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.
