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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

Gaia BH3 is the first observed dormant black hole (BH) with a mass of $\approx{30}$ M$_\odot$ and represents the first confirmation that such massive BHs are associated with metal-poor stars. Here, we explore the isolated binary formation channel for Gaia BH3 focusing on the old and metal-poor stellar population of the Milky Way halo. We use the MIST stellar models and our open-source population synthesis code SEVN to evolve $5.6 \times 10^8$ binaries exploring 20 sets of parameters. We find that systems like Gaia BH3 form preferentially from binaries initially composed of a massive star ($40-60$ M$_\odot$) and a low mass companion ($<1$ M$_\odot$) in a wide ($P>10^3$ days) and eccentric orbit ($e>0.6$). Such progenitor binary stars do not undergo any Roche-lobe overflow episode during their entire evolution, so that the final orbital properties of the BH-star system are determined at the core collapse of the primary star. Low natal kicks ($\lesssim$ 10~km/s) significantly favour the formation of Gaia BH3-like systems, but high velocity kicks up to $\approx 220$ km/s are also allowed. We estimate the formation efficiency for Gaia BH3-like systems in old ($t>10$ Gyr) and metal-poor ($Z<0.01$) populations to be $\sim 4 \times 10^{-8}$ M$_\odot^{-1}$ (for our fiducial model), representing $\sim 3\%$ of the whole simulated BH-star population. We expect up to $\approx 4000$ BH-star systems in the Galactic halo formed through isolated evolution, of which $\approx 100$ are compatible with Gaia BH3-like. Given the density profile of the Galactic halo we do not expect more than one at the observed distance of Gaia BH3. Our models show that, even if it was born inside a stellar cluster, Gaia BH3 is compatible with a primordial binary star that escaped from its parent cluster without experiencing significant dynamical interactions., Comment: new version after the review process (including suggestions and comments by the community). Accepted for publication in A&A

The degree of mass loss, i.e. the fraction of stars lost by globular clusters, and specifically by their different populations, is still poorly understood. Many scenarios of the formation of multiple stellar populations, especially the ones involving self-enrichment, assume that the first generation (FG) was more massive at birth than now to reproduce the current mass of the second generation (SG). This assumption implies that, during their long-term evolution, clusters lose around $90\%$ of the FG. We have tested whether such strong mass loss could take place in a massive globular cluster orbiting the Milky Way at $4\ {\rm kpc}$ from the centre and composed of two generations. We perform a series of $N$-body simulations for ${12\ \rm Gyr}$ to probe the parameter space of internal cluster properties. We have derived that, for an extended FG and a low-mass second one, the cluster loses almost $98\%$ of its initial FG mass and the cluster mass can be as much as 20 times lower after a Hubble time. Furthermore, under these conditions, the derived fraction of SG stars, $f_{\rm enriched}$, falls in the range occupied by observed clusters of similar mass ($\sim 0.6-0.8$). In general, the parameters that affect the most the degree of mass loss are the presence or not of primordial segregation, the depth of the central potential, $W_{0,FG}$, the initial mass of the SG, $M^{ini}_{SG}$, and the initial half-mass radius of the SG, $r_{h,SG}$. Higher $M^{ini}_{SG}$ have not been found to imply higher final $f_{\rm enriched}$ due to the deeper cluster potential well which slows down mass loss., Comment: 16 pages, 9 figures. Accepted for publication on Astronomy & Astrophysics

By means of 3D hydrodynamic simulations, we explore the effects of rotation in the formation of second-generation (SG) stars in globular clusters (GC). Our simulations follow the SG formation in a first-generation (FG) internally rotating GC; SG stars form out of FG asymptotic giant branch (AGB) ejecta and external pristine gas accreted by the system. We have explored two different initial rotational velocity profiles for the FG cluster and two different inclinations of the rotational axis with respect to the direction of motion of the external infalling gas, whose density has also been varied. For a low (10^-24 g cm^-3) external gas density, a disk of SG helium-enhanced stars is formed. The SG is characterized by distinct chemo-dynamical phase space patterns: it shows a more rapid rotation than the FG with the helium-enhanced SG subsystem rotating more rapidly than the moderate helium-enhanced one. In models with high external gas density (10^-23 g cm^-3), the inner SG disc is disrupted by the early arrival of external gas and only a small fraction of highly enhanced helium stars preserves the rotation acquired at birth. Variations in the inclination angle between the rotation axis and the direction of the infalling gas and the velocity profile can slightly alter the extent of the stellar disc and the rotational amplitude. No significant variation has been found in the timespan of our simulations when changing the inclination angle between the rotation axis and the direction of the infalling gas, while different velocity profiles can slightly alter the extent of the stellar disc and the rotational amplitude. The results of our simulations illustrate the complex link between dynamical and chemical properties of multiple populations and provide new elements for the interpretation of observational studies and future investigations of the dynamics of multiple-population GCs., Comment: 16 pages, 13 figures, accepted for publication in MNRAS

