JP Michael wrote: ↑Wed Dec 23, 2020 2:26 am
Except no-one has explained a suitable mechanism as to why the corona is hotter than the photosphere, let alone a mechanism as to how the heat from the core radiates outward to the photosphere, cooling, then suddenly reheats at the corona.
There are two things here:
a) a mechanism for how the heat from the Sun radiates outward to the photosphere, cooling; and
b) a mechanism for how the corona is heated in a short distance to 1MK
With regard to a), I think there is an extremely credible mechanism (or rather two extremely credible mechansims which dominate in different regions). The first mechanism which operates throughout the sun is radiation and conduction (they amount to the same thing, the transfer of energy outwards by photon and electron collisions without the bulk flow of matter. If energy is being created in the core then, of course, the core temperature will be higher than the surface, and there will be a temperature gradient radially throughout the Sun. Since for any radial distance element the equilibrium radiation spectrum represents on average more energetic photons radially outwards than radially inwards, there is a net flow of energy outwards. By considering free-free absorption and Compton scattering for the various elements present, it is possible to determine the opacity at any depth and therefore the mean free path of a photon before absorption or scattering. The energy flux can then be calculated. For the Sun, radiation transport of energy is sufficient uop the bottom of the convection zone, but for more masssive stars radiation is insufficient to transport all the energy on its own and those stars have convective cores.
The second mechanism is therefore convection. Convective processes in compressible fluids cannot start until the temperature gradient is such that a rising element will not cool more rapidly adiabatically than the temperature of the surroundings falls with distance. At that point convection will become established. At the radial distance in the Sun where radiative transport becomes insufficient to transport all the heat, convective transport is intiated (although the actual temperature gradient for this condition is not very different from the adibatic temperature gradient) and continues up to the top of the photosphere where it is observed as granulation.
All of this is laid out in far more detail than I can possibly reproduce in a forum post in Tayler,
The Stars: their structure and evolution, which I have recommended before. If you are interested in solar physics, it's a great starting point, with no maths more difficult than calculus.
With regard to b), everyone of course is in the same boat, as the vast majority of the Sun's energy is radiated from the photosphere at about 5800K and therefore any alternative heating mechanism would have to heat the photosphere to 5800K, and then in a relatively short distance the corona to 1MK. It's not that there are no credible mechanisms to heat the corona, but that there isn't enough data to select between the hypotheses we do have. The amount of energy to heat the corona is tiny compared with the total energy output of the Sun, and observations fro SOHO indicate that the coronal heating energy is derived from the Sun's magnetic field, but the details remain a work in progress.
I don't think the coronal heating problem on its own is any impediment to the credible and tested means for generating 10^26W that requires no electrical heating of the photosphere, especially since the coronal problem exists independent of the source of heating of the photosphere.