The delay time distribution of Type-Ia supernovae in galaxy clusters:
  the impact of extended star-formation histories
  The delay time distribution (DTD) of Type-Ia supernovae (SNe Ia) is important
for understanding chemical evolution, SN Ia progenitors, and SN Ia physics.
Past estimates of the DTD in galaxy clusters have been deduced from SN Ia rates
measured in cluster samples observed at various redshifts, corresponding to
different time intervals after a presumed initial brief burst of star
formation. A recent analysis of a cluster sample at $z=1.13-1.75$ confirmed
indications from previous studies of lower-redshift clusters, that the DTD has
a power-law form, ${\rm DTD}(t)=R_1 (t/{\rm Gyr})^\alpha$, with amplitude
$R_1$, at delay $t=1~\rm Gyr$, several times higher than measured in
field-galaxy environments. This implied that SNe Ia are somehow produced in
larger numbers by the stellar populations in clusters. This conclusion,
however, could have been affected by the implicit assumption that the stars
were formed in a single brief starburst at high $z$. Here, we re-derive the DTD
from the cluster SN Ia data, but relax the single-burst assumption. Instead, we
allow for a range of star-formation histories and dust extinctions for each
cluster. Via MCMC modeling, we simultaneously fit, using stellar population
synthesis models and DTD models, the integrated galaxy-light photometry in
several bands, and the SN Ia numbers discovered in each cluster. With these
more-realistic assumptions, we find a best-fit DTD with power-law index
$\alpha=-1.09_{-0.12}^{+0.15}$, and amplitude $R_1=0.41_{-0.10}^{+0.12}\times
10^{-12}~{\rm yr}^{-1}{\rm M}_\odot^{-1}$. We confirm a cluster-environment DTD
with a larger amplitude than the field-galaxy DTD, by a factor $\sim2-3$ (at
$3.8\sigma$). Cluster and field DTDs have consistent slopes of
$\alpha\approx-1.1$.
