Weekly Seminars for February 2017 |

Tuesday, February 21, 2017 - h 15:30
at
ICRANet Pescara
Piazza della Repubblica 10, 65122 - Pescara (Italy)
ICRANet Seminars Speaker: Prof. Marco Merafina
Institution: Department of Physics, University of Rome La Sapienza, Italy
Title: "GRAVITY AND THERMODYNAMICS: A NEW
POINT OF VIEW IN THE ANALYSIS OF EQUILIBRIUM AND DYNAMICAL
EVOLUTION OF GLOBULAR CLUSTERS"
Abstract:
space mixing of stellar orbits. In this scenario, thermodynamics plays a central role in the gravitational equilibrium and stability of the clusters, being binary relaxation time shorter than the age of such systems. On the other hand, the observations of luminosity profiles of globular clusters, at different values of the central gravitational potential, show self similar curves that suggested a unique sequence of models with the same distribution function and different parameters during the dynamical evolution [1]. This feature was also confirmed by several numerical simulations of globular clusters existing in literature. This means that the evolution of globular clusters can be studied by considering small thermodynamic transformations which keep constant the functional form of the velocity distribution of stars like in the framework of the Boltzmann statistical mechanics. Here we construct models with a different approach by applying thermodynamic principles to a Boltzmann distribution function with an Hamiltonian function which contains an effective potential depending on the kinetic energy of the stars, due to the effect of tidal interactions induced by the hosting galaxy. This particular form of the Hamiltonian function derives from solving the Fokker-Planck equation in a different way with respect to the King approach. The distribution obtained also corresponds to a maximum of the entropy, and therefore implies a thermodynamical equilibrium based on collisions among stars in the Fokker-Planck approximation. This result is a real breakthrough point in the analysis of dynamical evolution of globular clusters. We obtain new relations for the thermodynamical equilibrium in presence of a gravitational potential, a different form of the virial theorem, and introduce the concept of thermodynamic and kinetic temperature, pressure and chemical potential (the intensive quantities). In addition, we can show that a globular cluster can be described as a model containing regions with positive and negative specific heat producing thermodynamic instabilities which drive the systems towards the gravothermal catastrophe, without the necessity of an external thermal bath. The influence of the effective potential on the virial theorem will be described, together with the related consequences on the gravothermal stability limit for star clusters through the analysis of the caloric curve and its critical points. This new limit is different from one obtained by Katz in 1978 [2] and now is in complete accordance with the value related to the maximum of cluster distribution constructed by data from Harris Catalogue for globular clusters [3], solving the unexplained discrepancy evidenced since forty years. This agreement between theory and observations is obtained also for small clusters, giving the conditions for the disruption of clusters, never obtained from the theoretical point of view, but observed in several clusters. Finally, new developments on N-body simulations for glubular clusters are presented. The results confirm the presence and the predicted form of the effective potential arising from tidal interactions between the cluster and the hosting galaxy, as well the possibility to verify this effect by complete observations of transverse and radial velocities of stars of a globular cluster even in one single shell at given radius. References 1. I.R. King, AJ, 71, 64 (1966). 2. J. Katz, MNRAS, 183, 765 (1978). 3. W.E. Harris, AJ, 112, 1487 (1996). |