To further increase the specificity of the present model, we can scrutinize the solar power output, and ask if the model would produce power in precisely that form.

All of the power from the Sun is in the form of electromagnetic radiation (i.e., photons), and the intensity per wavelength is a close match to a 5525 K blackbody curve.

Figure 1. Solar Spectrum

So what is a blackbody spectrum? Following in Balfour Stewart's footsteps, Gustav Kirchhoff canonized the essential characteristics of different types of EM radiation in his three laws of spectroscopy.1,2
1. A hot solid object produces light with a continuous spectrum (i.e., blackbody radiation). (Wilhelm Wien went on to say that the power distribution has a lop-sided bell curve that depends on the temperature, as in Figure 1.3)
2. A hot tenuous gas produces light with spectral lines at discrete frequencies, and in combinations that depend in a more complex way on the temperature. (Niels Bohr later developed the concept of electron shells, and traced the spectral lines down to the degrees of ionization in the gas, which are a function of temperature.4)
3. A hot solid object surrounded by a cool tenuous gas produces blackbody radiation, but with gaps at discrete frequencies, which are the same as the emission frequencies of the gas, and likewise depend on the degree of ionization.
Figure 2. Hydrogen emission wavelengths (in nm), given the energy levels traversed.
To fully understand this, we should focus first on the Bohr model of the atom (which explains the 2nd law, and part of the 3rd). Emission and absorption of specific frequencies in gases are the consequence of electrons changing states. (See Figure 2.) Electrons entering lower energy levels emit photons. This could be electron uptake by a positive ion, or it could be an electron in an outer shell settling into an inner shell. Either way, the sudden movement of the charged particle creates a disruption in the surrounding electric and magnetic fields, producing an EM wave that propagates outward at the speed of light. Since electron shells occur at specific radii, the waves are generated at specific frequencies, producing distinctive spectral lines. Different elements have a different number of protons in their nuclei, so the electron shells occur at different radii. Thus the frequency of photons can be used to determine the elements (and the degrees of ionization) that produced them. The reciprocal process is photon absorption. Any electron bound to an atom is capable of being photo-ionized, where the frequency of the photon that gets absorbed is the same as the photon that will be re-emitted when that electron settles back into its original state. But when it does, the direction of the new photon is random. Hence a cool tenuous gas "scatters" photons from a light source, producing absorption bands, even though it emits as many photons as it absorbs.

Blackbody radiation (as described in the 1st law) is obviously generated by a fundamentally different mechanism, since it is a smooth continuum of frequencies, not spectral lines. The standard explanation for BB radiation is abstract and complex. Before the Bohr model became accepted, scientists struggling to understand the nature of light, and disillusioned by the failure of Rayleigh-Jeans law to predict BB curves, concluded that there was no suitable mechanistic framework, and that the problem could only be solved with heuristic math.5,6,7 Yet we are in the pursuit of a mechanistic model of the Sun, and such constructs are not useful to us, as their structural members will never rest squarely on any solid foundation.8:73 To integrate BB radiation into our physical model of the Sun, so that we can double-check the energy sources, we first need a physical model of BB radiation.

The only attempt at a physical model in the mainstream literature has the solar BB curve as the sum of a large number of individual spectral lines.9 But the chance of so many discrete processes consistently adding up to a smooth curve is too slight.10 With no better alternatives,11:36 we are free to explore new possibilities.

Figure 3. Atomic vibrations due to heat.
Some work has been done on a new conception of BB radiation at the quantum level.12 But we need not introduce such complexity into the present problem domain, which is already sufficiently broad. At the next level up there is a possible explanation for BB radiation based on simple atomic theory. Atoms in a molecule above absolute zero are in constant vibration, within the limits of their covalent bonds. (See Figure 3.) This movement of positively charged nuclei generates EM waves.13 The frequency is a direct function of the speed of the atoms, as they bounce back and forth within the lattice. We might think that the regularity of the lattice would determine a single frequency of oscillation, but the atomic motions in a solid are semi-random. So there will be a center frequency, predictable by the dimensions of the lattice and by the temperature, but all frequencies will be present, producing a continuous spectrum instead of individual lines.

