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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

We present a high resolution chemical study of a representative sample of 21 luminous giant stars of Liller~1, a complex stellar system in the Galactic bulge, based on H band spectra acquired with the Near InfraRed Spectrograph at KeckII. 15 stars turn out to have a subsolar iron abundance and enhanced [$\alpha$/Fe] and [Al/Fe], likely old that formed early and quickly from gas mainly enriched by type~II supernovae, and 6 stars with supersolar iron and roughly solar-scaled [$\alpha$/Fe] and [Al/Fe], likely younger, thus formed at later epochs from gas also enriched by type~Ia supernovae. Moreover, both subpopulations show enhanced [N/Fe], as in the bulge field, about solar-scaled [V/Fe], and depletion of [C/Fe] and $^{12}$C/$^{13}$C with respect to the solar values, indicating the occurrence of significant mixing in the stellar interiors of these evolved stars. The current study has also made evident that the sub-solar subpopulation shows some structuring, and the presence of a third subcomponent with iron content and [$\alpha$/Fe] enhancement somewhat intermediate between the metal-poor and metal-rich main subpopulations, has been statistically assessed, providing the chemical signature of an extended star formation with multiple bursts and of some self-enrichment., Comment: Accepted for pubblication in A&A

By using high-resolution spectra acquired with FLAMES-GIRAFFE at the ESO/VLT, we measured radial and rotational velocities of 115 stars in the Galactic globular cluster M55. After field decontamination based on the radial velocity values, the final sample of member stars is composed of 32 blue straggler stars (BSSs) and 76 reference stars populating the red giant and horizontal branches of the cluster. In agreement with previous findings, the totality of red giant branch stars has negligible rotation ($<$ 10 km s$^{-1}$), and horizontal branch stars have rotational velocities of 40 km s$^{-1}$ at most. In contrast, the BSS rotational velocity distribution shows a long tail extending up to $\sim$ 200 km s$^{-1}$, with 15 BSSs (out of 32) spinning faster than 40 km s$^{-1}$. By defining the threshold for fast rotating BSSs at 40 km s$^{-1}$, this sets the percentage of these stars at 47 $\pm$ 14 %. Such a large value has never been found before in any globular clusters. It is roughly comparable to that measured in other loose systems ($\omega$ Centauri, M4, and NGC 3201) and significantly larger than that observed in high-density clusters (as 47 Tucanae, NGC 6397, NGC 6752, and M30). This evidence supports a scenario where recent BSS formation is occurring in low-density environments. We also find that the BSS rotational velocity tends to decrease for decreasing luminosity, as found for another loose cluster of the sample (namely, NGC 3201)., Comment: Accepted for publication in A&A

A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn-Hilliard equation. A specialized, physics-inspired architecture is proven to provide close accordance between the predicted evolutions and the ground truth ones obtained via conventional integration schemes. The method can closely reproduce the evolution of microstructures not represented in the training set at a fraction of the computational costs. Extremely long-time extrapolation capabilities are achieved, up to reaching the theoretically expected equilibrium state of the system, despite the training set containing only relatively-short, initial phases of the evolution. Quantitative accordance with the decay rate of the Free energy is also demonstrated up to late coarsening stages, providing an example of a data-driven, physically consistent and high-accuracy Machine Learning method for the long timescale simulation of materials., Comment: 10 pages, 6 main text figures, 2 appendix figures

We used near-infrared spectroscopy at medium-high resolution (R=8,000$-$25,000) to perform the first comprehensive chemical study of the intermediate luminosity bulge globular cluster Terzan~6. We derived detailed abundances and abundance patterns of 27 giant stars, likely members of Terzan~6, based on their accurate Hubble Space Telescope proper motions and line-of-sight radial velocities. From the spectral analysis of these stars, we determined an average heliocentric radial velocity of 143.3$\pm$1.0 km s$^{-1}$ with a velocity dispersion of 5.1$\pm$0.7 km s$^{-1}$ and an average [Fe/H]=$-0.65\pm0.01$ and a low 1$\sigma$ dispersion of 0.03 dex. We also measured some depletion of [Mn/Fe] with respect to the solar-scaled values and enhancement of for [Ca/Fe], [Si/Fe], [Mg/Fe], [Ti/Fe], [O/Fe], [Al/Fe], [Na/Fe], and, to a lower extent, for [K/Fe], consistent with previous measurements of other bulge globular clusters and favoring the scenario of a rapid bulge formation and chemical enrichment. Some spread in the light element abundances suggest the presence of first- and second-generation stars, typical of genuine globulars. Finally, we measured some depletion of carbon and low $\rm ^{12}C/^{13}C$ isotopic ratios, as in previous studies of field and cluster bulge giants, indicating that extra-mixing mechanisms should be at work during the post main sequence evolution in the high metallicity regime as well., Comment: 8 pages, 5 figures, accepted for publication in Astronomy and Astrophysics

