From CC's paper: "Preview" http://www.qdl.scs-inc.us/?top=8469
This is Charles' recent summary of the reasoning for his model.

[Proof That the Sun's Distinct Limb Is Not Due to Gravity]

The standard model of the Sun fails to explain even the simplest of solar observations.

At its visible surface, the Sun is 75% hydrogen and 25% helium, with just traces of heavier elements.

Figure 1 [at http://www.qdl.scs-inc.us/?top=8469] shows the surface of the Sun on the limb, and in the primary wavelength emitted by hydrogen.

Notice that the edge of the photosphere is very distinct, topped by the tenuous plasma in the chromosphere and transition region.

Above that, the solar atmosphere is transparent.

The full transition, from opacity to transparency, occurs in only 7 Mm [7,000 km of the photosphere].

(Figure 1. The solar limb seen in H-α (6563 Å), 2007-05-27, courtesy Fred Bruenjes.)

Further evidence of a distinct surface are the s-waves sometimes caused by solar flares.

S-waves only occur at the boundary between layers with dramatically different densities.2:73 (See Figure 2.)

(Figure 2. Waves propagating after a solar flare, 1996-07-09, courtesy SOHO.)
(The images show an area 200 Mm [200,000 km] across.)

Yet in the standard model, a distinct surface just isn't possible.

If the organizing principle is gravity, balanced only by hydrostatic pressure, the density gradient should be set deterministically by the ideal gas laws. (See Figure 3.)

(Figure 3. The density gradient of the Sun in the Dalsgaard model, based on the ideal gas laws, with gravity supplying the pressure.)
(The X axis shows the decimal of the solar radius starting from the center, and above is the percentage of the solar volume, starting from the surface.)
(The Y axis shows g/cm3.)

The model density at 1.0 R is 2×10^−4 kg/m^3 (i.e., a good laboratory vacuum), increasing steadily to the density of STP air at a depth of 13.22 Mm.

In such a gradient, there is no distinct edge.

Analogously, the Earth's atmosphere traverses the same gradient from the top of the mesosphere (i.e., the dashed red line in (Figure 4) down to sea level.3

Even when only partially back-lit by the Sun, the [Earth's] mesosphere is transparent.

In full daylight, even the troposphere is transparent.

(Figure 4. Earth's atmosphere back-lit at sunrise, courtesy NASA.)
(The pale blue-green color is from water vapor in the troposphere.)
(The dark blue is from nitrogen and oxygen in the stratosphere.)
(The dashed red line shows the top of the transparent mesosphere.)
(Figure 5. ESO 325-G004)

Hence the plasma on the limb of the Sun should still be quite transparent at a depth [of] 13.22 Mm, and the opacity should increase steadily with depth, without producing a distinct edge.

With an internal light source, the Sun should look like headlights in the fog, with the luminosity gradually tapering off to nothing at some distance from the center (similar to the luminosity from elliptical galaxies (for different reasons), as in (Figure 5.))

Since the ideal gas laws leave no room for reinterpretation, the only possible conclusion is that forces other than just gravity and hydrostatic pressure are responsible for the sharp increase in density going from the chromosphere to the photosphere.

At the macroscopic level, there are two candidates: the electric force, and the magnetic force.