Search

Nearly all star clusters younger than ~600 Myr exhibit extended main sequence turn offs and split main sequences (MSs) in their color-magnitude diagrams. Works based on both photometry and spectroscopy have firmly demonstrated that the red MS is composed of fast-rotating stars, whereas blue MS stars are slow rotators. Nevertheless, the mechanism responsible for the formation of stellar populations with varying rotation rates remains a topic of debate. Potential mechanisms proposed for the split MS include binary interactions, early evolution of pre-main sequence stars, and the merging of binary systems, but a general consensus has yet to be reached. These formation scenarios predict different fractions of binaries among blue- and red-MS stars. Therefore, studying the binary populations can provide valuable constraints that may help clarify the origins of the split MSs. We use high-precision photometry from the Hubble Space Telescope (HST) to study the binaries of three young Magellanic star clusters exhibiting split MS, namely NGC 1818, NGC 1850, and NGC 2164. By analyzing the photometry in the F225W, F275W, F336W, and F814W filters for observed binaries and comparing it to a large sample of simulated binaries, we determine the fractions of binaries within the red and the blue MS. We find that the fractions of binaries among the blue MS are higher than those of red-MS stars by a factor of ~1.5, 4.6, and ~1.9 for NGC 1818, NGC 1850, and NGC 2164, respectively. We discuss these results in the context of the formation scenarios of the split MS., Comment: 8 pages, 7 figures, accepted for publication in Astronomy & Astrophysics

We present the first comprehensive analysis of the internal dynamics of multiple stellar populations (MPs) in 28 Galactic Globular Clusters (GCs) across a wide field of view, extending from the innermost regions to the clusters' outskirts. Using astro-photometric catalogs from ground-based observations, Gaia, and the Hubble Space Telescope (HST), we identify first- (1P) and second-population (2P) stars, and study the internal dynamics of MPs using high-precision Gaia DR3 and HST proper motions. Our results reveal that while the 1P transitions from isotropy to slight tangential anisotropy toward the outer regions, 2P stars become increasingly radially anisotropic beyond the half-light radius. We also explore the connection between the dynamics of MPs and the clusters' structural and dynamical properties, finding statistically significant differences in the anisotropy profiles of dynamically young and non-relaxed clusters, particularly beyond the 1-2 half-light radii. In these regions, 1P stars transition from isotropic to slightly tangentially anisotropic motion, while 2P stars become more radially anisotropic. In contrast, dynamically older clusters, with mixed MPs, exhibit weaker relative differences. Furthermore, clusters with orbits closer to the Galactic center exhibit larger dynamical differences between 1P and 2P stars than those with larger peri-Galactic radii. These findings are consistent with a scenario where 2P stars form in a more centrally concentrated environment, where the interaction with the Milky Way tidal field plays a crucial role in the dynamical evolution of MPs, especially of 1P., Comment: 19 pages, 13 figures (4 pages and 9 figures will be online supplementary material). Submitted to MNRAS, comments welcome

In this paper, we study the Cauchy problem for the linear plate equation with mass term and its applications to semilinear models. For the linear problem we obtain $L^p-L^q$ estimates for the solutions in the full range $1\leq p\leq q\leq \infty$, and we show that such estimates are optimal. In the sequel, we discuss the global in time existence of solutions to the associated semilinear problem with power nonlinearity $|u|^\alpha$. For low dimension space $n\leq 4$, and assuming $L^1$ regularity on the second datum, we were able to prove global existence for $\alpha> \max\{\alpha_c(n), \tilde\alpha_c(n)\}$ where $\alpha_c = 1+4/n$ and $\tilde \alpha_c = 2+2/n$. However, assuming initial data in $H^2(\mathbb{R}^n)\times L^2(\mathbb{R}^n)$, the presence of the mass term allows us to obtain global in time existence for all $1<\alpha \leq (n+4)/[n-4]_+$. We also show that the latter upper bound is optimal, since we prove that there exist data such that a non-existence result for local weak solutions holds when $\alpha > (n+4)/[n-4]_+$.

The pseudo two-color diagram, known as chromosome map (ChM), is a valuable tool for identifying globular clusters (GCs) that consist of single or multiple stellar populations (MPs). Recent surveys of Galactic GCs using the ChM have provided stringent observational constraints on the formation of GCs and their stellar populations. However, these surveys have primarily focused on GCs at moderate distances from the Galactic center and composed of MPs. In this paper, we present the first detailed study of the stellar composition of four GCs in the outer halo of the Milky Way: Arp 2, Ruprecht 106, Terzan 7, and Terzan 8. Our analysis is based on high-precision photometry obtained from images collected with the Hubble Space Telescope in the F275W, F336W, F438W, F606W, and F814W bands. We find that Ruprecht 106 and Terzan 7 are composed solely of a single stellar population, whereas Arp 2 and Terzan 8 host both first- and second-population stars. In these clusters, the second population comprises about half and one-third of the total number of GC stars, respectively. The results from this paper and the literature suggest that the threshold in the initial GC mass, if present, should be smaller than approximately 10^5 M$_{\odot}$. The first-population stars of Arp 2 and Terzan 8, along with the stars of the simple-population GCs Ruprecht 106 and Terzan 7, exhibit intrinsic F275W - F814W color spreads, likely indicative of [Fe/H] variations of approximately 0.05 -- 0.30 dex. This suggests that star-to-star metallicity variations are a common feature of star clusters, regardless of the presence of MPs., Comment: Accepted for publication in ApJ, 17 pages, 7 figures

