Similarly, the polarization solutions follow from the radial decomposition of the
Thus the structures of , ,and shown in Figs. 3 and 4 directly reflects the angular power of the sources and P(m). There are several general results that can be read off the radial functions. Regardless of the source behavior in k, the B-parity polarization for scalars vanishes, dominates by a factor of 6 over the electric parity at for the vectors, and is reduced by a factor of 8/13 for the tensors at [see Eqn. (23)].
Furthermore, the power spectra in can rise no faster than
Features in k-space in the moment at fixed time are increasingly well preserved in -space as |m| increases, but may be washed out if the source is not well localized in time. Only sources involving the visibility function are required to be well localized at last scattering. However even features in such sources will be washed out if they occur in the moment, such as the scalar dipole and the vector quadrupole (see Fig. 3). Similarly features in the vector E and tensor B modes are washed out.
The geometric properties of the temperature-polarization cross power spectrum can also be read off the integral solutions. It is first instructive however to rewrite the integral solutions as
The cross power spectrum contains two pieces: the relation between the temperature and polarization sources and P(m) respectively and the differences in their projection as anisotropies on the sky. The latter is independent of the model and provides interesting consequences in conjunction with tight coupling and causal constraints on the sources. In particular, the sign of the correlation is determined by 
These integral solutions are also useful in calculations. For example, they may be employed with approximate solutions to the sources in the tight coupling regime to gain physical insight on anisotropy formation (see §IV and [22,23]). Seljak & Zaldarriaga  have obtained exact solutions through numerically tracking the evolution of the source by solving the truncated Boltzmann hierarchy equations. Our expression agree with [3,4,24] where they overlap.