The complexity of the dark matter sheet

Abstract

One of the most important open questions of modern physics is: What is dark matter? Astrophysical approaches to learn more about the nature of dark matter rely upon the numerical modelling of the dark matter fluid in cosmological simulations. In this thesis we develop new mathematical tools and numerical simulation techniques to understand and predict the evolution of the dark matter fluid and its phase space distribution. Dark matter has an unknown, but small primordial velocity dispersion. Therefore the dark matter fluid effectively occupies a three dimensional Lagrangian submanifold in the six dimensional phase space - also know as the dark matter sheet. This has many implications for fine-grained features in the density field, the formation of structures and numerical simulation possibilities. We develop new tools to identify and understand different largescale structures types (single-stream regions, pancakes, filaments and haloes) from a phase space perspective. Further, we develop an excursion set approach for single-stream regions which is used to answer the question “what is the median density of the universe?” and to investigate whether single-stream regions form a connected percolating complex or distinct isolated regions. Further we introduce a “sheet + release” simulation approach to make reliable cosmological warm dark matter simulations possible. This combines a sheet-based phase space interpolation scheme (Hahn & Angulo, 2016) which is used in low density regions (like single-stream regions, pancakes and filaments) with a combined N-body + geodesic deviation equation simulation approach in complex high-density regions (like haloes). Thereby this overcomes problems in pure sheet-schemes (which become untraceably complex inside haloes) and N-body simulations (which tend to fragment in low-density regions). Further, we introduce a novel scheme for calculating forces from an oct-tree of cubes, which makes it possible to use the sheet + release scheme at high force resolution. Thereby we present the first scheme which makes possible warm dark matter simulations that are reliable from low-density regions up to the very dense and complex centers of haloes – and this while following a lot of fine-grained phase space information. As a first test case we apply this simulation scheme in a “zoom-in” simulation of a small warm dark matter halo. The simulation shows no artificial structures and the radial density structure of the halo converges well. The density profile seems to be consistent with an NFW-profile and does not differ significantly from an N-body simulation (which shows artificial fragments in the density field). In a final part of this thesis we discuss the possibility of following warm and hot phase space distributions by reconstructing the phase space locally around cold sheets in phase space. This could allow to simulate warm dark matter while explicitly modelling the thermal smoothing due to the primordial velocity dispersion. Further, it might be used to simulate the cosmic neutrino background with a relatively small number of required resolution elements