We present the first spectroscopic estimates of the chemical abundance of M dwarf stars in a globular cluster (GC), namely 47 Tucanae. By exploiting NIRSpec on board the James Webb Space Telescope (JWST) we gathered low-resolution spectra for 28 stars with masses in the range ~0.4-0.5 solar masses. The spectra are strongly affected by the H2O water vapour bands which can be used as indicators of the oxygen abundance. The spectral analysis reveals that the target stars feature a different O abundance, with a difference of ~0.40 dex between first and the most-polluted second population. The observed range is similar to that observed among red giant stars. This result reinforces previous findings based on the analysis of photometric diagrams, including the ``chromosome maps'', providing a first, and more direct, evidence of light element variations in the M dwarfs' mass regime. The observation that the multiple populations, with their variations in light elements, exhibit the same patterns from the lower main sequence all the way to the red giant branch further strengthens the notion that multiple stellar populations in globular clusters formed in a series of bursts of star formation., Comment: 9 pages, 4 figures, 2 tables, accepted for publication in ApJ Letters

Understanding the formation of multiple populations in globular clusters (GCs) represents a challenge for stellar population studies. Nevertheless, the outermost cluster regions, likely to hold clues about the initial configuration of GC stars, remain underexplored. We use synthetic spectra reflecting the chemical compositions of first- and second-population (1P, 2P) stars in 47Tucanae to identify spectral regions sensitive to these populations. This led us to define new photometric bands that effectively distinguish 1P and 2P giant stars using Gaia XP spectra. Testing these filters, we constructed the pseudo two-color diagrams dubbed chromosome maps (ChMs) and, for the first time, identified 1P and 2P stars in the cluster's outermost regions and beyond its tidal radius. We constructed similar diagrams for NGC3201, NGC6121, NGC6752, and NGC6397, thus exploring GCs with different metallicities. The ChMs effectively distinguished multiple populations in the outer regions of all clusters, except for the metal-poor NGC6397. Our findings, together with literature results from more-internal regions, show that the 2P stars of 47Tucanae are more-centrally concentrated than the 1P. A similar pattern is seen for 2P stars with extreme chemical composition of NGC3201. The multiple populations of NGC6121, and NGC6752 share the same radial distributions. These radial behaviors are consistent with the GC formation scenarios where 2P stars originate in the central regions. Noticeably, results on NGC3201 are in tension with the conclusion from recent work that its 1P is more centrally concentrated than the 2P and might form with more central concentration., Comment: 12 pages, 12 figures, accepted for publication in MNRAS

We present early-phase good-cadence (hour-to-day) simultaneous multiband ($ugi$ and $vrz$ bands) imaging of the nearby supernova SN~2024ggi, which exploded in the nearby galaxy, NGC 3621. A quick follow-up was conducted within less than a day after the explosion and continued $\sim$23 days. The $uvg$ band light curves display a rapid rise ($\sim$1.4 mag day$^{-1}$) to maximum in $\sim$4 days and absolute magnitude $M_{g}\sim$--17.75 mag. The post-peak decay rate in redder bands is $\sim$0.01 mag day$^{-1}$. Different colors (e.g., $u-g$ and $v-r$) of SN~2024ggi are slightly redder than SN 2023ixf. A significant rise ($\sim$12.5 kK) in black-body temperature (optical) was noticed within $\sim$2 days after the explosion, which successively decreased, indicating shock break out inside a dense circumstellar medium (CSM) surrounding the progenitor. Using semianalytical modeling, the ejecta mass and progenitor radius were estimated as 1.2 $M_\odot$ and $\sim$550 $R_\odot$. The archival deep images ($g,r,i and z$ bands) from the Dark Energy Camera Legacy Survey were examined, and a possible progenitor was detected in each band ($\sim$22--22.5 mag) and had a mass range of 14--17 $M_\odot$., Comment: Pages 12, Table 1, Figures 7

Globular cluster (GC) stars composed of pristine material (first-generation, 1G, stars) are not chemically homogeneous, as they exhibit extended sequences in the "Chromosome Map" (ChM). Recent studies characterized 1G stars within the center of 55 Galactic GCs, revealing metallicity variations. Despite this progress, several unanswered questions persist, particularly concerning the link between the 1G metallicity spread and factors such as the radial distance from the cluster center or the host GC parameters. Additionally, it remains unclear whether the extended 1G sequence phenomenon is exclusive to old Galactic GCs with multiple populations. This work addresses these open issues, examining 1G stars in different environments. First, we combine Hubble Space Telescope (HST) and James Webb Space Telescope photometry of the GC 47 Tucanae to study 1G stars at increasing distances from the cluster center. We find that metal-rich 1G stars are more centrally concentrated than metal-poor ones, suggesting a metallicity radial gradient. Additionally, the two groups of 1G stars share similar kinematics. Since our analysis focuses on giant stars in the cluster center and M dwarfs in external fields, we discuss the possibility that the metallicity distribution depends on stellar mass. Subsequently, we analyze HST multi-band photometry of two simple-population clusters, NGC 6791 and NGC 1783, revealing elongated sequences in the ChM associated with metallicity variations. Finally, we investigate the 1G color distribution in 51 GCs, finding no connections with the host cluster parameters. These results shed light on the complex nature of 1G stars, providing insights into the GC formation environment., Comment: 15 pages, 14 figures, accepted for pubblication in Astronomy & Astrophysics

