Theoretical Astrophysics

Introduction

The analysis of the spectra of astrophysical systems provides valuable information about their composition and dynamics. The purpose of this brief chapter is to introduce some basic concepts of atomic and molecular spectroscopy that are needed to appreciate the role played by spectra in astrophysics. The ideas developed in this chapter will be used in the study of stellar atmospheres, the interstellar medium (Vol. II), and in extragalactic astronomy (Vol. III).

Width of Spectral Lines

When a system makes a transition between two discrete energy levels E2 and E1 emitting a single photon, the frequency of the photon should be equal to ω = (E2 - E1)/ħ. Such a transition should lead to a sharp spectral line of infinite intensity and zero width. In reality, the frequency of the photon that is emitted is not precisely determined and the observed spectral line will have a finite width and intensity. The nature of the width of the spectral line contains important information about the state of the physical system.

The finite width of the spectral line can arise because of several reasons, among which three particular processes are of importance in astrophysics. To begin with, all energy levels (except the ground state) have a finite intrinsic width, that is, the energy of an excited state can be ascertained within only a finite accuracy ΔE2 around a mean value E2. This is because all excited states have a nonzero probability per second P for making a spontaneous transition to lower energy levels.