9.1: Introduction

In Part I, we discussed the internal structure and history of stars with little reference to the actual appearance of the stars themselves. Yet virtually all we know of stars rests on the information that we receive from their surfaces, and so we need to understand those processes that affect the light radiated into space. At several points in the evolution of stars, their evolution was determined by the efficiency with which radiation could be lost from their atmospheres. Thus, the structure of the atmosphere may be expected to play a role in the evolution of the star itself. In addition, for some stars, the region which we call the atmosphere represents a substantial fraction of the radial extent of the star, so that the surface boundary conditions on the equations of stellar structure are set by the atmospheric structure. When this fact is important, the very meaning of a stellar radius becomes intertwined with the details of the atmospheric structure. With the absence of a clearly defined radius, the notion of an effective temperature linked to the stellar luminosity and radius becomes meaningless. Thus, the physical situation near the surface of a star must be treated differently from that of the interior. This transition zone from the relatively simple physics of the stellar interior to the emptiness of interstellar space is commonly known as the stellar atmosphere.

There is a tendency to think of the difference between the interior and the atmosphere of a star as distinct, as it is with earth. To be sure, the relative extent of the solar atmosphere compared to the interior is similar to that of earth, but the similarity ends there. There is no sharp interface between stellar atmospheres and interiors as commonly exist with planets. There is no material phase change at the interface. Indeed, for stars, the distinction between atmospheres and interiors is denoted by the failure of certain assumptions used in the study of stellar interiors.

The solution of the problem posed by the surface layers of a star is similar to that for the interior. We have to describe the behavior of the state variables \(\mathrm{P}\), \(\mathrm{T}\), and \(\rho\) with position in the star. However, an additional problem is posed by the atmosphere. We have to describe the energy distribution of photons as they leave the star, for this specifies the appearance of the star which is the fundamental tie with observation. Only if this description of the stellar spectrum agrees with that which is observed can we say that we have provided a successful description of the star.

The approach to finding the structure of the atmosphere can be largely divided into two parts. First, one determines the flow of radiation through the atmosphere, given the structure of the atmosphere. Second, having determined the radiation field throughout the surface layers, one corrects the atmospheric structure so that energy is conserved at all levels of the atmosphere. Since most of the energy is carried by radiation, the second condition usually amounts to the imposition of radiative equilibrium throughout the atmosphere. One then uses the improved structure to correct the radiation field and repeats the process until a self-consistent model is found. To carry out this procedure it is necessary to make some assumptions about the conditions that prevail in this transition zone between the interior and the space surrounding the star.