We present the results of a study aimed at characterizing the kinematics of the inner regions of the halo globular cluster M75 (NGC 6864) based on data acquired as part of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters. Our analysis includes the first determination of the line-of-sight velocity dispersion profile in the core region of M75. By using MUSE/NFM observations, we obtained a sample of $\sim 1900$ radial velocity measurements from individual stars located within $16''$ (corresponding to about $r < 3 r_c$ where $r_c$ is the estimated core radius of the system) from the cluster center. After an appropriate selection of the most accurate velocity measures, we determined the innermost portion of the velocity dispersion profile, finding that it is characterized by a constant behavior and a central velocity dispersion of $\sigma_0\sim 9$ km s$^{-1}$. The simultaneous King model fitting to the projected velocity dispersion and density profiles allowed us to check and update previous determinations of the main structural parameters of the system. We also detected a mild hint of rotation in the central $\sim 7''$ from the center, with an amplitude of just $\sim 1.0$ km s$^{-1}$ and a position angle of the rotation axis of PA$_0 = 174\deg$. Intriguingly, the position angle is consistent with that previously quoted for the suspected rotation signal in the outer region of the cluster. Taking advantage of the high quality of the photometric catalog used for the analysis of the MUSE spectra, we also provide updated estimates of the cluster distance, age, and reddening., Comment: Accepted for publication in A&A

In the context of the study of the size-age relationship observed in star clusters in the Large Magellanic Cloud and the investigation of its origin, here we present the determination of the structural parameters and the dynamical age of the massive cluster NGC 1835. We have used a powerful combination of optical and near-ultraviolet images acquired with the WFC3 onboard the HST to construct the star density profile from resolved star counts, determining the values of the core, half-mass and tidal radii through the comparison with the King model family. The same data also allowed us to evaluate the dynamical age of the cluster by using the 'dynamical clock'. This is an empirical method that quantifies the level of central segregation of blue stragglers stars (BSSs) within the cluster half-mass radius by means of the A+ parameter, which is defined as the area enclosed between the cumulative radial distribution of BSSs and that of a reference (lighter) population. The results confirm that NGC 1835 is a very compact cluster with a core radius of only 0.84 pc. The estimated value of A+ ($0.30\pm 0.04$) is the largest measured so far in the LMC clusters, providing evidence of a highly dynamically evolved stellar system. NGC 1835 nicely fits into the correlation between A+ and the central relaxation time and in the anti-correlation between A+ and the core radius defined by the Galactic and the Magellanic Cloud clusters investigated to date., Comment: Accepted for publication in A&A

A Deep Learning approach is devised to estimate the elastic energy density $\rho$ at the free surface of an undulated stressed film. About 190000 arbitrary surface profiles h(x) are randomly generated by Perlin noise and paired with the corresponding elastic energy density profiles $\rho(x)$, computed by a semi-analytical Green's function approximation, suitable for small-slope morphologies. The resulting dataset and smaller subsets of it are used for the training of a Fully Convolutional Neural Network. The trained models are shown to return quantitative predictions of $\rho$, not only in terms of convergence of the loss function during training, but also in validation and testing, with better results in the case of the larger dataset. Extensive tests are performed to assess the generalization capability of the Neural Network model when applied to profiles with localized features or assigned geometries not included in the original dataset. Moreover, its possible exploitation on domain sizes beyond the one used in the training is also analyzed in-depth. The conditions providing a one-to-one reproduction of the ground-truth $\rho(x)$ profiles computed by the Green's approximation are highlighted along with critical cases. The accuracy and robustness of the deep-learned $\rho(x)$ are further demonstrated in the time-integration of surface evolution problems described by simple partial differential equations of evaporation/condensation and surface diffusion., Comment: 15 pages, 9 figures