The James Webb Space Telescope (JWST) observations have been demonstrated to be efficient in detecting globular clusters' (GCs) multiple stellar populations in the low mass regime of M dwarfs. We present an overview, and first results, of different projects that can be explored by using the JWST observations gathered under the GO2560 for 47 Tucanae, a first program entirely devoted to the investigation of multiple populations in very low mass stars, which includes spectroscopic data for the faintest GC stars for which spectra are available. Our color-magnitude diagram (CMD) shows some substructures for ultracool stars, including gaps and breaks in slope. In particular, we observe both a gap and a minimum in the F322W2 luminosity function less than one magnitude apart, and discuss which one could be associated with the H-burning limit. We detect stars fainter than this minimum, very likely the brown dwarfs. We corroborate the ubiquity of the multiple populations across different masses, from ~0.1 solar masses up to red giants (~0.8 solar masses). The oxygen range inferred from the M dwarfs, both from the CMD and from the spectra of two M dwarfs associated with different populations, is similar to that observed in giants. We have not detected any difference between the fractions of stars in distinct populations across stellar masses >~0.1 solar masses. This work demonstrates the JWST's capability in uncovering multiple populations within M dwarfs and illustrates the possibility to analyse very low-mass stars in GCs approaching the H-burning limit and the brown-dwarf sequence., Comment: 19 pages, 10 figures, 2 tables, accepted for publication in ApJ

The paper reports the results of an experiment aimed at testing to what extent ChatGPT 3.5 and 4 is able to answer questions regarding privacy policies designed in the new format that we propose. In a world of human-only interpreters, there was a trade-off between comprehensiveness and comprehensibility of privacy policies, leading to the actual policies not containing enough information for users to learn anything meaningful. Having shown that GPT performs relatively well with the new format, we provide experimental evidence supporting our policy suggestion, namely that the law should require fully comprehensive privacy policies, even if this means they become less concise.

The "chromosome maps" (ChMs) of globular clusters (GCs) have revealed that these ancient structures are not homogeneous in metallicity in various ways, and in different natures. The Type II GCs generally display larger variations, sometimes coupled with slow neutron capture (s) element enrichment on the ChMs redder sequences, which has been interpreted as due to multiple generations of stars. On the other hand, most GCs have inhomogeneous first populations (1P) in the form of large ranges in the Delta(F275W,F814W) values, pointing towards a not fully mixed pristine molecular cloud. We analyse the chemical composition the GC 47 Tucanae, which shows both inhomogeneous 1P stars and, although not formally a Type II GC, hosts a small number of stars distributed on a red side of the main stream of ChM stars. Our results suggest that 1P stars are not homogeneous in the overall metallicity, with variations of the order of ~0.10 dex in all the chemical species. The anomalous stars distributed on a redder sequence of the ChM, are further enriched in metals, but without any evidence for a significant enrichment in the s elements. Our three second population stars located on the normal component of the map, have metallicities similar to those of the metal-richer 1P group, suggesting that this population formed from these stars. Although three stars is a too-small sample to draw strong conclusions, the low spread in metals of these objects might point towards a formation in a fully mixed medium, possibly after a cooling flow phase., Comment: 16 pages, 6 figures, 8 tables. Accepted for publication in ApJ

Binary stars play a major role in determining the dynamic evolution of star clusters. We used images collected with the Hubble Space Telescope to study fourteen Magellanic Clouds star clusters that span an age interval between $\sim 0.6$ and $2.1$ Gyr and masses of $10^{4}-10^{5}$ M$_{\odot}$. We estimated the fraction of binary systems composed of two main-sequence stars and the fraction of candidate blue-straggler stars (BSSs). Moreover, we derived the structural parameters of the cluster, including the core radius, the central density, the mass function, and the total mass. We find that the fraction of binaries with a mass ratio larger than 0.7 ranges from $\sim$7%, in NGC1846, to $\sim$20%, in NGC2108. The radial and luminosity distribution can change from one cluster to another. However, when we combine the results from all the clusters, we find that binaries follow a flat radial trend and no significant correlation with the mass of the primary star. We find no evidence for a relation between the fractions of binaries and BSSs. We combined the results on binaries in the studied Magellanic Cloud clusters with those obtained for 67 Galactic globular clusters and 78 open clusters. We detect a significant anti-correlation between the binary fraction in the core and the mass of the host cluster. However, star clusters with similar masses exhibit a wide range of binary fractions. Conversely, there is no evidence of a correlation between the fraction of binaries and either the cluster age or the dynamic age., Comment: 16 figures, 18 pages, accepted for publication in Astronomy and Astrophysics

