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Abstract We exploit the astro‐photometric dataset of the multi‐epoch infrared parallel field of aHubble Space TelescopeLarge 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 , 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. 

ABSTRACT We present an analysis of the degree of energy equipartition in a sample of 101 Monte Carlo numerical simulations of globular clusters (GCs) hosting either a system of stellar-mass black holes (BHS), an intermediate-mass black hole (IMBH) or neither of them. For the first time, we systematically explore the signatures that the presence of BHS or IMBHs produces on the degree of energy equipartition and if these signatures could be found in current observations. We show that a BHS can halt the evolution towards energy equipartition in the cluster centre. We also show that this effect grows stronger with the number of stellar-mass black holes in the GC. The signatures introduced by IMBHs depend on how dominant their masses are to the GCs and for how long the IMBH has co-evolved with its host GCs. IMBHs with a mass fraction below 2 per cent of the cluster mass produce a similar dynamical effect to BHS, halting the energy equipartition evolution. IMBHs with a mass fraction larger than 2 per cent can produce an inversion of the observed mass-dependence of the velocity dispersion, where the velocity dispersion grows with mass. We compare our results with observations of Galactic GCs and show that the observed range of the degree of energy equipartition in real clusters is consistent with that found in our analysis. In particular, we show that some Galactic GCs fall within the anomalous behaviour expected for systems hosting a BHS or an IMBH and are promising candidates for further dynamical analysis. 

ABSTRACT 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 ∼ 103–105 cm−3). The sites where star formation ignites are characterized by maximum densities of the order of 105 cm−3 and gravitational pressures Pgrav/k >107 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 3.4$$\times 10^7~\rm M_{\odot }$$, in satisfactory agreement with the observed stellar mass of the observed systems. The most massive clumps have masses of $$\sim 10^6~\rm M_{\odot }$$ 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 orders 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. 

ABSTRACT By means of 3D hydrodynamic simulations, we explore the effects of rotation in the formation of second-generation (SG) stars in globular clusters (GC). Our simulations follow the SG formation in a first-generation (FG) internally rotating GC; SG stars form out of FG asymptotic giant branch (AGB) ejecta and external pristine gas accreted by the system. We have explored two different initial rotational velocity profiles for the FG cluster and two different inclinations of the rotational axis with respect to the direction of motion of the external infalling gas, whose density has also been varied. For a low (10−24 g cm−3) external gas density, a disc of SG helium-enhanced stars is formed. The SG is characterized by distinct chemo-dynamical phase space patterns: it shows a more rapid rotation than the FG with the helium-enhanced SG subsystem rotating more rapidly than the moderate helium-enhanced one. In models with high external gas density ($$10^{-23}\, {\rm g\ cm^{-3}}$$), the inner SG disc is disrupted by the early arrival of external gas and only a small fraction of highly enhanced helium stars preserves the rotation acquired at birth. Variations in the inclination angle between the rotation axis and the direction of the infalling gas and the velocity profile can slightly alter the extent of the stellar disc and the rotational amplitude. The results of our simulations illustrate the complex link between dynamical and chemical properties of multiple populations and provide new elements for the interpretation of observational studies and future investigations of the dynamics of multiple-population GCs. 

The formation of compact high-redshift star-forming clumps, along with the physical processes driving their evolution and their potential connection to present-day globular clusters (GCs), are key open questions in studies of galaxy formation. In this work, we aim to shed light on these aspects using the SImulating the Environment where Globular clusters Emerged (SIEGE) project, a suite of cosmological zoom-in simulations with subparsec resolution that is specifically designed to investigate the physical conditions behind the origin of compact stellar systems in high-redshift environments. The simulations analyzed in this study are focused on a dwarf galaxy with a virial mass of a few 10⁹M_⊙atz= 6.14, where the spatial resolution reaches 0.3 pc h⁻¹. Individual stars are formed directly by sampling the initial mass function, with a 100% star formation efficiency. This setup is designed to explore the impact of a high star formation efficiency under high-redshift conditions. The simulation reveals the emergence of numerous stellar clumps with sizes of 1–3 pc, stellar surface densities up to almost 10⁴M_⊙pc⁻², and masses predominantly spanning 10³M_⊙to several 10⁴M_⊙, with a few reaching 10⁵M_⊙and up to 10⁶M_⊙. All clumps form during intense, short bursts of star formation lasting less than a megayear, without noticeable signs of second peaks of star formation or accretion, often with negligible dark matter content (i.e., dark-to-stellar mass ratios below 1 within three times their effective radii). We measured a clear correlation between mass and size, with a clump mass function described by a power law with a slope of −2. Star formation conditions in the simulation reveal a behaviour that is similar to that of a feedback-free starburst scenario, where dense clumps form due to inefficient stellar feedback over small timescales. Notably, some clumps exhibit properties that closely resemble those of present-day globular clusters, highlighting their potential evolutionary connection. 

