What we know of the coronas of stars we know primarily by observing the Sun. The corona of the Sun is a very hot and tenuous wind blowing away from the Sun. The temperature of the solar corona is typically above 1 million degrees Kelvin, which is much higher than the 5800°K effective temperature of the solar photosphere. This wind is very complex and variable, with a structure that changes both with the eleven-year sun spot cycle and with the generation of magnetic structures at the Sun's photosphere. This complexity is masked when we observe the coronas of other stars, which limits what we can learn by studying the coronas of stars other than the Sun.
The existence of a corona is only possible because the outer layers of stars the size of the Sun and smaller are very dynamic; if a star were stable, so that the gas in the star was fixed in place, the energy trapped at its core would escape to the photosphere through the diffusion of radiation. This mechanism only transports energy from hot regions to cooler regions. This means that the temperature of a static star can only decrease with distance from the core, and the temperature away from the photosphere can only drop below the temperature at the photosphere. This is a consequence of thermodynamics. The conservation of energy and the imperative of systems not to decrease their entropy—which means they evolve so that energy is distributed among atoms, electrons, and radiation in the most probable manner—are central tenants of physics. In practice it implies that energy flows from high temperature regions to low temperature regions unless work is done on the system. For static stellar systems, this means that energy in the form of black-body radiation flows from the interior, where the temperature exceed 107 °K, to the surface, where the temperature is generally below 104°K, and into space, which is filled by 2.7° K black-body radiation. For a star to have a corona that is hotter than the photosphere, a dynamic mechanism must be present that channels energy from the interior to the corona through a non-radiative mechanism; for it to emit x-rays, it must produce a temperature above about 106°K.
In stars the size of the Sun and smaller, the engine that drives this alternative channel for energy flow is convection. If these stars were static, the temperature gradient in the outer layers of their interior would be so steep that they would be unstable to convection, so these stars boil, and energy is transported from the interior to the photosphere as hot gas from the interior swells and rises to the photosphere and cool surface gas at the photosphere shrinks and sinks to the interior. From the standpoint of thermodynamics, the system has a higher entropy—a more-probable state—if the outer regions of the star convect energy to the surface. In this state, energy exists not only in the thermal energy and radiation within the gas, but in the bulk motion of the gas as it flows to the surface and then sinks back to the interior.
On its face, this may seem a small point, because the bulk of the energy in the convective envelope is still in the form of radiation and thermal energy. But an ionized gas that is convected has another place to stick energy, and this is in a large-scale magnetic field. Conducting fluids in motion can generate a magnetic field, driving some of the energy associated with convective motion into the magnetic field. As the convection does more work on the magnetic field, driving more energy into the magnetic field, the magnetic field strength increases (the energy density of a magnetic field is proportional to the square of its strength).
A fact about a plasma threaded by a magnetic field is that the stronger the magnetic field becomes, the more buoyant the plasma becomes. Magnetic fields exert a pressure in the plasma without contributing an appreciable density (none under Newtonian gravity, and slight under general relativity). This means that if we create a localized magnetic field in a plasma, the gas containing the magnetic field will expand until the pressure of the gas and magnetic field in the magnetized region equals the gas pressure of the surrounding plasma. This means that the density of the gas in the magnetized region is less than in the surrounding plasma, so the region with magnetic field is buoyant.
The magnetic field continues to strengthen until its buoyancy can overcome the convective motion of the star's atmosphere. A star loses energy trapped in the magnetic field when the plasma carrying the magnetic field rises to the surface of the star. This expulsion of magnetic field appears as sun spots at the photosphere of a star and in the loops of magnetic field connecting these spots. This produces the familiar prominence, which is a loop of cool gas and magnetic field arching over the photosphere of a star. These expelled magnetic fields are the energy source that heats the corona to such extraordinary temperatures.
So convection splits the flow of energy from a star's interior into two channels: the transport of hot gas to the photosphere and cold gas to the interior, which transports the bulk of the energy released by a star, and the creation and expulsion of energy-dense magnetic fields.
How the energy in a magnetic field is converted into the thermal energy seen in the corona of the Sun and other stars remains a topic of active research. Many theories have been developed to explain how the magnetic fields at the Sun's photosphere convert their energy into the thermal energy seen in the solar corona, but current instruments cannot fully test all of these theories. The main point is that the magnetic fields have a lower energy density than the surrounding gas when they are under the photosphere, but they have a much greater energy density once they rise above the photosphere into the tenuous atmosphere, so when a magnetic field dissipates its energy into the surrounding gas, it can raise the temperature of the gas far above the temperature of the photosphere.
With temperatures above 106°K, the coronas of the Sun and other stars emits x-rays. The dominant mechanisms are bremsstrahlung, which is the release of light when an electron passes by an ion, and atomic line radiation. The luminosity of a star in the x-ray ranges from 1027 to 1031 ergs s-1, which contrasts with the total luminosity of 4× 033 ergs s-1 of the Sun. The x-ray emission from a star is therefore always a very small fraction of the total energy generated by a star.
By measuring the power and the spectrum of x-rays emitted by a star, we can measure the density, temperature, and composition of the star's corona. This has been accomplished for many star; the current crop of x-ray observatory has enabled us to measure to high precision the spectral lines produced by electron transitions within elements such as iron. Clearly the measurement of temperature and density give us information about a star that is different from the measurements of temperature we get through optical observations, which is a measurement of conditions at the photosphere of a star.
Measure of composition may seem redundant, because why would the composition differ from the composition at the photosphere? In fact, the composition of the corona is different, and the reason is that the forces that drive matter from the photosphere into the corona depend both on the mass and the charge of the ions in the plasma. For instance, as a magnetic field changes its structure, it generates electric fields that accelerate ions with a high ratio of electric charge to mass more that ions with a low ratio. Measuring the difference in composition between the corona and the photosphere of a star tells us something about the processes converting magnetic field into hot plasma.