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Star clusters stand at the crossroads between galaxies and single stars. Resolving the formation of star clusters in cosmological simulations represents an ambitious and challenging goal, since modelling their internal properties requires very high resolution. This paper is the third of a series within the SImulating the Environment where Globular clusters Emerged (SIEGE) project, where we conduct zoom-in cosmological simulations with sub-parsec resolution that include the feedback of individual stars, aimed to model the formation of star clusters in high-redshift proto-galaxies. We investigate the role of three fundamental quantities in shaping the intrinsic properties of star clusters, i. e., i) pre-supernova stellar feedback (continuous or instantaneous ejection of mass and energy through stellar winds); ii) star formation efficiency, defined as the fraction of gas converted into stars per freefall time, for which we test 2 different values (epsi_ff=0.1 and 1), and iii) stellar initial mass function (IMF, standard vs top-heavy). All our simulations are run down to z=10.5, which is sufficient for investigating some structural properties of the emerging clumps and clusters. [Abridged] The prescription for a continuous, low-intensity feedback, along with the adoption of epsi_ff=1, produces star clusters with maximum stellar density values up to 10^4 M_sun pc^(-2), in good agreement with the surface density-size relation observed in local young star clusters (YSCs). Therefore, a realistic stellar wind description and a high star formation effiency are the key ingredients that allow us to achieve realistic star clusters characterised by properties comparable to those of local YSCs. In contrast, the other models produce too diffuse clusters, in particular the one with a top-heavy IMF., Comment: 20 pages, 14 pages

We present the results of Monte Carlo simulations aimed at exploring the evolution towards energy equipartition of first- (1G) and second-generation (2G) stars in multiple-population globular clusters and how this evolution is affected by the initial differences between the spatial distributions of the two populations. Our results show that these initial differences have fundamental implications for the evolution towards energy equipartition of the two populations. We find that 2G stars, which are assumed to be initially more centrally concentrated than 1G stars, are generally characterized by a more rapid evolution towards energy equipartition. The evolution towards energy equipartition depends on the velocity dispersion component and is more rapid for the tangential velocity dispersion. The extent of the present-day differences between the degree of energy equipartition of 2G and 1G stars depends on the cluster's dynamical age and may be more significant in the tangential velocity dispersion and at intermediate distances from the cluster's center around the half-mass radius., Comment: 13 pages, 13 figures, Published in MNRAS

We present observations of the two closest globular clusters, NGC 6121 and NGC 6397, taken with the NIRISS detector of JWST. The combination of our new JWST data with archival Hubble Space Telescope (HST) images allows us to compute proper motions, disentangle cluster members from field objects, and probe the main sequence (MS) of the clusters down to <0.1 $M_\odot$ as well as the brighter part of the white-dwarf sequence. We show that theoretical isochrones fall short in modeling the low-mass MS and discuss possible explanations for the observed discrepancies. Our analysis suggests that the lowest-mass members of both clusters are significantly more metal-rich and oxygen-poor than their higher-mass counterparts. It is unclear whether the difference is caused by a genuine mass-dependent chemical heterogeneity, low-temperature atmospheric processes altering the observed abundances, or systematic shortcomings in the models. We computed the present-day local luminosity and mass functions of the two clusters; our data reveal a strong flattening of the mass function indicative of a significant preferential loss of low-mass stars in agreement with previous dynamical models for these two clusters. We have made our NIRISS astro-photometric catalogs and stacked images publicly available to the community., Comment: 15 pages, 12 figures, 2 tables. Accepted for publication in A&A on September 04, 2024. Astro-photometric catalogs and stacked images will be available at the CDS after the paper will be published

We present a study of the white dwarf (WD) cooling sequence (CS) in the globular cluster (GC) Omega Centauri, the primary goal of a dedicated Hubble Space Telescope (HST) programme. Our analysis has revealed that the peak at the termination of the WD CS is located at $m_{\rm F606W}$=30.1$\pm$0.2 (equivalent to $V$$\sim$31). The brighter part of Omega Centauri's WD CS is consistent with the presence of massive He-core WDs, in agreement with previous HST analyses with ultraviolet and blue filters. Comparative analyses of the WD luminosity function (LF) with theoretical counterparts have shown that a single-age population for the cluster is compatible with the data. However, an analysis of just the WD LF cannot entirely exclude the possibility of an age range, due to uncertainties in the present-day WD mass function, with a star formation history potentially spanning up to 5 billion years, predominantly comprising stars about 13 Gyr old, and with just a minority potentially as young as 8 Gyr. This underscores the need for global spectroscopic and photometric investigations that include simultaneously the WD populations together with the previous evolutionary phases to fully understand the cluster's diverse chemical compositions and ages., Comment: 10 pages, 9 figures. Accepted for publication in Astronomy & Astrophysics on Sep 5, 2024

We present the first 3D kinematic analysis of multiple stellar populations (MPs) in a representative sample of 16 Galactic globular clusters (GCs). For each GC in the sample we studied the MP line-of-sight, plane-of-the-sky and 3D rotation as well as the velocity distribution anisotropy. The differences between first- (FP) and second-population (SP) kinematic patterns were constrained by means of parameters specifically defined to provide a global measure of the relevant physical quantities and to enable a meaningful comparison among different clusters. Our analysis provides the first observational description of the MP kinematic properties and of the path they follow during the long-term dynamical evolution. In particular, we find evidence of differences between the rotation of MPs along all velocity components with the SP preferentially rotating faster than the FP. The difference between the rotation strength of MPs is anti-correlated with the cluster dynamical age. We observe also that FPs are characterized by isotropic velocity distributions at any dynamical age probed by our sample. On the contrary, the velocity distribution of SP stars is found to be radially anisotropic in dynamically young clusters and isotropic at later evolutionary stages. The comparison with a set of numerical simulations shows that these observational results are consistent with the long-term evolution of clusters forming with an initially more centrally concentrated and more rapidly rotating SP subsystem. We discuss the possible implications these findings have on our understanding of MP formation and early evolution., Comment: 26 pages, 22 figures, 3 tables; accepted for publication in A&A on September 2 2024

Context. Globular clusters (GCs) are suggested to host many stellar-mass black holes (BHs) at their centers, thus resulting in ideal testbeds for BH formation and retention theories. BHs are expected to play a major role in GC structural and dynamical evolution and their study has attracted a lot of attention. In recent years, several works attempted to constrain the BH mass fraction in GCs typically by comparing a single observable (for example mass segregation proxies) with scaling relations obtained from numerical simulations. Aims. We aim to uncover the possible intrinsic degeneracies in determining the BH mass fraction from single dynamical parameters and identify the possible parameter combinations that are able to break these degeneracies. Methods. We used a set of 101 Monte Carlo simulations sampling a large grid of initial conditions. In particular, we explored the impact of different BH natal kick prescriptions on widely adopted scaling relations. We then compared the results of our simulations with observations obtained using state-of-the-art HST photometric and astrometric catalogs for a sample of 30 Galactic GCs. Results. We find that using a single observable to infer the present-day BH mass fraction in GCs is degenerate, as similar values could be attained by simulations including different BH mass fractions. We argue that the combination of mass-segregation indicators with GC velocity dispersion ratios could help us to break this degeneracy efficiently. We show that such a combination of parameters can be derived with currently available data. However, the limited sample of stars with accurate kinematic measures and its impact on the overall errors do not allow us to discern fully different scenarios yet., Comment: 9 pages, 7 figures, accepted for publication by A&A

