Residual error in calibration coefficients corresponding to observed CMB maps is an important issue while estimating a pure CMB signal. A component separation method, if these errors in the input foreground contaminated CMB maps are not properly taken into account, may lead to bias in the cleaned CMB map and estimated CMB angular power spectrum. But the inability to exactly determine the calibration coefficients corresponding to each observed CMB map from any CMB experiment makes it very difficult to incorporate their exact and actual values in a component separation analysis. Hence the effect of any random and residual calibration error on the cleaned CMB map and its angular power spectrum of a component separation problem can only be understood by performing detailed Monte Carlo simulations. In this paper, we investigate the impact of using input foreground contaminated CMB maps with random calibration errors on posterior density of cleaned CMB map and theoretical CMB angular power spectrum over large angular scales of the sky following the Gibbs ILC method proposed by \cite{Sudevan:2018qyj}. By performing detailed Monte Carlo simulations of WMAP and Planck temperature anisotropy observations with calibration errors compatible with them we show that the best-fit map corresponding to posterior maximum is minimally biased in Gibbs ILC method by a CMB normalization bias and residual foreground bias. The bias in best-fit CMB angular power spectrum with respect to the case where no calibration error is present are $\sim 28 \mu K^2$ and $-4.7 \mu K^2$ respectively between $2 \le \ell \le 15$ and $16 \le \ell \le 32$. The calibration error induced error in best-fit power spectrum causes an overall $6\%$ increase of the net error when added in quadrature with the cosmic variance induced error.

中文翻译：

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随机残差校准误差对大角尺度 Gibbs ILC CMB 估计的影响

在估计纯 CMB 信号时​​，与观察到的 CMB 地图相对应的校准系数中的残余误差是一个重要问题。一种分量分离方法，如果未正确考虑输入前景污染的 CMB 图中的这些误差，可能会导致清洁的 CMB 图中和估计的 CMB 角功率谱出现偏差。但是，无法从任何 CMB 实验中准确确定与每个观察到的 CMB 图相对应的校准系数，因此很难将它们的准确值和实际值合并到组分分离分析中。因此，只有通过执行详细的蒙特卡罗模拟才能理解任何随机和残余校准误差对清洁的 CMB 图及其分量分离问题的角功率谱的影响。在本文中，我们根据\cite{Sudevan:2018qyj} 提出的Gibbs ILC 方法，研究了使用带有随机校准误差的输入前景污染CMB 地图对清洁CMB 地图的后验密度和大天空角尺度上的理论CMB 角功率谱的影响。通过对 WMAP 和普朗克温度各向异性观测值进行详细的蒙特卡罗模拟，校准误差与之兼容，我们表明与后验最大值对应的最佳拟合图在 Gibbs ILC 方法中通过 CMB 归一化偏差和残余前景偏差最小偏差。在不存在校准误差的情况下，最佳拟合 CMB 角功率谱中的偏差分别为 $\sim 28 \mu K^2$ 和 $-4.7 \mu K^2$ 之间的 $2 \le \ell \ le 15$ 和 $16 \le \ell \le 32$。