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Chapter 1: Astrophysics

Frequency of the Cosmic Background

Dear Dr. SETI:
I was talking with my professor about Radio Astronomy and he asked me about the temperature of the microwave cosmic background radiation, and what frequency that would be. I did a little research and found that the background radiation is about 2.7 degrees Kelvin, but it does seem to me that energy, even at that low temperature, should peak (be strongest) at a given frequency. However, I could find no further information on this, or a method of conversion.

Stephen (member of Society of Amateur Radio Astronomers)

The Doctor Responds:
Of course, your professor knew the answer, Stephen; he was trying to get you to do a little research. So, asking another professor is really cheating, isn't it? Nevertheless, I will attempt a response:

The short answer is that there is indeed a peak in the amplitude of the cosmic background radiation, and that it occurs at around 279.5 GHz.

The long answer is found by assuming a thermal radiation curve with a blackbody temperature of the stated 2.7 Kelvins. Planck's law (e = h f) tells us that e, the kinetic energy per photon, varies with frequency f according to Planck's Constant h. Since energy varies with frequency, a thermal energy curve should logically peak in amplitude at some specific frequency, which varies as a function of temperature.

From Wien's Law (a special case of Planck's Law), we find that the product of equivalent blackbody temperature times peak wavelength is a constant, which we call Wien's Constant A:

A = Lambda (peak) x Teq

When the peak wavelength Lambda is expressed in meters, Teq is the equivalent thermal blackbody temperature, in Kelvins, Wien's Constant comes out to something like 2.898 x 10-3 meters times Kelvins. Thus, we can solve for peak wavelength:

Lambda (peak) = A / Teq

For the cosmic microwave background,

Lambda (peak) = (2.898 x 10-3 m . K) / (2.7 K)

Note that the Kelvins in the numerator cancels the Kelvins in the denominator, and wavelength thus comes out simply in meters.

Given your stated temperature, the wavelength peak is thus about seven percent more than 1 mm. Dividing this into the speed of light (300 million meters per second), we find the equivalent frequency to be just seven percent lower than 300 GHz, or around 279.5 GHz. So, if you're looking to receive the peak of the cosmic microwave background radiation with your radio telescope, tune it below 300 GHz and look around. Only, a thermal blackbody emission of just 2.7 Kelvins is going to be pretty weak, and not all that easy to detect, even at its amplitude peak.

You may recall that, at Holmdel in 1963, Penzias and Wilson first detected the cosmic microwave background radiation (research which won them the Nobel Prize). They were receiving at a frequency around 4 GHz -- well below the amplitude peak, but still detectable with their huge horn antenna and cryogenically cooled maser amplifier. Four decades later, even using the best equipment available to advanced amateurs, the measurement still presents a challenge. May you rise to it!

Note: for an alternative solution to the peak frequency problem, see this subsequent column.

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