We present the first comprehensive chemical study of a representative sample of 27 luminous red giant branch (RGB) stars belonging to Liller 1, a complex stellar system in the Galactic bulge. This study is based on medium-resolution near-infrared spectra acquired with X-shooter at the Very Large Telescope. We found a subpopulation counting 22 stars with subsolar metallicity ($<$[Fe/H]$>=-0.31\pm0.02$ and 1$\sigma$ dispersion of 0.08 dex) and with enhanced [$\alpha$/Fe], [Al/Fe], and [K/Fe] that likely formed early and quickly from gas that was mainly enriched by type II supernovae, and a metal-rich population counting 5 stars with supersolar metallicity ($<$[Fe/H]$>$=+0.22$\pm$0.03 and 1$\sigma$ dispersion of 0.06 dex) and roughly solar-scaled [$\alpha$/Fe], [Al/Fe], and [K/Fe] that formed at later epochs from gas that was also enriched by type Ia supernovae. Moreover, both subpopulations show enhanced [Na/Fe], as in the bulge field, about solar-scaled [V/Fe], and depletion of [C/Fe] and $^{12}$C/$^{13}$C with respect to the solar values. This indicates that mixing and extra-mixing processes during the RGB evolution also occur at very high metallicities. Notably, no evidence of a Na-O anticorrelation, which is considered the fingerprint of genuine globular clusters, has been found. This challenges any formation scenarios that invoke the accretion of a molecular cloud or an additional stellar system onto a genuine globular cluster. The results of this study underline the strong chemical similarity between Liller 1 and Terzan 5 and support the hypothesis that these complex stellar systems might be fossil fragments of the epoch of Galactic bulge formation., Comment: Accepted for pubblication in A&A

We recently introduced three new parameters that describe the shape of the normalized cumulative radial distribution (nCRD) of the innermost stars in globular clusters and trace the clusters dynamical evolution. Here we extend our previous investigations to the case of a large set of Monte Carlo simulations of globular clusters, started from a broad range of initial conditions. All the models are analyzed at the same age of 13 Gyr, when they have reached different evolutionary phases. The sample of models is well representative of the structural properties of the observed population of Galactic globular clusters. We confirm that the three nCRD parameters are powerful tools to distinguish systems in early stages of dynamical evolution, from those that already experienced core collapse. They might also help disentangle clusters hosting a low-mass intermediate-mass black hole of a few hundred solar masses, from cases with large concentrations of dark remnants in their centers. With respect to other dynamical indicators, the nCRD parameters offer the advantage of being fully empirical and easier to measure from observational data., Comment: Accepted for publication in ApJ, 15 pages, 10 figures, 1 table

We present a high angular resolution multi-wavelength study of the massive globular cluster NGC 1835 in the Large Magellanic Cloud. Thanks to a combination of optical and near ultraviolet images acquired with the WFC3 on board the HST, we performed a detailed inspection of the stellar population in this stellar system adopting a ``UV-guided search'' to optimize the detection of relatively hot stars. This allowed us to discover a remarkably extended horizontal branch (HB), spanning more than 4.5 magnitudes in both magnitude and colour from the region redder than the instability strip, up to effective temperatures of 30,000 K, and including a large population of RR Lyrae (67 confirmed variables, and 52 new candidates). This is the first time that such a feature has been detected in an extra-Galactic cluster, demonstrating that the physical conditions responsible for the formation of extended HBs are ubiquitous. The acquired dataset has been also used to redetermine the cluster distance modulus, reddening, and absolute age, yielding $(m-M)_0=18.58$, $E(B-V)=0.08$, and $t=12.5$ Gyr, respectively., Comment: Accepted for publication in A&A

High-resolution Hubble Space Telescope (\textit{HST}) optical observations have been used to perform the deepest photometric study of the poorly studied Galactic globular cluster NGC 6284. The deep colour-magnitude diagram (CMD) that we obtained reaches 6 magnitudes below the main sequence turn-off. We provide the first determination of the gravitational centre ($C_{\rm grav}$) and density profile of the system from resolved stars. $C_{\rm grav}$ is significantly offset (by $1.5-3''$) from the values in the literature. The density profile shows the presence of a steep central cusp, unambiguously indicating that the cluster experienced the core-collapse phase. Updated values of the structural parameters and relaxation times of the system are provided. We also constructed the first high-resolution reddening map in the cluster direction, which allowed us to correct the evolutionary sequences in the CMD for the effects of differential reddening. Isochrone fitting to the corrected CMD provided us with new estimates of the cluster age, average colour excess, metallicity, and distance. We find an absolute age of $13.3 \pm 0.4$ Gyr, an average colour excess $E(B-V) = 0.32 \pm 0.01$, a metallicity [Fe/H]$= -1.36 \pm 0.01$, and a true distance modulus $(m-M)_0 = 15.61 \pm 0.04$ that sets the cluster distance at $13.2 \pm 0.2$ kpc from the Sun. The superb quality of the CMD allowed a clear-cut identification of the Red Giant Branch (RGB) bump, which is clearly distinguishable along the narrow RGB. The absolute magnitude of this feature turns out to be $\sim 0.2$ mag fainter than previous identification., Comment: 11 pages, 9 figures, 2 tables. Accepted for publication in A&A

