Cosmic Microwave Background Radiation

Question

I'm going through the NRAO Essential Radio Astronomy course and on the section about Cosmic Microwave Background Radiation, it mentions that BB radiation is $T_0 = 2.725 \pm 0.002$ K equating to "frequency of peak brightness" ~ 160 GHz.

Could someone spell out the factors that give this result please? I have seen this figure quoted in another answer to a CMB question, but cannot find the factors.

What do you mean by "factors that give this result"? Which result? The temperature is determined by observation. Are you asking how 2.7K corresponds to 160 GHz? — enumaris, Jul 11 '18 at 21:31
Your search might be more fruitful if you ask why a "blackbody spectrum" corresponding to $2.7,\mathrm{K}$ has a peak frequency near $160,\mathrm{GHz}$. — dmckee --- ex-moderator kitten, Jul 11 '18 at 22:02
This is a measured property of the CMB that was measured by the FIRAS instrument on COBE. — Sean E. Lake, Jul 12 '18 at 02:52

score 5 · Answer 1 · edited Jul 13 '18 at 10:07

5

The spectral radiance of a blackbody, $$ B_\nu\left(\nu,\,T\right)=\frac{2 h \nu^3}{c^2}\frac{1}{\exp\left(\frac{h\nu}{k_BT}\right)-1}, $$ peaks around $\nu=$160GHz when $T=$2.725K. See the Wikipedia article Planck's law.

edited Jul 13 '18 at 10:07

Kyle Kanos

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answered Jul 12 '18 at 02:36

G. Smith

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Cosmic Microwave Background Radiation

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