A Partial-sky Gibbs ILC Approach for the Estimation of CMB Posterior over Large Angular Scales of the Sky

In this article we present a formalism for incorporating the partial-sky maps into the Gibbs ILC algorithm to estimate the joint posterior density of the cosmic microwave background (CMB) signal and the theoretical CMB angular power spectrum given the observed CMB maps. In order to generate the partial-sky maps, we mask all the observed CMB maps provided by the WMAP and Planck satellite full-sky mission using a mask that removes 22% of the entire sky. The mask we use is based on the strength of the thermal dust emissions in the Planck 353 GHz map. While implementing the Gibbs ILC method on the partial-sky maps, we convert the partial-sky-cleaned angular power spectrum into the full-sky angular power spectrum using the mode-mode coupling matrix estimated from the smoothed mask. The main products of our analysis are a partial-sky cleaned best-fit CMB map and an estimate of the underlying full-sky theoretical CMB angular power spectrum in the multipole range 2 ≤ ℓ ≤ 32 along with their error estimates. We validate the method by performing detailed Monte Carlo simulations after using realistic models of foregrounds and detector noise consistent with the WMAP and Planck frequency channels used in our analysis. We can estimate the posterior density and full-sky theoretical CMB angular power spectrum without any need to explicitly model the foreground components from partial-sky maps using our method. Another important feature of this method is that the power spectrum results along with the error estimates can be directly used for cosmological parameter estimations.