2015ApJ...810..137J

The nature of the Type Ia supernova (SN Ia) progenitors remains uncertain. This is a major issue for galaxy evolution models since both chemical and energetic feedback plays a major role in the gas dynamics, star formation, and therefore the overall stellar evolution. The progenitor models for the SNe Ia available in the literature propose different distributions for regulating the explosion times of these events. These functions are known as the delay time distributions (DTDs). This work is the first one in a series of papers aiming at studying five different DTDs for SNe Ia. Here we implement and analyze the single-degenerate (SD) scenario in galaxies dominated by a rapid quenching of the star formation, displaying the majority of the stars concentrated in the bulge component. We find a good fit to both the present observed SN Ia rates in spheroidal-dominated galaxies and the [O/Fe] ratios shown by the bulge of the Milky Way. Additionally, the SD scenario is found to reproduce a correlation between the specific SN Ia rate and the specific star formation rate (sSFR), which closely resembles the observational trend, at variance with previous works. Our results suggest that SN Ia observations in galaxies with very low and very high sSFRs can help to impose more stringent constraints on the DTDs and therefore on SN Ia progenitors.