© Charles Chandler
The objective of this project is to provide a calculation engine for checking the consistency of solar models, given the proposed densities, pressures, temperatures, and elements. The strategy is to use finite element analysis, mainly for its conceptual transparency. If we divide the Sun into small enough pieces, we can calculate the fundamental forces acting on each piece with simple arithmetic, and then just add it all up to get the net results. This eliminates the complexities (and the attendant possibility of undetected errors) in the relevant integral calculus formulas.
Distribution of points generated by the Golden Spiral method.
This engine divides the Sun into 1000 pyramids, with "bases" equal to 1/1000 the area of the solar surface (shown as inwardly pointed cones in Figure 1
). The pyramids are sub-divided into 100 equal-volume truncations. (See Figure 2
. Note that the pyramids all have the same volume, even though in 2D, they don't have the same area.) The truncated pyramids are the discrete parcels used in the FEA calculations.
It doesn't matter that the square bases of the pyramids do not form a regular polyhedron, as we just need equally spaced centroids for the calculation of the gravitational and electric forces between the parcels. It also doesn't matter that there is no perfect distribution of an arbitrary number of points on a sphere, as the results are averaged from all of the parcels.
With the Sun divided into 100,000 parcels, we can then assign the model densities, pressures, temperatures, and elements to the respective parcels, and check the physical properties of the model.
- Is the model in equilibrium, given the gravitational, hydrostatic, and electrostatic forces?
- Do the energy sources look realistic, given the model temperatures?
- Will the model produce helioseismic shadows at .27 and .70 SR?
- Will the model produce a granular layer, 4 Mm deep?
- Will the model produce 4600 K blackbody radiation on the limb, and 6400 K BBR normal to the surface?
Within each model, more specific questions can be asked. For example, if the model states that the 4600~6400 K BBR is generated by ohmic heating in high-pressure plasma, what is the depth at which the necessary pressure is achieved? Given that pressure, what is the spacing between the atoms? Knowing the spacing, and knowing the frequency of photons, we can calculate the atomic speeds. Are those speeds realistic, for that amount of ohmic heating? What is the source of the current? Will the overlying plasma generate the necessary resistance for that much ohmic heating? And above the level at which the 4600 K BBR is being generated, will the plasma be cool enough to only produce absorption lines?