Why is the Sun's Corona so Hot?
The corona around the sun measures a lot hotter than the sun. However, the question shouldn't be worded "Why the Sun's Corona so Hot?", temperature isn't in the formula E=MC2; the question should be worded, "In the Sun's Corona, why are the Atoms Moving so Fast?".
By Douglas Krantz
Starting out, there is no such thing as temperature. At the small scale of atoms, temperature is just a term we civies use for a "Chaotic Relative Motion times Mass". Even though we think of the sun's corona as very hot, each atom making up the corona is just moving very fast.
When we talk about the temperature of a gas in a container, we are really referring to the motion of each atom moving at a certain speed "C2", combined with its atomic weight "M" (atomic weight is kinda referred to as mass). This "temperature" works out to a relative measurement of the amount energy "E".
Albert Einstein gave us a formula: "E=MC2". Each of the letters in the formula isn't a magical unknown, each of the letters in the formula is a representation of a number. When two of the letters have been exchanged for numbers, the number in the third letter can be figured out.
The Sun is Plasma
I'm talking about the sun, because, the sun that affects us directly is an easier concept to grasp than a star somewhere out there.
The sun is a weighty subject. It is so weighty that its gravitational forces pull the atoms very close together. The atoms have speed, at least relative to each other, and being that close together, their electrons keep getting bumped off. This "bumped off" from all the individual atoms means the sun is made up of atom-nuclei (positively charged particles) and free electrons (negatively charged particles).
From the observer's perspective, the electrons are moving at a speed closer to the speed of light. Compared to the movement the electrons, though, the nuclei may as well be just sitting there, in their position.
Because the electrons are moving so fast, at least compared to the nuclei, a few of the electrons on the edge of the sun are continually escaping into space, never to return. These escaped electrons make up part of the "Solar Wind".
The freed electrons, with their electromagnetic and gravitational forces, whiz past the atoms making up the sun's corona. These atoms have their own electromagnetic and gravitational forces. Because both the electrons and the atoms are connected together by these forces, they exchange a little speed as the electron whizzes past the atom.
OK, the electrons are moving very fast compared to the atoms of the corona, and the electrons have very little mass compared to the atoms of the corona, but each time an electron whizzes even near an atom of the corona, the atom is sped up ever so little and the electron is slowed down ever so little.
"Each time" doesn't affect either speed very much. As far as the electrons are concerned, once the electrons have left the area of the corona, there really isn't a lot of any other mass with which to exchange speed. Space is kinda empty.
On the other hand, the atoms making up the corona are slow compared to the electrons. The individual electrons leaving the sun don't hang around very long, but newly escaped electrons keep coming and coming. The speed exchange from each electron is very small, but the speed exchange from the electrons that keep coming and coming accumulates. This increases the atoms' speed, and makes the perceived temperature, of the atoms in the sun's corona, hotter.
There is a problem with this "theory". In order to be an electrically balanced atom, there has to be the same number of electrons as there are protons. There are a lot of protons in the sun; in order for the sun to have electrical balance, though, the sun requires the exact same number of electrons as protons.
With the electrons continually streaming off the sun, never to return, the sun would become very positive. Other words for positive are "not enough electrons for all of the protons".
The sun has to regularly rebalance itself - electrically.
Sun spots, or solar storms, are mostly made up of "atom nuclei" or "positive ions". These positive ions are being expelled from the sun, in the form of sun-spots, on a semi-regular basis. Because the sun keeps making these bursts of ions, the sun would tend to become very negative. Other words for negative are "too many electrons for all of the protons".
Going negative is a relative term. It could mean "going from positive to negative", "going from greatly positive to less positive", or "going from less negative to greatly negative".
Going positive is also a relative term. It could mean "going from negative to positive", "going from greatly negative to less negative", or "going from less positive to greatly positive".
But the sun has to remain electrically balanced.
It could be that the streaming and escaping electrons are causing the sun to rebalance electrically, using sun spots (or solar storms); it could be that sun spots are causing the sun to rebalance electrically, by constantly steaming off the escaping electrons; it could be a combination of each effect, the sun spots and the streaming, escaping electrons, are affecting the other.
How it actually balances is a subject for another thesis.
Heating Up the Corona (Speeding Up the Atoms)
The corona appears to be hotter than what the sun should make it. However, because "heat" really means a "Chaotic Relative Motion times Mass", we really mean that the individual atoms of the corona are moving faster than can be explained by the chaotic motion of the atoms in the sun.
When adding the constant streaming of the escaping electrons, though, this extra "heat' is explained, at least to some extent.