As we pointed out in §1.6, most of our knowledge about the astrophysical Universe is based on the electromagnetic radiation that reaches us from the sky. By analysing this radiation, we infer various characteristics of the astrophysical systems from which the radiation was emitted or through which the radiation passed. Hence an understanding of how radiation interacts with matter is very vital in the study of astrophysics. Such an interaction between matter and radiation can be studied at two levels: macroscopic and microscopic. At the macroscopic level, we introduce suitably defined emission and absorption coefficients, and then try to solve our basic equations assuming these coefficients to be given. This subject is known as radiative transfer. At the microscopic level, on the other hand, we try to calculate the emission and absorption coefficients from the fundamental physics of the atom. Much of this chapter is devoted to the macroscopic theory of radiative transfer. Only in §2.6, do we discuss how the absorption coefficient of matter can be calculated from microscopic physics. The emission coefficient directly follows from the absorption coefficient if the matter is in thermodynamic equilibrium, as we shall see in §2.2.4.
Theory of radiative transfer
Let us first consider how we can provide the mathematical description of radiation at a given point in space. It is particularly easy to give a mathematical description of blackbody radiation, which is homogeneous and isotropic inside a container.