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We recently introduced three new parameters that describe the shape of the normalized cumulative radial distribution (nCRD) of the innermost stars in globular clusters (GCs) and trace the clusters’ dynamical evolution. Here, we extend our previous investigations to the case of a large set of Monte Carlo simulations of GCs, 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 GCs. We confirm that the three nCRD parameters are powerful tools to distinguish systems in the early stages of dynamical evolution from those that have 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.

We used high-resolution spectra acquired with 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 straggler stars (BSSs) and reference stars in different evolutionary stages (main-sequence turnoff, subgiant, red giant, and asymptotic giant branches). The average radial velocity value (〈 V _r 〉 = 494.5 ± 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 has 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 ∼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 ∼28%. Such a percentage is roughly comparable to that measured in other loose systems ( ω 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.

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′ from the cluster, we detected the small stellar system KMK 88-10. 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 r _c = 4″ (0.97 pc), a half-mass radius r _hm = 12″ (2.9 pc), and a concentration parameter c ∼ 1.3 corresponding to a truncation radius r _t ∼ 81″ (19.5 pc). We also derived its integrated absolute magnitude ( M _V = −0.71) and total mass ( M ∼ 80–160 M _⊙ ). The most intriguing feature emerging from this analysis is that KMK 88-10 presents a structure elongated in the direction of NGC 1835, with an intracluster overdensity 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.

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 we predict 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 toward the cluster center, rather than being stripped by the strong tidal forces exerted by the Milky Way in the outer regions.

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 Ca II 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 subsolar component at [Fe/H] = −0.48 dex ( σ = 0.22) and a supersolar component at [Fe/H] = +0.26 dex ( σ = 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 that 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, Liller 1 is also a Bulge Fossil Fragment.

Recently, slowly cooling white dwarfs (WDs) are a new class of WD that have 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 originate 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 investigated 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 was found 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.

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 straggler stars (BSSs) within the cluster half-mass radius by means of the ${A}_{\mathrm{rh}}^{+}$ 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 ${A}_{\mathrm{rh}}^{+}$ currently includes 59 clusters: 52 old GCs in the Milky Way (including the three investigated here), five old clusters in the Large Magellanic Cloud, and two young systems in the Small Magellanic Cloud. The three objects studied here nicely nest into the correlation between ${A}_{\mathrm{rh}}^{+}$ 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 dynamical evolution of a star cluster in different galactic environments. Finally, we discuss the advantages of using the dynamical clock as an indicator of the dynamical ages of star clusters, compared to the present-day central relaxation time.

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 data set acquired in the context of the ESO-VLT Multi-Instrument Kinematic Survey 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 subsample 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 $\sim 20^{\prime} $ 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″ < r < 90″, corresponding to 2 r _c < r < 4.5 r _c ), but additional data are required to properly assess this possibility.

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-UV 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 ± 0.02 M _⊙ , a surface temperature of 11,500 ± 1900 K, and a very young cooling age of only 200 ± 100 Myr. The mass and the age of the companion are compatible with a progenitor star of about 0.87 M _⊙ , which started transferring mass to the primary during its evolution along the subgiant 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 ± 0.06 M _⊙ , thus suggesting a highly nonconservative 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.

In the context of the ESO-VLT Multi-Instrument Kinematic Survey 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 ∼1800 individual stars distributed over the entire cluster extension, from ∼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 σ _0 ∼ 12 km s ^−1 ) and no evidence of a central cusp or other significant deviations. Our data allowed us 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 ∼132° ± 2° and an amplitude of ∼3 km s ^−1 (corresponding to V _rot / σ _0 ∼ 0.3). In addition, a flattening of the system qualitatively consistent with the rotation signal has been detected in the central region.

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 turnoff, subgiant 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 ± 0.5 Gyr, consistent with the age of 47 Tucanae, an average color excess E ( B − V ) = 0.64 ± 0.01, and a true distance modulus ( m − M ) _0 = 15.27 ± 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] ≈ −0.9, which is ∼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.

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% of 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 an 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 without initial BH retention. Conversely, in the model that retains a large number of BHs for an 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 lower values of the three parameters found in this case might be used to indirectly infer the possible presence of BHs in the cluster.