About one-fifth of the Galactic globular clusters (GCs), dubbed Type II GCs, host distinct stellar populations with different heavy elements abundances. NGC 1851 is one of the most studied Type II GCs, surrounded by several controversies regarding the spatial distribution of its populations and the presence of star-to-star [Fe/H], C+N+O, and age differences. This paper provides a detailed characterization of its stellar populations through Hubble Space Telescope (HST), ground-based, and Gaia photometry. We identified two distinct populations with different abundances of s-process elements along the red-giant branch (RGB) and the sub-giant branch (SGB) and detected two sub-populations among both s-poor (canonical) and s-rich (anomalous) stars. To constrain the chemical composition of these stellar populations, we compared observed and simulated colors of stars with different abundances of He, C, N, and O. It results that the anomalous population has a higher CNO overall abundance compared to the canonical population and that both host stars with different light-element abundances. No significant differences in radial segregation between canonical and anomalous stars are detected, while we find that among their sub-populations, the two most chemical extremes are more centrally concentrated. Anomalous and canonical stars show different 2D spatial distributions outside ~3 arcmin, with the latter developing an elliptical shape and a stellar overdensity in the northeast direction. We confirm the presence of a stellar halo up to ~80 arcmin with Gaia photometry, tagging 14 and five of its stars as canonical and anomalous, respectively, finding a lack of the latter in the south/southeast field., Comment: Accepted for publication on MNRAS

Ancient Galactic Globular Clusters (GCs) have long fascinated astronomers due to their intriguing multiple stellar populations characterized by variations in light-element abundances. Among these clusters, Type-II GCs stand out as they exhibit stars with large differences in heavy-element chemical abundances. These enigmatic clusters, comprising approximately 17\% of analyzed GCs with MPs, have been hypothesized to be the remnants of accreted dwarf galaxies. We focus on one of the most debated Type~II GCs, NGC1851, to investigate its MPs across a wide spatial range of up to 50 arcmin from the cluster center. By using Gaia DR3 low-resolution XP spectra, we generate synthetic photometry to perform a comprehensive analysis of the spatial distribution and kinematics of the canonical and anomalous populations within this GC. By using appropriate CMDs from the synthetic photometry in the BVI bands and in the $\rm f415^{25}$ band introduced in this work, we identify distinct stellar sequences associated with different heavy-element chemical composition. Our results suggest that the canonical and the anomalous populations reside both inside and outside the tidal radius of NGC1851, up to a distance that exceeds by 3.5 times its tidal radius. However, $\sim$80\% of stars outside the tidal radius are consistent with belonging to the canonical population, emphasizing its dominance in the cluster's outer regions. Remarkably, canonical stars exhibit a more circular on-sky morphology, while the anomalous population displays an elliptical shape. Furthermore, we delve into the kinematics of the multiple populations. Our results reveal a flat/increasing velocity dispersion profile in the outer regions and hints of a tangentially anisotropic motion in the outer regions, indicating a preference for stars to escape on radial orbits., Comment: 13 pages, 10 figures, accepted for publication in A&A

Young and intermediate-age star clusters of both Magellanic Clouds exhibit complex color-magnitude diagrams. In addition to the extended main-sequence turn-offs (eMSTOs), commonly observed in star clusters younger than ~2 Gyr, the clusters younger than ~800 Myr exhibit split main sequences (MSs). These comprise a blue MS, composed of stars with low-rotation rates, and a red MS, which hosts fast-rotating stars. While it is widely accepted that stellar populations with different rotation rates are responsible for the eMSTOs and split MSs, their formation and evolution are still debated. A recent investigation of the ~1.7 Gyr old cluster NGC1783 detected a group of eMSTO stars extremely dim in UV bands. Here, we use multi-band Hubble Space Telescope photometry to investigate five star clusters younger than ~200 Myr, including NGC1805, NGC1818, NGC1850, and NGC2164 in the Large Magellanic Cloud, and the Small-Magellanic Cloud cluster NGC330. We discover a group of bright MS stars in each cluster that are significantly dim in the F225W and F275W bands, similar to what is observed in NGC1783. Our result suggests that UV-dim stars are common in young clusters. The evidence that most of them populate the blue MS indicates that they are slow rotators. As a byproduct, we show that the star clusters NGC1850 and BHRT5b exhibit different proper motions, thus corroborating the evidence that they are not gravitationally bound., Comment: 11 pages, 8 figures, accepted for publication in MNRAS

Recent work on metal-intermediate globular clusters (GCs) with [Fe/H]=$-1.5$ and $-0.75$ has illustrated the theoretical behavior of multiple populations in photometric diagrams obtained with the James Webb Space Telescope (JWST). These results are confirmed by observations of multiple populations among M-dwarfs of 47 Tucanae. Here, we explore the multiple populations in metal-poor GCs with [Fe/H]=$-$2.3. We take advantage of synthetic spectra and isochrones that account for the chemical composition of multiple populations to identify photometric diagrams that separate the distinct stellar populations of GCs. We derived high-precision photometry and proper motion for main-sequence stars in the metal-poor GC M 92 from JWST and Hubble Space Telescope (HST) images. We identified a first generation (1G) and two main groups of second-generation stars (2G$_{\rm A}$ and 2G$_{\rm B}$) and investigated their kinematics and chemical composition. We find isotropic motions with no differences among the distinct populations. The comparison between the observed colors of M 92 stars and the colors derived by synthetic spectra reveals that helium abundance of 2G$_{\rm A}$ and 2G$_{\rm B}$ stars are higher than that of the 1G by $\Delta Y \sim 0.01$ and $0.04$, respectively. The $m_{\rm F090W}$ vs. $m_{\rm F090W}-m_{\rm F277W}$ color-magnitude diagram shows that below the knee, MS stars exhibit a wide color broadening due to multiple populations. We constrain the amount of oxygen variation needed to reproduce the observed MS width, which is consistent with results on red-giant branch stars. We conclude that multiple populations with masses of $\sim$0.1-0.8$M_{\odot}$ share similar chemical compositions., Comment: 15 pages, 9 figures. Published 2023 August 2 in ApJ

