Topics in Galaxy Formation: Pairwise Velocities of Dark Matter Halos and Molecular Hydrogen Regulated Star Formation in Cosmological Simulations

In this dissertation we investigate two distinct challenges within the concordance LCDM model and an unrelated project. The first is a discrepancy between theory and observation. A massive galaxy sub-cluster known as the `bullet\u27 has fallen through a more massive parent galaxy cluster at a redshift of z=0.296. Theory finds that in order to reproduce the observational quantities of this cluster, an unusually high relative velocity of v12=3000 km/s between the two cluster\u27s parent halos is required. We quantify the statistical probability of producing a `bullet-like\u27 halo pair within large N-body simulations, and conclude that either the LCDM model is currently incompatible with observations, or the inferred relative velocity must be revised to a lower value. Recent improvements to the observed mass estimates provide hope that we may be able reconcile the differences in the future. The second challenge is on the topic of galaxy formation within cosmological smoothed particle hydrodynamic simulations. Recent observational evidence suggests that star formation correlates tightly with the presence of molecular hydrogen (H2). New analytic models have emerged allowing us to calculate the mass fraction of H2 at virtually no computational cost. We can then regulate star formation within our simulations by the local abundance of H2, rather than the gas density. A comparison study between the new H2-based star formation prescription and previous models is presented, detailing the advantages and disadvantages of the new model. Finally we discuss the construction of a galactic halo and disk with the goal of exploring and developing a better method for implementing supernova feedback in small scale hydrodynamic simulations. This proves to be a non-trivial process, and ultimately an unrealistic method to construct galaxies in a cosmological context