Average Spectral Properties of Type Ia Supernova Host Galaxies

We construct average spectra of host galaxies of slower, faster, bluer, and redder Type Ia Supernovae (SNe Ia) from the SDSS-II supernova survey. The average spectrum of slower declining (broader light-curve width or higher stretch) SN Ia hosts shows stronger emission lines compared to the average spectrum of faster declining (narrower light-curve width or lower stretch) SN Ia hosts. Using pPXF, we find that hosts of slower declining SNe Ia have metallicities that are, on average, 0.24 dex lower than average metallicities of faster declining SN Ia hosts. Similarly, redder SN Ia hosts have slightly higher metallicities than bluer SN Ia hosts. Lick index analysis of metallic lines and Balmer lines show that faster declining SN Ia hosts have relatively higher metal content and have relatively older stellar populations compared with slower declining SN Ia hosts. We calculate average $\rm H_{\alpha}$ Star Formation Rate (SFR), stellar mass, and the specific-SFR (sSFR) of host galaxies in these subgroups of SNe Ia. We find that slower declining SN Ia hosts have significantly higher ($>5\sigma$) sSFR than faster declining SN Ia hosts. A Kolmogorov-Smirnov test shows that these two types of hosts originate from different parent distributions. Our results, when compared with the models of \cite{childress14}, indicate that slower declining SNe Ia, being hosted in actively star-forming galaxies, are young (prompt) SNe Ia, originating from similar progenitor age groups.