Harmonic in-painting of CMB sky by constrained Gaussian realization

The presence of astrophysical emissions between the last scattering surface and our vantage point requires us to apply a foreground mask on CMB sky map, leading to large cut around the Galactic equator and numerous holes. Since many CMB analyses, including non-Gaussianity study may be performed on a whole sky map in a more straightforward and reliable manner, it is of utmost importance to develop an efficient method to in-paint the CMB sky map, while still preserving statistical properties. In this letter, we consider Monte-Carlo simulation of constrained Gaussian field and derive it for CMB anisotropy in harmonic space, where a feasible implementation is possible with good approximation. We applied our method to the simulated data, which confirms the masked area is in-painted in a way compliant with the expected statistical properties. Subsequently, we applied our method to the WMAP foreground-reduced maps and investigated the anomalous alignment between quadrupole and octupole components. From our investigation, we find the alignment in the foreground-reduced maps is even higher than the ILC map. In particular, we find the highest alignment in the V band map, which has less foreground contamination than other bands. Therefore, we find it hard to attribute the alignment to residual foregrounds. Our method will be complementary to other efforts on in-painting or reconstructing the masked CMB data, and of great use to Planck surveyor and future missions.