The formation of the firsts stars some 100-300 Myr after the Big Bang marked the end of the cosmic darks ages and created the elemental building blocks of not only rocky planets but eventually us. Understanding their formation, lifetimes, and contributions to the evolution of our universe is one of the current frontiers in astronomy and astrophysics.

In this work I present an improved model for following the formation of Pop III stars, their effects on early galaxy evolution, and how we might search for them. I make use of a new subgrid model of turbulent mixing to accurately follow the time scales required to mix supernova (SN) ejecta -- enriched with heavy elements -- into the pristine gas. I implement this model within a large-scale cosmological simulation and follow the fraction of gas with metallicity below a critical value marking the boundary between Pop III and metal enriched Population II (Pop II) star formation. I demonstrate that accounting for subgrid mixing results in a Pop III stars formation rate that is 2-3 times higher than standard models with the same physical resolution.

I also implement and track a new "Primordial metals" (PM) scalar that tracks the metals generated by Pop III SNe. These metals are taken up by second generation stars and likely result in a subclass of carbon-enhanced, metal-poor (CEMP) stars. By tracking both regular metals and PM, I can model, in post-processing, the elemental abundances of simulation stars. I find good agreement between observations of CEMP-no Milky Way halo stars and second generation stars within the simulation when assuming the first stars had a typical mass of 60 M☉, providing clues as to the Pop III initial mass function.

I combine, compare, and contrast the results from two different numerical techniques (grid vs. particle methods) studying multi-scale processes in galaxy and structure formation. I produce a method for recreating identical initial conditions for one method from those of the other, and explore methodologies necessary for making these two methods as consistent as possible. With this, I first study the impact of streaming velocities of baryons with respect to dark matter, present at the epoch of reionization, on the ability for small halos to accrete gas at high redshift. With the inclusion of this stream velocity, I find the central density profile of halos is reduced, overall gas condensation is delayed, and infer a delay in the inevitable creation of stars.

I then combine the two numerical methods to study starburst outflows as they interact with satellite halos. This process leads to shocks catalyzing the formation of molecular coolants that lead to bursts in star formation, a process that is better captured in grid methods. The resultant clumps of stars are removed from their initial dark matter halo, resemble precursors to modern-day globular clusters, and their formation may be observable with upcoming telescopes.

Finally, I perform two simulation suites, comparing each numerical method's ability to model the impact of energetic feedback from accreting black holes at the core of giant clusters. With these comparisons I show that black hole feedback can maintain a hot diffuse medium while limiting the amount of gas that can condense into the interstellar medium, reducing the central star formation by up to an order of magnitude.

3D models of white dwarf collisions are used to assess the likelihood of double-degenerate mergers as progenitors for Type Ia supernovae (henceforth SNIa) and to identify observational signatures of double-degenerate collisions. Observations of individual SNIa, SNIa rates in different galaxy types, and double white dwarf binary systems suggest that mergers or collisions between two white dwarfs play a role in the overall SNIa population. Given the possibility of two progenitor systems (single-degenerate and double-degenerate), the sample of SNIa used in cosmological calcula- tions needs to be carefully examined. To improve calculations of cosmological parameters, the development of calibrated diagnostics for double-degenerate progenitor SNIa is essential. Head-on white dwarf collision simulations are used to provide an upper limit on the Ni-56 production in white dwarf collisions. In chapter II, I explore zero impact parameter collisions of white dwarfs using the Eulerian grid code FLASH. The initial 1D white dwarf profiles are created assuming hydrostatic equilibrium and a uniform composition of 50% C-12 and 50% O-16. The masses range from 0.64 to 0.81 solar masses and have an isothermal temperature of 10^7 K. I map these 1D models onto a 3D grid, where the dimensions of the grid are each eight times the white dwarf radius, and the dwarfs are initially placed four white dwarf radii apart (center to center). To provide insight into a larger range of physical possibilities, I also model non-zero impact parameter white dwarf collisions (Chapter III). Although head-on white dwarf collisions provide an upper limit on Ni-56 production, non-zero impact parameter collisions provide insight into a wider range of physical scenarios. The initial conditions (box size, initial separation, composition, and initial temperature) are identical to those used for the head-on collisions (Chapter II) for the same range of masses. For each mass pair- ing, collision simulations are carried out at impact parameters b=1 and b=2 (grazing). Finally, I will address future work to be performed (Chapter IV).