By means of 3D hydrodynamic simulations, we study how Type Ia supernovae (SNe) explosions affect the star formation history and the chemical properties of second generation (SG) stars in globular clusters (GC). SG stars are assumed to form once first generation asymptotic giant branch (AGB) stars start releasing their ejecta; during this phase, external gas is accreted by the system and SNe Ia begin exploding, carving hot and tenuous bubbles. Given the large uncertainty on SNe Ia explosion times, we test two different values for the 'delay time'. We run two different models for the external gas density: in the low-density scenario with short delay time, the explosions start at the beginning of the SG star formation, halting it in its earliest phases. The external gas hardly penetrates the system, therefore most SG stars present extreme helium abundances (Y > 0.33). The low-density model with delayed SN explosions has a more extended SG star formation epoch and includes SG stars with modest helium enrichment. On the contrary, the high-density model is weakly affected by SN explosions, with a final SG mass similar to the one obtained without SNe Ia. Most of the stars form from a mix of AGB ejecta and pristine gas and have a modest helium enrichment. We show that gas from SNe Ia may produce an iron spread of $\sim 0.14$ dex, consistent with the spread found in about 20% of Galactic GCs, suggesting that SNe Ia might have played a key role in the formation of this sub-sample of GCs., Comment: 19 pages, 12 figures, Accepted for publication in MNRAS

We study the effects of the integrated galactic initial mass function (IGIMF) and dust evolution on the abundance patterns of high redshift starburst galaxies. In our chemical models, the rapid collapse of gas clouds triggers an intense and rapid star formation episode, which lasts until the onset of a galactic wind, powered by the thermal energy injected by stellar winds and supernova explosions. Our models follow the evolution of several chemical elements (C, N, $\alpha$-elements and Fe) both in the gas and dust phases. %The most recent stellar yield and dust prescriptions are adopted. We test different values of $\beta$, the slope of the embedded cluster mass function for the IGIMF, where lower $\beta$ values imply a more top-heavy initial mass function (IMF). The computed abundances are compared to high-quality abundance measurements obtained in lensed galaxies and from composite spectra in large samples of star-forming galaxies in the redshift range $2 \lesssim z \lesssim 3$. The adoption of the IGIMF causes a sensible increase of the rate of star formation with respect to a standard Salpeter IMF, with a strong impact on chemical evolution. We find that in order to reproduce the observed abundance patterns in these galaxies, either we need a very top-heavy IGIMF ($\beta < 2$) or large amounts of dust. In particular, if dust is important, the IGIMF should have $\beta \ge 2$, which means an IMF slightly more top-heavy than the Salpeter one. The evolution of the dust mass with time for galaxies of different mass and IMF is also computed, highlighting that the dust amount increases with a top-heavier IGIMF., Comment: 21 pages, 14 Figures. Accepted for publication in MNRAS

Stacked analyses of galaxy clusters at low-to-intermediate redshift show signatures attributable to dust, but the origin of this dust is uncertain. We test the hypothesis that the bulk of cluster dust derives from galaxy ejecta. To do so, we employ dust abundances obtained from detailed chemical evolution models of galaxies. We integrate the dust abundances over cluster luminosity functions (one-slope and two-slope Schechter functions). We consider both a hierarchical scenario of galaxy formation and an independent evolution of the three main galactic morphologies: elliptical/S0, spiral and irregular. We separate the dust residing within galaxies from the dust ejected in the intracluster medium. To the latter, we apply thermal sputtering. The model results are compared to low-to-intermediate redshift observations of dust masses. We find that in any of the considered scenarios, elliptical/S0 galaxies contribute negligibly to the present-time intracluster dust, despite producing the majority of gas-phase metals in galaxy clusters. Spiral galaxies, instead, provide both the bulk of the spatially-unresolved dust and of the dust ejected into the intracluster medium. The total dust-to-gas mass ratio in galaxy clusters amounts to $10^{-4}$, while the intracluster medium dust-to-gas mass ratio amounts to $10^{-6}$ at most. These dust abundances are consistent with the estimates of cluster observations at $0.2 < z <1$. We propose that galactic sources, spiral galaxies in particular, are the major contributors to the cluster dust budget., Comment: MNRAS. Accepted on Feb 11th, 2020. 13 pages, 4 figures