Gross, Axel2025-01-282025-01-282024-08https://hdl.handle.net/11299/269666University of Minnesota Ph.D. dissertation. August 2024. Major: Physics. Advisor: Yong-Zhong Qian. 1 computer file (PDF); x, 135 pages.In this thesis, after a general introduction to galaxy formation and its subsequent chemical evolution, we explore two topics contained within this field: the structure of dark matter haloes and the inference of r-process production patterns. The flattening of galactic rotation curves suggests that visible galaxies are surrounded by dark matter haloes. Much of what we have learned about the internal structure of these haloes has come from N-body simulations. Significantly, in 1997, Navarro, Frenk, and White showed that dark matter haloes have a universal density profile. Despite many attempts, theoretical motivation for the existence of this simple analytical form has not been demonstrated. In 2010, Hjorth and Williams developed DARKexp, an analytical form of the energy distribution theoretically motivated by the principles of statistical mechanics which has been shown to match those of simulated haloes. Using the formalism of the isotropic distribution function, which allows relation between the density profile, energy distribution, and distribution function, we perform a detailed comparison between the NFW density profile, DARKexp energy distribution, and a sample of N-body simulated haloes. We determine that both the NFW density profile and DARKexp energy distribution fit well not only in their density and energy distribution, respectively, but also in the other quantities which are inferred from their fits. We also find a connection between the characteristic parameters of the NFW and DARKexp profiles, which connects them together and hints at motivation for the existence of the universal halo structure. We also present new scaling relations for the distribution function and energy distribution from the inversion of the gravitational potential, which are universally satisfied by simulated dark matter haloes. These scaling relations allow for simple numerical calculation of the distribution function and energy distribution from only the gravitational potential. We connect these scaling relationships to the secondary infall model, the isothermal sphere, and other scaling relations that have been discovered, and demonstrate that these scaling relations are inexorably tied to the universal halo structure evidenced by the NFW density profile and DARKexp energy distribution. In the second part, we consider the r-process, which involves nucleosynthesis far from equilibrium in extreme environments. Therefore, this nucleosynthetic production is inherently difficult to understand. We present a new method for inferring the nucleosynthetic production templates of r-process sources directly from the abundance data of metal-poor stars. From a small test dataset, we derive the production ratios for two r-process sources, which we identify as Core-Collapse Supernovae and Neutron Star Mergers, respectively, and compare the ratios that we have inferred to ab-initio studies of r-process nucleosynthesis, finding general consistency. We also demonstrate approximate consistency between our model and the solar system nucleosynthetic inventory.enThesis or Dissertation