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Holger Baumgardt

Publications and source records attributed to Holger Baumgardt.

At least 19 recordsLinked to original sources

The Delegate Survey: KOALA/AAOmega-IFU spectroscopy of three nearby dwarf galaxies

Assessing the cosmological typicality of the Local Group is crucial for establishing whether its dwarf galaxy population is representative. To this end, the Delegate Survey targets dwarf galaxies in Local Group analogues for systematic comparison. As a pilot study for the Delegate Survey, we obtained integral-field spectra of three dwarf galaxies, GAMA 79098, GAMA 569709, and HIPASS J1159-19 S2, in two nearby galaxy groups using the KOALA instrument on the AAT. The galaxies were mapped at a spatial sampling of 1.25 arcsec per spaxel, providing two-dimensional spectral coverage of both the stellar and ionised gas components. Using continuum and emission-line maps, we investigate the ionisation structure, star-forming properties, metallicity, star formation histories, and velocity fields of each system. GAMA 79098 exhibits properties closely analogous to the SMC, with ongoing star formation superimposed on an old stellar population and moderate rotational support. GAMA 569709 resembles transition-type Local Group (LG) dwarfs such as NGC 147 and NGC 185, showing predominantly an old stellar population. HIPASS J1159-19 S2 is dominated by young stars and intense star-forming complexes, consistent with a dynamically young, gas-rich galaxy group environment. The two GAMA dwarfs follow the LG stellar mass-metallicity relation within uncertainties, while HIPASS J1159-19 S2 appears approximately 0.5 dex more metal-rich for its stellar mass. Overall, the structural, chemical, and kinematic properties of these dwarfs overlap substantially with analogous LG dwarfs.

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HRMOS: A High-Resolution Multi-Object Spectrograph for the VLT

This White Paper presents the scientific rationale and instrument concept for HRMOS (High-Resolution Multi-Object Spectrograph), a next-generation instrument proposed for the ESO Very Large Telescope within the VLT 2030 roadmap. Current and planned facilities offer either multi-object spectroscopy or ultra-high spectral resolution, but not both. HRMOS fills this gap by combining very high spectral resolution, multi-object capability, and radial-velocity stability, enabling transformative studies in Galactic and extragalactic astrophysics. The baseline design provides a resolving power of R = 80000, radial-velocity precision of 10 m s-1 (goal: 5 m s-1), simultaneous observations of 50-60 targets, and broad optical coverage down to 385 nm. These capabilities enable precise measurements of elemental abundances, isotopic ratios, line profiles, and radial velocities for large stellar samples, including crowded fields, star clusters, the Galactic bulge, and nearby dwarf galaxies. HRMOS will address key questions on the age of the oldest stellar populations through nucleocosmochronology, the formation and survival of planetary systems, the assembly history of the Milky Way and satellites, the origin of the heaviest elements, stellar evolution, and the chemical and dynamical properties of the interstellar and circumgalactic medium. It will bridge large spectroscopic surveys and the next generation of extremely large telescopes, with strong synergies with 4MOST, Gaia, TESS, PLATO, the proposed Haydn mission, and future ELT instruments. Building on VLT/FLAMES heritage, HRMOS represents a strategic investment for European astronomy in the 2030s.

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JWST Observations of the Double Nucleus in NGC 4486B: Possible Evidence for a Recent Binary SMBH Merger and Recoil

A recent study of the compact elliptical galaxy NGC 4486B using JWST-NIRSpec IFU kinematics confirmed a supermassive black hole (SMBH) of mass $M_{BH}=3.6\pm0.7\times10^8$ (~8% of the stellar mass). In addition to its double nucleus, the nuclear kinematics show pronounced asymmetries: a velocity-dispersion peak displaced by 6 pc from the galaxy center and a ~16 km/s offset in the mean stellar line-of-sight velocity near the SMBH. We examine the origin of the 12 pc double nucleus and these asymmetries and show that the observations favor an SMBH surrounded by an eccentric nuclear disk (END). END formation models require the SMBH to experience a gravitational wave (GW) recoil following a binary SMBH merger. Our orbit-superposition models contain ~50% retrograde stars at the edge of the nuclear region, in striking agreement with END-formation simulations. We infer a pre-merger mass ratio q>0.15 and a recoil kick of ~340 km/s. Our N-body simulations show that with such a kick, the SMBH returns to the center within ~30 Myr. Its flat central core is also consistent with earlier binary black hole scouring. We test two alternative mechanisms-buoyancy-driven oscillations and a pre-merger SMBH binary-but neither reproduces the observed offsets, favoring the GW-kick scenario. Our direct N-body simulations further show that a prograde SMBH binary in a rotating host can stall in a corotation resonance, delaying coalescence. Thus, although NGC 4486B is an old, relaxed galaxy near the Virgo cluster center, its SMBH appears to have merged only recently, making its nucleus a rare nearby laboratory for studying post-merger SMBH dynamics.

