= Photon temperature perturbation
{title2=$\Theta=\delta T/\bar T$}
A direction-dependent fractional photon temperature change. For a thermal spectrum, $f(\epsilon)=\bar f(\epsilon)-\Theta\epsilon\bar f'(\epsilon)$ is its linear expansion at fixed comoving energy. For a nonthermal spectrum the same ansatz is a brightness dilation, rather than necessarily a thermodynamic temperature. In unweighted <Legendre polynomial> multipoles, $\Theta=\sum_\ell(-i)^\ell\Theta_\ell P_\ell$, the photon density, velocity and <anisotropic stress> are $\delta_\gamma=4\Theta_0$, $v_\gamma=-\Theta_1$ and $\Pi_\gamma=-3\Theta_2/5$.
Back to article page