= Temperature-only tight-coupling quadrupole
{title2=$\Theta_2=-20k\Theta_1/(27\tau^{\prime})$}
For $\Theta(\mu)=\sum_\ell(-i)^\ell\Theta_\ell P_\ell(\mu)$ and a Thomson collision operator omitting polarization feedback, the quadrupole relaxes with rate $(9/10)\Gamma_T$, where $\Gamma_T=-\tau'>0$. Balancing its leading streaming source gives $\Theta_2=20k\Theta_1/(27\Gamma_T)$. This differs from <photon quadrupole in tight coupling with polarization>; the two formulas expand different collision operators.
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