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Binary disruption during the early phase of open clusters

The binary fraction in young open clusters exceeds that of field stars, making the study of binary dynamical evolution in clusters essential for understanding the origins and evolution of field binaries. Using N-body simulations based on Gaia DR3 open cluster observations and assuming a 100\% primordial binary fraction, we investigated the early evolution of binary survival fractions in open clusters. We find that binary disruption has two stages, an initial rapid decline followed by a slower decrease, well described by two piecewise linear functions. The early disruption rate, $k_1$, follows a power-law relation with the cluster's initial density ($ ρ_\mathrm{0} $), with an index of approximately 0.56, driven by the disruption of wide binaries via close encounters. The transition time between the two phases, $t_\mathrm{b}$, also exhibits a power-law dependence on $ρ_\mathrm{0}$ with an index of about -0.46. The disruption rate also depends on binary parameters: high-$q$ and wide binaries are disrupted faster, while the dependence on eccentricity $e$ is less clear, likely due to its strong evolution. We developed and publicly released a Python tool to predict binary survival fraction evolution based on $ρ_0$, $P$ and $q$. Additionally, we also investigate how open cluster binaries contribute to the field population, and find that the escaped stars have a systematically lower binary fraction, likely due to mass segregation. Both populations show similar distributions of $ P $ and $e$, but lower-$q$ systems preferentially remain bound within clusters, the origin of which remains uncertain.

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Spatial mixing of stellar populations in globular clusters via binary-single star scattering

The majority of Galactic globular star clusters (GCs) have been reported to contain at least two populations of stars (we use P1 for the primordial and P2 for the chemically-enriched population). Recent observational studies found that dynamically-old GCs have P1 and P2 spatially mixed due to relaxation processes. However, in dynamically-young GCs, where P2 is expected to be more centrally concentrated from birth, the spatial distributions of P1 and P2 are sometimes very different from system to system. This suggests that more complex dynamical processes specific to certain GCs might have shaped those distributions. We aim to investigate the discrepancies between the spatial concentration of P1 and P2 stars in dynamically-young GCs. Our focus is to evaluate whether massive binary stars (e.g. BHs) can cause the expansion of the P2 stars through binary-single interactions in the core, and whether they can mix or even radially invert the P1 and P2 distributions. We use a set of theoretical and empirical arguments to evaluate the effectiveness of binary-single star scattering. We then construct a set of direct N-body models with massive primordial binaries to verify our estimates further and gain more insights into the dynamical processes in GCs. We find that binary-single star scatterings can push the central P2 stars outwards within a few relaxation times. While we do not produce radial inversion of P1 and P2 for any initial conditions we tested, this mechanism systematically produces clusters where P1 and P2 look fully mixed even in projection. The mixing is enhanced 1) in denser GCs, 2) in GCs containing more binary stars, and 3) when the mass ratio between the binary components and the cluster members is higher. Binary-single star interactions seem able to explain the observable properties of some dynamically-young GCs (e.g. NGC4590 or NGC5904) where P1 and P2 are fully radially mixed.

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A Supermassive Black Hole in a Diminutive Ultra-compact Dwarf Galaxy Discovered with JWST/NIRSpec+IFU

