Constraining SN Ia Progenitors from the Observed Fe-peak Elemental Abundances in the Milky Way Dwarf Galaxy Satellites

Chemical abundances of iron-peak elements in the red giants of ultra-faint dwarf galaxies (UFD) and dwarf spheroidal galaxies (dSph) are among the best diagnostics in the cosmos to probe the origin of Type Ia Supernovae (SNe Ia). We incorporate metallicity-dependent SN Ia nucleosynthesis models for different progenitor masses in our inhomogeneous galactic chemical evolution model, {\tt{i-GEtool}}, to recreate the observed elemental abundance patterns and their spread in a sample of UFD and dSph galaxies with different average metallicities and star formation histories. Observations across different environments indicate that [Mn/Mg] increases on average with metallicity while [Ni/Mg] remains nearly constant. The average dispersion of [X/Mg] from our UFD model ranges between $0.20$ and $0.25$ for iron-peak elements, with the exception of [Sc/Mg] that has $\sigma \approx 0.39$. Chemical evolution models assuming Chandrasekhar mass (M$_{\text{Ch}}$) SN Ia progenitors produce similar [Mn/Mg]-[Fe/H] and [Ni/Mg]-[Fe/H] abundance patterns to those observed in the examined UFD and dSph galaxies, without the need to invoke a substantial fraction of sub-M$_{\text{ch}}$ progenitors that change across different environments, as claimed by some previous chemical evolution studies. Sub-M$_{\text{ch}}$ progenitors in our dSph models under produce both [Ni/Mg]-[Fe/H] and [Ni/Mg]-[Fe/H] abundance patterns, with the $1\,\text{M}_{\odot}$ sub-M$_{\text{ch}}$ model explaining a number of outliers in [Ni/Mg]-[Fe/H], while the outliers in [Mn/Mg]-[Fe/H] require higher sub-M$_{\text{ch}}$ progenitor masses.