There is no consensus on the progenitors of Type Ia supernovae (SNe Ia) despite their importance for cosmology and chemical evolution. We address this question by using our previously published catalogs of Mg, Si, Ca, Cr, Fe, Co, and Ni abundances in dwarf galaxy satellites of the Milky Way to constrain the mass at which the white dwarf explodes during a typical SN Ia. We fit a simple bi-linear model to the evolution of [X/Fe] with [Fe/H], where X represents each of the elements mentioned above. We use the evolution of [Mg/Fe] coupled with theoretical supernova yields to isolate what fraction of the elements originated in SNe Ia. Then, we infer the [X/Fe] yield of SNe Ia for all of the elements except Mg. We compare these observationally inferred yields to recent theoretical predictions for two classes of Chandrasekhar-mass (M_Ch) SN Ia as well as sub-M_Ch SNe Ia. Most of the inferred SN Ia yields are consistent with all of the theoretical models, but [Ni/Fe] is consistent only with sub-M_Ch models. We conclude that the dominant type of SN Ia in ancient dwarf galaxies is the explosion of a sub-M_Ch white dwarf. The Milky Way and dwarf galaxies with extended star formation histories have higher [Ni/Fe] abundances, which could indicate that the dominant class of SN Ia is different for galaxies where star formation lasted for at least several Gyr.
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