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What was the Intensity of the Cosmic Background Radiation Just After Recombination?

-- simon | May 3, 2020

Question:

What was the intensity of the cosmic background radiation just after recombination ? What, to our eyes, would appear similar brightness to the CBR just after recombination ?

I know:
Now it is roughly 10^(-18) erg/s/cm^2/ster/Hz ( previous answer)
It has been redshifted by z = 1100 since recombination.
Just after recombination its black body temp was about 3000 K

Thanks !

-- simon

Answer:

Since the cosmic microwave background emits as a black body, we start with the spectral radiance of a black body at frequency and temperature T, which is given by the Planck Function:

If we integrate the Planck Function over all frequencies, we get the Stefan-Boltzmann Law:

To calculate the intensity of the cosmic microwave background radiation at the epoch of recombination, when the black body temperature was about 3000K, and knowing that the intensity of the cosmic microwave background today, where the black body temperature is 2.726K, we take the ratio of the Stefan-Boltzmann Law at the two black body temperatures:

For a cosmic microwave background intensity of 10^{-18} erg s^{-1} cm^{-2} ster^{-1} Hz^{-1}, the above ratio indicates that the intensity of the cosmic microwave background at the epoch of reionization would be 10^{-18} x 1.5×10^{12} = 1.5×10^{-6} cm^{-2} ster^{-1} Hz^{-1}.

-- Jeff Mangum

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