Low-multipole kernel of polarization potentials
= Low-multipole kernel of polarization potentials
{title2=$\ker(\eth^2)=\{\ell=0,1\}$}
Twice-applied spin-raising or lowering annihilates the ordinary spherical-harmonic multipoles $\ell=0,1$. Polarization potentials therefore have a four-dimensional monopole/dipole ambiguity on the sphere. For an axisymmetric mode it is $A+B\cos\theta$. Setting these components to zero defines the observable $\ell\ge2$ potentials without changing $Q$ or $U$.