The idea behind sunspots, in mainstream theory, is that is the location of a 'tangle' in the magnetic field.
That would technically be true as I see things as well.
This could very well be the source of many coronal loops, as the sunspots are believed to be a place where the magnetic field pops out (or into) the photosphere in unusually high densities.
I tend to agree that the loop originate beneath the photosphere. This brings me I suppose the the notion of 'solar moss', and articles I've read on this topic. It seems to me that the base of the loops, and also the solar moss activity begin underneath the photosphere.
When you talk about "density" here are you referring to the strength of the magnetic field, the density of the plasma in the loops, or a combination of both of these things?
The reason the sunspot itself is cooler than the surrounding region is dependent upon how the photosphere gets it's energy from the interior. This is believed to be via convection (helio-siesmology supports this idea btw).
I agree that convection is bringing heat to the surface of the photosphere, but those same heliosiesmology studies suggest that the plasma flows "flatten out" about 4800KM, and show a "stratification subsurface" located about about .995R which varies with the solar cycle.
When the convection current rises and finds this magnetic tangle, it gets diverted, shut down, disturbed, etc. The end result is less efficient energy transport to that particular region, so it cools slightly compared to it's surroundings.
I suppose the part that doesn't seem to "add up" to me is the fact that the higher energy wavelengths require that these loops reach millions (sometimes up to 20 million) degrees Kelvin to be able to emit such photons. That seem consistent with 'hot' plasma, but not cooler regions. From a visual perspective, the sunspots themselves also seem to have a distinct edge (seen in penumbral filaments) that stop emitting light at particular depth, including all the edges of the sunspot. I have however seen plenty of evidence that these regions do show evidence of cooler plasma, and that must be "explained" in some way shape or form.
This cooling mechanism is independent from any heating mechanism any coronal loops may have on the corona.
Hmm. It might make sense to suggest that coronal loops "carry away" some of the heat and distribute it in the corona, so I'm not sure how you're certain that they are "independent" processes.
And we don't entirely understand how the coronal loops heat the corona in the first place, but my guess is that's it's due in part to the loops moving rapidly through it, due to the suns rotation and the loop's changing geometry.
The one thing that seems clear to me about this sunspot/coronal loop relationship is that there are many times where "activity" can be observed in 195A, and nothing much is happening as it relates to sunspot activity. All sunspots however tend to be congregated, in and around these active regions. The may not be directly related, but there is an "indirect" relationship between them. The other thing that seems rather clear is that these active regions are emitting energy that is consistent with plasma that has been heated to millions of degrees, and the energy received on Earth *increases* during sunspot activity and active solar cycles. There is excess energy being released in the active part of the solar cycle, and the sunspots are somehow related to this high energy activity.