Note that this BB model will not suffer the same fate as the Rayleigh-Jeans law, which naïvely predicted that the power distribution should vary with the temperature over the wavelength. Thus decreasing wavelengths should have resulted in power that hyperbolically approached infinity, but what we actually see is a bell curve, and in the UV band, the power drops back down to nothing. So T/λ just isn't going to work. But the present contention is that the waves are caused by oscillating particles, and their physical characteristics need to be taken into account. Specifically, the particles have mass, and their kinetic energy varies with the square of the velocity (Ek = ½·m·v2). Hence it takes exponentially more thermal energy to generate higher frequencies, and this attenuates the power in the UV band. So simple atomic oscillators remain a reasonable model for blackbody radiation from solids.2,10:98

But what about gases and plasmas?

Outside of the complexities in a crystal lattice, discrete gas molecules vibrate only at characteristic frequencies, producing well-known emission/absorption lines in the infrared band. (Other gaseous degrees of freedom, such as translation and rotation, do not produce EM waves, as the protons and electrons translate and rotate together, and the field perturbations cancel out.) So gases don't produce continuous spectra like blackbody solids. Rather, they only emit photons of specific wavelengths.

Plasmas do not have molecular vibrations or rotations, but the translation of an ion should generate a wave. Theoretically it does, but the mean free path between atoms is typically so long that the blackbody radiation is in the ELF band, and the power is extremely weak, due to the low density. The emission lines from electron uptake in plasmas are far more powerful.

Hence gases and plasmas are known by their distinct emission/absorption frequencies, and their lack of blackbody radiation.

Yet we know that the Sun issues BB radiation, and that the temperature is roughly 5525 K. The only elements that are still solid at 5525 K are tantalum, tungsten, and rhenium, but these are not present in sufficient quantities to dominate the spectrum. So what produces the BB radiation?

More recent research has demonstrated that supercritical fluids, well above their boiling points but under sufficient pressure to still be at or near their liquid densities, produce BB radiation.14,15,16:21,17:445,18,19 Instead of covalent bonds constraining the motion of atoms, Coulomb forces between closely packed ions do the same thing. So instead of a crystal lattice, it's a Coulomb lattice, so to say. The greater the pressure, the closer the atoms, and the higher the frequency of vibration, even with the same atomic speeds. So the 4th law of spectroscopy should be that a supercritical fluid does not produce spectral lines (because electron uptake isn't happening), but it does produce BB radiation (from the oscillations of atomic nuclei in short mean free paths).

So let's apply this law to the photosphere. The temperature averages 5525 K. The physical instantiation of temperature is particle motion, which for hydrogen at 5525 K works out to 1.29 × 104 m/s. The dominant wavelength is 500 nm, which is the same as 6.00 × 1014 Hz, or 1.67 × 10−15 seconds per cycle. How far will a particle moving at 1.29 × 104 m/s travel in 1.67 × 10−15 s? That works out to 2.15 × 10−11 m, which is about 1/4 of the spacing between the atoms in an H2 molecule (7.40 × 10−11 m), and which would be a reasonable oscillation distance. Note that particles in ionized matter don't collide the way neutrally charged molecules do — the Coulomb force between ions affects a rebound long before the collision would have occurred.

But BB radiation coming from supercritical hydrogen causes more problems than it solves for the standard model. Most astronomers believe that the Sun is transparent down to a depth of at least 300 km, and possibly to a depth of 700 km.9 This leaves them with no choice but to assert that the 5525 K BB radiation comes from within 700 km of the surface. But the same model also states that plasma at that depth, and down to a depth of 13 Mm, is thinner than the Earth's atmosphere at sea level, and laboratory studies show that such tenuous plasmas produce only spectral lines. Any BB radiation should be extremely weak, and in the ELF band, signifying extremely low temperatures. This, of course, is not at all the nature of the radiation from the Sun.

