Groups, clusters and superclusters of galaxies
Galaxies are observed in a diverse range of associations. Understanding the dynamical, statistical and clustering properties of aggregations of galaxies forms the main body of this thesis. On the smallest scale, we use a model for the Local Group to study the formation of a typical galaxy system and to understand the mass distribution within the Local Group. Our model is a binary system excised from numerical simulation of a Universe dominated by cold dark matter which has similar radial velocity and separation as M31 and the Milky Way. We find that the timing argument provides a reliable method for placing a lower limit to the mass of the Local Group. The anisotropy parameter of the particle orbits within the dark halos of CDM are predicted to radially biased. To reconcile the mass of the Milky Way with the predictions from the timing argument and the mass of our model halo, the satellites of our Galaxy must be on circularly biased orbits. The asymptotic values of the rotation curves of the two halos match very closely those of M31 and the Milky Way, as the halos come closer together the curves become very distorted. A simple treatment of gas within our model extends the rotation curves into the central regions of the halos. In our model, M31 and the Milky Way collide 2.5 Gyrs from the present time, a fraction of the current crossing time. Intermediate scales are probed using a statistical analysis of groups of galaxies identified using well defined selection criteria from the CfA redshift survey. The grouping algorithm is optimised using artificial galaxy catalogues constructed from N-body simulations which have similar low order correlations to the original survey. We develop a method of estimating the total luminosity of groups of galaxies identified within magnitude limited redshift surveys and use it to calculate the luminosity function of galactic systems. This statistic measures the abundance of gravitationally bound structures, independent of the detailed arrangement of the luminous material within them. We find that this function has a smooth transition from single galajdes to rich clusters. The distribution of group velocity dispersions shows a discontinuity at the transition between groups and rich clusters. The correlation function of groups is found to depend on the mass range of the sample, luminous groups are more strongly correlated than faint groups. We compare these results with predictions from the CDM model and have extended to intermediate scales the previous success of the model on galactic and cluster scales. On large scales we have used an all sky redshift survey of galaxies detected by IRAS to investigate the topology of the Universe to a depth of 200h(^-1) Mpc. Qualitatively, the distribution of galaxies out to this distance appears similar to a Gaussian density field with a sponge-like topology. High and low density regions are topologically similar and surfaces of constant density are interconnected. Quantitatively, we have used the genus-threshold density relation of Hamilton et al. to measure the slope of the power spectrum over a range of length scales between l0 (^-1) Mpc and 50h(^-1) Mpc. To constrain the slope of the power spectrum we used artificial "galaxy" catalogues constructed from N-body simulations and a variety of Monte-Carlo and bootstrap techniques. Our topological analysis is consistent with a spectrum of power-law form with n ~ -1 (in δk(^2) x k(^n)) over the range of scales considered. Values of n < -1.8 and n > 0 are strongly ruled out by our data. The inferred power spectrum of the distribution of IRAS galaxies is similar to the predicted mass spectrum in the standard cold dark matter model on scales <15 h(^-1) Mpc, but falls off less steeply on larger scales. This discrepancy is significant at over 2σ and implies that structure identified by IRAS galaxies is coherent over scales larger than expected from the CDM model.