The presence of differential reddening in the direction of Galactic globular clusters (GCs) has proven to be a serious limitation in the traditional colour-magnitude diagram (CMD) analysis. Here, we estimate local reddening variations in the direction of 56 Galactic GCs. To do that, we use the public catalogs derived as part of the Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters, which include photometry in the F275W, F336W, F438W, F606W, and F814W filters. We correct photometry for differential reddening finding that for 21 out of 56 GCs the adopted correction procedure significantly improves the CMDs. Moreover, we measure the reddening law in the direction of these clusters finding that $R_{V}$ exhibits a high level of variability within the Galaxy, ranging from $\sim2.0$ to $\sim4.0$. The updated values of $R_{V}$ have been used to improve the determination of local reddening variations and derive high-resolution reddening maps in the direction of the 21 highly-reddened targets within our sample. To compare the results of the different clusters, we compute the 68$^{\rm th}$ percentile of the differential-reddening distribution, $\sigma_{\Delta A_{\rm F814W}}$. This quantity ranges from 0.003 mag to 0.030 mag and exhibits a significant anti-correlation with the absolute module of the Galactic latitude and a strong correlation with the average reddening in the direction of each cluster. Therefore, highly-reddened GCs located in the proximity of the Galactic plane typically show higher differential-reddening variations across their field of view., Comment: 14 pages, 14 figures, accepted for pubblication in MNRAS. The photometric catalogs corrected for differential reddening are publicly available at this website: http://progetti.dfa.unipd.it/GALFOR/

Binary stars play a crucial role in our understanding of the formation and evolution of star clusters and their stellar populations. We use Gaia Data Release 3 to homogeneously analyze 78 Galactic open clusters and the unresolved binary systems they host, each composed of two main sequence (MS) stars. We first investigated the structural parameters of these clusters, such as the core radius and the central density, and determined the cluster mass function (MF) and total mass by interpolating the density profile of each cluster. We measured the fraction of binaries with a large mass ratio and the fraction of blue straggler stars (BSSs), and finally investigated possible connections between the populations of binary stars and BSSs with the main parameters of the host cluster. {Remarkably, we find that the MFs of 78 analyzed open clusters follow a similar trend and are well reproduced by two single power-law functions, with a change in slope around masses of 1$M_{\odot}$. The fraction of binary stars ranges from $\sim$15\% to more than $\sim$60\% without significant correlation with the mass and the age of the host cluster. Moreover, we detect hints of a correlation between the total fraction of binary stars and the central density of the host cluster. We compared the fraction of binary stars with that of BSSs, finding that clusters with high and low central density exhibit different trends. The fraction of binaries does not significantly change with the mass of the primary star and the mass ratio. The radial distribution of binary stars depends on cluster age. The binaries of clusters younger than $\sim$800\,Myr typically show a flat radial distribution, with some hints of a double peak. In contrast, the binaries of the remaining clusters are more centrally concentrated than the single stars, which is similar to what is observed in globular clusters., Comment: 27 pages, 27 figures, accepted for publication in Astronomy & Astrophysics

We use images collected with the near-infrared camera (NIRCam) on board the James Webb Space Telescope and with the Hubble Space Telescope (HST) to investigate multiple populations at the bottom of the main sequence (MS) of 47 Tucanae. The F115W vs. F115W-F322W2 CMD from NIRCam shows that, below the knee, the MS stars span a wide color range, where the majority of M-dwarfs exhibit blue colors, and a tail of stars are distributed toward the red. A similar pattern is observed from the F160W vs. F110W-F160W CMD from HST, and multiple populations of M-dwarfs are also visible in the optical F606W vs. F606W-F814W CMD. The NIRCam CMD shows a narrow sequence of faint MS stars with masses smaller than 0.1 solar masses. We introduce a chromosome map of M-dwarfs that reveals an extended first population and three main groups of second-population stars. By combining isochrones and synthetic spectra with appropriate chemical composition, we simulate colors and magnitudes of different stellar populations in the NIRCam filters (at metallicities [Fe/H]=-1.5 and [Fe/H]=-0.75) and identify the photometric bands that provide the most efficient diagrams to investigate the multiple populations in globular clusters. Models are compared with the observed CMDs of 47 Tucanae to constrain M-dwarfs' chemical composition. Our analysis suggests that the oxygen range needed to reproduce the colors of first- and second-population M-dwarfs is similar to that inferred from spectroscopy of red giants, constraining the proposal that the chemical variations are due to mass transfer phenomena in proto-clusters., Comment: 21 pages, 17 figures, accepted for publication in MNRAS

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

Pseudo two-colour diagrams or Chromosome maps (ChM) indicate that NGC 2808 host five different stellar populations. The existing ChMs have been derived by the Hubble Space Telescope photometry, and comprise of stars in a small field of view around the cluster centre. To overcome these limitations, we built a ChM with U,B,I photometry from ground-based facilities that disentangle the multiple stellar populations of NGC 2808 over a wider field of view. We used spectra collected by GIRAFFE@VLT in a sample of 70 red giant branch (RGB) and seven asymptotic giant branch (AGB) stars to infer the abundances of C, N, O, Al, Fe, and Ni, which combined with literature data for other elements (Li, Na, Mg, Si, Ca, Sc, Ti, Cr and Mn), and together with both the classical and the new ground-based ChMs, provide the most complete chemical characterisation of the stellar populations in NGC 2808 available to date. As typical of the multiple population phenomenon in globular clusters, the light elements vary from one stellar population to another; whereas the iron peak elements show negligible variation between the different populations (at a level of $\lesssim0.10$~dex). Our AGB stars are also characterised by the chemical variations associated with the presence of multiple populations, confirming that this phase of stellar evolution is affected by the phenomenon as well. Intriguingly, we detected one extreme O-poor AGB star (consistent with a high He abundance), challenging stellar evolution models which suggest that highly He-enriched stars should avoid the AGB phase and evolve as AGB-manqu\'e star., Comment: Accepted for publication in MNRAS. 19 pages and 13 figures

