A new approach of estimating the Galactic thermal dust and synchrotron polarized emission template in the microwave bands

The Internal Linear Combination (ILC) method has been extensively used to extract the cosmic microwave background (CMB) anisotropy map from foreground contaminated multi-frequency maps. However, the performance of simple ILC is limited and can be significantly improved by heavily constraint equations, dubbed cILC. The standard ILC and cILC works on the spin-0 field. Recently, a generalized version of ILC is developed to estimate polarization maps in which the quantity $Q \pm iU$ is combined at multiple frequencies using complex coefficients called Polarization ILC (PILC). A statistical moment expansion method has recently been developed for high precision modelling of the Galactic foregrounds. This paper develops a semi-blind component separation method combining the moment approach of foreground modelling with a generalized version of the PILC method for heavily constraint equations. The algorithm is developed in pixel space and performs for a spin-2 field. We employ this component separation technique in simultaneous estimation of Stokes $Q$, $U$ maps of the thermal dust at 353 GHz and synchrotron at 30 GHz over 78 % of the sky. We demonstrate the performance of the method on three sets of absolutely calibrated simulated maps at WMAP and planck frequencies with varying foreground models.