The Milky Way (MW) Galaxy in which we live offers an opportunity to study the details of galaxy evolution at a level unattainable in external galaxies, as the stars in the MW can be individually resolved and observed. The detailed chemical abundances of a star indicate the enrichment processes that polluted the gas that formed that star. By analyzing the chemical abundances of stars across the entire MW, one can understand the MW's star formation history and chemical evolution. This thesis uses chemical abundances derived from stellar spectra obtained as part of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) to answer questions about the chemical evolution of the Sagittarius Dwarf Galaxy (Sgr), the MW stellar halo. and the MW disk. This thesis is comprised of four main projects. In project one, we present the detection and characterization of 10 spectral lines of neodymium in the APOGEE spectral region. allowing for the exploration of the contribution of asymptotic giant branch (AGB) stars to the chemical evolution of the MW. In project two, we present the APOGEE chemical abundance patterns of the Sagittarius Dwarf Galaxy, and find that Sgr is deficient in all chemical abundances relative to the MW. We find that the more metal-rich Sgr stars likely formed from gas lacking metals from the most massive Type II supernovae, suggesting a top-light initial mass function in the past. In project 3, we exploit the unique chemical abundance patterns of Sgr to find Sgr stars across the MW halo, demonstrating that it is possible to find Sgr stars in chemical space, i.e. without any position/dynamic information. In project 4, we analyze carbon to nitrogen abundances (often expressed as [C/N]) of stars across the MW disk, which serves as an age indicator for red giant stars, allowing for a temporal exploration of the stellar populations of the MW disk. We find no age-metallicity anti-correlation, as one might expect from simple chemical evolution, and conclude that radial migration played a significant role in shaping the stellar population distribution of the MW.
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