Power spectrum of H i 21-cm radiation is one of the promising probes to study large scale structure of the universe and understand galaxy formation and evolution. The presence of foregrounds, that are orders of magnitude larger in the same frequency range of the redshifted 21-cm signal has been one of the largest observational challenges. The foreground contamination also hinders the calibration procedures and introduces residual calibration errors in the interferometric data. It has been shown that the calibration errors can introduce bias in the 21-cm power spectrum estimates and introduce additional systematics. In this work, we assess the efficacy of 21-cm power spectrum estimation for the uGMRT Band-3 observations of the ELAIS-N1 field. We first evaluate the statistics of the residual gain errors and perform additional flagging based on these statistics. We then use an analytical method to estimate the bias and variance in the power spectrum. We found that (a) the additional flagging based on calibration accuracy help reduce the bias and systematics in the power spectrum, (b) the majority of the systematics at the lower angular scales, ℓ< 6000, are due to the residual gain errors, (c) for the uGMRT baseline configuration and system parameters, the standard deviation is always higher than the bias in the power spectrum estimates. Based on our analysis we observe that for an angular multipole of ℓ∼3000, 2000 hours of `on source time' is required with the uGMRT to detect redshifted 21-cm signal at 3-σ significance from a redshift of 2.55. In this work we only consider the power spectrum measurement in the plane of the sky, an assessment of residual gain statistics and its effect on multifrequency angular power spectrum estimation for the uGMRT and the SKA like telescopes will be presented in a companion paper.

中文翻译：

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再电离历元 21 厘米信号观测的校准要求。第三部分。 uGMRT ELAIS-N1 场功率谱的偏差和方差


H i 21-cm辐射的功率谱是研究宇宙大尺度结构、了解星系形成和演化的有前景的探测器之一。前景的存在（在红移 21 厘米信号的相同频率范围内要大几个数量级）一直是最大的观测挑战之一。前景污染还会阻碍校准程序并在干涉数据中引入残余校准误差。研究表明，校准误差可能会在 21 厘米功率谱估计中引入偏差，并引入额外的系统性。在这项工作中，我们评估了 21 厘米功率谱估计对 ELAIS-N1 场 uGMRT Band-3 观测的有效性。我们首先评估残余增益误差的统计数据，并根据这些统计数据执行附加标记。然后，我们使用分析方法来估计功率谱中的偏差和方差。我们发现（a）基于校准精度的附加标记有助于减少功率谱中的偏差和系统性，（b）较低角度尺度（ℓ< 6000）的大多数系统性是由于残余增益误差造成的， (c) 对于 uGMRT 基线配置和系统参数，标准偏差始终高于功率谱估计中的偏差。根据我们的分析，我们观察到，对于 ℓ∼3000 的角度多极子，uGMRT 需要 2000 小时的“源时间”才能从红移 2.55 检测到红移 21-cm 信号，显着性为 3-σ。 在这项工作中，我们只考虑天空平面上的功率谱测量，剩余增益统计的评估及其对 uGMRT 和 SKA 等望远镜的多频角功率谱估计的影响将在另一篇论文中介绍。