Indeed, there will always be detailed corrections to any overall simplifying description. The real world does not have sharp boundaries, but they are still useful in our minds. (There isn't even a "depth from which we see the Sun"-- an occasional photon can come from very much deeper!)

Thanks Tim.

Here is a set of lecture notes ("Stellar atmospheres (PHY305)") which seems to cover much of what's been discussed so far in this thread.

It's 3rd year undergrad university level, so the math may be somewhat daunting to some readers ...

Bearing in mind its stated scope, does anyone feel there's anything in this set of material that may be misleading (or downright wrong)*, wrt the scope of this thread?

*Of course, much of it is well beyond the scope of this thread!

A quick look doesn't find any problems, but it's very "mathy"-- sort of, here's the equations, here's what you get when you solve them. Most people won't find that terribly illuminating, but when instead "explanations" are given, they are sometimes wrong-- so this is kind of the "safe" approach to the subject.

Thanks, Nereid. The sixth lecture was very relevant and interesting: Stellar Opacity (hydrogen).

The binding energy of the extra electron on the H^- ion is 0.754 eV. Photons with wavelengths of 1640 nm (Infrared) or less can ionize the ion back to neutral H. The extra electrons needed to form H^- ions come from ionized matals such as Ca⁺. But only 2 out of every 10⁸ hydrogen atoms is a H^- ion.

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I hadn't seen that part-- those do sound like quite helpful explanations! It does look generally like a pretty complete and well organized course.

Doesn't fusion aggravate the free electron problem by eating two electrons to convert to one He? This raises an interesting question, Eroica.

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Yes, but all that is in the core, not the atmosphere. Unless you are talking about very highly evolved stars!

So you think a 400,000 km non-convective zone might insulate it enough? You have my vote! [Does the core develop a large postive net charge?]

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No-- the helium eats protons too!

Ah, that makes sense; those are my favorite.

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Protons taste like Chicken.

Hmmm Protons!

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Have you tried the croutons? They come in a lattice.

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I recommend the quark-gluon soup.

Which of the six flavors are best?

Meanwhile, back to asking about black-body radiation from a white-body radiator ....Neried's link to another (305-2) states that opacity is inversely proportional to the mean free path of a photon, so I'm still a bit confussed.

Summarizing only the basics of what is happening given a view into a cylindrical region penetrating directly toward the solar center....

1) The vast majority of the light is from the photons generated as the weakly bound electrons become attached to the atom.

2) The near blackbody radiation from the Sun is due to the extensive range of kinetic energies of the free electrons allowing such a wide distribution of photon energies. These photons form when free electrons combine with hydrogen atoms to form the hydrogen ion (H^-).

3) The visible depth into the atmosphere is approximately the depth of the photosphere. The scale height more accurately sets the actual depth.

4) The rising adiabatic convective cells from the lower convective zone become turbulent and non-adiabatic in the photosphere.

5) A slight majority of the light comes from the lower-half region of the scale height due to the higher density in this lower region.

6) The total energy flux of the Sun from its surface is the same as the energy flux from the core.

7) The photon flux of the Sun from its surface is far greater than that of the core.

8) Normal absorption lines will be found with some blurring due to minor Doppler, Zeeman, and pressure broadening effects.

9) Hydrogen and helium constitute over 99% of the surface atoms.

10) The other elements produce the majority of the absorption lines in the spectrum.

11) The number of absorption lines exceed 25,000.

12) Emission lines are also found in the spectrum.

13) The peak energy intensity is near 455nm (blue, almost violet).

14) The photon flux distribution is almost flat across the visible spectrum.

15) The net color of this region, with proper attenuation for the observing eye, is.....white or bluish-white.


Original attempt:
1) The vast majority of the light is from the photons generated as the weakly bound electrons become attached to the atom.
[I assume it is too cold for Helium ions?]
2) The near bb radiation is due to the extensive range of photon energies allowable because of the same extensive range of electron states of the outer electron of the hydrogen ion.
3) The visible depth into the atmosphere is the region known as the photosphere.
4) The depth of the photosphere is the scale height for this region, ignoring some variations such as covection currents.
5) A slight majority of the light comes from the lower-half region of the scale height due to the higher density in this lower region.
6) The total energy flux of the Sun from its surface is the same as the energy flux from the core.
7) The photon flux of the Sun from its surface is far greater than that of the core.
8) Normal absorption lines will be found with some blurring due to minor Doppler effects.
9) Additional blurring of the absorption bands may occur due to magnetic activity (Zeeman effect).
10) Hydrogen and helium constitute about 98%(?) of the surface atoms.
11) The other elements produce the majority of the absorption bands in the spectrum.
12) The number of absorption bands exceed 25,000. [I didn't count them!]
13) Emission bands are also found in the spectrum.
14) The peak energy intensity is near 455nm (blue, almost violet).
15) The photon flux distribution is almost flat across the visible spectrum.
16) The net color of this region, with proper attenuation for the observing eye, is.....white or bluish-white.

