An Accurate Reconstruction of CMB E Mode Signal over Large Angular
  Scales using Prior Information of CMB Covariance Matrix in ILC Algorithm
  In the recent years, the internal-linear-combination (ILC) method was
investigated extensively in the context of reconstruction of Cosmic Microwave
Background (CMB) temperature anisotropy signal using observations obtained by
WMAP and Planck satellite missions. In this article, we, for the first time,
apply the ILC method to reconstruct the large scale CMB E mode polarization
signal, which serves as the unique probe of ionization history of the Universe,
using simulated observations of 15 frequency CMB polarization maps of future
generation COrE satellite mission. We find that usual ILC cleaned E mode map is
highly erroneous due to presence of a chance-correlation between CMB and
astrophysical foreground components in the empirical covariance matrix which is
used to estimate the weight factors. The cleaned angular power spectrum for E
mode is strongly biased and erroneous due to these chance correlation factors.
In order to address the issues of bias and errors we extend and improve the
usual ILC method for CMB E mode reconstruction by incorporating prior
information of theoretical E mode angular power spectrum while estimating the
weights for linear combination of input maps. Using the E mode covariance
matrix effectively suppresses the CMB-foreground chance correlation power
leading to an accurate reconstruction of cleaned CMB E mode map and its angular
power spectrum. We provide a comparative study of the performance of the usual
ILC and the new method over large angular scales of the sky and show that the
later produces significantly statistically improved results than the former.
The new E mode CMB angular power spectrum contains neither any significant
negative bias at the low multipoles nor any positive foreground bias at
relatively higher mutlipoles. The error estimates of the cleaned spectrum agree
very well with the cosmic variance induced error.
