  The chemical composition of galaxies offers vital insights into their
formation and evolution. A key aspect of this study is the correlation between
helium abundance (He/H) and metallicity, which is instrumental in estimating
the primordial helium generated by Big Bang nucleosynthesis. We study the
chemical enrichment history of low-metallicity galaxies, specifically focusing
on extremely metal-poor galaxies (EMPGs) and the first galaxies, using the
one-zone model and cosmological hydrodynamic simulations. Our one-zone model,
using the Limongi & Chieffi (2018) yield, aligns well with observed high He/H
ratios at low metallicities and reproduces Fe/O ratios akin to EMPGs.
Conversely, the Nomoto et al. (2013) yield does not fully match the high Fe/O
ratios seen in EMPGs. Our cosmological hydrodynamic simulations of the first
galaxy successfully replicate the stellar mass and star formation rate of
galaxies like GN-z11 but fail to produce metallicity and high He/H at low O/H.
This is consistent with the results of the one-zone model, which shows that the
slope of the He/H-O/H relation is moderate in young, actively star-forming
galaxies, suggesting the importance of using galaxies with similar star
formation histories for the fit. These results highlight the need for
high-resolution simulations and expanded observational datasets to refine our
understanding of early galactic chemical evolution.
