How Do Radio Astronomical Measurements Convert to Temperature (Kelvin)?

[Martin1957]

How does one convert measurements in radio astronomical terms to temperature (Kelvin)? Specifically: Penzias & Wilson's measurement of CMB was "excess temperature at 4080 Mc/s." HOW does this yield a "value of about 3.5 degrees Kelvin higher than expected?" Basically, how do you get from Mc/s to K?

 

[smallphi]

I've never seen 'Mc/s' before but at the end of the original paper http://adsabs.harvard.edu/abs/1965ApJ...142..419P they mention it's a measure of frequency so probably means 'Mega cycles/ second' which is MHz nowadays.

The CMB temperature characterizes the whole spectrum, it is the spectrum that would be emmited by a perfect black body radiator at that temperature. They probably measured the energy falling on unit area per unit time and in unit solid angle and then used the formula (Planck's law) for a black body radiator that predicts that energy:

http://en.wikipedia.org/wiki/Black_body

Knowing the energy density that was measured, you can invert the formula and solve for the temperature.