We used ultra-deep observations obtained with the NIRCam aboard the James Webb Space Telescope to explore the stellar population of NGC 6440: a typical massive, obscured and contaminated globular cluster formed and orbiting within the Galactic bulge. Leveraging the exceptional capabilities of this camera, we sampled the cluster down to ~5 magnitudes below the main-sequence turn-off in the (mF115W , mF115W - mF200W ) colour-magnitude diagram. After carefully accounting for differential extinction and contamination by field interlopers, we find that the main sequence splits into two branches both above and below the characteristic knee. By comparing the morphology of the colour-magnitude diagram with a suitable set of isochrones, we argue that the upper main-sequence bi-modality is likely due to the presence of a He-enriched stellar population with a helium spread of DeltaY = 0.04. The lower main-sequence bi-modality can be attributed to variations in the abundance of water (i.e., oxygen) with Delta[O/Fe] ~ -0.4. This is the first evidence of both helium and oxygen abundance variations in a globular cluster purely based on JWST observations. These results open the window for future in-depth investigations of the multiple population phenomenon in clusters located in the Galactic bulge, which were previously unfeasible with near-UV observations, due to prohibitive reddening and crowding conditions., Comment: Accepted for publication in A&A

With the goal of untangling the origin of extended main-sequence turnoffs (eMSTOs) and extended red clumps (eRCs) in star clusters, in this work we present the study of the intermediate-age cluster NGC 419, situated along the Bridge of the Small Magellanic Cloud. To this aim, we analyzed multi-epoch, high angular resolution observations acquired with the Hubble Space Telescope for this dynamically young cluster, which enabled the determination of precise proper motions and therefore the assessment of the cluster membership for each individual star in the field of view. With this unprecedented information at hand, we first studied the radial distribution of kinematically selected member stars in different eMSTO subregions. The absence of segregation supports the rotation scenario as the cause for the turnoff color extension and disfavors the presence of a prolonged period of star formation in the cluster. A similar analysis on the eRC of NGC 419 confirms the absence of segregation, providing further evidence against an age spread, which is at odds with previous investigations. Even so, the currently available evolutionary models including stellar rotation fail at reproducing the two photometric features simultaneously. We argue that either shortcomings in these models or a different origin for the red clump feature, such as a nonstandard differential mass loss along the red giant branch phase, are the only way to reconcile our observational findings with theoretical expectations., Comment: 6 pages, 8 figures, Accepted for publication on A&A

We used high resolution spectra acquired at the Magellan Telescope to measure radial and rotational velocities of approximately 200 stars in the Galactic globular cluster NGC 3201. The surveyed sample includes Blue Stragglers Stars (BSSs) and reference stars in different evolutionary stages (main sequence turn-off, sub-giant, red giant and asymptotic giant branches). The average radial velocity value ($\langle V_r\rangle = 494.5 \pm 0.5$ km s$^{-1}$) confirms a large systemic velocity for this cluster and was used to distinguish 33 residual field interlopers. The final sample of member stars counts 67 BSSs and 114 reference stars. Similarly to what is found in other clusters, the totality of the reference stars has negligible rotation ($<20$ km s$^{-1}$), while the BSS rotational velocity distribution shows a long tail extending up to $\sim 200$ km s$^{-1}$, with 19 BSSs (out of 67) spinning faster than 40 km s$^{-1}$. This sets the percentage of fast rotating BSSs to $\sim 28\%$. Such a percentage is roughly comparable to that measured in other loose systems ($\omega$ Centauri, M4 and M55) and significantly larger than that measured in high-density clusters (as 47 Tucanae, NGC 6397, NGC 6752 and M30). This evidence supports a scenario where recent BSS formation (mainly from the evolution of binary systems) is occurring in low-density environments. We also find that the BSS rotational velocity tends to decrease for decreasing luminosity and surface temperature, similarly to what is observed in main sequence stars. Hence, further investigations are needed to understand the impact of BSS internal structure on the observed rotational velocities., Comment: Accepted for pubblication in ApJ: 14 pages, 10 figures

