"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.