Two-point Correlation Function of WMAP 9 year data

Using an optimal estimator for the CMB Angular Power Spectrum we compute the temperature two-point correlation function of WMAP 9 year at low resolution. Supported by realistic Monte-Carlo simulations, we evaluate how such observed function depends on the Galactic mask. We find that it is more and more consistent with zero (i.e. no correlation) as the Galactic mask is increased. In particular we estimate that such a behavior happens very rarely in a $\Lambda$CDM model, i.e. $<0.01$ of the realizations when we adopt a mask which leaves 46% of observed sky. This is evaluated for the so called $S_{1/2}$ estimator, already well known in literature \citep{Spergel:2003cb}. Also for its generalization to the whole angular range $[0, \pi]$, namely $S_{1}$, we find a very unlikely behavior which is $\lesssim 0.04$ C.L. for the considered masks that cover at least $\sim 54$ of the sky.