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.

A study of extended radio galaxies in the Shapley concentration core

Extended cluster radio galaxies show different morphologies com- pared to those found isolated in the field. Indeed, symmetric double radio galaxies are only a small percentage of the total content of ra- dio loud cluster galaxies, which show mainly tailed morphologies (e.g. O’Dea & Owen, 1985). Moreover, cluster mergers can deeply affect the statistical properties of their radio activity. In order to better understand the morphological and radio activity differences of the radio galaxies in major mergeing and non/tidal-merging clusters, we performed a multifrequency study of extended radio galax- ies inside two cluster complexes, A3528 and A3558. They belong to the innermost region of the Shapley Concentration, the most massive con- centration of galaxy clusters (termed supercluster) in the local Universe, at average redshift z ≈ 0.043. We analysed low frequency radio data performed at 235 and 610 MHz with Giant Metrewave Radio Telescope (GMRT) and we combined them with proprietary and literature observations, in order to have a wide frequency range (150 MHz to 8.4 GHz) to perform the spectral analysis. The low frequency images allowed us to carry out a detailed study of the radio tails and diffuse emission found in some cases. The results in the radio band were also qualitatively compared with the X-ray information coming from XMM-Newton observations, in order to test the interaction between radio galaxies and cluster weather. We found that the brightest central galaxies (BCGs) in the A3528 cluster complex are powerful and present substantial emission from old relativistic plasma characterized by a steep spectrum (α > 2). In the light of observational pieces of evidence, we suggest they are possible re-started radio galaxies. On the other hand, the tailed radio galaxies trace the host galaxy motion with respect to the ICM, and our find- ings is consistent with the dynamical interpretation of a tidal interaction (Gastaldello et al. 2003). On the contrary, the BCGs in the A3558 clus- ter complex are either quiet or very faint radio galaxies, supporting the hypothesis that clusters mergers quench the radio emission from AGN.