| This dissertation focuses on the evolution and structure of dark matter halos of galaxies, groups and clusters of galaxies. I explore the dependence of the final halo's properties on the initial conditions and the physical processes that guide the halo to equilibrium, with special focus on the power-law nature of the &rgr;/sigma3 profile, where &rgr; is the density profile and sigma is the velocity dispersion profile. As the astronomy community does not yet fully understand these processes, this research expands our understanding of collisionless, gravitationally-interacting systems.;In the initial chapters, I study the collisionless semi-analytic halo simulations and show that the final properties are sensitive to the initial conditions, such as the power-spectra filtering scale, the secondary velocities' magnitudes and directions, and the accretion rate. The general conclusions are that semi-analytic halos are in hydrostatic equilibrium and have a power-law &rgr;/sigma 3 profile. If there were discontinuities in the initial conditions, the power-law feature in &rgr;/sigma3 breaks. Because of this, hydrostatic equilibrium is a less restrictive condition than the &rgr;/sigma 3 profile. These halos can recover from moderate discontinuities by either correcting a single profile by sacrificing other quantities or by sufficient post-accretion.;Finally, I compare collisionless semi-analytic and N-body simulations directly. This novel comparison is useful because these techniques use different physics to collapse the proto-halo. The physical differences between these two methods are used to determine causes of the final halo profiles. Specifically, I find the NFW density profile and power-law &rgr;/sigma3 are due to the slow rate of evolution, which is determined from the initial conditions and cosmology. The density slope-velocity anisotropy relationship is dependent, rather, on the physical processes (notably the radial orbit instability) and three-dimensional evolution used to collapse the proto-halos. We also find that the slow-evolution halos do not undergo violent relaxation (large changes in the global potential). Thus we suggest that slow, collisionless relaxation is responsible for creating the power-law feature &rgr;/sigma 3. |
