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Originally Posted by George
I would be highly interested in learning how the scale height affects the spectrum from the observers point of view here on Earth. The center-to-limb variation (CLV) reveals a significant difference in temperature of about 1400K between limb and the central zone of the disk.
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That's not really an effect of the scale height per se, in that you could increase or reduce the scale height without altering the limb darkening. Yes, it does relate to the temperature gradient over the scale height, but the logic goes the other way-- the physics of diffusive radiation causes
both the limb darkening
and the temperature gradient; neither of those cause the other. You can use either to
establish the other, but the logical
cause is simply the physics of radiative diffusion in radiative equilibrium. That's why changing the scale height will change the temperature gradient so as to end up with the same limb darkening.
The limb darkening is
caused by the fact that diffusive radiation is more likely to emerge more or less directly out of the boundary than into a similar-sized angular bin that is at a steep angle from the boundary. The same would hold for drunken people stumbling through the doorway of a bar.
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If, however, a spectral irradiance observation is obtained of only a small region of the Sun, then a much nicer Planck distribution should be found, right?
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Yes, you would then be sampling less of that region of temperature gradient, or "drunkards" who had followed a more similar stumbling history.
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What is unclear to me is whether or not the central disk temperature of 6400K will produce a very nice Planck distribution for that temperature (ignoring the emission & absorption bands)? In other words, would scattering or other effects [observable to the bottom of the photosphere] complicate the Planck result?
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Scattering, and opacity variations due to lines etc.,
always complicate the Planck result, whenever not in strict thermodynamic equilibrium.