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

Abstract: 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.