A popular approach to model galaxies is Schwarzschild’s method. For this method, a grid of sample orbits of stars in an external potential is calculated, and a model for the stellar system is obtained through attributing specific weights to the orbits in a superposition of them. The models created with Schwarzschild’s method can fit many observed properties of the modeled stellar system with high precision. However, systems that are stationary as Schwarzschild models may therefore exhibit a strong time evolution if they are translated into more realistic self-gravitating models. The issue is highlighted with the Galactic center as an example.

Spectroscopy and photometry have revealed existence, complexity and properties of the multiple stellar populations (mPOPs) hosted in Galactic globular clusters. However, the conundrum of the formation and evolution of mPOPs is far from being completely exploited: the available pieces of information seem not enough to shed light on these topics. Astrometry, and in particular high-precision proper motions, can provide us the sought-after answers about how mPOPs formed and have evolved in these ancient stellar systems. In the following, I present a brief overview of the observational results on the internal kinematics of the mPOPs in some GCs thanks to Hubble Space Telescope high-precision proper motions.

The VISCACHA (VIsible Soar photometry of star Clusters in tApii and Coxi HuguA†) Survey is an ongoing project based on deep and spatially resolved photometric observations of Magellanic Cloud star clusters, collected using the SOuthern Astrophysical Research (SOAR) telescope together with the SOAR Adaptive Module Imager. So far we have used >300h of telescope time to observe ∼150 star clusters, mostly with low mass (M < 104M⊙) on the outskirts of the LMC and SMC. With this high-quality data set, we homogeneously determine physical properties using deep colour-magnitude diagrams (ages, metallicities, reddening, distances, mass, luminosity and mass functions) and structural parameters (radial density profiles, sizes) for these clusters which are used as a proxy to investigate the interplay between the Magellanic Clouds and their evolution. We present the VISCACHA survey and its initial results, based on our first two papers. The project’s long term goals and expected legacy to the community are also addressed.

The blooming era of precision astrometry for Galactic studies truly brings the rich internal dynamics of globular clusters to the centre stage. But several aspects of our current understanding of fundamental collisional stellar dynamics cannot match such new-generation data and the theoretical ambitions they trigger. This rapidly evolving context offers the stimulus to address a number of old and new questions concerning the phase space properties of this class of stellar systems.

I review the methods, mostly developed in the last decade, that are commonly used to identify and characterize multiple populations (MPs) in Globular Clusters (GCs) based on photometry. I summarize the results from the recent surveys of MPs with the Hubble Space Telescope (HST) and ground-based facilities and provide a list of the main properties of MPs as inferred from these studies.

The Asymptotic Giant Branch (AGB) scenario for the formation of multiple populations has been quantitatively studied in the course of the last twenty years, examining the aspects both of nucleosynthesis and of the dynamics of formation of new stars in a cooling flow at the center of the first generation cluster, and of the following N–body evolution. The large complexity of these studies finds many validations in the properties of multiple populations. Here I shortly summarize recent accomplishments in the study of the evolution of massive AGBs and super–AGBs including the explanation of anomalous high lithium abundances in ‘extreme’ second generation stars in ω Cen and NGC 2808.

We have performed photometric analysis of four Galactic globular clusters (GGCs): NGC 4147, NGC 4590, NGC 5053 and NGC 7492 using far-UV and near-UV filters of the Ultraviolet Imaging Telescope (UVIT) on-board AstroSat. With the help of color-magnitude diagrams (CMDs), we have identified ~150 blue horizontal branch stars (BHBs), and ~40 blue straggler stars (BSS) in the four GGCs. We study the temperature and radial distribution of BHBs and BSS for the four GGCs.

In the context of the STRucture and Evolution of the GAlaxy survey, we describe the preliminary results obtained for the fields around the globular cluster Pal 3 (about 2.75 square degrees), by exploiting the obtained g, r, i time series photometry. The final aim is to use variable stars as tools to verify and study the presence of streams around Pal 3. We found 20 candidate variable stars of which 7 RR Lyrae stars possibly belonging to Pal 3, also at large distance from the center. The distribution of the candidate RR Lyrae seems to confirm a preferential distribution in the north-east direction, confirming previous results in literature.

Recent observations of globular clusters imposed major revisions to the previous paradigm, in which they were considered to be isotropic in velocity space and non-rotating. However, the theory of collisionless spheroids with some kinematic richness has seldom been studied. We present here a first step in this direction, owing to new results regarding the linear stability of rotating Plummer spheres, with varying anisotropy in velocity space and total amount of angular momentum. We extend the well-known radial orbit instability to rotating systems, and discover a new regime of instability in fast rotating, tangentially anisotropic systems.

We review spectroscopic results concerning multiple stellar populations in globular clusters. The cluster initial mass is the most important parameter determining the fraction of second generation stars. The threshold for the onset of the multiple population phenomenon is 1–3×105 M⊙. Nucleosynthesis is influenced by metallicity: Na/O and Mg/Al anti-correlations are more extended in metal-poor than in metal-rich clusters. Massive clusters are more complex systems than the smaller ones, with several populations characterized by different chemical compositions. The high Li abundance observed in the intermediate second generation stars strongly favours intermediate mass AGB stars as polluters for this class of stars; however, it is well possible that the polluters of extreme second generation stars, that often do not have measurable Li, may be fast rotating massive stars or super-massive stars. The mass budget factor should be a function of the cluster mass, and needs to be large only in massive clusters.