Thanks to its exceptional near-infrared photometry, JWST can effectively contribute to the discovery, characterization, and understanding of multiple stellar populations in globular clusters, especially at low masses where the Hubble Space Telescope (HST) faces limitations. This paper continues the efforts of the JWST GO-1979 program in exploring the faintest members of the globular cluster NGC 6397. Here we show that the combination of HST and JWST data allows us to identify two groups of MS stars (MSa, the first-generation, and MSb, the second-generation group). We measured the ratio between the two groups and combined it with measurements from the literature focused on more central fields and more massive stars compared to our study. We find that the MSa and MSb stars are present in a $\approx$30-70 ratio regardless of the distance from the centre of the cluster and the mass of the stars used so far., Comment: 7 pages, 6 figures, 1 table, A&A accepted

We exploit the astro-photometric dataset of the multi-epoch infrared parallel field of a $\textit{Hubble Space Telescope}$ Large Programme aimed at studying the faintest stars of the globular cluster NGC$\,$6752 to determine the luminosity and mass functions of the multiple stellar populations of this cluster. Thanks to the measurement of proper motions and deeper completeness, the results presented in this paper represent a significant improvement over those of previous studies. We successfully derived membership probabilities reaching stars as faint as $m_{\rm F160W} \sim 25$, allowing us to reliably distinguish the three main stellar populations detected within this cluster. We employed a new set of model isochrones that have been individually fit to the colour-magnitude diagram of each population. We present a comprehensive analysis of the luminosity and mass functions for three stellar populations within NGC$\,$6752. Notably, our findings reveal differences in the present-day luminosity and mass functions of first-generation and second-generation stars; these differences are consistent with the manifestation of the effects of dynamical processes acting on populations with different initial spatial distributions. Finally, we publicly release the catalogues with positions, photometry, proper motions, and memberships probabilities, as well as the stacked-image atlases and all newly calculated stellar models., Comment: 25 pages, 17 figures, 5 tables. Accepted for publication in AN

We explore the possibility that the N-rich young proto-galaxy GN-z11 recently observed at z=10.6 by the James Webb Space Telescope is the result of the formation of second generation stars from pristine gas and Asymptotic Giant Branch (AGB) ejecta in a massive globular cluster or nuclear star cluster. We show that a second generation forming out of gas polluted by the ejecta of massive AGB stars and mixed with gas having a standard composition accounts for the unusually large N/O in the GN-z11 spectrum. The timing of the evolution of massive (4-7.5M$_{\odot}$) AGBs also provides a favourable environment for the growth of a central stellar mass black hole to the Active Galactic Nucleus stage observed in GN-z11. According to our model the progenitor system was born at an age of the Universe of $\simeq 260 - 380$Myr, well within the pre-reionization epoch., Comment: 6 pages, 3 figures, accepted for publication on A&A Letters

We use zoom-in, hydrodynamical, cosmological $N$-body simulations tracing the formation of the first stellar clumps from the SImulating the Environments where Globular clusters Emerged (SIEGE) project, to study key structural properties of dark matter haloes when the Universe was only $0.92$ Gyr old. The very high-resolution (maximum physical resolution 0.3 h$^{-1}$ pc at $z=6.14$, smallest dark-matter particle mass $164\,M_{\odot}$) allows us to reach the very low mass end of the stellar-to-halo mass relation ($M_{\rm vir}=10^{7.5-9.5}\,M_{\odot}$) to study the processes that mould dark matter haloes during the first stages of structure formation. We investigate the role of baryonic cooling and stellar feedback, modeled from individual stars, in shaping haloes, and of environmental effects as accretion of dark matter along cosmic filaments and mergers. We find that the onset of star formation (typically for $\log M_{\rm vir}/M_{\odot}\simeq7.6$) causes the inner cusp in the haloes density profile to flatten into a core with constant density and size proportionally to the halo virial mass. Even at these mass scales, we confirm that baryons make haloes that have formed stars rounder in the central regions than haloes that have not formed stars yet, with median minor-to-major $\langle q \rangle$ and intermediate-to-major $\langle s \rangle$ axes 0.66 and 0.84, respectively. Our morphological analysis shows that, at $z=6.14$, haloes are largely prolate in the outer parts, with the major axis aligned along filaments of the cosmic web or towards smaller sub-haloes, with the degree of elongation having no significant dependence on the halo mass., Comment: 20 pages, 11 figures. Accepted for publication in MNRAS

The Color Magnitude Diagram (CMD) morphology of the "extended" main sequence turnoff (eMSTO) and upper main sequence (MS) of the intermediate age ($\lesssim 2$ Gyr) Large Magellanic Cloud Cluster NGC 1783 shows the presence of a small group of UV-dim stars, that, in the ultraviolet Hubble Space Telescope filters, are located at colors on the red side of the typical "fan" shape displayed by the eMSTO. We model the UV-dim stars by assuming that some of the stars which would intrinsically be located on the left side of the eMSTO are obscured by a ring of dust due to grain condensation at the periphery of the excretion disc expelled when they spin at the high rotation rates typical of stars in the Be stage. A reasonably low optical depth at 10$\mu$ is necessary to model the UV-dim group. Introduction of dust in the interpretation of the eMSTO may require a substantial re-evaluation of previous conclusions concerning the role of age and/or rotation spreads in the MC clusters: the entire eMSTO can be populated by dusty stars, and the reddest UV-dim stars simply represents the tail of the distribution with both maximum obscuration and the dust ring seen along the line of sight. The model stars having higher rotational projected velocity ($v \sin$ i) are predicted to be preferentially redder than the slowly-rotating stars. The mass loss responsible for the dust may also cause the non-monotonic distribution of stars in the upper main sequence, with two peaks and gaps showing up in the UV CMD., Comment: 11 pages, 13 figures. This is a pre-copyedited, author-produced PDF of an article (stad851) accepted for publication in MNRAS following peer review

Several observational studies have shown that many Galactic globular clusters (GCs) are characterised by internal rotation. Theoretical studies of the dynamical evolution of rotating clusters have predicted that, during their long-term evolution, these stellar systems should develop a dependence of the rotational velocity around the cluster's centre on the mass of stars, with the internal rotation increasing for more massive stars. In this paper we present the first observational evidence of the predicted rotation-mass trend. In our investigation, we exploited the $\mathit{Gaia}$ Data Release 3 catalogue of three GCs: NGC 104 (47 Tuc), NGC 5139 ($\omega$ Cen) and NGC 5904 (M 5). We found clear evidence of a cluster rotation-mass relation in 47 Tuc and M 5, while in $\omega$ Cen, the dynamically youngest system among the three clusters studied here, no such trend was detected., Comment: 6 pages, 4 figures, 1 table. Accepted for publication in MNRAS Letters

