Séminaire / Seminar GReCO |
| « Large scale structure formation with the Schrödinger method » |
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C. Uhlemann |
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When describing large-scale structure formation of collisionless dark matter one is interested in the dynamics of a large collection of identical point particles that interact only gravitationally. Via gravitational instability initially small density perturbations evolve into eventually bound structures, like dark matter halos that are distributed along the cosmic web. Even though this problem seems quite simple from a conceptual point of view, no sufficiently general solution of the underlying equation, the collisionless Boltzmann equation coupled to the Poisson equation, is known. Therefore one usually has to resort to N-body simulations which tackle the problem numerically. Analytical methods to describe structure formation are in general based on the dust model which describes cold dark matter as a pressureless fluid characterized by density and velocity. This model works quite well up to the quasi-linear regime but eventually fails when multiple streams form that are especially important for halo formation but lead to singularities in the model.
We employ the so-called Schrödinger method to develop a model which is able to describe multi-streaming and therefore can serve as replacement for the dust model. The Schroedinger method is based on the coarse-grained Wigner probability distribution obtained from a wave function fulfilling the Schroedinger-Poisson equation. We show that its evolution equation approximates the Vlasov equation in a controlled way, cures the shell-crossing singularities of the dust model and is able to describe regions of multi-streaming which are crucial for halo formation. This feature has already been employed in cosmological simulations of large-scale structure formation by Widrow & Kaiser (1993). We explain how the coarse-grained Wigner ansatz allows to calculate all higher moments analytically from density and velocity, thereby incorporating higher cumulants in a self-consistent manner. On this basis we show that the Schroedinger method automatically closes the hierarchy of cumulants and that it suffices to solve the Schroedinger-Poisson instead of the Vlasov-Poisson system to directly determine density and velocity and all higher cumulants. |
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lundi 28 septembre 2015 - 11:00 Salle des séminaires Évry Schatzman Institut d'Astrophysique de Paris |
| Pages web du séminaire / Seminar's webpage |