Stellar and dynamical evolution in Globular Clusters

Globular Clusters (GCs) are stellar systems orbiting around galaxies, that present a spherical shape and are characterized by an intriguing dynamical evolution. The high stellar density makes gravitational encounters between stars frequent, driving these system toward two-body relaxation. This process alters the structural, spatial, and kinematic properties of stars during the long life of GCs, that is ∼ 10 Gyr. In this work, we first present and examine the past and current knowledge on Galactic GCs (Chapter 1). We begin by considering these systems as made of a single stellar population, to introduce the physical effects connected with relaxation, such as energy equipartition and mass segregation as well as stellar evaporation, produced by the Galactic tidal field. The already intricate evolution of GCs is further complicated by the presence of Multiple Populations (MPs), that is, generations of stars showing a different chemical content, detected in almost all GCs. The scenario behind their formation is still not known and widely discussed, as are the early conditions and their impact in the following evolution of these systems and the Galactic environment. We outline the observational evidence, the proposed formation scenarios, and MPs evolution, focusing on the main open problems. In Chapter 2 we present the methods and tools used for studying the evolution of GCs and their dynamical state. As collisional systems, GCs evolution must be described through direct N-body simulations, that integrate the N-point mass dynamics subject to the mutual gravitational attraction between stars, as we outline in Sect. 2.1. In addition, also stellar evolution must be taken into account, as it alters the properties of individual objects, causing important effects on the system behavior, in particular in the early phases. Furthermore, dynamical models offer a robust tool to analyze and describe GCs and their physical process. In Sect. 2.2, we present our multi-mass King-like dynamical model, that can appropriately predict and quantify mass-based processes, such as energy equipartition and mass segregation. In particular, we use the model to estimate the energy equipartition degree in a subset of Galactic GCs, for which we fit the available data on internal kinematics (Sect. 2.3). Our work reveals that the multi-mass model equilibrium parameter Φ_0, connected with the gravitational potential and the dynamical state, correlates with the equipartition mass m_eq, an empirical estimator of the energy equipartition degree adopted in the literature, as well as other structural quantities. In addition, we successfully fit the observed surface brightness profiles of the same GCs, further validating our approach and confirming the goodness of our description. Concerning mass segregation, we find that our dynamical model can predict its degree through the relation between the half-mass radius and stellar mass. The shape of this function predicted by the model is also well described by a linear relation, whose slope β is an empirical quantifier of the segregation degree and results correlated with Φ_0 (Sect. 2.4.2). As a consequence, we use our model to determine initial conditions for N-body simulations (Sect. 2.5), to set an initial degree of primordial segregation in GCs, as expected from the violent relaxation phase, that is, the early dynamical evolution that sets the monolithic structure of the system after stellar formation. In Chapter 3, we take advantage of the aforementioned results to simulate the dynamical evolution of MPs, assuming one of the most appealing formation scenarios, the AGB one. It sees a First Generation (FG) formed by the original cluster composition. Once AGB stars of the FG evolve, they pollute the cluster with a chemically altered material, that contributes to the formation of a Second Generation (SG). We consider for the first time the impact of a primordial segregation degree in FG stars, imprinted by the violent relaxation phase. We also take into account the age of FG stars after the formation of SG stars, that is ∼ 100 Myr in the AGB pollution scenario. In addition, we explore the effects of a different relative spatial concentration between MPs in the initial conditions, taking advantage of quantitative estimates from SG formation studies. Our results highlight that primordial segregation and age difference alter the early dynamical evolution, that is, the feedback from stellar evolution (Sect. 3.3). The expansion of FG stars is stronger for the aged cases and weaker for segregated ones. This affects the MPs radial mixing efficiency and the evolution toward mass segregation and energy equipartition, with the SG typically showing a higher degree of both. Interestingly, our different initial conditions also affect the behavior of the half-mass radius of FG black holes, which sink in the core. Furthermore, a higher initial relative concentration between MPs severely changes the early dynamics, bringing to a strong predominance of SG stars in the most extreme case, that also show a more advanced dynamical state (Sect. 3.4). Finally, we discuss the challenges of more realistic simulations in Sect. 3.5, targeting the mass budget problem with direct N-body simulations, likely requiring a very high number of stars and several computational resources to perform simulations where both the strong early loss of FG stars as well as the final internal dynamics are well described. Our work underline the importance of considering the effect of a primordially segregated and aged FG, aspects that both influence the observational and structural features of MPs observable today. Thus, future research should focus on setting more realistic and consistent initial conditions, taking advantage of multi-mass dynamical models and appropriately considering the initial differences between FG and SG. This would shed further light on the formation scenario of MPs, the early conditions of GCs and the role of these systems in the galactic context.