# What is the diameter of the sun as a function of wavelength/frequency (around 10GHz)?

I have this vague recollection of being told that the diameter of the apparent surface of the sun is a function of what band you observe it in. I'm looking for a model of this that works for bands in the 1-100GHz range.

If the "surface of the sun" has no formal definition, then it might as well be something that will be useful to my case: use something like the surface where a tangential radio transmission link (using "very narrow beam" antennas, <.01 deg) will see a 3dB reduction in the signal-to-noise ratio from the combination of solar radiation and signal attenuation.

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The apparent surface you are describing is the photosphere, which is indeed dependent on the frequency you're looking at. The simplest answer is that the radius (as a function of frequency) is very nearly constant --- because the density profile of sun near the photosphere is very sharp.

The photosphere is approximately the location where the optical depth to light (at the frequency of interest) is 2/3 (most people just round to 1). The optical depth is a function of the density and opacity. You could calculate the photosphere radius as a function of frequency, using the density profile of the sun, and something like kramer's opacity law.

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What are the bounds on the validity of that model? Does that still apply in the RF ranges? IIRC absorption at optical wavelengths is an interaction with single electrons whereas with RF wavelengths it's dealing with conduction inside conductive materials. – BCS Aug 15 '12 at 22:59
@BCS That's much more correct for atomic phases of matter than for plasmas. In the latter case nearly all of the electrons are free so there are no intrinsic limitations on the energy of photon--electron interactions caused by atomic or molecular energy level concerns. – dmckee Aug 16 '12 at 1:46
@BCS the calculation that I outlined is applicable to all wavelengths --- the only issue is using an appropriate opacity in that realm. Kramer's opacity law is very general, and while I don't know any of the details, it definitely has regions where it will over/under estimate the opacity. For more completeness, full simulations of the stellar atmosphere are needed (e.g. something like MESA - arxiv.org/abs/1009.1622) – DilithiumMatrix Aug 16 '12 at 14:18