Ages of Type Ia Supernovae Over Cosmic Time

We derive empirical models for galaxy mass assembly histories, and convolve these with theoretical delay time distribution (DTD) models for Type Ia supernovae (SNe Ia) to derive the distribution of progenitor ages for all SNe Ia occurring at a given epoch of cosmic time. In actively star-forming galaxies, the progression of the star formation rate is shallower than a $t^{-1}$ SN Ia DTD, so mean SN Ia ages peak at the DTD peak in all star-forming galaxies at all epochs of cosmic history. In passive galaxies which have ceased star formation through some quenching process, the SN Ia age distribution peaks at the quenching epoch, which in passive galaxies evolves in redshift to track the past epoch of major star formation. Our models reproduce the SN Ia rate evolution in redshift, the relationship between SN Ia stretch and host mass, and the distribution of SN Ia host masses in a manner qualitatively consistent with observations. Our model naturally predicts that low-mass galaxies tend to be actively star-forming while massive galaxies are generally passive, consistent with observations of galaxy "downsizing". Consequently, the mean ages of SNe Ia undergo a sharp transition from young ages at low host mass to old ages at high host mass, qualitatively similar to the transition of mean SN Ia Hubble residuals with host mass. The age discrepancy evolves with redshift in a manner currently not accounted for in SN Ia cosmology analyses. We thus suggest that SNe Ia selected only from actively star-forming galaxies will yield the most cosmologically uniform sample, due to the homogeneity of young SN Ia progenitor ages at all cosmological epochs.