Hubble Space Telescope (HST) photometry is providing an extensive analysis of globular clusters (GCs). In particular, the pseudo two-colour diagram dubbed 'chromosome map (ChM)' allowed to detect and characterize their multiple populations with unprecedented detail. The main limitation of these studies is the small field of view of HST, which makes it challenging to investigate some important aspects of the multiple populations, such as their spatial distributions and the internal kinematics in the outermost cluster regions. To overcome this limitation, we analyse state-of-art wide-field photometry of 43 GCs obtained from ground-based facilities. We derived high-resolution reddening maps and corrected the photometry for differential reddening when needed. We use photometry in the U, B, and I bands to introduce the $\Delta c_{\rm U,B,I}$ vs. $\Delta_{\rm B,I}$ ChM of red-giant branch (RGB) and asymptotic-giant branch (AGB) stars. We demonstrate that this ChM, which is built with wide-band ground-based photometry, is an efficient tool to identify first- and second-generation stars (1G and 2G) over a wide field of view. To illustrate its potential, we derive the radial distribution of multiple populations in NGC 288 and infer their chemical composition. We present the ChMs of RGB stars in 29 GCs and detect a significant degree of variety. The fraction of 1G and 2G stars, the number of subpopulations, and the extension of the ChMs significantly change from one cluster to another. Moreover, the metal-poor and metal-rich stars of Type II GCs define distinct sequences in the ChM. We confirm the presence of extended 1G sequences., Comment: 19 pages, 15 figures

The origin of young star clusters represents a major challenge for modern stellar astrophysics. While stellar rotation partially explains the colour spread observed along main-sequence turn-offs, i.e. where stars leave the main-sequence after the exhaustion of hydrogen in their core, and the multiple main sequences in the colour-magnitude diagrams of stellar systems younger than approximately 2 Gyr, it appears that an age difference may still be required to fulfill the observational constraints. Here we introduce an alternative approach that exploits the main-sequence turn-on, i.e. the point alongside the colour-magnitude diagram where pre-main-sequence stars join the main-sequence, to disentangle between the effects of stellar rotation and age to assess the presence, or lack thereof, of prolonged star formation in the approximately 40-Myr-old cluster NGC1818. Our results provide evidence for a fast star formation, confined within 8 Myr, thus excluding age differences as responsible for the extended main-sequence turn-offs, and leading the way to alternative observational perspectives in the exploration of stellar populations in young clusters., Comment: 9 pages, 5 figures, published on Nature Communications DOIhttps://doi.org/10.1038/s41467-022-31977-y

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

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

Evidence that the multiple populations (MPs) are common properties of globular clusters (GCs) is accumulated over the past decades from clusters in the Milky Way and in its satellites. This finding has revived GC research, and suggested that their formation at high redshift must have been a much-more complex phenomenon than imagined before. However, most information on MPs is limited to nearby GCs. The main limitation is that most studies on MPs rely on resolved stars, facing a major challenge to investigate the MP phenomenon in distant galaxies. Here we search for integrated colors of old GCs that are sensitive to the multiple-population phenomenon. To do this, we exploit integrated magnitudes of simulated GCs with MPs, and multi-band Hubble Space Telescope photometry of 56 Galactic GCs, where MPs are widely studied, and characterized as part of the UV Legacy Survey of Galactic GCs. We find that both integrated $C_{\rm F275W,F336W,F438W}$ and $m_{\rm F275W}-m_{\rm F814W}$ colors strongly correlate with the iron abundance of the host GC. In second order, the pseudo two-color diagram built with these integrated colors is sensitive to the MP phenomenon. In particular, once removed the dependence from cluster metallicity, the color residuals depend on the maximum internal helium variation within GCs and on the fraction of second-generation stars. This diagram, which we define here for Galactic GCs, has the potential of detecting and characterizing MPs from integrated photometry of old GCs, thus providing the possibility to extend their investigation outside the Local Group., Comment: 17 pages, 10 figures, 2 tables

