Cosmological Halo Formation and Mergers

My research has centred around establishing the nature of dark matter haloes by investigating their abundance as a function of halo mass, the formation his- tory of each halo, commonly called the merger tree, and the internal structure of the halo, in terms of their radial density profiles and angular momentum. In the first part of this thesis, I present a new algorithm which groups the subhaloes found in cosmological N-body simulations by structure finders such as subfind into dark matter haloes whose formation histories are strictly hier- archical. One advantage of these ‘Dhaloes’ over the commonly used friends-of- friends (FoF) haloes is that they retain their individual identity in cases when FoF haloes are artificially merged by tenuous bridges of particles or by an over- lap of their outer diffuse haloes. Dhaloes are thus well suited for modelling galaxy formation and their merger trees form the basis of the Durham semi- analytic galaxy formation model, galform. Applying the Dhalo construction to the ΛCDM Millennium-2 simulation we find that approximately 90% of Dhaloes have a one-to-one, bijective match with a corresponding FoF halo. The remaining 10% are typically secondary components of large FoF haloes. Although the mass functions of both types of haloes are similar, the mass of Dhaloes correlates much more tightly with the virial mass, M200, than FoF masses. Approximately 80% of FoF and bijective and non-bijective Dhaloes are relaxed according to standard criteria. For these relaxed haloes all three types have similar concentration– M200 relations and, at fixed mass, the concentration distributions are described accurately by log-normal distributions. In the second part of this thesis, I present distributions of orbital parameters of infalling satellite haloes at the time of crossing the virial radius of their host halo. Detailed investigation of the orbits is crucial as it represents the initial conditions which determine the later evolution of the substructure within the host. I use merger trees in a high resolution cosmological N-body simulation to trace the satellite haloes and measure their orbits when they first infall into the host halo. I find that there is a trend of the orbital parameters with the ratio between the satellite halo mass and the host halo mass at infall. I find that the more massive satellites move along more eccentric orbits with lower specific angular momentum than less massive satellites. I also search for possible correlations between different orbital parameters and provide accurate fitting formulae for the two independent orbital parameters (the total velocity and the radial-to-total velocity ratio). Using combinations of these formulae, we successfully fit all the other orbital parameters