We report on the identification of a massive ($\sim10^5$ M$_\odot$) sub-structured stellar system in the Galactic Perseus complex likely undergoing hierarchical cluster assembly. Such a system comprises nine star clusters (including the well-known clusters NGC 654 and NGC 663) and an extended and low-density stellar halo. Gaia-DR3 and available spectroscopic data show that all its components are physically consistent in the 6D phase-space (position, parallax, and 3D motion), homogeneous in age (14 $-$ 44 Myr), and chemical content (half-solar metallicity). In addition, the system's global stellar density distribution is that of typical star clusters and shows clear evidence of mass segregation. We find that the hierarchical structure is mostly contracting towards the center with a speed of up to $\simeq4-5$ km s$^{-1}$, while the innermost regions expand at a lower rate (about $\simeq1$ km s$^{-1}$) and are dominated by random motions. Interestingly, this pattern is dominated by the kinematics of massive stars, while low-mass stars ($M<2$ M$_\odot$) are characterized by contraction across the entire cluster. Finally, the nine star clusters in the system are all characterized by a relatively flat velocity dispersion profile possibly resulting from ongoing interactions and tidal heating. We show that the observational results are generally consistent with those found in $N$-body simulations following the cluster violent relaxation phase strongly suggesting that the system is a massive cluster in the early assembly stages. This is the second structure with these properties identified in our Galaxy and, following the nomenclature of our previous work, we named it LISCA II., Comment: 21 pages, 24 figures, 1 table; accepted for publication in A&A

Our understanding of the kinematic properties of multiple stellar populations (mPOPs) in Galactic globular clusters (GCs) is still limited compared to what we know about their chemical and photometric characteristics. Such limitation arises from the lack of a comprehensive observational investigation of this topic. Here we present the first homogeneous kinematic analysis of mPOPs in 56 GCs based on high-precision proper motions computed with Hubble Space Telescope data. We focused on red-giant-branch stars, for which the mPOP tagging is clearer, and measured the velocity dispersion of stars belonging to first (1G) and second generations (2G). We find that 1G stars are generally kinematically isotropic even at the half-light radius, whereas 2G stars are isotropic at the center and become radially anisotropic before the half-light radius. The radial anisotropy is induced by a lower tangential velocity dispersion of 2G stars with respect to the 1G population, while the radial component of the motion is comparable. We also show possible evidence that the kinematic properties of mPOPs are affected by the Galactic tidal field, corroborating previous observational and theoretical results suggesting a relation between the strength of the external tidal field and some properties of mPOPs. Although limited to the GCs' central regions, our analysis leads to new insights into the mPOP phenomenon, and provides the motivation for future observational studies of the internal kinematics of mPOPs., Comment: 10 pages, 4 figures, 2 tables. Accepted for publication on ApJ

In the past years, we have undertaken an extensive investigation of LMC and SMC star clusters based on HST data. We present photometry and astrometry of stars in 101 fields observed with the WFC/ACS, UVIS/WFC3 and NIR/WFC3 cameras. These fields comprise 113 star clusters. We provide differential-reddening maps and illustrate various scientific outcomes that arise from the early inspection of the photometric catalogs. In particular, we provide new insights on the extended main-sequence turn-off (eMSTO) phenomenon: i) We detected eMSTOs in two clusters, KMHK361 and NGC265, which had no previous evidence of multiple populations. This finding corroborates the conclusion that the eMSTO is a widespread phenomenon among clusters younger than ~2 Gyr. ii) The homogeneous color-magnitude diagrams (CMDs) of 19 LMC clusters reveal that the distribution of stars along the eMSTO depends on cluster age. iii) We discovered a new feature along the eMSTO of NGC1783, which consists of a distinct group of stars going on the red side of the eMSTO in CMDs composed of ultraviolet filters. Furthermore, we derived the proper motions of stars in the fields of view of clusters with multi-epoch images. Proper motions allowed us to separate the bulk of bright field stars from cluster members and investigate the internal kinematics of stellar populations in various LMC and SMC fields. As an example, we analyze the field around NGC346 to disentangle the motions of its stellar populations, including NGC364 and BS90, young and pre-MS stars in the star-forming region associated with NGC346, and young and old field stellar populations of the SMC. Based on these results and the fields around five additional clusters, we find that young SMC stars exhibit elongated proper-motion distributions that point toward the LMC, thus bringing new evidence for a kinematic connection between the LMC and SMC., Comment: 37 pages, 27 figures, accepted for publication in Astronomy & Astrophysics

We present our final study of the white dwarf cooling sequence (WD CS) in the globular cluster NGC 6752. The investigation is the main goal of a dedicated Hubble Space Telescope large Program, for which all the observations are now collected. The WD CS luminosity function (LF) is confirmed to peak at m_F606W = 29.3+/-0.1, consistent within uncertainties with what has been previously reported, and is now complete down to m_F606W~29.7. We have performed robust and conclusive comparisons with model predictions that show how the theoretical LF for hydrogen envelope WD models closely follow the shape of the empirical LF. The magnitude of the peak of the observed LF is matched with ages between 12.7 and 13.5 Gyr, consistent with the cluster age derived from the main sequence turn off and subgiant branch. We also find that the impact of multiple populations within the cluster on the WD LF for m_F606W below 27.3 is negligible, and that the presence of a small fraction of helium envelope objects is consistent with the data. Our analysis reveals a possible hint of an underestimate of the cooling timescales of models in the magnitude range 28.1 < m_F606W < 28.9. Finally, we find that hydrogen envelope models calculated with a new tabulation of electron conduction opacities in the transition between moderate and strong degeneracy provide WD ages that are too small in comparison to the Main Sequence turnoff age., Comment: 16 pages, 13 figures. Accepted for publication in MNRAS on 2022, November 4. Associated files soon at this https://web.oapd.inaf.it/bedin/files/PAPERs_eMATERIALs/NGC6752_IV/

We introduce a new set of zoom-in cosmological simulations with sub-pc resolution, intended to model extremely faint, highly magnified star-forming stellar clumps, detected at z=6.14 thanks to gravitational lensing. The simulations include feedback from individual massive stars (in both the pre-supernova and supernova phases), generated via stochastic, direct sampling of the stellar initial mass function. We adopt a modified 'delayed cooling' feedback scheme, specifically created to prevent artificial radiative loss of the energy injected by individual stars in very dense gas (n~10^3-10^5 cm^{-3}). The sites where star formation ignites are characterised by maximum densities of the order of 10^5 cm^{-3} and gravitational pressures P/k>10^7 K/cm^3, corresponding to the values of the local, turbulent regions where the densest stellar aggregates form. The total stellar mass at z=6.14 is 3.4x10^7 M_sun, in satisfactory agreement with the observed stellar mass of the observed systems. The most massive clumps have masses of ~10^6 M_sun and half-mass sizes of ~100 pc. These sizes are larger than the observed ones, including also other samples of lensed high-redshift clumps, and imply an average density one order of magnitude lower than the observed one. In the size-mass plane, our clumps populate a sequence that is intermediate between the ones of observed high-redshift clumps and local dSph galaxies., Comment: MNRAS, accepted for publication. 24 pages, 17 figures

