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Relaxation of isolated self-gravitating systems in one and three dimensions

Abstract : Although Newtonian gravity plays an essential role in the evolution of celestial objects in the universe, the understanding of its dynamics is still limited. In this thesis we present a theoretical study of the dynamics of self-gravitating systems in one and three dimensions. The main question we study, using extensive numerical simulations, is whether existing statistical mechanical theories can describe their dynamical behavior. In one dimension we study principally two questions: the relaxation toward thermal equilibrium and the "violent relaxation" toward so-called "quasi-stationary states" (QSS). The first question considers the relaxation toward a state corresponding to the thermal equilibrium in the micro-canonical or canonical ensemble, where the analytical solution is known. We introduce the order parameters which can probe the relaxation. More specifically we establish that the characteristic time of this relaxation is correlated with fluctuations in the quasi-stationary state and scaled linearly with the particle number, independently of the initial condition. The second question considers the violent relaxation starting from different initial conditions, and the comparison with the violent relaxation theory of Lynden-Bell. This theory turns out to describe to a good approximation the properties of quasi-stationary states when the energy is close to the degenerate limit, or, more generally, when the initial conditions are such that the relaxation is "gentle". The breakdown of the theory on the other hand is correlated to the emergence of "core-halo" structure. Finally we study the same question for self-gravitating systems in three dimensions. For this case the theory of Lynden-Bell gives, in absence of a confining box, a solution of infinite mass. We show however that the solution is only weakly sensitive to the box size close to the degenerate limit. It can thus be compared with the (more physical) case of systems with open boundary conditions, which we simulate numerically. We observe as in one dimension a good agreement with the theory of Lynden-Bell in the regime close to the degenerate limit, and otherwise the emergence of core-halo structure when it breaks down. Keywords:
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Submitted on : Monday, July 11, 2011 - 11:22:01 AM
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  • HAL Id : tel-00607774, version 1


T. Worrakitpoonpon. Relaxation of isolated self-gravitating systems in one and three dimensions. Astrophysics [astro-ph]. Université Pierre et Marie Curie - Paris VI, 2011. English. ⟨tel-00607774⟩



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