In this chapter we shall develop fundamental concepts for describing relativistic astrophysical outflows. In order for a flow to be accelerated to high Lorentz factors the internal energy per baryon at the flow injection point must largely exceed unity. This internal energy may have a thermal origin as, e.g., in hydrodynamical fireball models, or a magnetic origin, as in pulsar winds and outflows from rotating black holes. A basic question in the former case is how to avoid excessive mass loading. A key issue in the latter case is the conversion of magnetic energy to kinetic energy. Observations seem to indicate that collimation is a generic feature of astrophysical outflows, suggesting that confinement by the ambient medium may play an important role in the dynamics of the system. In the following only steady flows will be considered, for which simple analytic solutions can be obtained.

Hydrodynamic fireballs

Let us consider first an unmagnetized spherical wind. In general, the wind may consist of a mixture of baryons, radiation and electron–positron plasma, which in sufficiently compact regions can be taken to be in local equilibrium. The flow is then characterized by the proper baryon density nb, pressure p, temperature T and velocity uμ = (γ, γv). We further assume that the flow is adiabatic and not subject to any external forces, including gravity (the effect of gravity will be considered in the following sections).