A number of studies based on data collected by the $\textit{Hubble Space Telescope}$ ($\textit{HST}$) GO-13297 program "HST Legacy Survey of Galactic Globular Clusters: Shedding UV Light on Their Populations and Formation" have investigated the photometric properties of a large sample of Galactic globular clusters and revolutionized our understanding of their stellar populations. In this paper, we expand previous studies by focusing our attention on the stellar clusters' internal kinematics. We computed proper motions for stars in 56 globular and one open clusters by combining the GO-13297 images with archival $\textit{HST}$ data. The astro-photometric catalogs released with this paper represent the most complete and homogeneous collection of proper motions of stars in the cores of stellar clusters to date, and expand the information provided by the current (and future) $\textit{Gaia}$ data releases to much fainter stars and into the crowded central regions. We also census the general kinematic properties of stellar clusters by computing the velocity-dispersion and anisotropy radial profiles of their bright members. We study the dependence on concentration and relaxation time, and derive dynamical distances. Finally, we present an in-depth kinematic analysis of the globular cluster NGC 5904., Comment: 33 pages, 19 figures, 6 tables. Accepted for publication on ApJ. Astro-photometric catalogs, velocity-dispersion values and profiles are available at https://archive.stsci.edu/hlsp/hacks

We introduce a new prescription for the evolution of globular clusters (GCs) during the initial embedded gas phase into a Monte Carlo method. With a simplified version of the Monte Carlo MOCCA code embedded in the AMUSE framework, we study the survival of GCs after the removal of primordial gas. We first test our code and show that our results for the evolution of mass and Lagrangian radii are in good agreement with those obtained with N-body simulations. The Monte Carlo code enables a more rapid exploration of the evolution of systems with a larger number of stars than N-body simulations. We have carried out a new survey of simulations to explore the evolution of globular clusters with up to $N = 500000$ stars for a range of different star formation efficiencies and half-mass radii. Our study shows the range of initial conditions leading to the clusters' dissolution and those for which the clusters can survive this early evolutionary phase., Comment: 13 pages, 6 figures

Disentangling distinct stellar populations along the red-giant branches (RGBs) of Globular Clusters (GCs) is possible by using the pseudo two-color diagram dubbed chromosome map (ChM). One of the most intriguing findings is that the so-called first-generation (1G) stars, characterized by the same chemical composition of their natal cloud, exhibit extended sequences in the ChM. Unresolved binaries and internal variations in helium or metallicity have been suggested to explain this phenomenon. Here, we derive high-precision Hubble Space Telescope photometry of the GCs NGC6362 and NGC6838 and build their ChMs. We find that both 1G RGB and main-sequence (MS) stars exhibit wider ChM sequences than those of second-generation (2G). The evidence of this feature even among unevolved 1G MS stars indicates that chemical inhomogeneities are imprinted in the original gas. We introduce a pseudo two-magnitude diagram to distinguish between helium and metallicity, and demonstrate that star-to-star metallicity variations are responsible for the extended 1G sequence. Conversely, binaries provide a minor contribution to the phenomenon. We estimate that the metallicity variations within 1G stars of 55 GCs range from less than [Fe/H]~0.05 to ~0.30 and mildly correlate with cluster mass. We exploit these findings to constrain the formation scenarios of multiple populations showing that they are qualitatively consistent with the occurrence of multiple generations. In contrast, the fact that 2G stars have more homogeneous iron content than the 1G challenges the scenarios based on accretion of material processed in massive 1G stars onto existing protostars., Comment: 18 pages, 13 figures, accepted for publication in MNRAS

We present an investigation of the internal kinematic properties of M79 (NGC 1904). Our study is based on radial velocity measurements obtained from the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters for more than 1700 individual stars distributed between $\sim 0.3^{\prime\prime}$ and $770^{\prime\prime}$ ($\sim14$ three-dimensional half-mass radii), from the center. Our analysis reveals the presence of ordered line-of-sight rotation with a rotation axis almost aligned along the East-West direction and a velocity peak of $1.5$ km s$^{-1}$ at $\sim 70^{\prime\prime}$ from the rotation axis. The velocity dispersion profile is well described by the same King model that best fits the projected density distribution, with a constant central plateau at $\sigma_0\sim 6$ km s$^{-1}$. To investigate the cluster rotation in the plane of the sky, we have analyzed the proper motions provided by the Gaia EDR3, finding a signature of rotation with a maximum amplitude of $\sim 2.0$ km s$^{-1}$ at $\sim 80^{\prime\prime}$ from the cluster center. Analyzing the three-dimensional velocity distribution, for a sub-sample of 130 stars, we confirm the presence of systemic rotation and find a rotation axis inclination angle of $37${\deg} with respect to the line-of-sight. As a final result, the comparison of the observed rotation curves with the results of a representative N-body simulation of a rotating star cluster shows that the present-day kinematic properties of NGC 1904 are consistent with those of a dynamically old system that has lost a significant fraction of its initial angular momentum., Comment: 30 pages, 20 figures, 8 tables, accepted for publication in ApJ

Recent work has shown that NIR Hubble Space Telescope (HST) photometry allows us to disentangle multiple populations (MPs) among M dwarfs of globular clusters (GCs) and investigate this phenomenon in very low-mass (VLM) stars. Here, we present the color-magnitude diagrams (CMDs) of nine GCs and the open cluster NGC 6791 in the F110W and F160W bands of HST, showing that the main sequences (MSs) below the knee are either broadened or split thus providing evidence of MPs among VLM stars. In contrast, the MS of NGC 6791 is consistent with a single population. The color distribution of M-dwarfs dramatically changes between different GCs and the color width correlates with the cluster mass. We conclude that the MP ubiquity, variety, and dependence on GC mass are properties common to VLM and more-massive stars. We combined UV, optical, and NIR observations of NGC 2808 and NGC 6121 (M 4) to identify MPs along with a wide range of stellar masses (~ 0.2 - 0.8M ), from the MS turn off to the VLM regime, and measured, for the first time, their mass functions (MFs). We find that the fraction of MPs does not depend on the stellar mass and that their MFs have similar slopes. These findings indicate that the properties of MPs do not depend on stellar mass. In a scenario where the second generations formed in higher-density environments than the first generations, the possibility that the MPs formed with the same initial MF would suggest that it does not depend on the environment., Comment: 22 pages, 15 figures. Accepted for publication in ApJ

We present a numerical study, based on Monte Carlo simulations, aimed at defining new empirical parameters measurable from observations and able to trace the different phases of star cluster dynamical evolution. As expected, a central density cusp, deviating from the King model profile, develops during the core collapse (CC) event. Although the slope varies during the post-CC oscillations, the cusp remains a stable feature characterizing the central portion of the density profile in all post-CC stages. We then investigate the normalized cumulative radial distribution (nCRD) drawn by all the cluster stars included within one half the tridimensional half-mass radius (R<0.5 rh), finding that its morphology varies in time according to the cluster's dynamical stage. To quantify these changes we defined three parameters: A5, the area subtended by the nCRD within 5% of the half-mass radius, P5, the value of the nCRD measured at the same distance, and S2.5, the slope of the straight line tangent to the nCRD measured at R=2.5% rh. The three parameters evolve similarly during the cluster's dynamical evolution: after an early phase in which they are essentially constant, their values rapidly increase, reaching their maximum at the CC epoch and slightly decreasing in the post-CC phase, when their average value remains significantly larger than the initial one, in spite of some fluctuations. The results presented in the paper suggest that these three observable parameters are very promising empirical tools to identify the star cluster's dynamical stage from observational data., Comment: 18 pages, 11 figures, accepted for publication in ApJ