In the standard model, these problems cannot be solved. Only considering gravity and hydrostatic pressure, the density gradient is dictated by the ideal gas laws, with no room for reinterpretation. So they have no choice but to contend that the energy source is nuclear fusion in the core, and that the gamma rays are absorbed and re-emitted at successively lower frequencies that, when taken together, just happen to add up to a 5525 K BB curve. But this presents several impossibilities.10
• If the standard model is correct, the Sun is composed of 75% hydrogen and 25% helium. This means that
• there is no way of accounting for the overall mass of the Sun, given the electron degeneracy pressure, and
• the wide variety of elemental species necessary to convert gamma rays to BB radiation shouldn't be present.
• If a wide variety of species (including heavier elements) were present,
• the chance of many non-BB processes adding up to a smooth BB curve is effectively nil, and
• the heavier elements would settle into the core, where the pressure is insufficient for fusion, meaning that there shouldn't be any gamma rays.
Clearly, the standard model just doesn't work, and cannot be made to work. So the model constraints need to be removed, and we need to look directly at the data and the physical properties of the plasma. We know that the solar BB radiation can only be coming from high-pressure plasma, so the opacity can be set by the pressure gradient. This creates another impossibility for the standard model, where supercritical hydrogen occurs only at depths greater than 100 Mm. All photons having to travel through 100 Mm will surely be scattered. But the standard model assumes that it is only gravity that compresses the plasma. When electrostatic potentials between charged double-layers are taken into account, the forces are much greater, and supercritical hydrogen occurs much closer to the surface.

References

1. Kirchhoff, G. (1860): Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht. Annalen der Physik und Chemie, 109: 275-301

2. Robitaille, P. M. (2003): On the validity of Kirchhoff's law of thermal emission. IEEE Transactions on Plasma Science, 31 (6): 1263-1267

3. Wien, W.; Lummer, O. (1895): Methode zur Prüfung des Strahlungsgesetzes absolut schwarzer Körper. Annalen der Physik, 292 (11): 451-456

4. Bohr, N. (1913): On the Constitution of Atoms and Molecules. Philosophical Magazine, 26: 1-25

5. Einstein, A. (1905): Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik, 322 (6): 132-148

6. Planck, M.; Masius, M. (1914): The theory of heat radiation. Philadelphia: P. Blakiston's Son & Co

7. Kuhn, T. S. (1987): Black-Body Theory and the Quantum Discontinuity, 1894-1912. Chicago: University of Chicago Press

8. Robitaille, P. (2007): A High Temperature Liquid Plasma Model of the Sun. Progress in Physics, 1: 70-81

9. Iglesias, C. A.; Rogers, F. J. (1996): Updated Opal Opacities. The Astrophysical Journal, 464: 943

10. Robitaille, P. (2011): Stellar Opacity: The Achilles' Heel of the Gaseous Sun. Progress in Physics, 3: 93-99

11. Robitaille, P. (2008): Blackbody Radiation and the Carbon Particle. Progress in Physics, 3: 36-55

12. Lucas, C. W. (2003): A Physical Model for Atoms and Nuclei, Part 4: Blackbody Radiation and the Photoelectric Effect. Foundations of Science, 6 (3)

13. Robitaille, P. (2009): Blackbody Radiation and the Loss of Universality: Implications for Planck's Formulation and Boltzman's Constant. Progress in Physics, 4: 14-16

14. Tsintsadze, L. N.; Callebaut, D. K.; Tsintsadze, N. L. (1996): Black-body radiation in plasmas. Journal of Plasma Physics, 55: 407-413

15. Davis, W. C.; Salyer, T. R.; Jackson, S. I.; Aslam, T. D. (2006): Explosive-driven shock waves in argon. Proceedings of the 13th International Detonation Symposium, 1035-1044

16. Meyer, R.; Köhler, J.; Homburg, A. (2007): Explosives. John Wiley & Sons

17. Ray, S. F. (1999): Scientific Photography and Applied Imaging. Focal Press

18. Vazquez, G.; Camara, C.; Putterman, S.; Weninger, K. (2001): Sonoluminescence: nature’s smallest blackbody. Optics Letters, 26 (9): 575-577

19. Levi, B. G. (2005): Evidence for a Plasma Inside a Sonoluminescing Bubble. Physics Today, 21-23