Cosmological theories that include a non-baryonic dynamically cold dark matter\ud (CDM) have been stunningly successful at explaining observations of the universe on\ud large scales. On the scale of individual galaxies, however, observations have been made which call into question the CDM paradigm.\ud \ud In particular, simulations of structure formation show CDM haloes with a density\ud “cusp”, such that in the centre of the halo d ln ρ/d ln r ~1 − 1.5. In contrast, observational studies suggest that CDM haloes have constant density cores.\ud \ud In this thesis I use gravitational N-body simulations to investigate the claim that the\ud dark matter halo cusp can be removed by angular momentum transport from a rotating\ud bar in a disc galaxy. I find that the simulations which were used to support this claim were seriously flawed, and similar simulations designed to mitigate these flaws suggest that this is unlikely to be a mechanism for turning a cusp into a core.\ud \ud In the interests of further work on dark matter haloes, and on other problems in\ud astrophysics, I design and implement a new method for constructing model galaxies\ud with halo, bulge, and disc components. This method avoids the use of an approximation\ud to a Maxwellian velocity distribution. I show that this creates stable galaxy models, well suited to many applications.\ud \ud As an example of these applications, I conduct a thorough investigation of the structural and kinematic properties of the haloes of the remnants of 1:1 mass ratio mergers. I determine that the merger has virtually no effect on the halo cusp strength, but a substantial effect on the halo velocity distribution. The remnant haloes are significantly less spherical that those described in studies of mergers which consider gas cooling. Other properties of the remnants are noted and discussed
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