We present the results of a study aimed at exploring, by means of N-body simulations, the evolution of rotating multi-mass star clusters during the violent relaxation phase, in the presence of a weak external tidal field. We study the implications of the initial rotation and the presence of a mass spectrum for the violent relaxation dynamics and the final properties of the equilibria emerging at the end of this stage. Our simulations show a clear manifestation of the evolution towards spatial mass segregation and evolution towards energy equipartition during and at the end of the violent relaxation phase. We study the final rotational kinematics and show that massive stars tend to rotate more rapidly than low-mass stars around the axis of cluster rotation. Our analysis also reveals that during the violent relaxation phase, massive stars tend to preferentially segregate into orbits with angular momentum aligned with the cluster's angular momentum, an effect previously found in the context of the long-term evolution of star clusters driven by two-body relaxation., Comment: 18 pages, 20 figures, 1 appendix. Accepted for publication in MNRAS

In the fourth paper of this series, we present -- and publicly release -- the state-of-the-art catalogue and atlases for the two remaining parallel fields observed with the Hubble Space Telescope for the large programme on omega Centauri. These two fields are located at ~12' from the centre of the globular cluster (in the West and South-West directions) and were imaged in filters from the ultraviolet to the infrared. Both fields were observed at two epochs separated by about 2 years that were used to derive proper motions and to compute membership probabilities., Comment: 15 pages, 11 figures (low resolution). Electronic on-line material at this url https://web.oapd.inaf.it/bedin/files/PAPERs_eMATERIALs/wCen_HST_LargeProgram/P04/ ; Accepted for publication in MNRAS on 2021 May 18th, available at this url https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.3549S/abstract

We present a detailed 3D kinematic analysis of the central regions ($R<30''$) of the low-mass and dynamically evolved galactic globular cluster NGC 6362. The study is based on data obtained with ESO-VLT/MUSE used in combination with the adaptive optics module and providing $\sim3000$ line-of-sight radial velocities, which have been complemented with Hubble Space Telescope proper motions. The quality of the data and the number of available radial velocities allowed us to detect for the first time a significant rotation signal along the line of sight in the cluster core with amplitude of $\sim 1$ km/s and with a peak located at only $\sim20''$ from the cluster center, corresponding to only $\sim10\%$ of the cluster half-light radius. This result is further supported by the detection of a central and significant tangential anisotropy in the cluster innermost regions. This is one of the most central rotation signals ever observed in a globular cluster to date. We also explore the rotational properties of the multiple populations hosted by this cluster and find that Na-rich stars rotate about two times more rapidly than the Na-poor sub-population thus suggesting that the interpretation of the present-day globular cluster properties require a multi-component chemo-dynamical approach. Both the rotation amplitude and peak position would fit qualitatively the theoretical expectations for a system that lost a significant fraction of its original mass because of the long-term dynamical evolution and interaction with the Galaxy. However, to match the observations more quantitatively further theoretical studies to explore the initial dynamical properties of the cluster are needed., Comment: 13 pages, 12 figures, 2 tables; accepted for publication in MNRAS

The amount of mass lost by stars during the red-giant branch (RGB) phase is one of the main parameters to understand and correctly model the late stages of stellar evolution. Nevertheless, a fully-comprehensive knowledge of the RGB mass loss is still missing. Galactic Globular Clusters (GCs) are ideal targets to derive empirical formulations of mass loss, but the presence of multiple populations with different chemical compositions has been a major challenge to constrain stellar masses and RGB mass losses. Recent work has disentangled the distinct stellar populations along the RGB and the horizontal branch (HB) of 46 GCs, thus providing the possibility to estimate the RGB mass loss of each stellar population. The mass losses inferred for the stellar populations with pristine chemical composition (called first-generation or 1G stars) tightly correlate with cluster metallicity. This finding allows us to derive an empirical RGB mass-loss law for 1G stars. In this paper we investigate seven GCs with no evidence of multiple populations and derive the RGB mass loss by means of high-precision {\it Hubble-Space Telescope} photometry and accurate synthetic photometry. We find a cluster-to-cluster variation in the mass loss ranging from $\sim$0.1 to $\sim$0.3 $M_{\odot}$. The RGB mass loss of simple-population GCs correlates with the metallicity of the host cluster. The discovery that simple-population GCs and 1G stars of multiple population GCs follow similar mass-loss vs. metallicity relations suggests that the resulting mass-loss law is a standard outcome of stellar evolution., Comment: 10 pages, 7 figures, 3 tables, accepted for publication on MNRAS

We have carried out a set of Monte Carlo simulations to study a number of fundamental aspects of the dynamical evolution of multiple stellar populations in globular clusters with different initial masses, fractions of second generation (2G) stars, and structural properties. Our simulations explore and elucidate: 1) the role of early and long-term dynamical processes and stellar escape in the evolution of the fraction of 2G stars and the link between the evolution of the fraction of 2G stars and various dynamical parameters; 2) the link between the fraction of 2G stars inside the cluster and in the population of escaping stars during a cluster's dynamical evolution; 3) the dynamics of the spatial mixing of the first-generation (1G) and 2G stars and the details of the structural properties of the two populations as they evolve toward mixing; 4) the implications of the initial differences between the spatial distribution of 1G and 2G stars for the evolution of the anisotropy in the velocity distribution and the expected radial profile of the 1G and 2G anisotropy for clusters at different stages of their dynamical history; 5) the variation of the degree of energy equipartition of the 1G and the 2G populations as a function of the distance from the cluster's centre and the cluster's evolutionary phase., Comment: 16 pages, 19 figures. Accepted for publication in MNRAS

We present the first detailed observational picture of a possible ongoing massive cluster hierarchical assembly in the Galactic disk as revealed by the analysis of the stellar full phase-space (3D positions and kinematics and spectro-photometric properties) of an extended area ($6^{\circ}$ diameter) surrounding the well-known $\it h$ and $\chi$ Persei double stellar cluster in the Perseus Arm. Gaia-EDR3 shows that the area is populated by seven co-moving clusters, three of which were previously unknown, and by an extended and quite massive ($M\sim10^5 M_{\odot}$) halo. All stars and clusters define a complex structure with evidence of possible mutual interactions in the form of intra-cluster over-densities and/or bridges. They share the same chemical abundances (half-solar metallicity) and age ($t\sim20$ Myr) within a small confidence interval and the stellar density distribution of the surrounding diffuse stellar halo resembles that of a cluster-like stellar system. The combination of these evidences suggests that stars distributed within a few degrees from $\it h$ and $\chi$ Persei are part of a common, sub-structured stellar complex that we named LISCA I. Comparison with results obtained through direct $N$-body simulations suggest that LISCA I may be at an intermediate stage of an ongoing cluster assembly that can eventually evolve in a relatively massive (a few $10^5 M_{\odot}$) stellar system. We argue that such cluster formation mechanism may be quite efficient in the Milky Way and disk-like galaxies and, as a consequence, it has a relevant impact on our understanding of cluster formation efficiency as a function of the environment and redshift., Comment: 19 pages, 8 figures, 1 table; accepted for publication in ApJ

