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, DTD(t) = R1(t/Gyr)α, with amplitude R1, 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 modelling, 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-fitting 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 ∼2–3 (at 3.8σ). Cluster and field DTDs have consistent slopes of α ≈ −1.1.

中文翻译：

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星系团中 Ia 型超新星的延迟时间分布：扩展恒星形成历史的影响

Ia 型超新星 (SNe Ia) 的延迟时间分布 (DTD) 对于理解化学演化、SN Ia 前身和 SN Ia 物理学非常重要。过去对星系团中 DTD 的估计是根据在各种红移下观测到的星团样本中测量的 SN Ia 速率推导出来的，对应于假定的初始短暂恒星形成爆发后的不同时间间隔。最近对 z = 1.13–1.75 的星团样本的分析证实了先前对较低红移星团的研究表明，DTD 具有幂律形式，DTD(t) = R1(t/Gyr)α，幅度为 R1，在延迟 $t=1\,\rm Gyr$ 时，比在场星系环境中测量的要高几倍。这意味着 SNe Ia 是由星团中的恒星群体以某种方式大量产生的。然而这个结论，可能受到隐含假设的影响，即恒星是在高 z 的一次短暂的星暴中形成的。在这里，我们从集群 SN Ia 数据中重新推导 DTD，但放宽单突发假设。相反，我们允许每个星团有一系列恒星形成历史和尘埃灭绝。通过 MCMC 建模，我们使用恒星种群合成模型和 DTD 模型同时拟合多个波段中的集成星系光光度测量，以及在每个星团中发现的 SN Ia 数。通过这些更现实的假设，我们找到了幂律指数 $\alpha =-1.09_{-0.12}^{+0.15}$，幅度 $R_1=0.41_{-0.10}^{ +0.12}\times 10^{-12}\,{\rm yr}^{-1}\, {\rm M}_\odot ^{-1}$。我们确认了一个比场星系 DTD 振幅更大的集群环境 DTD，系数约为 2-3（在 3.8σ 处）。