We are assuming here that and are parallel, also for photons emitted with . This is clearly a good approximation, because the distance corresponds to a redshift , while the radius of the emitting region is of the order of magnitude of a few light seconds. Thus, as a preliminary consideration and approximation, we assume that photons are in equilibrium at the same temperature T with electron-positron pairs before and at decoupling.
T is the temperature in the comoving frame.
The non-thermal spectrum due to multiple inverse Compton scattering may slightly modify these assumptions. We can now use Eq. By using Eq. Note that the radiation flux is axially symmetric with respect to the axis directed towards the detector.