Inhomogeneous Galactic Chemical Evolution: Modelling Ultra-Faint Dwarf Galaxies of the Large Magellanic Cloud

Ultra-faint dwarf galaxies are among the oldest and most metal-poor galaxies in the cosmos, observed to contain no gas and a high dark matter mass fraction. Understanding the chemical abundance dispersion in such extreme environments could shed light on the very first generations of stars. We present a novel inhomogeneous chemical evolution model, {\tt i-GEtool}, that we apply to two ultra-faint dwarf galaxies, Carina II and Reticulum II, both satellites of the Large Magellanic Cloud. Our model is based on the Monte Carlo sampling of the initial mass function as star formation proceeds in different gas cells of the galaxy volume. We account for the chemical enrichment of Supernova bubbles as they spread in the interstellar medium, causing dispersion in the elemental abundances. We recreate the abundance patterns of $\alpha$- and odd-$\textit{Z}$ elements, predicting two sequences in [C/Fe] and [N/Fe] at all metallicities. Our models underestimate [C/Fe] and [Ti/Fe] because of the large uncertainty in the adopted stellar nucleosynthesis yields. We discuss that the observed C and N abundances had likely been affected by internal mixing processes, which changed the initial surface abundances in the red giants. Our Supernova feedback scheme is responsible for driving galactic outflows, which quench the star formation activity at early times. We predict an average outflow mass-loading factor $\approx 10^{3}$, which extrapolates towards very low galaxy stellar masses the trend observed at high masses. Finally, by combining our model with the MIST isochrone database, we compare our synthetic colour-magnitude diagrams to observations.