The integral-field unit mode of the Near-Infrared Spectrograph (NIRSpec+IFU) mounted on the James Webb Space Telescope has now enabled kinematic studies of smaller and less massive compact stellar systems in which to search for central massive black holes (BHs) than ever before. We present here the first such detection using NIRSpec+IFU in its highest resolution (R~2700) mode. We report a $3σ$ detection of a central black hole with mass ${\cal M}_{BH}=2.2\pm1.1\times10^6\,M_\odot$ in UCD736 orbiting within the Virgo galaxy cluster based on Schwarzschild's modeling of the 1D kinematic profile. The presence of such a massive BH strongly argues against a globular cluster origin of this UCD, and rather suggests a tidally stripped formation route from a former $\gtrsim10^9\,M_\odot$ dwarf galaxy host. Two other methods produce results consistent with Schwarzschild's modelling, but can only provide upper-limits on ${\cal M}_{BH}$. This represents the detection of a BH in the most compact ($r_h\approx15\,{\rm pc}$) stellar system to date, with a ${\cal M}_{BH}$ corresponding to ~9 percent of the system's stellar mass, roughly in line with previously reported UCD BH detections and comparable to the BH detected in the compact elliptical galaxy NGC4486B.

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On the connection between nitrogen-enhanced field stars and the Galactic globular clusters

As sites of some of the most efficient star formation in the Universe, globular clusters (GCs) have long been hypothesized to be the building blocks of young galaxies. Within the Milky Way, our best tracers of the contribution of GCs to the proto-Galaxy are stars with such anomalous overabundance in nitrogen and depletion in oxygen ("high-[N/O] stars") that they can be identified as having originated in a cluster long after they have escaped. We identify associations between these high-[N/O] field stars and GCs using integrals of motion and metallicities and compare to chemically typical halo stars to quantify any excess association, enabling a population-level exploration of the formation sites of the nitrogen-enhanced stars in the field. Relative to the halo as a whole, high-[N/O] stars show stronger associations with the most initially massive, inner Galaxy GCs, suggesting that many nitrogen-rich stars formed in these environments. However, when compared to a sample matched in orbital energy, the excess largely disappears: high-[N/O] stars are, on average, no more associated with surviving GCs than energy-matched halo stars, despite their [N/O] abundances indicating GC origins, consistent with a scenario in which a substantial fraction of low-energy inner-halo stars originate in GCs, so an energy-matched control dilutes any differential excess. We argue that associations between high-[N/O] stars and their parent GCs are further weakened because dynamical friction and the Galactic bar have altered integrals of motion, limiting the reliability of precise present-day associations and, especially, individual star-to-cluster tagging.

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Insights into spatial mixing of multiple populations in dynamically-young globular clusters

Many galactic globular clusters (GCs) contain at least two stellar populations. Recent observational studies found that the radial distributions of the first (P1) and second population (P2) differ in dynamically-young GCs. Since P2 is conventionally assumed to form more centrally concentrated, the rapid mixing (or even inversion) in some GCs but not others is puzzling. We investigate whether dynamical processes specific to certain GCs might cause this. Specifically, we evaluate the expansion of P2 by binary-single interactions in the cluster core and whether these can mix the P1/P2 radial distributions, using a set of toy-models with varying numbers and masses of primordial binaries. We find that even one massive binary star can push the central P2 outwards, but multiple binaries are required to fully mix P1 and P2 within a few relaxation times. We also compare our results to observed properties of mixed young GCs (NGC 4590, 5053, or 5904).

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Origin of High Dark Remnant Fractions in Milky Way Globular Clusters: The Crucial Role of Initial Black Hole Retention

Comparing the dynamical and stellar masses of Milky Way (MW) globular clusters (GCs) reveals a discrepancy exceeding a factor of two. Since this substantial invisible mass is concentrated in the cluster centre, it is attributed to stellar remnants. The majority of mass in remnants consists of white dwarfs (WDs). Allocating over half of a GC's current mass to WDs could significantly restrict the dynamical evolution scenarios governing stellar clusters. As the most massive stars in GCs, black holes (BHs) exert a substantial effect on the escape rate of lower mass stars, such as WDs. This paper aims to identify which scenarios of BH natal kicks can accurately reproduce the notable dark remnant fraction observed in MW GCs. We compare the observed remnant fraction of MW GCs with a comprehensive grid of direct \Nbody simulations while adjusting the natal kick received by BHs. Our results reveal that simulations employing low natal kicks to BHs are the only ones capable of mirroring the remnant fraction of MW GCs. According to the Spitzer instability, the presence of a BH population prompts the formation of a BH sub-system (BHSub) at the centre of a star cluster. The BHSub serves as an energetic power plant, continually releasing kinetic energy through few-body encounters between single and binary BHs, and transferring the generated energy to the entire stellar population. This energy induces a significant difference in the ejection rate of stellar remnants and luminous stars, ultimately increasing the fraction of dark remnants within the star cluster.