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Is that your final answer?

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It is a subtle shout for a call-to-arms!!! Which is it: white or bluish-white? [Sad that it isn't green. ]

I hope the answer comes after the heliochromology textbooks are printed -- I should have enough for 6 or 7 pages of text (50 or 60 with sunset pictures). Offering them for sale after the fact would be of little use except as collector items. Perhaps we could add Poor Pluto's story in a chapter, too. I could use some sympathetic padding.

[Added. BTW, I recall it was you, Eroica, that presented us with the 25000 lines in the solar spectrum (Item 12). Do I have that correct?]

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The extensive range is in the free electron energies, prior to making an ion of much more definite energy.
Unless defined in terms of the energy equation. If we use your definition, we still need a name for what lies between the convection zone and the photosphere.
The currents at the surface aren't really convection, they are mechanically driven by dynamical energy releases, i.e., they are not adiabatic like standard convection.
There is also some blurring due to "pressure broadening" by the perturbing effect of high density, especially important in dwarfs. Indeed, this effect is pretty much the way that dwarfs are identified, though I expect we'd know the Sun was one anyway!
Even more.
Note the word "line" is better than "band", unless dealing with molecules.

Ah, that's a little different than I thought. It is those energies posessed by the free electrons that correlate to the spectral distrubtion. Is this correct?

Maybe that is why I have not seen a very specific depth stated for the photosphere. I suppose "the phovectosphere" would not eschew obfuscation. How 'bout "the blueocline" for its distincitive color (once established, that is)? [Perhaps whoever came up with "the tachocline", for the intermediary zone between the convective and the radiative zones, could help, as their term does make some sense (it is a rotational speed interface boundary). ]

Interesting, though I don't get it. Are the convective currents stable, similar to a laminar flow, until they reach the photosphere where they, apparently, become turbulent?

Ok. Is there a specific term for it?

You mean...... a yellow dwarf!

Yes.

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Yes, the electrons can be characterized by a single local electron temperature, and that shows up in the blackbody radiation they are responsible for, for all energies above the binding energy of H minus.
Convection is pretty turbulent everywhere, but the need to carry a heat flux is just a tiny "hitchhiking" effect that maintains the instability, it doesn't alter the buoyancy-controlled structure that drives the turbulence. In contrast, the flows at the surface are highly non-adiabatic-- they are getting heated and cooled will nilly and following ballistic trajectories due to "squirting" and/or "explosive" types of forces that are highly out of force balance (unlike buoyancy). So the gas in the convection zone is all at the same entropy, pretty much, but above that the entropy becomes very dynamical.
Yeah-- pressure broadening!
Of course, just ask kindergardners.

Is the binding energy for H^- a set value as found in the other transition levels? If so, then is the photon energy simply the difference in this energy state and the free electron's kinetic energy?

So does this mean that somewhere below the photosphere that the convective cells are essentially adiabatic?

Wow, deja vu, I am sure I have recently heard this very term. I think, however, it deserves a scientific name. Even the acronym looks wimpy.

Alas, we arrive finally at a first cause issue in astronomy!

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Yes and yes. The energy was stated earlier in the thead, a bit under 1 eV as I recall.
Yes, pretty much throughout the convective region, except at the top and bottom where you convert back to and from radiative energy flux. Note this implies that the convection zone is a lot like a very poor efficiency Carnot engine. Where does the work go? A lot of it, apparently, into magnetic activity (solar flares and so forth).

Nice oxymoron. I never thought I'd see a Carnot engine and now you've shown me another; the first in the Cepheid ionization zones, possibly.

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Yes, they really have two uses, one to find the maximal efficiency, but another to just see a general mechanism that is approximately followed, to some good or poor level, by a host of periodic and quasi-periodic phenomena that are driven by heat flow.