On the evolution of small scale Cosmic structure

In this thesis, we use a variety of high resolution cosmological
$N$--body simulations to study the formation and evolution of
highly non--linear objects in our universe. In Chapter~2, we study
the systematics of dark matter subhalo populations. For the first
time, we give a picture for the evolution of subhalo populations: a
substantial fraction of the mass of most haloes has been added at
relatively recent redshifts, and this mass is accreted in clumpy
form with a halo mass distribution similar to that of the Universe
as a whole. Since tidal stripping rapidly reduces the mass of
subhaloes, the population at any given mass is dominated by objects
which fell in recently and so had lower mass (and thus more
abundant) progenitors. The orbits of recently accreted objects
spend most of their time in the outer halo, so that subhaloes of
given mass are substantially less centrally concentrated than the
dark matter as a whole. Subhaloes which are seen near halo centre
have shorter period orbits and so must have fallen in earlier. They
thus retain a relatively small fraction of their initial mass. Our
results suggest that any comparison with galaxies in real clusters
is only possible if the formation of the luminous component is
modelled appropriately. Extending the work of Chapter~2, in
Chapter~3 we study the relationship between the subhalo and the
galaxy population by combining $10$ high resolution resimulations
of cluster--sized dark haloes with semi--analytic galaxy formation
modelling. In particular, we compare the number density and
velocity profiles of cluster galaxies and those of subhaloes. While
the radial distribution of galaxies follows closely that of the
dark matter, the distribution of dark matter subhaloes is much less
centrally concentrated. We find there is a complex and strongly
position--dependent relation between galaxies and the subhaloes in
which they reside. This relation can be properly modelled only by
appropriate physical representation of the galaxy formation
process. In Chapter~4, we study the assembly of the central cusps
of $\Lambda$CDM haloes. The primary conclusion is that the inner
cores of galaxies tend to a universal density profile for their
collisionless mixture of stars and dark matter through multiple
mergers. Our result may alleviate some apparent challenges to the
CDM model for structure formation. Firstly, it could in principle
explain the observed absence of a cusp in the central dark matter
distribution of nearby galaxies and galaxy clusters. Secondly, it
would allow consistency of the comoving number density of massive
haloes as a function of velocity dispersion with SDSS observations
of the counts of galaxies as a function of stellar velocity
dispersion. In the final Chapter, we have carried out a sequence of
$N$--body resimulations of individual haloes at various redshifts
within a {\em cosmological volume} $(0.68{\rm Gpc})^3$ with the aim
of resolving the first bound objects which could potentially host
the first stars in a cold dark matter dominated universe. Our
simulations succeed in resolving rare but relatively massive haloes
spanning a very broad redshift range[$z=80$, $z=0$] with ultra-high
resolution. The highest resolution achieved in our final level
simulation has a particle mass of $0.8{\rm M_{\odot}}$ and a force
softening of $\epsilon=7.8$pc in comoving units. Our results
indicate that initial structure formation was extremely strongly
biased to overdense regions, and that this can be well understood
within the framework of extended Press-Schechter(EPS) theory. The
internal structure of these early haloes are quite similar to their
low redshift counterparts, although the NFW profile does not fit as
well. The halo mass function is examined at redshift $z=50$ and
$z=30$. We find an excellent agreement between the predictions and
the simulations. Because our simulation volume is not a small
periodic box we are able to simulate rarer and more massive halos
at any given redshift than previous work. We find that bound--free
cooling from atomic hydrogen can take place in haloes as early as
$z=32$ and that the comoving abundance of these halos is predicted
to be the same as for $10^{14}h^{-1}{\rm M_\odot}$ halos today. If
the first stars did form in haloes with mass $\sim 10^6{\rm
M_\odot}$, a large number would be born already at $z \sim 45$ with
a comoving abundance matching that of haloes with mass $M_*$ today.