NGC 2419 is likely the globular cluster (GC) with the lowest dynamical age in the Galaxy. This makes it an extremely interesting target for studying the properties of its multiple populations (MPs), as they have been likely affected only modestly by long-term dynamical evolution effects. Here we present for the first time a detailed analysis of the structural and morphological properties of the MPs along the whole extension of this remote and massive GC by combining high-resolution HST and wide-field ground-based data. In agreement with formation models predicting that second population (SP) stars form in the inner regions of the first population (FP) system, we find that the SP is more centrally concentrated than the FP. This may provide constraints on the relative concentrations of MPs in the cluster early stages of the evolutionary phase driven by two-body relaxation. In addition, we find that the fraction of FP stars is larger than expected from the general trend drawn by Galactic GCs. If, as suggested by a number of studies, NGC 2419 formed in the Sagittarius dwarf galaxy and was later accreted by the Milky Way, we show that the observed FP fraction may be explained as due to the transition of NGC 2419 to a weaker tidal field (its current Galactocentric distance is d_gc~95 kpc) and consequently to a reduced loss rate of FP stars., Comment: Accepted for publication in A&A

In the context of a project aimed at characterizing the dynamical evolution of old globular clusters in the Large Magellanic Cloud, we have secured deep HST/WFC3 images of the massive cluster NGC 1835. In the field of view of the acquired images, at a projected angular separation of approximately 2 arcmin from the cluster, we detected the small stellar system KMK88-10. The observations provided the deepest color-magnitude diagram ever obtained for this cluster, revealing that it hosts a young stellar population with an age of 600-1000 Myr. The cluster surface brightness profile is nicely reproduced by a King model with a core radius rc = 4 arcsec (0.97 pc), an half-mass radius rhm = 12 arcsec (2.9 pc), and a concentration parameter c~1.3 corresponding to a truncation radius rt~81 arcsec (19.5 pc). We also derived its integrated absolute magnitude (MV=-0.71) and total mass (M~80-160 Msun). The most intriguing feature emerging from this analysis is that KMK88-10 presents a structure elongated in the direction of NGC 1835, with an intracluster over-density that suggests the presence of a tidal bridge between the two systems. If confirmed, this would be the first evidence of a tidal capture of a small star cluster by a massive globular., Comment: Accepted for publication in ApJ

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test this approach by applying it to a prototypical stochastic process on a lattice. By suitably adding noise to the original data we succeed in bringing both the Generator and the Discriminator loss functions close to their ideal value. Importantly, the discreteness of the model is retained despite the noise. As typical for adversarial approaches, oscillations around the convergence limit persist also at large epochs. This undermines model selection and the quality of the generated trajectories. We demonstrate that a simple multi-model procedure where stochastic trajectories are advanced at each step upon randomly selecting a Generator leads to a remarkable increase in accuracy. This is illustrated by quantitative analysis of both the predicted equilibrium probability distribution and of the escape-time distribution. Based on the reported findings, we believe that GANs are a promising tool to tackle complex statistical dynamics by machine learning techniques, Comment: Main text and appendices, 10 pages and 10 figures Updated version: citations to previous work which was not known to the authors have been added, text has been re-organized and modified accordingly; supplemental material has been moved into appendices

Terzan 5 is a heavily obscured stellar system located in the inner Galaxy. It has been postulated to be a stellar relic, a Bulge Fossil Fragment witnessing the complex history of the assembly of the Milky Way bulge. In this paper, we follow the chemical enrichment of a set of putative progenitors of Terzan 5 to assess whether the chemical properties of this cluster fit within a formation scenario in which it is the remnant of a primordial building block of the bulge. We can explain the metallicity distribution function and the runs of different element-to-iron abundance ratios as functions of [Fe/H] derived from optical-infrared spectroscopy of giant stars in Terzan 5, by assuming that the cluster experienced two major star formation bursts separated by a long quiescent phase. We further predict that the most metal-rich stars in Terzan 5 are moderately He-enhanced and a large spread of He abundances in the cluster, Y = 0.26-0.335. We conclude that current observations fit within a formation scenario in which Terzan 5 originated from a pristine, or slightly metal-enriched, gas clump about one order of magnitude more massive than its present-day mass. Losses of gas and stars played a major role in shaping Terzan 5 the way we see it now. The iron content of the youngest stellar population is better explained if the white dwarfs that give rise to type Ia supernovae (the main Fe factories) sink towards the cluster center, rather than being stripped by the strong tidal forces exerted by the Milky Way in the outer regions., Comment: 14 pages, 2 tables, 8 figures, accepted for publication in ApJ

