| Deep in dark matter halos, galaxies are large factories that convert gas into stars. Gas is accreted from the expansive intergalactic medium (IGM); stars process this gas by fusing lighter elements into heavier ones. In this Dissertation, I combine both observations and theories from a variety of subfields of astrophysics with analytic and numerical models in an aim for a comprehensive understanding of the underlying physics of star formation feedback, galaxy chemical evolution, and the IGM.;The mass-metallicity relation is an observed tight correlation between the stellar masses and gas-phase oxygen abundances of star-forming galaxies. I show that while the intrinsic scatter in this relation is small, extreme outliers do exist; I argue that these outliers have unusual metallicities for their masses because they have unusual gas fractions for their masses. The low-mass high-metallicity galaxies appear to be nearing the end of their star formation, and thus should have abnormally small gas reservoirs with which to dilute their metals. On the other hand, the high-mass low-metallicity galaxies appear to be undergoing gas-rich galaxy mergers, implying that they have larger-than-normal amounts of gas diluting their metals.;I then show through analytic arguments that while gas fractions can have a large impact on observed metallicities, the low-redshift mass-metallicity relation is dominated by outflow properties because typical galaxies have relatively small gas fractions. Specifically, the mass-metallicity relation implies that the efficiency with which galaxies expel metals should scale steeply with galaxy mass. Combining this model with reasonable models for star formation feedback, I show that the outflow metallicity should likewise vary with galaxy mass; future measurements of wind metallicity can therefore inform models of the physics underlying galaxy winds.;The high-redshift IGM is primarily observed through the Lyman-alpha absorption of neutral hydrogen along the line of sight to a distant quasar. As samples of close quasar pairs increase, so does the amount of potential information in the Lya forest transverse to the line-of-sight. Using two cosmological hydrodynamic simulations with different photoionization heating rates and thus different IGM temperature-density relations, I show that the small-scale structure in the Lya forest along the line of sight is dominated by the current thermal state of the gas. On the other hand, the transverse signal is sensitive to---and thus could be used to place unique constraints on---the thermal history of the gas.;Finally, I investigate how a two-phase medium is treated in a suite of idealized smoothed particle hydrodynamic (SPH) simulations. I show that cold, dense spherical blobs become over-pressured relative to their hot, tenuous surroundings, arguing that this is because of an effective numerical surface tension owing to the un-resolveable density discontinuity. I then test one proposed modification to how pressure gradients are calculated in SPH, the so-called "relative pressure SPH" (rpSPH); while rpSPH leads to a more uniform pressure across the simulation, I show that it is ultimately unstable because of its lack of momentum conservation. |
