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Wang, Jie (2008): Simulating structure formation with N-Body and semi-analytic models. Dissertation, LMU München: Faculty of Physics
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Abstract

In this thesis, I study the formation of structure within the current standard cosmological model using two numerical methods: N-body simulations and semi-analytic models of galaxy formation. In Chapter 1 & 2, I will explain the motivations and objectives of the analysis presented in this thesis, and give a brief review of the relevant background. Chapter 3 is focused on the discreteness effects in $N$-body simulation: Hot/Warm Dark Matter (H/WDM) $N$-body simulations in which the initial uniform particle load is a cubic lattice, exhibit artefacts related to this lattice. In particular, the filaments which form in these simulations break up into regularly spaced clumps which reflect the initial grid pattern. Using numerical simulations, I demonstrate that a similar artefact is present even when the initial uniform particle load is not a lattice, but rather a glass with no preferred directions and no long-range coherence. My study shows that such regular fragmentation occurs also in simulations of the collapse of idealized, uniform filaments, but not in simulations of the collapse of infinite uniform sheets. In H/WDM simulations, all self-bound non-linear structures with masses much smaller than the free streaming mass appear to originate through spurious fragmentation of filaments. These artificial fragments form below a characteristic mass which scales as $M_p^{1/3}k^{-2}_{peak}$. This has the unfortunate consequence that the effective mass resolution of such simulations improves only as the cube root of the number of particles employed. In Chapter 4, I combine $N$-body simulations of structure growth with physical modelling of galaxy evolution to investigate whether the shift in cosmological parameters between the 1-year and 3-year results from the Wilkinson Microwave Anisotropy Probe (WMAP) affects predictions for the galaxy population. Structure formation is significantly delayed in the WMAP3 cosmology, because the initial matter fluctuation amplitude is lower on the relevant scales. The decrease in dark matter clustering strength is, however, almost entirely offset by an increase in halo bias, so predictions for galaxy clustering are barely altered. In both cosmologies, several combinations of physical parameters can reproduce observed, low-redshift galaxy properties; the star formation, supernova feedback, and AGN feedback efficiencies can be played off against each other to give similar results for a variety of combinations. Models which fit observed luminosity functions predict projected 2-point correlation functions which scatter by about 10-20 per cent on large scale and by larger factors on small scale, depending both on cosmology and on details of galaxy formation. Measurements of the pairwise velocity distribution prefer the WMAP1 cosmology, but careful treatment of the systematics is needed. Given current modelling uncertainties, it is not easy to distinguish the WMAP1 and WMAP3 cosmologies on the basis of low-redshift galaxy properties. Model predictions diverge more dramatically at high redshift. Better observational data at z>2 will better constrain galaxy formation and perhaps also cosmological parameters. In Chapter 5, I study whether the apparent universality of halo properties in hierarchical clustering cosmologies is a consequence of their growth through mergers. N-body simulations of Cold Dark Matter (CDM) have shown that, in this hierarchical structure formation model, dark matter halo properties, such as the density profile, the phase-space density profile, the distribution of axial ratio, the distribution of spin parameter, and the distribution of internal specific angular momentum follow `universal' laws or distributions. Here I study the properties of the first generation of haloes in a Hot Dark Matter (HDM) dominated universe, as an example of halo formation through monolithic collapse. I find all these universalities to be present in this case also. Halo density profiles are very well fit by the Navarro et al (1997) profile over two orders of magnitude in mass. The concentration parameter depends on mass as $c \propto M^{0.2}$, reversing the dependence found in a hierarchical CDM universe.However, the concentration-formation time relation is similar in the two cases: earlier forming haloes tend to be more concentrated than their later forming counterparts. Halo formation histories are also characterized by two phases in the HDM case: an early phase of rapid accretion followed by slower growth. Furthermore, there is no significant difference between the HDM and CDM cases concerning the statistics of other halo properties: the phase-space density profile; the velocity anisotropy profile; the distribution of shape parameters; the distribution of spin parameter, and the distribution of internal specific angular momentum are all similar in the two cases. Only substructure content differs dramatically. These results indicate that mergers do not play a pivotal role in establishing the universalities, thus contradicting models which explain them as consequences of mergers.