Structure, Containment And Coherence
Purpose of This Table
This document presents the first fully contextualized version of the solar brightness gradient table, offering not just numerical values but ontological meaning. These values are not thermal artifacts or perceptual illusions. They are the measurable result of containment loss in the Sun’s electromagnetic field structure. The table below marks the gradient by which light escapes not because of pressure or temperature, but because coherence is failing.
Definitions and Geometry
Each row represents a radial layer within the Sun, expressed as a fraction of the solar radius. The column μ = cos(θ) is a geometric translation of Angle of Encounter, the degree to which light meets the container surface at a perpendicular (μ = 1.0) or grazing (μ ≈ 0) angle. The final column, normalized intensity (I/I₀), expresses the fraction of light escaping from that radius compared to the full intensity at disk center. A drop in this value marks a weakening in containment.
Comparison with Theoretical Physics
Conventional solar physics attributes limb darkening to temperature gradients and optical depth. This framework, however, fails to address the underlying structure that causes brightness to drop geometrically. By contrast, this table is not an observation of light passing through hotter or cooler gases, it is a direct map of where electromagnetic coherence begins to fail.
Structural Application
This table forms the quantitative basis of the Lilborn field model for the Sun. It demonstrates that as one approaches the limb, coherence fails and brightness increases. As one moves inward, brightness fades not due to absorption, but due to structural containment. At the core, where μ approaches 1.0 and I/I₀ approaches 1.00, light is not emitted because it is fully retained.
Simulated Solar Brightness Table
| Relative Radius (r/R⊙) | μ = cos(θ) | Normalized Intensity (I/I₀) |
| 0.00 | 1.000 | 1.00 |
| 0.10 | 0.995 | 0.98 |
| 0.20 | 0.980 | 0.95 |
| 0.30 | 0.954 | 0.90 |
| 0.40 | 0.917 | 0.85 |
| 0.50 | 0.866 | 0.80 |
| 0.60 | 0.800 | 0.73 |
| 0.70 | 0.714 | 0.65 |
| 0.80 | 0.600 | 0.50 |
| 0.85 | 0.526 | 0.43 |
| 0.90 | 0.435 | 0.35 |
| 0.95 | 0.312 | 0.25 |
| 1.00 | 0.000 | 0.18 |
Produced by The Lilborn Equation Team:
Michael Lilborn-Williams
Daniel Thomas Rouse
Thomas Jackson Barnard
Audrey Williams