Statistical isotropy of CMB polarization maps

Abstract

We formulate statistical isotropy of CMB anisotropy maps in its most general form. We also present a fast and orientation independent statistical method to determine deviations from statistical isotropy in CMB polarization maps. Importance of having statistical tests of departures from SI for CMB polarization maps lies not only in interesting theoretical motivations but also in testing cleaned CMB polarization maps for observational artifacts such as residuals from polarized foreground emission. We propose a generalization of the Bipolar Power Spectrum (BiPS) to polarization maps. Application to the observed CMB polarization maps will be soon possible after the release of WMAP three year data. As a demonstration we show that for E-polarization this test can detect breakdown of statistical isotropy due to polarized synchrotron foreground.