Young star clusters are a promising environment for forming binary black holes. Such binaries may form dynamically or via binary star evolution or through the interplay of these two channels. To study these formation pathways, we have performed high precision direct N-body simulations of low-mass (M < 1000 M⊙) young star clusters. The simulations were carried out with the code Nbody6++GPU coupled with the population synthesis code MOBSE. Our results highlight the importance of dynamics to form massive black hole binaries even in low-mass young star clusters.

Over the last decade, our abilities to observe the internal kinematics of star clusters have drastically increased. Where a few years back only small numbers of bright stars with radial velocity measurements were available, we can nowadays study the three-dimensional motions of large stellar samples, thanks to the combined datasets gathered by state-of-art spectrographs and astrometric satellites. In this work, I summarise the contribution of integral-field spectrographs, in particular MUSE, to this paradigm change. Using dedicated software tools, we were able to overcome a fundamental limitation of spectroscopy and advance to the crowded cluster centres. This allowed us to study the central kinematics in unprecedented detail and to start uncovering the populations of black holes that reside in massive star clusters.

We present some preliminary results of our ongoing project about planetary systems around S-stars in the vicinity of Sgr A* black hole. Since S-stars might have migrated in the Galactic Centre (GC) from elsewhere, they probably still keep their planetary systems throughout their voyage. In this work, we study the destiny of their putative planetary systems after close interaction with the central black hole of our galaxy.

We investigate the old open cluster M67 using ultraviolet photometric data of Ultra-Violet Imaging Telescope in multi-filter far-UV bands. M67, well known for the presence of several blue straggler stars (BSS), has been put to detailed tests to understand their formation pathways. Currently, there are three accepted formation channels: mass transfer due to Roche-lobe overflow in binary systems, stellar mergers either due to dynamical collisions or through coalescence of close binaries. So far, there had not been any confirmed detection of a white dwarf (WD) companion to any of the BSSs in this cluster. Here, we present the detection of WD companions to 5 bright BSSs in M67. The multiwavelength spectral energy distributions covering 0.12 -11.5 μm range, were found to require binary spectral fits for 5 BSSs, consisting of a cool (BSS) and a hot companion. The parameters (Luminosity, Temperature, Radius and Mass) of the hot companions suggest them to be WDs with mass in the range 0.2 - 0.35 M⊙ with Teff ~11000 –24000 K.

In order to investigate the origin of multiple populations in globular clusters (GCs), we have constructed new chemical evolution models for proto-GCs where the supernova blast waves undergo blowout without expelling the ambient gas. Chemical enrichments in our models are then dictated by the winds of massive stars together with the asymptotic-giant-branch stars ejecta. We find that the observed Na-O anti-correlation can be reproduced when multiple episodes of starburst and enrichment are allowed to continue in proto-GCs. The “mass budget problem” is mostly resolved by our models without ad-hoc assumptions on star formation efficiency, initial mass function, and significant loss of first-generation stars. Interestingly, ages and chemical abundances predicted by this chemical evolution model are in good agreements with those independently obtained from our stellar evolution model for the horizontal-branch. We also discuss observational evidence for the GC-like multiple populations in the Milky Way bulge.

Gravitational wave direct detections suggest that 30 M⊙ binary black holes (BBHs) commonly exist in the universe. One possible formation scenario of such BBHs is dynamical three-body encounters in dense star clusters. We performed a series of direct N-body simulations with a mass of 2500 and 10000 M⊙ and found a new channel for the formation of BBHs which is dominant in open clusters. In open clusters, the core-collapse time is shorter than in globular clusters, and therefore massive main-sequence (MS) binaries can form before they evolve to BHs. These MS binaries experience common envelope evolution and evolve to hard BBHs, which can merge within the Hubble time. The number of BBH mergers per unit mass obtained from our simulations reached 20–50 % of that for globular clusters, assuming an initial cluster mass function. Thus, open clusters can be a dominant formation site of hard BBHs.

High resolution spectra of stars in the ≈200 Myr LMC globular cluster, NGC 1866, reveal rapidly rotating stars with variable H α emission and absorption, and signatures of outflowing material. The variable H α line can substantially affect photometric measurements obtained with HST/WFC3 narrow-band filters.

. We present a significantly improved version of our numerical code JASMINE, that can now solve the Jeans equations for axisymmetric models of stellar systems, composed of an arbitrary number of stellar populations, a Dark Matter halo, and a central Black Hole. The stellar components can have different structural (density profile, flattening, mass, scale length), dynamical (rotational support, velocity dispersion anisotropy), and population (age, metallicity, Initial Mass Function, mass-to-light ratio) properties. These models, when combined with observations, will allow to investigate important issues, such as quantifying the systematic effects of IMF variations, of mass-to-light ratio gradients, and of different stellar kinematic components (e.g. counter rotating disks, kinematically decoupled cores) on luminosity-weighted properties. The developed analytical and numerical framework aims at modeling Early-Type Galaxies, but it can also be applied to dwarf Spheroidal galaxies and Globular Clusters.

We recently discovered that NGC 3201 has characteristics that set it outside the current twofold classification scheme for Galactic globular clusters (GCs). Most GCs are mono-metallic and show light-element abundance variations (e.g., Na-O and C-N anti-correlations); but a minority of clusters also present variations in Fe correlating with s-process element and C+N+O abundances, and they possess multiple C-N sequences. These anomalous GCs also have a broad sub-giant branch (SGB) and follow the same mass-size relation as dwarf galaxies possibly evolving into GCs. We now revealed that NGC 3201 belongs to neither group. It has multiple C-N sequences, but no broad SGB, no strong evidence of a Fe-spread, and it does not follow the mass-size relation.