Blue stragglers are anomalously luminous core hydrogen-burning stars formed through mass-transfer in binary/triple systems and stellar collisions. Their physical and evolutionary properties are largely unknown and unconstrained. Here we analyze 320 high-resolution spectra of blue stragglers collected in eight galactic globular clusters with different structural characteristics and show evidence that the fraction of fast rotating blue stragglers (with rotational velocities larger than 40 km/s) increases for decreasing central density of the host system. This trend suggests that fast spinning blue stragglers prefer low-density environments and promises to open an unexplored route towards understanding the evolutionary processes of these stars. Since large rotation rates are expected in the early stages of both formation channels, our results provide direct evidence for recent blue straggler formation activity in low-density environments and put strong constraints on the timescale of the collisional blue straggler slow-down processes., Comment: Published in Nature Communications

In the context of a project aimed at characterizing the properties of the so-called Bulge Fossil Fragments (the fossil remnants of the bulge formation epoch), here we present the first determination of the metallicity distribution of Liller 1. For a sample of 64 individual member stars we used ESO- MUSE spectra to measure the equivalent width of the CaII triplet and then derive the iron abundance. To test the validity of the adopted calibration in the metal-rich regime, the procedure was first applied to three reference bulge globular clusters (NGC 6569, NGC 6440, and NGC 6528). In all the three cases, we found single-component iron distributions, with abundance values fully in agreement with those reported in the literature. The application of the same methodology to Liller 1 yielded, instead, a clear bimodal iron distribution, with a sub-solar component at $\text{[Fe/H]}= -0.48\,$dex ($\sigma = 0.22$) and a super-solar component at $\text{[Fe/H]}= +0.26\,$dex ($\sigma = 0.17$). The latter is found to be significantly more centrally concentrated than the metal-poor population, as expected in a self-enrichment scenario and in agreement with what found in another bulge system, Terzan 5. The obtained metallicity distribution is astonishingly similar to that predicted by the reconstructed star formation history of Liller 1, which is characterized by three main bursts and a low, but constant, activity of star formation over the entire lifetime. These findings provide further support to the possibility that, similar to Terzan 5, also Liller 1 is a Bulge Fossil Fragment., Comment: Accepted for publication in the ApJ, 15 pages, 9 figures

Recently, a new class of white dwarfs (dubbed ``slowly cooling WDs'') has been identified in two globular clusters (namely M13 and NGC 6752) showing a horizontal branch (HB) morphology with an extended blue tail. The cooling rate of these WDs is reduced by stable thermonuclear hydrogen burning in their residual envelope, and they are thought to be originated by stars that populate the blue tail of the HB and then skip the asymptotic giant branch phase. Consistently, no evidence of such kind of WDs has been found in M3, a similar cluster with no blue extension of the HB. To further explore this phenomenon, we took advantage of deep photometric data acquired with the Hubble Space Telescope in the near-ultraviolet and investigate the bright portion of the WD cooling sequence in M5, another Galactic globular cluster with HB morphology similar to M3. The normalized WD luminosity function derived in M5 turns out to be impressively similar to that observed in M3, in agreement with the fact that the stellar mass distribution along the HB of these two systems is almost identical. The comparison with theoretical predictions is consistent with the fact that the cooling sequence in this cluster is populated by canonical (fast cooling) WDs. Thus, the results presented in this paper provide further support to the scenario proposing a direct causal connection between the slow cooling WD phenomenon and the horizontal branch morphology of the host stellar cluster., Comment: 12 pages, 8 figures, accepted in the ApJ

In the context of a project aimed at characterizing the properties of star clusters in the Galactic bulge, here we present the determination of the internal kinematics and structure of the massive globular cluster NGC 6569. The kinematics has been studied by means of an unprecedented spectroscopic dataset acquired in the context of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters, combining the observations from four different spectrographs. We measured the line-of-sight velocity of a sample of almost 1300 stars distributed between ~0.8" and 770" from the cluster center. From a sub-sample of high-quality measures, we determined the velocity dispersion profile of the system over its entire radial extension (from ~ 5" to ~ 200" from the center), finding the characteristic behavior usually observed in globular clusters, with a constant inner plateau and a declining trend at larger radii. The projected density profile of the cluster has been obtained from resolved star counts, by combining high-resolution photometric data in the center, and the Gaia EDR3 catalog radially extended out to ~20' for a proper sampling of the Galactic field background. The two profiles are properly reproduced by the same King model, from which we estimated updated values of the central velocity dispersion, main structural parameters (such as the King concentration, the core, half-mass, and tidal radii), total mass, and relaxation times. Our analysis also reveals a hint of ordered rotation in an intermediate region of the cluster (40"

