David Van Blerkom, a professor of astronomy at the University of Massachusetts at Amherst, provides a nice overview, focusing on the second part of the query:
"The fact that the outermost region of the sun's atmosphere is at millions of degrees while the temperature of the underlying photosphere is only 6,000 kelvins (degrees C. above absolute zero) is quite nonintuitive. One would have expected a gradual cooling as one moves away from the central heat source. A related question is why, if the corona is so hot, it does not heat up the photosphere until it has an equally high temperature.
"I will address these questions in reverse order. Let us first ask what it means for a gas to have a high temperature. The answer is that temperature is a measure of the average kinetic energy of the gas atoms, that is, a measure of how fast they are moving. A high temperature gas has atoms with a larger average velocity than a low temperature gas of the same composition. We thus infer that the atoms in the corona are moving much more rapidly than those in the photosphere.
"In order for the corona to make the photospheric temperature rise, the coronal gas must cause the photospheric atoms to move faster. It could do so by colliding and mixing with the cooler gas and thus transfering some of its kinetic energy. Another way is also possible: At a temperature of millions of degrees, the gas in the corona is highly ionized, that is, electrons are stripped off neutral atoms and move freely. Because electrons are thousands of times less massive than atoms, the hot electrons have very high speeds. These electrons could travel into the photospheric gas and collide with the atoms there, again increasing their velocities. These two heating mechanisms are called convection and conduction, respectively.
"A gas at millions of degrees also radiates energy; much of it is emitted in the form of very high-energy x-ray photons. X-ray photons impinging on the photosphere could also transfer energy to the gas atoms there. This heating mechanism is radiation.
"Yet the three traditional methods of heating do not raise the photospheric temperature for a simple reason. Suppose, as a thought experiment, one had a thermometer that could measure temperatures of millions of degrees and placed it in the corona. In order to make a temperature measurement, the coronal atoms or electrons must strike the thermometer, or x-ray photons must impinge upon it. The corona, however, has such a low density that the thermometer will almost never be hit. So while the thermometer is technically sitting in a gas that is at 2,000,000 kelvins, it doesn't know it. The gas has a high temperature but a low heat content. There are just not enough atoms around to heat our hypothetical thermometer or the underlying photosphere.
"The question of why the corona has such a high temperature is harder to explain, and probably the last word on the physical mechanism has not yet been given. Most astronomers assume that the gas is heated by the magnetic field that pervades the corona. The solar magnetic field has long been known to cause the sunspot cycle, and the physical shape and activity in the corona also varies with the sunspot cycle. Magnetic fields are known to be able to transfer large amounts of energy to the solar atmosphere, sometimes explosively as in flares. Huge magnetic loops can be seen to rise far into the corona, and it is quite plausible that the solar magnetic field is the ultimate source of physical heating of the corona."
Vic Pizzo of the Space Environment Center in Boulder, Colo., reiterates how mysterious this process is:
"The precise mechanism by which the corona overlying the solar surface is heated to temperatures of one to two million kelvins remains one of the outstanding problems of solar physics. It has long been suspected that turbulent motions in the lower solar atmosphere are propagated outward as waves in some form, which ultimately shock the thin atmosphere above the surface (the photosphere). The shocks thereby dissipate mechanical energy in the waves as heat. When magnetic field lines reconnect, they release energy; some researchers suspect that fine-scale magnetic reconnections above the sun's surface provide the energy to heat the corona.
"Whatever the cause, some heat does indeed leak back toward the solar surface, but the total amount of energy so transported is really quite small, and cannot raise the photospheric temperature very much. The reason for this is the extremely rapid fall-off of mass density with height above the solar surface. That is, although the material in the corona is very hot, it is also very tenuous. Thus, the energy transported back toward the surface is dissipated into an ever increasing mass of material as it works its way down, whereas the heat transported outward is readily dissipated into the vacuum of space. "
Leo Connolly, the chair of the department of physics at California State University, San Bernardino, adds the following information:
"You are quite right about the corona being much hotter than the photosphere of the sun. The photosphere is the outer layer of the sun that produces the visible light we receive. The corona is a large, tenuous layer of gas whose structure is governed by the Sun's magnetic field. The gas in the corona is actually escaping from the Sun, forming the solar wind.
"What accelerates the atoms of gas to high velocity and temperature in the corona? It is likely that the solar magnetic field provides the necessary energy, but the mechanism is poorly understood. At the photosphere, the temperature is about 6,000 kelvins. The region of interest is above the top of the photosphere, where the temperature actually drops (to about 4,500 kelvins at a level of 500 kilometers above the photosphere). At 1,500 kilometers, the temperature starts to rise and by 10,000 kilometers above the photosphere the temperature reaches one million kelvins. Between 1,500 kilometers from the top of the photosphere and 10,000 kilometers is a region called the 'transition zone,' which is where the atoms are accelerated. The corona starts at 10,000 kilometers and extends out to about 10 million kilometers, where the gas finally escapes the sun's gravity and becomes part of the solar wind.
"We know that atoms, stripped of one or more electrons, are trapped by magnetic fields and move along the field lines. But what causes these atoms to be accelerated, producing the high temperatures of the corona, is not understood. All we know is that it definitely occurs in the transition zone."
Last but not least, Jay M. Pasachoff, Chair of the Department of Astronomy at Williams College in Williamstown, Mass., offers a perspective on some of the current attempts (including his own) to solve the riddle of the solar corona:
"One of the nice things about astronomy is that questions that are simply phrased often turn out to be profound. The manner in which the solar corona is heated to millions of degrees Celsius is one of the important unsolved problems of astrophysics. I have conducted experiments during a series of total solar eclipses to address the question, and there has been much theoretical work in this area recently. The problem was much addressed at a NATO Advanced Research Workshop on Observational and Theoretical Problems Related to Solar Eclipses, held in Bucharest, Romania in the first week of June 1996; the proceedings of that workshop will be available in a year or two.
"Basically, one cannot account for the heating of the corona by a radiative flow, so we think the corona is heated by some sort of magnetohydrodynamic (MHD) wave flowing out of lower levels of the sun. Images of the sun in the far ultraviolet and in X-rays (acquired most recently by the Solar and Heliospheric Observatory spacecraft, the Yohkoh satellite, and the NIXT rockets) show that the heating of the corona is localized in solar active regions, which indicates the important role played by the magnetic field. There are perhaps a dozen specific models that have been proposed to account for the high temperature of the corona. These models involve fast-mode MHD waves, slow-mode MHD waves, Alfren waves, et cetera. The older idea that acoustic waves flowing out of lower levels heats the corona was abandoned in the 1970s, when the Orbiting Solar Observatory 8 spacecraft did not see such waves in the chromosphere, the layer just above the photosphere (the apparent 'surface' of the sun in visible light). It remains possible, however, that some acoustic waves can be formed at higher levels.
"My work on the coronal heating problem is summarized in my chapter 'Measurements of 1-Hz coronal oscillations at total eclipses and their implications for coronal heating,' in Mechanisms of Chromospheric and Coronal Heating (Proceedings of the Heidelberg Conference), edited by P. Ulmschneider, E. R. Priest and R. Rosner (Springer-Verlag, 1991). The book also contains many other theoretical and observational papers.