The location of Galactic Globular Clusters' (GC) stars on the horizontal branch (HB) should mainly depend on GC metallicity, the "first parameter", but it is actually the result of complex interactions between the red giant branch (RGB) mass loss, the coexistence of multiple stellar populations with different helium content, and the presence of a "second parameter" which produces dramatic differences in HB morphology of GCs of similar metallicity and ages (like the pair M3--M13). In this work, we combine the entire dataset from the Hubble Space Telescope Treasury survey and stellar evolutionary models, to analyse the HBs of 46 GCs. For the first time in a large sample of GCs, we generate population synthesis models, where the helium abundances for the first and the "extreme" second generations are constrained using independent measurements based on RGB stars. The main results are: 1) the mass loss of first generation stars is tightly correlated to cluster metallicity. 2) the location of helium enriched stars on the HB is reproduced only by adopting a higher RGB mass loss than for the first generation. The difference in mass loss correlates with helium enhancement and cluster mass. 3) A model of "pre-main sequence disc early loss", previously developed by the authors, explains such a mass loss increase and is consistent with the findings of multiple-population formation models predicting that populations more enhanced in helium tend to form with higher stellar densities and concentrations. 4) Helium-enhancement and mass-loss both contribute to the second parameter., Comment: 29 pages, 30 figures, 4 tables. Accepted for publication in MNRAS

We present a study of the internal kinematics of two globular clusters, M10 (NGC 6254) and M71 (NGC 6838), using individual radial velocity (RV) measurements obtained from observations using the Hydra multi-object spectrograph on the WIYN 3.5 m telescope. We measured 120 RVs for stars in M10, of which 107 were determined to be cluster members. In M71, we measured 82 RVs and determined 78 of those measurements belonged to cluster members. Using the cluster members, we determine a mean RV of $75.9 \pm 4.0$ (s.d.) km s$^{-1}$ and $-22.9 \pm 2.2$ (s.d.) km s$^{-1}$ for M10 and M71, respectively. We combined the Hydra RV measurements with literature samples and performed a line-of-sight rotational analysis on both clusters. Our analysis has not revealed a statistically significant rotation in either of these clusters with the exception of the inner region (10\arcsec - 117\arcsec) of M10 for which we find hints of a marginally significant rotation with amplitude V$_{rot} = 1.14 \pm 0.18$ km s$^{-1}$. For M10, we calculate a central velocity dispersion of $\sigma_{0} = 5.44 \pm 0.61$ km s$^{-1}$, which gives a ratio of the amplitude of rotation to the central velocity dispersion $V_{rot}/\sigma_{0} = 0.21 \pm 0.04$. We also explored the rotation of the multiple stellar populations identified in M10 and M71 and found rotation (or lack thereof) in each population consistent with each other and the cluster global rotation signatures., Comment: 12 pages, 7 figures

A number of scenarios for the formation of multiple populations in globular clusters (GCs) predict that second generation (2G) stars form in a compact and dense subsystem embedded in a more extended first-generation (1G) system. If these scenarios are accurate, a consequence of the denser 2G formation environment is that 2G binaries should be more significantly affected by stellar interactions and disrupted at a larger rate than 1G binaries. The fractions and properties of binary stars can thus provide a dynamical fingerprint of the formation epoch of multiple-population GCs and their subsequent dynamical evolution. We investigate the connection between binaries and multiple populations in five GCs, NGC 288, NGC 6121 (M 4), NGC 6352, NGC 6362, and NGC 6838 (M 71). To do this, we introduce a new method based on the comparison of Hubble Space Telescope observations of binaries in the F275W, F336W, F438W, F606W and F814W filters with a large number of simulated binaries. In the inner regions probed by our data we do not find large differences between the local 1G and the 2G binary incidences in four of the studied clusters, the only exception being M 4 where the 1G binary incidence is about three times larger than the 2G incidence. The results found are in general agreement with the results of simulations predicting significant differences in the global 1G and 2G incidences and in the local values in the clusters' outer regions but similar incidences in the inner regions. The significant difference found in M 4 is consistent with simulations with a larger fraction of wider binaries. Our analysis also provides the first evidence of mixed (1G-2G) binaries, a population predicted by numerical simulations to form in a cluster's inner regions as a result of stellar encounters during which one component of a binary is replaced by a star of a different population., Comment: 13 pages, 11 figures, published in MNRAS

In the present work we analyzed seven globular clusters selected from their location in the Galactic bulge and with metallicity values in the range $-1.30\lesssim\rm{[Fe/H]}\lesssim-0.50$. The aim of this work is first to derive cluster ages assuming single stellar populations, and secondly, to identify the stars from first (1G) and second generations (2G) from the main sequence, subgiant and red giant branches, and to derive their age differences. Based on a combination of UV and optical filters used in this project, we apply the Gaussian mixture models to distinguish the multiple stellar populations. Applying statistical isochrone fitting, we derive self-consistent ages, distances, metallicities, and reddening values for the sample clusters. An average of $12.3\pm0.4$ Gyr was obtained both using Dartmouth and BaSTI (accounting atomic diffusion effects) isochrones, without a clear distinction between the moderately metal-poor and the more metal-rich bulge clusters, except for NGC 6717 and the inner halo NGC 6362 with $\sim 13.5$ Gyr. We derived a weighted mean age difference between the multiple populations hosted by each globular cluster of $41\pm170$ Myr adopting canonical He abundances; whereas for higher He in 2G stars, this difference reduces to $17\pm170$ Myr, but with individual uncertainties of $500$ Myr., Comment: 25 pages, 16 figures and 7 tables. Accepted for publication in ApJ

We studied the spatial distributions of multiple stellar populations (MPs) in a sample of 20 globular clusters (GCs) spanning a broad range of dynamical ages. The differences between first-population (FP) and second-population (SP) stars were measured by means of the parameter $A^+$, defined as the area enclosed between their cumulative radial distributions. We provide the first purely observational evidence of the dynamical path followed by MPs from initial conditions toward a complete FP-SP spatial mixing. Less dynamically evolved clusters have SP stars more centrally concentrated than FPs, while in more dynamically evolved systems the spatial differences between FP and SP stars decrease and eventually disappear. By means of an appropriate comparison with a set of numerical simulations, we show that these observational results are consistent with the evolutionary sequence expected by the long-term dynamical evolution of clusters forming with an initially more centrally concentrated SP sub-system. This result is further supported by the evidence of a trend between $A^+$ and the stage of GC dynamical evolution inferred by the ratio between the present-day and the initial mass of the cluster., Comment: 12 pages, 4 figures, 1 table; accepted for publication in ApJ Letters

