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The delay time distribution (DTD) of Type-Ia supernovae (SNe Ia) is importantfor understanding chemical evolution, SN Ia progenitors, and SN Ia physics.Past estimates of the DTD in galaxy clusters have been deduced from SN Ia ratesmeasured in cluster samples observed at various redshifts, corresponding todifferent time intervals after a presumed initial brief burst of starformation. A recent analysis of a cluster sample at $z=1.13-1.75$ confirmedindications from previous studies of lower-redshift clusters, that the DTD hasa 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 infield-galaxy environments. This implied that SNe Ia are somehow produced inlarger numbers by the stellar populations in clusters. This conclusion,however, could have been affected by the implicit assumption that the starswere formed in a single brief starburst at high $z$. Here, we re-derive the DTDfrom the cluster SN Ia data, but relax the single-burst assumption. Instead, weallow for a range of star-formation histories and dust extinctions for eachcluster. Via MCMC modeling, we simultaneously fit, using stellar populationsynthesis models and DTD models, the integrated galaxy-light photometry inseveral bands, and the SN Ia numbers discovered in each cluster. With thesemore-realistic assumptions, we find a best-fit DTD with power-law index$\alpha=-1.09_{-0.12}^{+0.15}$, and amplitude $R_1=0.41_{-0.10}^{+0.12}\times10^{-12}~{\rm yr}^{-1}{\rm M}_\odot^{-1}$. We confirm a cluster-environment DTDwith 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$\alpha\approx-1.1$.

The delay time distribution of Type-Ia supernovae in galaxy clusters: the impact of extended star-formation histories