= Photon multipole normalization change
For a fixed angular order $m$, write $\Theta=\sum_\ell C_\ell q_\ell Y_{\ell m}$. Streaming by $ik\mu$ contributes $ik(C_{\ell+1}/C_\ell)a_{\ell+1,m}q_{\ell+1}+ik(C_{\ell-1}/C_\ell)a_{\ell,m}q_{\ell-1}$. Thus rescaling the expansion coefficients also rescales the hierarchy couplings and source amplitudes. Replacing $C_\ell=(-i)^\ell\sqrt{(2\ell+1)/(8\pi)}$ by $\widetilde C_\ell=(-i)^\ell\sqrt{2\pi/(2\ell+1)}$ requires $\widetilde q_\ell=(2\ell+1)q_\ell/(4\pi)$; the temperature field is unchanged. This prevents mixing incompatible <photon temperature multipole> conventions.
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