Abstract
The baryonic content of galaxies is thought to grow through the interplay of accretion of gas from the intergalactic medium, processing of that gas through star formation, and feedback processes such as supernovae that heat gas and drive outflows, known collectively as the "cycle of baryons." Measuring the gas-phase metallicities of galaxies across multiple epochs in cosmic history is one of the most promising avenues to gain insight into the cycle of baryons controlling galaxy growth. I will present measurements of the stellar mass-gas-phase metallicity relation (MZR) and mass-star-formation rate-metallicity (M*-SFR-Z) relation at z~2-3.5 using data from the MOSDEF survey, and discuss implications for baryon cycling. Obtaining robust gas-phase metallicity estimates at any redshift requires an understanding of the systematic biases associated with interpreting emission-line ratios from galaxy spectra. To study redshift evolution, the effects of chemical evolution on line ratios must be disentangled from changes in other parameters, such as electron density, ionization parameter, and ionizing spectrum. Degeneracies between metallicity and other parameters can be broken using measurements of electron temperature-sensitive auroral lines, such as [OIII]4363, at high redshifts. I will present measurements of [OIII]4363 at z>2, and discuss implications for the evolution of metallicity calibrations with redshift. Future observations from the James Webb Space Telescope will provide more auroral line detections at high redshifts, leading to a clearer picture of the chemical evolution of galaxies than has been possible to date. Systematic biases affecting metallicity measurements at z=0 must also be carefully considered. I will demonstrate that diffuse ionized gas contamination significantly biases line ratio measurements from z~0 global galaxy spectra and present models that can correct for these biases, allowing for more robust evolutionary studies.