Lyman-alpha (Lyα) galaxies (LAEs) and Lyα blobs (LABs) are objects identified and studied due to their bright Lyα emission lines. This bright emission allows LAEs and LABs to be studied in the distant universe, providing a glimpse into the physical processes occuring in the early universe. This dissertation presents three complementary studies of LAEs and LABs at z ~ 3.1. The two main foci of this work are (1) to understand the gas kinematics in both classes of objects and (2) to improve spectral energy distribution (SED) fitting processes to better determine the physical characteristics of LAEs. Gas kinematics in this dissertation means looking for signatures of large-scale winds. This is an exciting astrophysical endeavor, because the results can provide insight into how Lyα photons escape distant galaxies and traverse the IGM, and the results have implications for how the epoch of reionization can be studied with the Lyα line and because winds can be a signature of powerful star formation events. In the first two studies we find signatures of winds in three LAEs by measuring the velocity offset between the redshifts of [OIII] and Lyα in these galaxies. The first two LAEs presented here represent the first ever measurements of [OIII] in Lyα-selected field galaxies. The third study reports no velocity offset between [OIII] and Lyα when the methodology is transferred to a z ~ 3.1 LAB. This lack of velocity offset is an interesting result, however, as powerful outflows and star formation events, which should impart a velocity offset, have been hypothesized as power sources for LABs. In addition to understanding the kinematics of these objects, we introduce a new parameter into the SED fitting process typically used to characterize LAEs. This new parameter enables better determination of characteristics like the age, mass, metallicity, dust content and star formation history of the galaxies in our sample. These characteristics provide a snapshot of galaxies in the universe ~ 11 billion years ago and also provide insight into how these characteristics compare to galaxies at other epochs.

Using high-resolution three-dimensional adaptive mesh refinement simulations I study the interaction between primordial minihalo, a clump of baryonic and dark matter with a virial temperature below the atomic cooling limit, and a galaxy outflow. In Chapter 2 I concentrate on the formation of molecular coolants and their effect on the evolution of the minihalo gas. Molecular coolants are important since they allow gas to cool below 10000 K. Therefore, I implement a primordial chemistry and cooling network that tracks the evolution and cooling from these species. I show that the shock from the galaxy outflow produces an abundance of coolants in the primordial gas which allows the gas to cool to below 10000 K. I also show that this interaction produces compact stellar clusters that are ejected from their parent dark matter halos. In Chapter 3 I look at the turbulent mixing of metals that occur between the minihalo and outflow. To do this, I develop a sub-grid model for turbulence that reproduces three primary fluid instabilities. I find that the metals from the outflow are well mixed throughout the minihalo gas. In addition, the metal abundance found roughly corresponds to the observed abundances in halo globular clusters. In Chapter 4, I conduct a suite of simulations that follow this interaction over a wide range of parameters. In almost all cases, the shocked minihalos form molecules and cool rapidly to become compact, chemically homogenous stellar clusters. Furthermore, I show that the unique properties of these clusters make them a prime observational target for study with the next generation of telescopes. Given the unique properties of these clusters there are reasons to suspect that their low-redshift counterparts are halo globular clusters. I outline this comparison in Chapter 5 and give my conclusions in Chapter 6. Finally, I summarize my current work in Chapter 7 and future extensions in Chapter 8. By the end, I hope to convince you that the interaction between a galaxy outflow and a primordial minihalo provides a formation pathway for present day halo globular clusters.