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A JWST View of the Overmassive Black Hole in NGC 4486B

We present a new stellar dynamical measurement of the supermassive black hole (SMBH) in the compact elliptical galaxy NGC 4486B, based on integral field spectroscopy with JWST/NIRSpec. The two-dimensional kinematic maps reveal a resolved double nucleus and a velocity dispersion peak offset from the photometric center. Utilizing two independent methods-Schwarzschild orbit-superposition and Jeans Anisotropic Modeling-we tightly constrain the black hole mass by fitting the full line-of-sight velocity distribution. Our axisymmetric Schwarzschild models yield a best-fit black hole mass of $M_{BH} = 3.6^{+0.7}_{-0.7} \times 10^8 \, M_{\odot}$, slightly lower but significantly more precise than previous estimates. However, since our models do not account for the non-equilibrium nature of the double nucleus, this value may represent a lower limit. Across all tested dynamical models, the inferred $M_{BH}/M_*$ ratio ranges from ~ 4-13%, providing robust evidence for an overmassive SMBH in NGC 4486B. Combined with the galaxy's location deep within the Virgo Cluster, our results support the interpretation that NGC 4486B is the tidally stripped remnant core of a formerly massive galaxy. As the JWST/NIRSpec field of view is insufficient to constrain the dark matter halo, we incorporate archival ground-based long-slit kinematics extending to 5 arcsec. While this provides some leverage on the dark matter content, the constraints remain relatively weak. We place only an upper limit on the dark matter fraction, with $M_{DM}/M_{*} < 0.5$ within 1 kpc-well beyond the effective radius. The inferred black hole mass remains unchanged with or without a dark matter halo.

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The coherent satellite velocity field around the interacting spiral galaxy pair NGC5713/19: signature of two galaxy groups merging

The luminous spirals NGC5713 and NGC5719 form an interacting galaxy pair 94 kpc apart and are connected by a straight, elongated neutral hydrogen structure extending over 200 kpc. Their 14 velocity-confirmed satellite galaxies and the two hosts separate into two distinct subgroups in their line-of-sight velocities and on-sky distribution revealing a prominent coherent kinematic structure with a velocity amplitude of 67+-12 kms-1 . We test four scenarios to explain the observed velocity field: isotropic motions in a dark matter halo, a plane of satellites seen nearly face-on, and a kinematically mixed satellite system with a co-rotating edge-on plane and an isotropic component, and a merger of two small galaxy groups. Taking the geometry and dynamical state of the NGC5713/19 pair into account together with their positions and motions in the Bootes Strip the most consistent picture is the infall of two satellite systems that follow their host galaxies along a cosmic filament. We believe this is the first clear example of an equal-mass L* disk galaxy merger where a kinematically coherent satellite system is in the process of formation. These observations reinforce the importance of major mergers as a channel for producing co-rotating satellite systems.

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RR Lyrae Stars in Intermediate-age Magellanic Clusters: Membership Probabilities and Delay Time Distribution

Recent works have challenged our canonical view of RR Lyrae (RRL) stars as tracers of exclusively old populations ($\gtrsim10$~Gyr) by proposing a fraction of these stars to be of intermediate ages ($\sim$2-5~Gyr). Since it is currently not possible to infer stellar ages directly for individual RRL stars, our goal in this work is to search for these in association to intermediate-age clusters whose reliable ages can then be safely be attributed to the RRL. We used the Gaia DR3 Specific Object Study and OGLE IV public catalogues to search for RRL stars around stellar clusters older than 1~Gyr in the Large and Small Magellanic Clouds. Modelling membership probabilities based on proper motion and photometric distance we obtained a list of 259 RRL stars associated with Magellanic clusters. Of these, 23 RRL are likely members of 10 intermediate-age clusters: 3 and 7 in the Small and Large Magellanic Clouds, respectively. By modelling the inferred expectation values of the number of RRL stars per cluster, we inferred the delay time distribution of the RRL in three age ranges. For the old population ($>8$~Gyr) we find $2.5^{+0.4}_{-0.3}$ RRL$/10^5 M_\odot$. For the young (1-2 Gyr) and intermediate age (2-8 Gyr) populations we find rates of $0.34^{+0.17}_{-0.12}$ and $0.071^{+0.073}_{-0.041}$ RRL$/10^5 M_\odot$, respectively, after further decontamination from control field tests. While radial velocities are necessary for definitively confirming cluster memberships, the high-probability list of intermediate-age RRL stars presented here offers a promising opportunity for the first direct confirmation of these enigmatic stars.

