Young, Anthony2018-08-142018-08-142018-05https://hdl.handle.net/11299/199029University of Minnesota Ph.D. dissertation. May 2018. Major: Astrophysics. Advisor: Liliya Williams. 1 computer file (PDF); 1 xviii, 92 pages.During the merger of two galaxies, the resulting system undergoes violent relaxation and seeks stable equilibrium. However, the details of this evolution are not fully understood. Before we address evolution, we examine two different classes of models that describe equilibrium, or steady-state dark matter halos, in order to look for clues regarding the dynamical state of the halo. Both classes exhibit non-monotonic changes in their density profile slopes which we call oscillations for short. We analyze these two unrelated classes separately. Class 1 consists of systems that have density oscillations and that are defined through their distribution function f(E), or differential energy distribution N(E), such as isothermal spheres, King profiles, or DARKexp, a theoretically derived model for relaxed collisionless systems. Systems defined through f(E) or N(E) generally have density slope oscillations. We then proceed to investigate the physical basis for these oscillations and the relationship with the dynamical state of the halo. Using Illustris simulation, we probe two physically related processes, mixing and relaxation. Though the two are driven by the same dynamics---global time-varying potential for the energy, and torques caused by asymmetries for angular momentum---we measure them differently. We define mixing as the redistribution of energy and angular momentum between particles of the two merging galaxies. We assess the degree of mixing as the difference between the shapes of their energy distributions, $N(E)$s, and their angular momentum distributions, $N(L^2)$s. We find that the difference is decreasing with time, indicating mixing. To measure relaxation, we compare $N(E)$ of the newly merged system to $N(E)$ of a theoretical prediction for relaxed collisionless systems, DARKexp, and witness the system becoming more relaxed, in the sense that $N(E)$ approaches DARKexp $N(E)$. Because the dynamics driving mixing and relaxation are the same, the timescale is similar for both. We measure two sequential timescales: a rapid, 1 Gyr phase after the initial merger, during which the difference in $N(E)$ of the two merging halos decreases by $\sim 80$\%, followed by a slow phase, when the difference decreases by $\sim 50$\% over $\sim 8.5$ Gyrs. This is a direct measurement of the relaxation timescale.enDark matter halosThesis or Dissertation