Recent work has revealed two classes of Globular Clusters (GCs), dubbed Type-I and Type-II. Type-II GCs are characterized by a blue- and a red- red giant branch composed of stars with different metallicities, often coupled with distinct abundances in the slow-neutron capture elements (s-elements). Here we continue the chemical tagging of Type-II GCs by adding the two least-massive clusters of this class, NGC1261 and NGC6934. Based on both spectroscopy and photometry, we find that red stars in NGC1261 are slightly enhanced in [Fe/H] by ~0.1 dex and confirm that red stars of NGC 6934 are enhanced in iron by ~0.2 dex. Neither NGC1261 nor NGC6934 show internal variations in the s-elements, which suggests a GC mass threshold for the occurrence of s-process enrichment. We found a significant correlation between the additional Fe locked in the red stars of Type-II GCs and the present-day mass of the cluster. Nevertheless, most Type II GCs retained a small fraction of Fe produced by SNe II, lower than the 2%; NGC6273, M54 and omega Centauri are remarkable exceptions. In the appendix, we infer for the first time chemical abundances of Lanthanum, assumed as representative of the s-elements, in M54, the GC located in the nucleus of the Sagittarius dwarf galaxy. Red-sequence stars are marginally enhanced in [La/Fe] by 0.10\pm0.06 dex, in contrast with the large [La/Fe] spread of most Type II GCs. We suggest that different processes are responsible for the enrichment in iron and s-elements in Type-II GCs., Comment: 22 pages, 10 figures, submitted

A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral decomposition of the former, considerable benefits are achieved. The integration requires the solution of a single equation in a single unknown, which is a considerable improvement as compared to the system of seven or four equations required by other approaches available in the literature for the Cauchy medium. The scheme also allows for a very efficient treatment of the singularity which affects the apex of most of the existing yield and plastic potential surfaces. Moreover, no complications arise when some of the principal stresses coincide. The algorithm has been implemented in a proprietary Finite Element program, and used for the constitutive model proposed in part I of this paper. Numerical analyses have been conducted to simulate a biaxial compression test and a shallow strip footing resting on a Tresca, Mohr-Coulomb, Matsuoka-Nakai and Lade-Duncan soil. The benefits of the Cosserat continuum over the Cauchy/Maxwell medium are discussed considering mesh refinement, non-associated flow and softening behaviour., Comment: submitted to the International Journal of Plasticity

The Cosserat continuum is used in this paper to regularize the ill-posed governing equations of the Cauchy/Maxwell continuum. Most available constitutive models adopt yield and plastic potential surfaces with a circular deviatoric section. This is a too crude an approximation which hinders the application of the Cosserat continuum into practice, particularly in the geotechnical domain. An elasto-plastic constitutive model for the linear formulation of the Cosserat continuum is here presented, which features non-associated flow and hardening/softening behaviour, whilst linear hyper-elasticity is adopted to reproduce the recoverable response. For the formulation of the yield and plastic potential functions, a definition of the \textit{equivalent von Mises stress} is used which is based on Hencky's interpretation of the von Mises criterion and also on the theory of representations. The dependency on the Lode's angle of both the yield and plastic potential functions is introduced through the adoption of a recently proposed \textit{Generalized classical} criterion, which rigorously defines most of the classical yield and failure criteria., Comment: Submitted to the International Journal of Plasticity

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

Multiple stellar populations (MPs) are a distinct characteristic of Globular Clusters (GCs). Their general properties have been widely studied among main sequence, red giant branch (RGB) and horizontal branch (HB) stars, but a common framework is still missing at later evolutionary stages. We studied the MP phenomenon along the AGB sequences in 58 GCs, observed with the Hubble Space Telescope in ultraviolet (UV) and optical filters. By using UV-optical color-magnitude diagrams, we selected the AGB members of each cluster and identified the AGB candidates of the metal-enhanced population in type II GCs. We studied the photometric properties of AGB stars and compared them to theoretical models derived from synthetic spectra analysis. We observe the following features: i) the spread of AGB stars in photometric indices sensitive to variations of light-elements and helium is typically larger than that expected from photometric errors; ii) the fraction of metal-enhanced stars in the AGB is lower than in the RGB in most of the type II GCs; iii) the fraction of 1G stars derived from the chromosome map of AGB stars in 15 GCs is larger than that of RGB stars; v) the AGB/HB frequency correlates with the average mass of the most helium-enriched population. These findings represent a clear evidence of the presence of MPs along the AGB of Galactic GCs and indicate that a significant fraction of helium-enriched stars, which have lower mass in the HB, does not evolve to the AGB phase, leaving the HB sequence towards higher effective temperatures, as predicted by the AGB-manqu\'e scenario., Comment: 32 pages, 19 figures, 3 tables

We exploit multi-band Hubble Space Telescope photometry to investigate multiple populations (MPs) along the red horizontal branches (HBs) and red clumps of fourteen metal-rich Globular Clusters (GCs), including twelve Milky Way GCs and the Magellanic Cloud GCs NGC 1978 and NGC 416. Based on appropriate two-color diagrams we find that the fraction of 1G stars in Galactic GCs correlates with cluster mass, confirming previous results based on red-giant branch (RGB) stars. Magellanic-Cloud GCs show higher fractions of 1G stars than Galactic GCs with similar masses, thus suggesting that the environment affects the MP phenomenon. We compared and combined our population fractions based on HB with previous estimates from MS and RGB, and we used ground-based UBVI photometry (available for NGC 104, NGC 5927, NGC 6366, NGC 6838) to extend the investigation over a wide field of view. All studied GCs are consistent with flat distributions of 1G and 2G stars within ~1 arcmin from the cluster center except NGC 416, where the 2G is more centrally concentrated. 2G stars of NGC 104 and NGC 5927 are more centrally-concentrated than the 1G, whereas the distribution is flat for NGC 6366 and NGC 6838. We discover that most of the analyzed GCs exhibit extended sequences of 1G stars along the red HB, not consistent with a simple population. The comparison between appropriate synthetic and observed CMDs reveals that these extended distributions are consistent with either star-to-star variation in helium or with an internal metallicity spread, recalling the inhomogeneity of 1G stars along the ChMs., Comment: 27 pages, 20 figures, 5 tables, accepted for pubblication 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

Recent work has demonstrated how data-driven AI methods can leverage consumer protection by supporting the automated analysis of legal documents. However, a shortcoming of data-driven approaches is poor explainability. We posit that in this domain useful explanations of classifier outcomes can be provided by resorting to legal rationales. We thus consider several configurations of memory-augmented neural networks where rationales are given a special role in the modeling of context knowledge. Our results show that rationales not only contribute to improve the classification accuracy, but are also able to offer meaningful, natural language explanations of otherwise opaque classifier outcomes.