By means of grid-based, 3D hydrodynamical simulations we study the formation of second generation (SG) stars in a young globular cluster (GC) of mass 10^7 Msun, the possible progenitor of an old GC with a present mass ~(1-5) * 10^6 Msun. The cluster accretes external gas as its first generation (FG) asymptotic giant branch (AGB) stars release their ejecta and SG stars form. We consider two models characterised by different densities of the external gas. In both cases, we find that a very compact SG subsystem with central density >10^5M sun/pc^3 forms in the innermost regions of the cluster. The low-density model forms a population of extreme SG stars with high helium enhancement, followed by the formation of another SG group out of a mix of pristine gas and AGB ejecta and characterised by a modest helium enhancement. On the other hand, the high-density model forms in prevalence SG stars with modest helium enhancement. Our simulations illustrate the dynamical processes governing the formation of SG populations in GCs and shed light on the structural properties emerging at the end of this phase. The newly born SG groups have different concentrations, with more extreme SG stars more centrally concentrated than those with less extreme chemical abundances. The very high density of the SG subsystems implies that SG massive stars, if formed, might suffer frequent close encounters, collisions and gas stripping, thus possibly contributing further gas to the SG formation., Comment: MNRAS, accepted for publication. 17 pages, 7 figures

The outer regions of globular clusters can enable us to answer many fundamental questions concerning issues ranging from the formation and evolution of clusters and their multiple stellar populations to the study of stars near and beyond the hydrogen-burning limit and to the dynamics of the Milky Way. The outskirts of globular clusters are still uncharted territories observationally. A very efficient way to explore them is through high-precision proper motions of low-mass stars over a large field of view. The Wide Field InfraRed Survey Telescope (WFIRST) combines all these characteristics in a single telescope, making it the best observational tool to uncover the wealth of information contained in the clusters' outermost regions., Comment: 8 pages, 3 figures

We used high-resolution optical HST/WFC3 and multi-conjugate adaptive optics assisted GEMINI GeMS/GSAOI observations in the near-infrared to investigate the physical properties of the globular cluster NGC 6569 in the Galactic bulge. We have obtained the deepest purely NIR color-magnitude diagram published so far for this cluster using ground-based observations, reaching $K_{s}$ $\approx$ 21.0 mag (two magnitudes below the main-sequence turn-off point). By combining the two datasets secured at two different epochs, we determined relative proper motions for a large sample of individual stars in the center of NGC 6569, allowing a robust selection of cluster member stars. Our proper motion analysis solidly demonstrates that, despite its relatively high metal content, NGC 6569 hosts some blue horizontal branch stars. A differential reddening map has been derived in the direction of the system, revealing a maximum color excess variation of about $\delta E(B-V)$ $\sim$ 0.12 mag in the available field of view. The absolute age of NGC 6569 has been determined for the first time. In agreement with the other few bulge globular clusters with available age estimates, NGC 6569 turns out to be old, with an age of about 12.8 Gyr, and a typical uncertainty of 0.8-1.0 Gyr., Comment: 25 pages, 16 Figures, 1 Table. Accepted for publication in ApJ

We present the analysis of the radial distributions and kinematic properties of the multiple stellar populations (mPOPs) hosted in the globular cluster (GC) NGC 6352 as part of the Hubble Space Telescope (HST) "UV Legacy Survey of Galactic Globular Clusters" program. NGC 6352 is one of the few GCs for which the mPOP tagging in appropriate color-magnitude diagrams is clear in all evolutionary sequences. We computed high-precision stellar proper motions for the stars from the cluster's core out to 75 arcsec ($\sim$1.5 core radii, or $\sim$0.6 half-light radii). We find that, in the region explored, first- and second-generation stars share the same radial distribution and kinematic properties. Velocity dispersions, anisotropy radial profiles, differential rotation, and level of energy equipartition, all suggest that NGC 6352 is probably in an advanced evolutionary stage, and any possible difference in the structural and kinematic properties of its mPOPs have been erased by dynamical processes in the core of the cluster. We also provide an estimate of the mass of blue stragglers and of main-sequence binaries through kinematics alone. In general, in order to build a complete dynamical picture of this and other GCs, it will be essential to extend the analyses presented in this paper to the GCs' outer regions where some memories of the initial differences in the mPOP properties, and those imprinted by dynamical processes, might still be present., Comment: 14 pages, 16 figures, 2 tables, accepted for publication in ApJ

Recent work, based on data from the Hubble Space Telescope (HST) UV Legacy Survey of Galactic Globular Clusters (GCs), has revealed that all the analyzed clusters host two groups of first- (1G) and second-generation (2G) stars. In most GCs, both 1G and 2G stars host sub-stellar populations with different chemical composition. We compare multi-wavelength HST photometry with synthetic spectra to determine for the first time the average helium difference between the 2G and 1G stars in a large sample of 57 GCs and the maximum helium variation within each of them. We find that in all clusters 2G stars are consistent with being enhanced in helium with respect to 1G. The maximum helium variation ranges from less than 0.01 to more than 0.10 in helium mass fraction and correlates with both the cluster mass and the color extension of the horizontal branch (HB). These findings demonstrate that the internal helium variation is one of the main (second) parameters governing the HB morphology., Comment: 26 pages, 19 figures, accepted for publications in MNRAS

As part of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters, we present a detailed investigation of the internal kinematics of NGC 5986. The analysis is based on about 300 individual radial velocities of stars located at various distances from the cluster center, up to 300 arcseconds (about 4 half-mass radii). Our analysis reveals the presence of a solid-body rotation extending from the cluster center to the outermost regions probed by the data, and a velocity dispersion profile initially declining with the distance from the cluster's center, but flattening and staying constant at ~5 km/s for distances larger than about one half-mass radius. This is the first globular cluster for which evidence of the joint presence of solid-body rotation and flattening in the outer velocity dispersion profile is found. The combination of these two kinematical features provides a unique opportunity to shed light on fundamental aspects of globular cluster dynamics and probe the extent to which internal relaxation, star escape, angular momentum transport and loss, and the interaction with the Galaxy tidal field can affect a cluster's dynamical evolution and determine its current kinematical properties. We present the results of a series of N-body simulations illustrating the possible dynamical paths leading to kinematic features like those observed in this cluster and the fundamental dynamical processes that underpin them., Comment: 22 pages, 8 figure, ApJ in press

We present a detailed analysis of the kinematic properties of the multiple populations (MPs) in the low-mass Galactic globular cluster NGC6362 based on a sample of about 500 member stars for which radial velocities (RVs), Fe and Na abundances have been homogeneously derived. At distances from the cluster center larger than about 0.5 $r_h$, we find that first (FG - Na-poor) and second generation (SG - Na-rich) stars show hints of different line-of-sight velocity dispersion profiles, with FG stars being dynamically hotter. This is the first time that differences in the velocity dispersion of MPs are detected by using only RVs. While kinematic differences between MPs in globular clusters are usually described in terms of anisotropy differences driven by the different radial distributions, this explanation seems hardly viable for NGC6362, where SG and FG stars are spatially mixed. We demonstrate that the observed difference in the velocity dispersion profiles can be accounted for by the effect of binary stars. In fact, thanks to our multi-epoch RV measurements we find that the binary fraction is significantly larger in the FG sample (f~14%) than in SG population (f<1%), and we show that such a difference can inflate the velocity dispersion of FG with respect to SG by the observed amount in the relevant radial range. Our results nicely match the predictions of state-of-the art $N$-body simulations of the co-evolution of MPs in globular clusters that include the effect of binaries., Comment: 18 pages, 6 figures; Accepted for publication in ApJ

