I dont follow. walk me through it.
Fair enough. I think it's *imperative* that we start with a *working model*. Please allow me to include that short explanation and video for anyone that hasn't already looked at it. It's absolutely necessary to understand the basic idea, and to see a working "corona" in action in the lab:
Now we can add a few double layers to Birkeland's model, and I think you'll be understand how his model can be applied to SDO images a lot better.
Let's start with there existing a temperature differential as you describe, with the core of the sun being cooler than the photosphere.
It might be easier to start with the video and notice the temperature differential between the surface of the solid sphere, and the corona around the sphere. The corona around the sphere may be "hot", but it's not particularly "dense" compared to the surrounding sphere. If all the molecules on the surface of the sphere were at the same temperature as the corona in that video, the spheres would melt. Fortunately that doesn't happen.
To properly understand the model that I'm proposing, you're going to have to add a few extra "double layers" between the blue corona that we can observe in that video, and the solid surface.
Each of the various double layers in the solar atmosphere is arranged by atomic weight.
The corona contains the lightest elements, mostly hydrogen, and the other "solar wind" particles that are flowing up from below. It also contains many "coronal loops", but we'll save the surface to surface discharge conversation for a later date.
The chromosphere is another current carrying double layer that is mostly made of helium, but like all layers, there's a constant flow of various particles through that plasma layer.
The "photosphere" is mostly composed of neon, but again a lot of various elements flow through it, and it's essentially "white" due to the emission of all the various wavelengths of the various elements that are present in the neon double layer.
Below that neon double layer that you're calling a "photosphere", sits another double layer of silicon plasma that is probably quite "deep" compared to any of the other double layers.
Each of the various double layers is more dense, and cooler as we work down from the corona towards the solid surface.
None of the various double layers are particularly "dense" compared to the solid surface itself.
The solid surface is still the cathode surface as it is with that video, and all the various double layers are "lit up" due to the flow of current through double layers.
The mainstream already concedes that the corona is hotter than the chromosphere, and the chromosphere is hotter than the surface of the photosphere. That is because the flow of current from the cathode is the ultimate source of heat, and it arrives in the form of kinetic energy that is transferred to material in the atmosphere by the high speed electrons flowing off the sphere.
The net result of the kinetic energy flow is a movement of particles up and away from the surface of the cathode, and toward "space".
the photosphere radiates heat, some of which escapes, some of which heats the core.
The corona in that video also "radiates heat", but the density of the material precludes it from "melting" the solid cathode.
How does the core get rid of that heat to prevent it from reaching thermal equalibrium with its surroundings?
It's technically ridding itself of heated particles by moving them away from the cathode surface. As the high speed electrons slam into particles in the atmosphere it pushes them outward, away from the cathode surface. We see that occurring rapidly at the surface of the photosphere. It gives the surface an appearance of "boiling water".
For example, the mainstream understanding is that the corona is heated by magnetic forces from the core,
So why is it that we sometimes observe much *cooler* material inside of "sunspots"?
The mainstream has a bad habit of denying the role of electrical *current* in solar physics and instead they try to make magnetic lines do all sorts of various heating and cooling "magic tricks". Alfven actually called their mathematical models "pseudoscience" till the day that he died. He actually made all "reconnection" maths completely irrelevant and obsolete with his double layer paper, not that the mainstream ever cared.
Alfven like Birkeland before him used *circuit theory* and electric fields to explain the temperature gradients in the solar atmosphere, not "magnetic lines".
as is the photosphere. because the photosphere is not as fully ionized, it is able to more effectively radiate that heat away to space. the corona is instead insulated in a way by the ionization and stays hot.
The corona (and other various double layers) are not staying hot because they are "insulated". The corona is staying "hot" because of the electrons (cathode rays) that are flowing through it, and the coronal loops that pump heat into all the various double layers. Just as is true with that working model in the video, the moment that we switch off the electric field, the plasma atmosphere ceases to exist, and the light show is over.