Simulating structure formation with N-Body and semi-analytic models

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.