We have used the ``dynamical clock'' to measure the level of dynamical evolution reached by three Galactic globular clusters (namely, NGC 3201, NGC 6316 and NGC 6440). This is an empirical method that quantifies the level of central segregation of blue stragglers stars (BSSs) within the cluster half-mass radius by means of the $A^+_{rh}$ parameter, defined as the area enclosed between the cumulative radial distribution of BSSs and that of a lighter population. The total sample with homogeneous determinations of $A^+_{rh}$ now counts a gran-total of 59 clusters: 52 old GCs in the Milky Way (including the three investigated here), 5 old clusters in the Large Magellanic Cloud, and 2 young systems in the Small Magellanic Cloud. The three objects studied here nicely nest into the correlation between $A^+_{rh}$ and the central relaxation time defined by the previous sample, thus proving and consolidating the use of the dynamical clock as an excellent tracer of the stage of star cluster dynamical evolution in different galactic environments. Finally, we discuss the advantages of using the dynamical clock as an indicator of star cluster dynamical ages, compared to the present-day central relaxation time., Comment: 16 pages and 8 figures, in press in the ApJ

We report on the discovery of the companion star to the millisecond pulsar PSR J1835-3259B in the Galactic globular cluster NGC 6652. Taking advantage of deep photometric archival observations acquired through the Hubble Space Telescope in near-ultraviolet and optical bands, we identified a bright and blue object at a position compatible with that of the radio pulsar. The companion is located along the helium-core white dwarf cooling sequence and the comparison with binary evolution models provides a mass of $0.17 \pm 0.02~M_\odot$, a surface temperature of $11500\pm1900$ K and a very young cooling age of only $200\pm100$ Myr. The mass and the age of the companion are compatible with a progenitor star of about $0.87~M_{\odot}$, which started transferring mass to the primary during its evolution along the sub-giant branch and stopped during the early red giant branch phase. Combining together the pulsar mass function and the companion mass, we found that this system is observed at an almost edge-on orbit and hosts a neutron star with a mass of $1.44 \pm 0.06~M_\odot$, thus suggesting a highly non-conservative mass accretion phase. The young age of the WD companion is consistent with the scenario of a powerful, relatively young MSP indicated by the earlier detection of gamma-rays from this system., Comment: 11 pages, 7 figures, accepted for publication in ApJ

By studying the normalized cumulative radial distribution (nCRD) of the stars in the central region of a Monte Carlo-simulated globular cluster, we recently defined three parameters able to pinpoint the stage of internal dynamical evolution reached by the system: $A_5$ (i.e., the area subtended by the nCRD within 5$\%$ the half-mass radius, $r_h$), $P_5$ (the value of the nCRD at 5$\%$ $r_h$), and $S_{2.5}$ (the slope of the nCRD at 2.5$\%$ $r_h$). Here we extend the analysis and explore the effects that different fractions (0$\%$, 10$\%$, and 20$\%$) of primordial binaries and stellar-mass black holes (BHs) induce on the dynamical history of the system. As expected, the gradual contraction of the cluster becomes milder and core collapse shallower for increasing binary fraction. Nevertheless, the cluster dynamical evolution is still properly traced by the three parameters. For models with a larger initial retention of stellar mass BHs the evolution depends on the timescale of their subsequent dynamical ejection. An early dynamical ejection of BHs results in a long-term evolution of the three parameters similar to that found in systems with no initial BH retention. Conversely, in the model that retains a large number of BHs for extended time (slow dynamical ejection of BHs), the system is characterized by a less concentrated structure and by the lack of significant temporal evolution of the three parameters. The smaller values of the three parameters found in this case might be used to indirectly infer the possible presence of BHs in the cluster., Comment: 15 pages, 12 figures, 1 table

In the context of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters, here we present the line-of-sight velocity dispersion profile of NGC 6440, a massive globular cluster located in the Galactic bulge. By combining the data acquired with four different spectrographs, we obtained the radial velocity of a sample of $\sim 1800$ individual stars distributed over the entire cluster extension, from $\sim$0.1$"$ to 778$"$ from the center. Using a properly selected sample of member stars with the most reliable radial velocity measures, we derived the velocity dispersion profile up to 250$"$ from the center. The profile is well described by the same King model that best fits the projected star density distribution, with a constant inner plateau (at ${\sigma}_0 \sim $ 12 km s$^{-1}$) and no evidence of a central cusp or other significant deviations. Our data allowed to study the presence of rotation only in the innermost regions of the cluster (r < 5$"$), revealing a well-defined pattern of ordered rotation with a position angle of the rotation axis of $\sim$132 $\pm$ 2{\deg} and an amplitude of $\sim$3 km s$^{-1}$ (corresponding to Vrot/${\sigma}_0 \sim$ 0.3). Also, a flattening of the system qualitatively consistent with the rotation signal has been detected in the central region., Comment: 20 pages, 11 figures, 4 tables, accepted for publication in ApJ

