The Neil Gehrels Swift observatory observes gamma-ray burst (GRB) plateaus in X-rays. We test the reliability of the closure relations through the fireball model when dealing with GRB plateau emissions. We analyze 455 X-ray light curves collected by Swift from 2005 January until 2019 August for which the redshifts are either known or unknown using the phenomenological Willingale 2007 model. Using these fits, we analyze the emission mechanisms and astrophysical environments of these GRBs through the closure relations within the time interval of the plateau emission. Finally, we test the three-dimensional fundamental plane relation (Dainotti relation) which connects the prompt peak luminosity, the time at the end of the plateau (rest frame), and the luminosity at that time, for the GRBs with redshift, concerning groups determined by the closure relations. This allows us to check if the intrinsic scatter σint of any of these groups is reduced compared to previous literature. The most fulfilled environments for the electron spectral distribution, p > 2, are wind slow cooling (SC) and interstellar material (ISM) slow cooling for cases in which the parameter q, which indicates the flatness of the plateau emission and accounts for the energy injection, is 0 and 0.5, respectively, in cases with both known and unknown redshifts. We also find that for short GRBs all ISM environments with q = 0 have the smallest σint = 0.04 ± 0.15 in terms of the fundamental plane relation holding a probability of occurring by chance of p = 0.005. We have shown that the majority of GRBs presenting plateau emission fulfill the closure relations, including the energy injection, with a particular preference for the wind SC environment. The subsample of GRBs that fulfill the given relations can be used as possible standard candles and can suggest a way to reduce the intrinsic scatter of these studied relationships.

中文翻译：

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Swift GRBs高原发射与基面的闭合关系

Neil Gehrels Swift 天文台在 X 射线中观察到伽马射线爆发 (GRB) 高原。在处理 GRB 高原排放时，我们通过火球模型测试了闭合关系的可靠性。我们使用现象学 Willingale 2007 模型分析了 Swift 从 2005 年 1 月到 2019 年 8 月收集的 455 条 X 射线光曲线，其中红移是已知的或未知的。利用这些拟合，我们通过高原发射时间间隔内的闭合关系分析了这些伽马暴的发射机制和天体物理环境。最后，我们检验了红移伽马暴的三维基本平面关系（Dainotti 关系），它连接了瞬时峰值光度、高原结束时间（静止帧）和当时的光度，关于由闭合关系确定的组。这使我们能够检查与以前的文献相比，这些组中的任何一个的固有散射 σint 是否减少。电子光谱分布最满足的环境，p > 图 2 是风缓冷 (SC) 和星际物质 (ISM) 缓冷，其中参数 q 表示高原发射的平坦度并说明能量注入，分别为 0 和 0.5，在有已知和未知的红移。我们还发现，对于短 GRB，所有 q = 0 的 ISM 环境都具有最小的 σint = 0.04 ± 0.15，就基本平面关系而言，其发生概率为 p = 0.005。我们已经表明，大多数呈现高原发射的 GRB 满足闭合关系，包括能量注入，特别偏爱风 SC 环境。满足给定关系的 GRB 子样本可以用作可能的标准蜡烛，并且可以提出一种减少这些研究关系的内在分散的方法。