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I have read that 3GHz is the best frequency at which to measure the sun's microwave output, but that measurements are made at 2.8GHz for historical reasons, however I can find no explanation of why 3GHz should be the best frequency. Could anyone tell me please?

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    $\begingroup$ Welcome to the Astronomy Stack Exchange! For some context to help people answer this, could you add details of where you read this to the question? $\endgroup$ – user24157 Aug 27 '20 at 13:43
  • $\begingroup$ 2.8 Ghz, or 2800 Mhz, electromagnetic radiation has a wavelength of 10.7 cm. Hour-long measurements of the Sun's output in a 100 Mhz band centered around 2800 Mhz form the basis for the F10.7 radio flux. $\endgroup$ – David Hammen Aug 27 '20 at 15:06
  • $\begingroup$ Thank you, thugh I'm afraid that I can't find the original quote about 3GHz being the best frequency, but according to K.F.Tapping, there is a "broad spectral peak" in the (slowly varying component of the) sun's microwave output at 10cm (3GHz), I should think that this answers my own question. $\endgroup$ – Shaun Ross Aug 27 '20 at 15:15
  • $\begingroup$ @ShaunRoss - That peak is so broad that (a) it is hard to say exactly where the peak is, and (b) any frequency in the region of that very broad peak does just fine. The peak is so broad (it spans over an order of magnitude in the frequency domain) that 3 GHz and 10 cm are used because they are nice round numbers that happen to lie close to the middle of the range in a logarithmic sense. $\endgroup$ – David Hammen Aug 27 '20 at 22:29
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From "The 10.7 cm solar radio flux ($F_{10.7}$)",

It has become clear that wavelengths in the region of 10 cm are best for monitoring the level of solar activity because solar emissions at these wavelengths are very sensitive to conditions in the upper chromo- sphere and at the base of the corona.

This is not saying that exactly 10 cm wavelength radiation (3.0 GHz) is optimal. Ten centimeters is being used in this context as a nice round number. 10.7 cm radiation is definitely in the "region of 10 cm". Schmahl and Kundu reported in "Microwave proxies for sunspot blocking and total irradiance" that anything in the range of 1000 MHz to 9400 MHz works quite nicely. 3.0 GHz (3000 MHz) is more or less in the middle of that range, logarithmically.

Measurements of the F10.7 radio flux go back to 1946. This was a serendipitous choice as a proxy for measuring variations in the Sun's output, not just in the microwave / radio frequencies, but also in very high frequencies (ultraviolet and X-rays).


References:

Tapping, K. F. "The 10.7 cm solar radio flux ($F_{10.7}$)." Space Weather 11.7 (2013): 394-406

Schmahl, E. J., and M. R. Kundu. "Microwave proxies for sunspot blocking and total irradiance." Journal of Geophysical Research: Space Physics 100.A10 (1995): 19851-19864

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