Almost all globular clusters (GCs) contain multiple stellar populations consisting of stars with varying helium and light-element abundances. These populations include first-population stars, which exhibit similar chemical compositions as halo-field stars with comparable [Fe/H], and second-population stars, characterized by higher helium and nitrogen abundances along with reduced levels of oxygen and carbon. Nowadays, one of the most intriguing open questions about GCs pertains to the formation and evolution of their multiple populations. Recent works based on N-body simulations of GCs show that the fractions and characteristics of binary stars can serve as dynamic indicators of the formation period of multiple-population GCs and their subsequent dynamical evolution. Nevertheless, the incidence of binaries among multiple populations is still poorly studied. Moreover, the few available observational studies focus only on the bright stars of a few GCs. We used deep images of the GC 47 Tucanae collected with theJames Webband theHubblespace telescopes to investigate the incidence of binaries among multiple populations of M dwarfs and bright main- sequence stars. To reach this objective, we used UV, optical, and near-infrared filters to construct photometric diagrams that allowed us to disentangle binary systems and multiple populations. Moreover, we compared these observations with a large sample of simulated binaries. In the cluster central regions, the incidence of binaries among first-population stars is only slightly higher than that of second- population stars. In contrast, in the external regions, the majority of the studied binaries (≳85%) are composed of first-population stars. These results are consistent with the GC formation scenarios in which the second-population stars originate in the cluster’s central region, forming a compact and dense stellar group within a more extended system of first-population stars. 

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 (ϵ_ff= 0.1 and 1), and (iii) stellar initial mass function (IMF, standard vs top-heavy). All our simulations are run down toz= 10.5, which is sufficient for investigating some structural properties of the emerging clumps and clusters. Among the analysed quantities, the gas properties are primarily sensitive to the feedback prescriptions. A gentle and continuous feedback from stellar winds originates a complex, filamentary cold gas distribution, opposite to explosive feedback, causing smoother clumps. The prescription for a continuous, low-intensity feedback, along with the adoption of ϵ_ff= 1, also produces star clusters with maximum stellar density values up to 10⁴M_ʘpc⁻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. 

Recent work withJWSThas demonstrated its capability to identify and chemically characterize multiple populations in globular clusters down to the H-burning limit. In this study, we explore the kinematics of multiple populations in the globular cluster 47 Tucanae by combining data fromJWST, HST, Gaia, and ground-based telescopes. We analyzed velocity dispersion and anisotropy profiles from the cluster center out to ∼10R_h. Our findings indicate that while first population (1G) stars’ motions are isotropic, second population (2G) stars’ motions are significantly radially anisotropic. These results align with the predictions of simulations of the dynamical evolution of clusters where 2G stars are initially more centrally concentrated than 1G stars. Furthermore, we subdivided the 2G population into two subpopulations: 2G_Aand 2G_B, with the latter being more chemically extreme. We compared their dynamical profiles and found no significant differences. For the first time, we measured the degree of energy equipartition among the multiple populations of 47 Tucanae. Overall, within the analyzed radial range (∼2–4R_h), both populations exhibit a low degree of energy equipartition. The most significant differences between 1G and 2G stars are observed in the tangential velocity component, where 2G stars are characterized by a stronger degree of energy equipartition than 1G stars. In the radial component, the behavior of 1G and 2G stars is more variable, with differences largely dependent on radius. Moreover, our analysis reveals that the ratio of rotational velocity to velocity dispersion is larger for the 2G population. Finally, we found that 1G stars exhibit a higher skewness in their tangential proper motions than 2G stars, providing additional evidence of kinematic differences between the two stellar generations. 

Aims. Globular clusters (GCs) are known to host distinct stellar populations, characterized by different chemical compositions. Despite extensive research, the origin of these populations remains elusive. According to many formation scenarios, the second population (2P) originated within a compact and denser region embedded in a more extended first population (1P) system. As a result, 2P binaries should be disrupted at a larger rate than 1P binaries. For this reason, binary systems offer valuable insight into the environments in which these stellar populations formed and evolved. Methods. We analyzed the fraction of binaries among 1P and 2P M dwarfs in the outer region of NGC 288 using Hubble Space Telescope data. We combined our results with those from a previous work, where we inferred the fraction of 1P and 2P binaries in the cluster center. Results. In the outer region, we find a predominance of 1P binaries (97₋₃⁺¹%) compared to 2P binaries (3 ± 1%) corresponding to an incidence of binaries with a mass ratio (i.e., the ratio between the masses of the primary and secondary star) greater than 0.5 equal to 6.4 ± 1.7% for the 1P and 0.3 ± 0.2% for the 2P. These binary fractions and incidences differ from those found in the cluster’s central region, where the 1P and 2P exhibit similar binary incidences and fractions. These results are in general agreement with the predictions of simulations following the evolution of binary stars in multiple-population GCs, starting with a dense 2P subsystem concentrated in the central regions of a 1P system. 

We explored the evolution of various properties of multiple-population globular clusters (GCs) for a broad range of initial conditions. We simulated over 200 GC models using theMOCCAMonte Carlo code and find that the present-day properties of core and half-light radii and the ratio of the number of second-generation (SG) stars to the total number of stars (N_SG/N_TOT) of these models cover the observed values of these quantities for Milky Way GCs. Starting with a relatively small value of the SG fraction (N_SG/N_TOT~ 0.25) and a SG system concentrated in the inner regions of the cluster, we find, in agreement with previous studies, that systems in which the first-generation (FG) is initially tidally filling or slightly tidally underfilling best reproduce the observed ratios of N_SG/N_TOTand have values of the core and half-light radii typical of those of many Galactic globular clusters. Models in which the FG is initially tidally underfilling retain values of N_SG/N_TOTclose to their initial values. These simulations expand previous investigations and serve to further constrain the viable range of initial parameters and better understand their influence on present-day GC properties. The results of this investigation also provide the basis for our future survey aimed at building specific models to reproduce the observed trends (or lack thereof) between the properties of multiple stellar populations and other cluster properties.