Dynamics of galaxies in the cluster environment: a resonant origin for the ISP?

The internal dynamics of elliptical galaxies in clusters depends on many factors, including the environment in which the galaxy is located. In addition to the strong encounters with the other galaxies, we can also consider the gravitational interaction with the ubiquitous Cluster Tidal Field (CTF). As recognized in many studies, one possible way in which CTF affects the dynamics of galaxies inside the cluster is related to the fact that they may start oscillating as ���rigid bodies��� around their equilibrium positions in the field, with the periods of these oscillations curiously similar to those of stellar orbits in the outer parts of galaxies. Resonances between the two motions are hence expected and this phenomenon could significantly contribute to the formation of the Intracluster Stellar Population (ISP), whose presence is abundantly confirmed by observations. In this thesis work, we propose to study the motion of an elliptical galaxy, modelled as a rigid body, in the CTF, especially when its center of mass traces a quasi-circular orbit in the cluster gravitational potential. This case extends and generalizes the previous models and findings, proceeding towards a much more realistic description of galaxy motion. In addition to this, the presence of a further oscillation, namely that of the entire galaxy along its orbit, will possibly increase the probability of having resonances and, consequently, the rate of ISP production nearly to observed values. Thus, after reviewing the dynamics of a rigid body in a generic force field, we will assess some physically relevant studies and report their main results, discussing their implications with respect to our problem. We will conclude our discussion focusing on the more realistic scenario of an elliptical galaxy whose center of mass moves on a quasi-circular orbit in a spherically symmetric potential. The derivation of the fundamental equations of motion will serve as the basis for future modelling and discussions.

A Comparative Analysis of Dynamical Models for Tidal Dissipation in Natural Satellite Ephemerides

The study of the tides of a celestial bodies can unveil important information about their interior as well as their orbital evolution. The most important tidal parameter is the Love number, which defines the deformation of the gravity field due to an external perturbing body. Tidal dissipation is very important because it drives the secular orbital evolution of the natural satellites, which is even more important in the case of the the Jupiter system, where three of the Galilean moons, Io, Europa and Ganymede, are locked in an orbital resonance where the ratio of their mean motions is 4:2:1. This is called Laplace resonance. Tidal dissipation is described by the dissipation ratio k2/Q, where Q is the quality factor and it describes the dampening of a system. The goal of this thesis is to analyze and compare the two main tidal dynamical models, Mignard's model and gravity field variation model, to understand the differences between each model with a main focus on the single-moon case with Io, which can help also understanding better the differences between the two models without over complicating the dynamical model. In this work we have verified and validated both models, we have compared them and pinpointed the main differences and features that characterize each model. Mignard's model treats the tides directly as a force, while the gravity field variation model describes the tides with a change of the spherical harmonic coefficients. Finally, we have also briefly analyzed the difference between the single-moon case and the two-moon case, and we have confirmed that the governing equations that describe the change of semi-major axis and eccentricity are not good anymore when more moons are present.