The origin of multiple stellar populations in Globular Clusters (GCs) is one of the greatest mysteries of modern stellar astrophysics. N-body simulations suggest that the present-day dynamics of GC stars can constrain the events that occurred at high redshift and led to the formation of multiple populations. Here, we combine multi-band photometry from the Hubble Space Telescope (HST) and ground-based facilities with HST and Gaia Data Release 2 proper motions to investigate the spatial distributions and the motions in the plane of the sky of multiple populations in the type II GCs NGC 5139 ($\omega\,$Centauri) and NGC 6656 (M 22). We first analyzed stellar populations with different metallicities. Fe-poor and Fe-rich stars in M 22 share similar spatial distributions and rotation patterns and exhibit similar isotropic motions. Similarly, the two main populations with different iron abundance in $\omega\,$Centauri share similar ellipticities and rotation patterns. When analyzing different radial regions, we find that the rotation amplitude decreases from the center towards the external regions. Fe-poor and Fe-rich stars of $\omega\,$Centauri are radially anisotropic in the central region and show similar degrees of anisotropy. We also investigate the stellar populations with different light-element abundances and find that their N-rich stars exhibit higher ellipticity than N-poor stars. In $\omega\,$Centauri Centauri both stellar groups are radially anisotropic. Interestingly, N-rich, Fe-rich stars exhibit different rotation patterns than N-poor stars with similar metallicities. The stellar populations with different nitrogen of M 22 exhibit similar rotation patterns and isotropic motions. We discuss these findings in the context of the formation of multiple populations., Comment: 24 pages, 13 figures, accepted for publication in ApJ

Historically, photometry has been largely used to identify stellar populations (MPs) in Globular Clusters (GCs) by using diagrams that are based on colours and magnitudes that are mostly sensitive to stars with different metallicities or different abundances of helium, carbon, nitrogen and oxygen. In particular, the pseudo two-colour diagram called chromosome map (ChM), allowed the identification and the characterization of MPs in about 70 GCs by using appropriate filters of the Hubble Space Telescope (HST) that are sensitive to the stellar content of He, C, N, O and Fe. We use here high-precision HST photometry from F275W, F280N, F343N, F373N, and F814W images of Omega Centauri to investigate its MPs. We introduce a new ChM whose abscissa and ordinate are mostly sensitive to stellar populations with different magnesium and nitrogen, respectively, in monometallic GCs. This ChM is effective in disentangling the MPs based on their Mg chemical abundances, allowing us to explore, for the first time, possible relations between the production of these elemental species for large samples of stars in GCs. By comparing the colours of the distinct stellar populations with the colours obtained from appropriate synthetic spectra we provide 'photometric-like' estimates of the chemical composition of each population. Our results show that, in addition to first generation (1G) stars, the metal-poor population of Omega Centauri hosts four groups of second-generation stars with different [N/Fe], namely, 2GA--D. 2GA stars share nearly the same [Mg/Fe] as the 1G, whereas 2GB, 2GC and 2GD stars are Mg depleted by ~0.15, ~0.25 and ~0.45 dex, respectively. We provide evidence that the metal-intermediate populations host stars with depleted [Mg/Fe]., Comment: 15 pages, 11 figures, accepted for publication in MNRAS

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

The 'chromosome map' diagram (ChM) proved a successful tool to identify and characterize multiple populations (MPs) in 59 Galactic Globular Clusters (GCs). Here, we construct ChMs for 11 GCs of both Magellanic Clouds (MCs) and with different ages to compare MPs in Galactic and extra-Galactic environments, and explore whether this phenomenon is universal through 'place' and 'time'. MPs are detected in five clusters. The fractions of 1G stars, ranging from about 50% to more than 80%, are significantly higher than those observed in Galactic GCs with similar present-day masses. By considering both Galactic and MC clusters, the fraction of 1G stars exhibits: (i) a strong anti-correlation with the present-day mass, and (ii) with the present-day mass of 2G stars; (iii) a mild anti-correlation with 1G present-day mass. All Galactic clusters without MPs have initial masses smaller than ~1.5 10^5 solar masses but a mass threshold governing the occurrence of MPs seems challenged by massive simple-population MC GCs; (iv) Milky Way clusters with large perigalactic distances typically host larger fractions of 1G stars, but the difference disappears when we use initial cluster masses. These facts are consistent with a scenario where the stars lost by GCs mostly belong to the 1G. By exploiting recent work based on Gaia, half of the known Type II GCs appear clustered in a distinct region of the integral of motions space, thus suggesting a common progenitor galaxy. Except for these Type II GCs,we do not find any significant difference in the MPs between clusters associated with different progenitors., Comment: 18 pages, 13 figures, accepted for publication in MNRAS