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