The supernova delay time distribution in galaxy clusters and implications for Type-Ia progenitors and metal enrichment

Knowledge of the supernova (SN) delay time distribution (DTD) - the SN rate versus time that would follow a hypothetical brief burst of star formation - can shed light on SN progenitors and physics. We compile recent measurements of the Type-Ia SN (SN Ia) rate in galaxy clusters at redshifts z=0-1.45. Together with the observed iron-to-stellar mass ratio in clusters, which constrains the time-integrated number of SN Ia events in clusters, we recover the DTD of SNe Ia in cluster environments. The DTD peaks at the shortest time-delay interval we probe, 0<t<2.2 Gyr, with a low tail out to delays of ~10 Gyr, and is remarkably consistent with several recent DTD reconstructions based on different methods, in different environments. We test DTD models from the literature, requiring that they simultaneously reproduce the observed cluster SN rates and the observed iron-to-stellar mass ratios. A power-law DTD of the form t^{-1.2+/-0.3}, extending to a Hubble time, can satisfy both constraints. Shallower power laws, such as t^{-1/2} cannot, assuming a single DTD, and a single star-formation burst (either brief or extended) at high z. This implies 50-85% of SNe Ia explode within 1 Gyr of star formation. DTDs from double-degenerate (DD) models, which generically have ~t^{-1} shapes over a wide range of timescales, match the data, but only if their predictions are scaled up by factors of 5-10. Single degenerate (SD) DTDs always give poor fits to the data, due to a lack of delayed SNe and overall low numbers of SNe. The observations also permit a combination of two SN Ia populations - prompt (e.g. SD) SNe Ia that explode within a few Gyr of star formation, and produce about 60% of the iron mass in clusters, and a DD population that contributes the events seen at z<1.4. Our results support the existence of a DD progenitor channel for SNe Ia, if the overall predicted numbers can be suitably increased.