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Nearby Supernova Rates from the Lick Observatory Supernova Search. IV. A Recovery Method for the Delay Time Distribution

The supernova (SN) delay-time distribution (DTD) - the SN rate versus time that would follow a brief burst of star formation - can shed light on SN progenitors, and on chemical enrichment timescales. Previous attempts to recover the DTD have used comparisons of mean SN rates vs. redshift to cosmic star-formation history (SFH), or comparison of SN rates among galaxies of different mean ages. We present an approach to recover the SN DTD that avoids such averaging. We compare the SFHs of individual galaxies to the numbers of SNe discovered in each galaxy (generally zero, sometimes one or a few SNe). We apply the method to a subsample of 3505 galaxies, hosting 82 SNe Ia and 119 core-collapse SNe (CC SNe), from the Lick Observatory SN Search (LOSS), with SFHs reconstructed from SDSS spectra. We find a >2sigma SN Ia DTD signal in our shortest-delay, "prompt", bin at <420 Myr. Despite a systematic error, due to the limited aperture of the SDSS spectroscopic fibres, which causes some of the prompt signal to leak to the later DTD bins, the data require prompt SNe Ia at the >99% confidence. We further find, at 4sigma, SNe Ia that are "delayed" by > 2.4 Gyr. Thus, the data support the existence of both prompt and delayed SNe Ia. The time integral over the CC SN DTD is 0.010+/-0.002 SNe per Msun, as expected if all stars of mass >8 Msun lead to visible SN explosions. This argues against a minimum mass for CC SNe of >10 Msun, and against a significant fraction of massive stars that collapse without exploding. For SNe Ia, the time-integrated DTD is 0.0023+/-0.0006 SNe per Msun formed, most of them with delays < 2.4 Gyr. We show, using simulations, that application of the method to the full existing LOSS sample, but with complete and unbiased SFH estimates for the survey galaxies, could provide a detailed measurement of the SN Ia DTD.