1.7 \%$. This indicates that there are no significant biases in either estimation method and provides an important validation of the stellar-evolution theory that underlies photometric distance estimates. The analysis also estimates dynamical M/L ratios for our clusters; on average, the dynamically-inferred M/L ratios agree with existing stellar-population-based M/L ratios that assume a Chabrier initial mass function (IMF) to within $-8.8 \pm 6.4 \%$, implying that such an IMF is consistent with our data. Our results are also consistent with a Kroupa IMF, but strongly rule out a Salpeter IMF. We detect no correlation between our M/L offsets from literature values and our distance offsets from literature values, strongly indicating that our methods are reliable and our results are robust.

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arXiv2015

The tilt of the velocity ellipsoid in the Milky Way disk

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.

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arXiv2015

Hubble Space Telescope proper motion (HSTPROMO) catalogs of Galactic globular clusters. II. Kinematic profiles and maps

We present kinematical analyses of 22 Galactic globular clusters using the Hubble Space Telescope proper motion (HSTPROMO) catalogues recently presented in Bellini et al. (2014). For most clusters, this is the first proper-motion study ever performed, and, for many, this is the most detailed kinematic study of any kind. We use cleaned samples of bright stars to determine binned velocity-dispersion and velocity-anisotropy radial profiles and two-dimensional velocity-dispersion spatial maps. Using these profiles, we search for correlations between cluster kinematics and structural properties. We find that: (1) more centrally-concentrated clusters have steeper radial velocity-dispersion profiles; (2) on average, at 1σconfidence in two dimensions, the photometric and kinematic centres of globular clusters agree to within ~1", with a cluster-to-cluster rms of 4" (including observational uncertainties); (3) on average, the cores of globular clusters have isotropic velocity distributions to within 1% (σ_t/σ_r = 0.992 +/- 0.005), with a cluster-to-cluster rms of 2% (including observational uncertainties); (4) clusters generally have mildly radially anisotropic velocity distributions (σ_t/σ_r ~ 0.8-1.0) near the half-mass radius, with bigger deviations from isotropy for clusters with longer relaxation times; (5) there is a relation between σ_minor/σ_major and ellipticity, such that the more flattened clusters in the sample tend to be more anisotropic, with σ_minor/σ_major ~ 0.9-1.0. Aside from these general results and correlations, the profiles and maps presented here can provide a basis for detailed dynamical modelling of individual globular clusters. Given the quality of the data, this is likely to provide new insights into a range of topics concerning globular cluster mass profiles, structure, and dynamics.

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