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

The parameter A+, defined as the area enclosed between the cumulative radial distribution of blue straggler stars (BSSs) and that of a reference population, is a powerful indicator of the level of BSS central segregation. As part of the Hubble Space Telescope UV Legacy Survey of Galactic globular clusters (GCs), here we present the BSS population and the determination of A+ in 27 GCs observed out to about one half-mass radius. In combination with 21 additional clusters discussed in a previous paper this provides us with a global sample of 48 systems (corresponding to \sim 32\% of the Milky Way GC population), for which we find a strong correlation between A+ and the ratio of cluster age to the current central relaxation time. Tight relations have been found also with the core radius and the central luminosity density, which are expected to change with the long-term cluster dynamical evolution. An interesting relation is emerging between A+ and the ratio of the BSS velocity dispersion relative to that of main sequence turn-off stars, which measures the degree of energy equipartition experienced by BSSs in the cluster. These results provide further confirmation that BSSs are invaluable probes of GC internal dynamics and A+ is a powerful dynamical clock., Comment: Accepted for publication in the ApJ

In the context of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters, we present the line-of-sight rotation curve and velocity dispersion profile of M5 (NGC 5904), as determined from the radial velocity of more than 800 individual stars observed out to 700" (~ 5 half-mass radii) from the center. We find one of the cleanest and most coherent rotation patterns ever observed for globular clusters, with a very stable rotation axis (having constant position angle of 145^o at all surveyed radii) and a well-defined rotation curve. The density distribution turns out to be flattened in the direction perpendicular to the rotation axis, with a maximum ellipticity of 0.15. The rotation velocity peak (~3 km/s in projection) is observed at ~0.6 half-mass radii, and its ratio with respect to the central velocity dispersion (~0.3-0.4 at 4 projected half-mass radii) indicates that ordered motions play a significant dynamical role. This result strengthens the growing empirical evidence of the kinematic complexity of Galactic globular clusters and motivates the need of fundamental investigations of the role of angular momentum in collisional stellar dynamics., Comment: 27 pages, 11 figures, ApJ submitted. Text overlap with arXiv:1804.08618 because the two papers are part of the MIKiS Survey series

We present the first results of the Multi-Instrument Kinematic Survey of Galactic Globular Clusters, a project aimed at exploring the internal kinematics of a representative sample of Galactic globular clusters from the radial velocity of individual stars, covering the entire radial extension of each system. This is achieved by exploiting the formidable combination of multi-object and integral field unit spectroscopic facilities of the ESO Very Large Telescope. As a first step, here we discuss the results obtained for 11 clusters from high and medium resolution spectra acquired through a combination of FLAMES and KMOS observations. We provide the first kinematical characterization of NGC 1261 and NGC 6496. In all the surveyed systems, the velocity dispersion profile declines at increasing radii, in agreement with the expectation from the King model that best fits the density/luminosity profile. In the majority of the surveyed systems we find evidence of rotation within a few half-mass radii from the center. These results are in general overall agreement with the predictions of recent theoretical studies, suggesting that the detected signals could be the relic of significant internal rotation set at the epoch of the cluster's formation., Comment: 39 pages, 12 figures, ApJ, in press

We present a detailed analysis of the radial distribution of light-element multiple populations (LE-MPs) in the massive and dense globular cluster M80 based on the combination of UV and optical Hubble Space Telescope data. Surprisingly, we find that first generation stars (FG) are significantly more centrally concentrated than extreme second generation ones (SG) out to $\sim 2.5 r_h$ from the cluster center. To understand the origin of such a peculiar behavior, we used a set of $N$-body simulations following the long-term dynamical evolution of LE-MPs. We find that, given the advanced dynamical state of the cluster, the observed difference does not depend on the primordial relative distributions of FG and SG stars. On the contrary, a difference of $\sim 0.05-0.10 M_{\odot}$ between the average masses of the two sub-populations is needed to account for the observed radial distributions. We argue that such a mass difference might be the result of the higher He abundance of SG stars (of the order of $\Delta Y\sim 0.05-0.06$) with respect to FG. Interestingly, we find that a similar He variation is necessary to reproduce the horizontal branch morphology of M80. These results demonstrate that differences in mass among LE-MPs, due to different He content, should be properly taken into account for a correct interpretation of their radial distribution, at least in dynamically evolved systems., Comment: 19 pages, 9 figures, 1 table; Accepted for publication in ApJ

The split main sequences (MSs) and extended MS turnoffs (eMSTOs) detected in a few young clusters have demonstrated that these stellar systems host multiple populations differing in a number of properties such as rotation and, possibly, age.We analyze Hubble Space Telescope photometry for thirteen clusters with ages between ~40 and ~1000 Myrs and of different masses. Our goal is to investigate for the first time the occurrence of multiple populations in a large sample of young clusters. We find that all the clusters exhibit the eMSTO phenomenon and that MS stars more massive than ~1.6 solar masses define a blue and red MS, with the latter hosting the majority of MS stars. The comparison between the observations and isochrones suggests that the blue MSs are made of slow-rotating stars, while the red MSs host stars with rotational velocities close to the breakup value. About half of the bright MS stars in the youngest clusters are H-alpha emitters. These Be stars populate the red MS and the reddest part of the eMSTO thus supporting the idea that the red MS is made of fast rotators. We conclude that the split MS and the eMSTO are a common feature of young clusters in both Magellanic Clouds. The phenomena of a split MS and an eMSTO occur for stars that are more massive than a specific threshold which is independent of the host-cluster mass. As a by-product, we report the serendipitous discovery of a young SMC cluster, GALFOR1., Comment: 22 pages, 20 figures, accepted for publication in MNRAS

Dynamical evolution drives globular clusters toward core collapse, which strongly shapes their internal properties. Diagnostics of core collapse have so far been based on photometry only, namely on the study of the concentration of the density profiles. Here we present a new method to robustly identify core-collapsed clusters based on the study of their stellar kinematics. We introduce the \textit{kinematic concentration} parameter, $c_k$, the ratio between the global and local degree of energy equipartition reached by a cluster, and show through extensive direct $N$-body simulations that clusters approaching core collapse and in the post-core collapse phase are strictly characterized by $c_k>1$. The kinematic concentration provides a suitable diagnostic to identify core-collapsed clusters, independent from any other previous methods based on photometry. We also explore the effects of incomplete radial and stellar mass coverage on the calculation of $c_k$ and find that our method can be applied to state-of-art kinematic datasets., Comment: Accepted for publication in MNRAS Letter

As part of the Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters, 110 parallel fields were observed with the Wide Field Channel of the Advanced Camera for Surveys, in the outskirts of 48 globular clusters, plus the open cluster NGC 6791. Totalling about $0.3$ square degrees of observed sky, this is the largest homogeneous Hubble Space Telescope photometric survey of Galalctic globular clusters outskirts to date. In particular, two distinct pointings have been obtained for each target on average, all centred at about $6.5$ arcmin from the cluster centre, thus covering a mean area of about $23\,{\rm arcmin^{2}}$ for each globular cluster. For each field, at least one exposure in both F475W and F814W filters was collected. In this work, we publicly release the astrometric and photometric catalogues and the astrometrised atlases for each of these fields., Comment: 30 pages, 23 figures. Accepted by MNRAS