On Minkowski Functionals of CMB polarization

Abstract

CMB polarization data is usually analyzed using Eand Bmodes because they are scalar quantities under rotations along the lines of sight and have distinct physical origins. We explore the possibility of using the Stokes parameters Qand Ufor complementary analysis and consistency checks in the context of searches for non-Gaussianity. We show that the Minkowski Functionals (MFs) of Q,Uare invariant under local rotations along the lines of sight even though Q,Uare spin-2 variables, for full sky analysis. The invariance does not hold for incomplete sky. For local type primordial non-Gaussianity, when we compare the non-Gaussian deviations of MFs for Q,Uto what is obtained for Emode or temperature fluctuations, we find that the amplitude is about an order of magnitude lower and the shapes of the deviations are different. This finding can be useful in distinguishing local type non-Gaussianity from other origins of non-Gaussianity in the observed data. Lastly, we analyze the sensitivity of the amplitudes of the MFs for Q,Uand the number density of singularities of the total polarization intensity to the tensor-to-scalar ratio, r, and find that all of them decrease as rincreases