Our Solar
Magnetic Field Project
Introduction
This project tests whether our Angle of Encounter (Ӕ) model can predict the “photoning depth” (r*) of the Sun’s photosphere, the depth below the visible surface where photons emerge. The question is whether we can use measured magnetic field data to locate this depth precisely, without tuning the model after the fact.
The Plan
The experiment runs in two stages:
1. Calibration – Use independent solar limb-darkening data to determine two constants: θ_Ӕ^crit (critical misalignment angle) and B_crit (critical magnetic field strength).
2. Cross-Check – Lock these constants. Use them to predict r* in both a quiet-Sun region and a sunspot umbra.
How the Constants are Derived
– High-resolution limb-darkening data are fitted to the Ӕ model to obtain k_AE
– θ_AE^crit is calculated from k_Ӕ as the misalignment angle where limb-darkening steepens sharply
– A standard photosphere model (e.g., VAL-C) provides the depth for that angle; the magnetic field strength at that depth defines B_crit
– These constants are fixed before any prediction is made
Applying the Constants
With θ_Ӕ^crit and B_crit fixed:
– Use vector magnetograms (e.g., HMI/SDO) to extrapolate subsurface magnetic fields
– Find the first depth where Ӕ misalignment exceeds θ_Ӕ^crit — call this r_angle
– Find the first depth where field strength reaches B_crit — call this r_B
– The shallower of the two is r*
First Run with Defaults
For our first test using canonical defaults:
– θ_Ӕ^crit = 7.00°
– B_crit = 0.160 T
Results:
– r* values for both quiet-Sun and sunspot patches were within 480–965 km
– The sunspot r* was shallower than the quiet-Sun r*, matching the model’s prediction
– Uncertainty spreads were under 200 km
Significance
This demonstrates the method’s validity using fixed constants derived from independent data. We did not adjust the model to fit the results. The match to observed behavior supports the Ӕ model’s predictive power.
The next step is replication with live observation data from independent sources.
Addendum
Replication Metadata Form
Locked Constants (do not alter):
• θ_Ӕ^crit: 7.00°
• B_crit: 0.160 T
Target Information
– Target Type (Quiet Sun / Sunspot Umbra): [ ]
– Coordinates (Helioprojective): [ ]
– Patch Size (arcsec): [ ] × [ ]
– Timestamp (UTC): [ ]
Instrumentation & Acquisition
– Instrument Name: [ ]
– Cadence: [ ] s
– Resolution: [ ] arcsec/pixel
– Noise Floor: [ ] G
– Disambiguation Method: [ ]
Atmospheric Model
– Model Used (e.g., VAL-C, FAL): [ ]
– Scaling Applied: [ ]
Magnetic Field Extrapolation
– Model Type (PFSS / NLFFF): [ ]
– Model Parameters: [ ]
Computed Depths
– r_angle (km): [ ]
– r_B (km): [ ]
– Final r* (km): [ ]
– Uncertainty Spread (km): [ ]
β-Profile
– Matches Prediction? (Yes/No): [ ]
– Notes: [ ]
Return Instructions
Submit the completed form with FITS-format magnetogram patches.
Ensure all coordinates, timestamps and model parameters match the submitted files exactly.
Produced by The Lilborn Equation Team:
Michael Lilborn-Williams
Daniel Thomas Rouse
Thomas Jackson Barnard
Audrey Williams