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Reevaluating UMa3/U1: star cluster or the smallest known galaxy?

Ursa Major III/UNIONS 1 (UMa3/U1) is the faintest Milky Way satellite discovered to date, exhibiting a half-light radius of 3 $\pm$ 1 pc and an absolute V-band magnitude of +2.2 $\pm$ 0.4. Previous studies suggest UMa3/U1 is a dwarf galaxy, based on its large internal velocity dispersion and the improbability (indicated by dynamical cluster simulations) of its long-term survival if it were a dark-matter-free star cluster. In this paper, we model the evolution of UMa3/U1 as a star cluster using collisional N-body simulations that include a description of stellar evolution and the external tidal field of the Milky Way, with some simulations including primordial binaries. We find that UMa3/U1 has a substantial remaining lifetime of 2.7 $\pm$ 0.4 Gyr, primarily due to the retention of compact stellar remnants within the cluster. This retention is facilitated by mass segregation and the preferential loss of low-mass stars. Furthermore, we demonstrate that the observed large velocity dispersion of UMa3/U1 can be successfully reproduced. These results support the possibility that UMa3/U1 is a self-gravitating star cluster. Our simulations reveal that modelling UMa3/U1 as a dark matter free star cluster produces a markedly altered present-day mass function, driven by a strong depletion of low-mass stars. However, the degree of mass segregation among the visible stars is not statistically significant. We therefore recommend that future observations of UMa3/U1 and other very small Milky Way satellites focus on measuring their present-day mass functions to determine their nature.

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oMEGACat. VI. Analysis of the overall kinematics of Omega Centauri in 3D: velocity dispersion, kinematic distance, anisotropy, and energy equipartition

Omega Centauri ($ω$ Cen) is the Milky Way's most massive globular cluster and is likely the stripped nucleus of an accreted dwarf galaxy. In this paper, we analyze $ω$ Cen's kinematics using data from oMEGACat, a comprehensive catalog of $ω$ Cen's central regions, including 1.4 million proper motion measurements and 300,000 spectroscopic radial velocities. Our velocity dispersion profiles and kinematic maps are consistent with previous work but improve on their resolution, precision, and spatial coverage. The cluster's 3D dispersion is isotropic in the core, with increasing radial anisotropy at larger radii. The 2D kinematic maps show an elongation of the velocity dispersion field comparable to the flattening observed photometrically. We find good agreement between proper motions and line-of-sight velocity dispersion and measure a kinematic distance of 5494$\pm$61 pc, the most precise kinematic distance to $ω$ Cen available. The subset of data with precise metallicity measurements shows no correlation between metallicity and kinematics, supporting the picture of well-mixed stellar populations within the half-light radius of $ω$ Cen. Finally, we study the degree of energy equipartition using a large range of stellar masses. We find partial energy equipartition in the center that decreases towards large radii. The spatial dependence of the radial energy equipartition is stronger than the tangential energy equipartition. Our kinematic observations can serve as a new reference for future dynamical modeling efforts that will help to further disentangle the complex mass distribution within $ω$ Cen.

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Multiple stellar populations at less evolved stages. IV. evidence of helium enrichments in four Magellanic globular clusters

Most globular clusters in the local group show multiple stellar populations, a pattern defined by variations of several light elements, with some also displaying dispersions in heavy elements. Since helium is the most immediate product of hydrogen burning, almost all models suggest that second-generation stars should show different levels of helium enrichment than first-generation stars. Therefore, investigating helium enrichment in stellar populations of globular clusters can constrain different theoretical models. Using the deep photometry carried out by the {\sl Hubble} Space Telescope, we have analyzed the morphologies of the main sequences of four Large Magellanic Cloud globular clusters, Hodge 11, NGC 1841, NGC 2210, and NGC 2257. We aim to constrain the helium distributions among their main sequence stars. We found a clear broadening of main sequences in all four clusters. After excluding the effects of photometric errors, differential reddening, unresolved binaries, and metallicity dispersions, this broadening would suggest a substantial helium enrichment in their star populations, ranging from $δ{Y}=0.08$ to $δ{Y}\geq0.12$, depending on the presumed helium distributions. Helium-enriched stars are comparable in number to normal stars within these clusters, and may even dominate, comprising approximately $\sim$40\% to over 80\% of the total stellar population. However, given the great distance of the Large Magellanic Cloud, it is difficult to rule out the significant impact of crowding, so our results may only represent an upper limit.

