On the evolution of small scale Cosmic structure
b'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.\\n\\nIn 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\\nthat 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\\ntheir 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.\\n\\nExtending the work of Chapter~2, in Chapter~3 we study the\\nrelationship 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\\nappropriate physical representation of the galaxy formation\\nprocess.\\n\\nIn Chapter~4, we study the assembly of the central cusps of\\n$\\\\Lambda$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.\\nSecondly, it would allow consistency of the comoving number\\ndensity of massive haloes as a function of velocity dispersion with SDSS observations of the counts of galaxies as a function of stellar velocity dispersion.\\n\\n\\n\\nIn 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 \\nvery 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\\nwell. 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\\nto 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.'