The purpose of this chapter is to describe and explain some of the fundamental properties of the stellar wind models. This is done by deriving the equations for idealized simple winds. For these simple models the equation of motion can be solved easily so that the velocity and density structures of the wind are known. The solutions show how the velocities and densities depend on the forces in the wind. They also show that the mass loss rate of a stationary wind model is uniquely determined by the solution of the equations, i.e., given the lower boundary conditions in the wind and the forces and energy gains and losses, a physically realistic solution exists for only one specific value of the mass loss rate. The simple solutions discussed in this chapter show how this so-called critical solution depends on the forces and the energy of the wind. Although only simplified models are considered in this chapter, the conclusions are qualitatively valid for the more complicated and detailed models which will be described in later chapters.
Section 3.1 describes the simplest possible model of an isothermal wind in which gas pressure provides the outward force. In §§ 3.2, 3.3 and 3.4 the effects of additional forces in isothermal wind models are considered; first as simple analytic expressions, such as a force which varies as r-2, or as v dv/dr, and later in more general terms.