The Heating of the Solar Chromosphere, Plages, and Corona by Magnetohydrodynamic Waves.

The energy radiated from the chromosphere, the corona, and the upper chromosphere is approximately estimated from observational data. The energy carried upward by sound waves generated in the hydrogen convection zone is estimated and found sufficient to balance these losses, though the numerical result is highly uncertain because of its great dependence on the turbulent velocity field The spectrum of this noise is a broad band with maximum near the frequency of 0 Ol cps. The waves propagate in the so-called "fast" mode and become increasingly magnetohydrodynamic in character as they run out through the chromosphere, because of the negative density gradient. Little, if any, energy is emitted by the hydrogen convection zone in the "slow" or "Allve'n" modes, and these modes are, in addition, strongly absorbed in the photosphere. The cross-sections for collisions between neutral atoms and ions in the chromosphere is large, and, as a result, the dissipation of the fast-mode waves by the frictional damping mechanism is very small. The waves build up to shocks, and the dissipation of these shocks is the main energy source for the chromosphere The dissipation of the shocks is worked out by using a similarity principle, in a way analogous to the Brinkley-Kirkwood theory of the dissipation of pure gas- dynamic shocks At great heights, where the magnetic field dominates, the shocks become weaker, the dissipation decreases, and the rays are refracted back downward toward the photosphere. However, at these heights, collisions between shocks must be expected to feed some energy into the slow mode and the Alfve'n mode, and these modes then propagate straight up the magnetic line of force, with essentially no weakening by refraction, and carry energy into the corona. The plages are regions of larger magnetic field, where there is extra generation of noise in the hydrogen convection zone below and where the refraction and shock-collision effects are more important. The spicules seen at the limb of the sun are interpreted as slow-mode disturbances carrying chromospheric material up along the magnetic lines of force into the corona.