## Elements of radiation transport theory

Radiation is being emitted and absorbed in the Sun in all layers. However, we see radiation mostly from the surface. Most radiation from below is absorbed before it reaches the surface. To understand what we are seeing when we look at the Sun, we need to understand about the interaction between radiation and matter. For example, much of what we know about the solar atmosphere comes from studying spectral lines as well as the continuum. In studying how radiation interacts with matter, known as radiation transport theory, we see how to use spectral lines

The Sun. [NOAO/AURA/NSF]

The Sun. [NOAO/AURA/NSF]

Corona

Photosphere Chromosphere]

Corona

Photosphere Chromosphere]

Basic structure of the Sun.

Basic structure of the Sun.

= N a to extract detailed information about the solar atmosphere.

We first look at the absorption of radiation by atoms in matter. We can think of the atoms as acting like small spheres, each of radius r (Fig. 6.3). Each sphere absorbs any radiation that strikes it. To any beam of radiation, a sphere looks like a circle of projected area vr2. If the beam is within that circle, it will strike the sphere and be absorbed. We say that the cross section for striking a sphere is a = ^r2. The concept of a cross section carries over into quantum mechanics. Instead of the actual size of an atom, we use the effective area over which some process (such as absorption) takes place. So then r would be how close the photon would have to be to the atom in order to be absorbed.

We consider a cylinder of these spheres, with the radiation entering the cylinder from one end. We would like to know how much radiation is absorbed, and how much passes through to the far end. We let n be the number of spheres per unit volume. The cylinder has length l and area A, so the volume is Al. The number of spheres in the cylinder is

In making this definition, we have assumed that the incoming beam can "see" all the spheres. No sphere blocks or shadows another. We are assured of little shadowing if the spheres occupy a small fraction of the area, as viewed from the end. That is a(tot)

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