Analytical and numerical studies of dark matter halos

Abstract

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 ρ/σ3 profile, where ρ is the density profile and σ 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 powerspectra 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 ρ/σ3 profile. If there were discontinuities in the initial conditions, the power-law feature in ρ/σ3 breaks. Because of this, hydrostatic equilibrium is a less restrictive condition than the ρ/σ3 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 ρ/σ3 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 ρ/σ3.