On the Impact of Random Residual Calibration Error on the Gibbs ILC CMB Estimates over Large Angular Scales

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Abstract Residual errors in calibration coefficients corresponding to observed cosmic microwave background (CMB) maps are an important issue when estimating a pure CMB signal. These errors in the input-foreground-contaminated CMB maps, if not properly taken into account in a component separation method, 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 a multifrequency CMB experiment makes it very difficult to incorporate their exact and actual values during the component separation method. Hence, the effect of any random and residual calibration error in 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-observed CMB maps with random calibration errors on the posterior density of a cleaned CMB map and theoretical CMB angular power spectrum over large angular scales of the sky following the Gibbs Internal-Linear-Combination (ILC) method. By performing detailed Monte Carlo simulations of WMAP and Planck temperature anisotropy observations, including their estimate on calibration errors, we show that the best-fit map corresponding to the posterior maximum is minimally biased in the Gibbs ILC method by a CMB normalization bias and residual foreground bias. The residual calibration-induced error in the best-fit power spectrum causes an overall 6% increase of the net error when added in quadrature with the cosmic-variance-induced error.