High-resolution Hubble Space Telescope optical observations have been used to analyze the stellar population and the structure of the poorly investigated bulge globular cluster NGC 6316. We constructed the first high-resolution reddening map in the cluster direction, which allowed us to correct the evolutionary sequences in the color magnitude diagram (CMD) for the effects of differential reddening. A comparison between the CMDs of NGC 6316 and 47 Tucanae revealed strikingly similar stellar populations, with the two systems basically sharing the same turn-off, sub-giant branch, and horizontal branch morphologies, indicating comparable ages. The red giant branch in NGC 6316 appears slightly bluer than in 47 Tucanae, suggesting a lower metal content. This has been confirmed by the isochrone fitting of the observed CMD, which provided us with updated values of the cluster age, distance, average color excess, and metallicity. We estimated an absolute age of 13.1 $\pm$ 0.5 Gyr, consistent with the age of 47 Tucanae, an average color excess E(B-V) = 0.64 $\pm$ 0.01, and a true distance modulus (m-M)0 = 15.27 $\pm$ 0.03 that sets the cluster distance at 11.3 kpc from the Sun. In addition, the photometric estimate of the cluster metallicity suggests [Fe/H]$\approx$ -0.9, which is $\sim$ 0.2 dex smaller than that of 47 Tucanae. We also determined the gravitational center and the density profile of the system from resolved stars. The latter is well reproduced by a King model. Our results confirm that NGC 6316 is another extremely old relic of the assembly history of the Galaxy., Comment: 14 pages, 8 figures, 2 tables. Accepted for publication on ApJ

We used a combination of high-resolution optical images acquired with the Hubble Space Telescope and near-IR wide-field data to investigate the stellar density profile and the population of blue straggler star (BSS) in the Galactic globular cluster NGC6256, with the aim of probing its current stage of internal dynamical evolution. We found that the inner stellar density profile significantly deviates from a King model while is well reproduced by a steep cusp with a power-law slope alpha=-0.89, thus implying that the cluster is currently in the post core-collapse (PCC) phase. This is also confirmed by the very high segregation level of the BSS population measured through the A+ parameter. We also found that the distribution of BSSs in the color-magnitude diagram is characterized by a collimated blue sequence and a red more sparse component, as already observed in other three PCC clusters. The comparison with appropriate collisional models demonstrates that the vast majority of the BSSs lying along the collimated blue sequence is consistent with a generation of coeval (1 Gyr-old) stars with different masses originated by an event that highly enhanced the collisional rate of the system (i.e. the core collapse). This study confirms that the segregation level of BSSs is a powerful dynamical diagnostic also of star cluster in a very advanced stage of dynamical evolution. Moreover, it pushes forward the possibility of using the morphology of the BSS in the color-magnitude diagram as a tracer of the core-collapse and subsequent dynamical evolutionary phases., Comment: Accepted for publication in ApJ

Liller 1 and Terzan 5 are two massive systems in the Milky-Way bulge hosting populations characterized by significantly different ages ($\Delta t>7-8$ Gyr) and metallicities ($\Delta$[Fe/H]$\sim1$ dex). Their origin is still strongly debated in the literature and all formation scenarios proposed so far require some level of fine-tuning. The detailed star formation histories (SFHs) of these systems may represent an important piece of information to assess their origin. Here we present the first attempt to perform such an analysis for Liller 1. The first key result we find is that Liller 1 has been forming stars over its entire lifetime. More specifically, three broad SF episodes are clearly detected: 1) a dominant one, occurred some 12-13 Gyr ago with a tail extending for up to $\sim3$ Gyr, 2) an intermediate burst, between 6 and 9 Gyr ago, 3) and a recent one, occurred between 1 and 3 Gyr ago. The old population contributes to about $70\%$ of the total stellar mass and the remaining fraction is almost equally split between the intermediate and young populations. If we take these results at a face value, they would suggest that this system unlikely formed through the merger between an old globular cluster and a Giant Molecular Cloud, as recently proposed. On the contrary, our findings provide further support to the idea that Liller 1 is the surviving relic of a massive primordial structure that contributed to the Galactic bulge formation, similarly to the giant clumps observed in star-forming high-redshift galaxies., Comment: 23 pages, 14 figures; accepted for publication in ApJ