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

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SUMMARY

The conversion of radio astronomical measurements to temperature in Kelvin involves understanding the relationship between frequency and energy density. Specifically, Penzias & Wilson's measurement of the Cosmic Microwave Background (CMB) at 4080 Mc/s indicates an "excess temperature" of approximately 3.5 degrees Kelvin. This conversion utilizes Planck's law, which relates the energy emitted by a black body radiator to its temperature. By measuring energy per unit area and applying the appropriate formulas, one can derive the temperature from frequency measurements.

PREREQUISITES
  • Understanding of Planck's law and black body radiation
  • Familiarity with radio frequency measurements (e.g., Mc/s or MHz)
  • Basic knowledge of energy density concepts
  • Experience with astronomical measurement techniques
NEXT STEPS
  • Study Planck's law in detail to understand its application in astrophysics
  • Research the relationship between frequency and temperature in black body radiation
  • Explore methods for measuring energy density in astronomical contexts
  • Investigate the historical context and significance of Penzias & Wilson's findings
USEFUL FOR

Astronomers, astrophysicists, and students studying cosmology or radio astronomy will benefit from this discussion, particularly those interested in the conversion of radio measurements to thermal properties.

Martin1957
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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?
 
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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.
 

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