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Fast-moving stars around an intermediate-mass black hole in Omega Centauri

Black holes have been found over a wide range of masses, from stellar remnants with masses of 5-150 solar masses (Msun), to those found at the centers of galaxies with $M>10^5$ Msun. However, only a few debated candidate black holes exist between 150 and $10^5$ Msun. Determining the population of these intermediate-mass black holes is an important step towards understanding supermassive black hole formation in the early universe. Several studies have claimed the detection of a central black hole in $ω$ Centauri, the Milky Way's most massive globular cluster. However, these studies have been questioned due to the possible mass contribution of stellar mass black holes, their sensitivity to the cluster center, and the lack of fast-moving stars above the escape velocity. Here we report observations of seven fast-moving stars in the central 3 arcseconds (0.08 pc) of $ω$ Centauri. The velocities of the fast-moving stars are significantly higher than the expected central escape velocity of the star cluster, so their presence can only be explained by being bound to a massive black hole. From the velocities alone, we can infer a firm lower limit of the black hole mass of $\sim$8,200 Msun, making this a compelling candidate for an intermediate-mass black hole in the local universe.

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Direct N-body simulations of NGC 6397 and its tidal tails

We have performed a series of direct N-body simulations that study the evolution of the Galactic globular cluster NGC 6397 under the combined influence of two-body relaxation, stellar evolution and the Milky Way's tidal field. Our simulations follow the evolution of the cluster over the last several Gyr up to its present-day position in the Milky Way in order to allow us to derive present-day cluster parameters and the distribution of its extra-tidal stars. We have also determined a new density profile of NGC 6397 by selecting stars from Gaia DR3 using Gaia DR3 proper motions, parallaxes and photometry to discriminate cluster members from non-members. This allows us to derive the surface density profile of NGC 6397 and the location of its tidal tails up to 10 degrees of the cluster centre, well beyond the tidal radius of NGC 6397. Our results show that the current state of NGC 6397 in terms of surface density, velocity dispersion profile and stellar mass function can be matched by a cluster model evolving from a standard initial mass function and does not require an additional central cluster of dark remnants. We also find good agreement in the location and absolute number of the extra-tidal stars between our simulations and the observations, making it unlikely that NGC 6397 is surrounded by a dark matter halo.

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The Kinematics of 30 Milky Way Globular Clusters and the Multiple Stellar Populations within

The spectroscopic and photometric classification of multiple stellar populations (MPs) in Galactic globular clusters (GCs) has enabled comparisons between contemporary observations and formation theories regarding the initial spatial configurations of the MPs. However, the kinematics of these MPs is an aspect that requires more attention. We investigated the 3D kinematics of 30 Galactic GCs, extending to 3-5 half-light radii, as well as their MPs, in order to uncover clues of the initial conditions of GCs and the MPs within. We have combined Hubble Space Telescope and Gaia DR3 proper motions together with a comprehensive set of line-of-sight velocities to determine the 3D rotation amplitudes, rotation axes, and anisotropy profiles of the clusters. We include radial velocities from new IFU observations of NGC 5024 and an analysis of archival MUSE data of NGC 6101. We compare our kinematic results with structural and orbital parameters of each cluster, reporting the most significant correlations and common features. We find significant rotation in 21 GCs, with no significant differences between the total rotational amplitudes of the MPs, except for NGC 104. We find no significant differences in the position angles or inclination angles. We find that the 3D rotational amplitude is strongly correlated with mass, relaxation time, enriched star fraction and concentration. We determine the anisotropy profiles of each cluster and the MPs where possible. We investigate correlations with the structural parameters, orbital parameters and accretion history of the clusters, finding that the dynamically young clusters with the highest central concentrations of primordial stars show radial anisotropy in their outer regions ($>2$ half-light radii). The dynamically young clusters with a central concentration of enriched stars show significant tangential anisotropy or isotropy in their outer regions.

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