标题： 超新星相关伽马射线暴的低红移过量检测 显示英文标题

标题： Detection of Low-Redshift Excess in Supernova-Linked Gamma-Ray Bursts

摘要： 伽马射线暴（GRBs）传统上根据其 $T_{90}$被分为长持续时间（lGRBs）和短持续时间（sGRBs），由于lGRBs与核心坍缩超新星的观测关联，通常被用作宇宙恒星形成率（SFR）的示踪器。然而，最近一些lGRBs伴随千新星的探测挑战了这一假设，表明可能存在来自致密双星合并的污染。在这里，我们超越传统的 $T_{90}$基分类，仅关注直接与超新星相关的GRBs——这些是大质量恒星坍缩的最直接标志——以重新评估它们与SFR的联系。使用一个SN/GRBs样本，我们构建了光度-红移（$L$-$z$）平面，并揭示了这些变量之间的显著相关性。为了考虑观测偏差，我们应用 $\tau$统计方法和Lynden-Bell的 $C^{-}$方法来推导固有光度函数和形成率。我们的分析显示，即使在这个定义明确的子样本中，SN/GRB的形成率在低红移（$z < 1$）仍超过SFR。这些发现表明，低红移的GRBs可能不能作为SFR的可靠示踪器，需要更大的样本进一步研究这种差异。 显示英文摘要

摘要： Gamma-ray bursts (GRBs) are traditionally classified into long (lGRBs) and short (sGRBs) durations based on their $T_{90}$, with lGRBs widely used as tracers of the cosmic star formation rate (SFR) due to their observed association with core-collapse supernovae. However, recent detections of kilonovae accompanying some lGRBs challenge this assumption, suggesting potential contamination from compact binary mergers. Here, we move beyond the conventional $T_{90}$-based classification and focus exclusively on GRBs directly associated with supernovae - the most direct signatures of massive stellar collapse - to reassess their connection to the SFR. Using a sample of SN/GRBs, we construct the luminosity - redshift ($L$-$z$) plane and uncover a significant correlation between these variables. To account for observational biases, we apply the $\tau$ statistic and Lynden-Bell's $C^{-}$ method to derive the intrinsic luminosity function and formation rate. Our analysis reveals that even among this well-defined subsample, the SN/GRB formation rate still exceeds the SFR at low redshifts ($z < 1$). These findings suggest that GRBs at low redshift may not serve as reliable tracers of the SFR, and that larger samples are required to further investigate this discrepancy.