On wind-type flows in astrophysical jets. III - Temporal evolution of perturbations and the formation of shocks

The temporal evolution of disturbances in a spherically symmetric polytropic wind from a central object is studied. Such disturbances may be due to localized momentum addition/subtraction, as, for example, by MHD waves, heating/cooling mechanisms in the outflow, or localized deviations from spherical symmetric expansion. The evolution of an initial perturbed state to a continuous or discontinuous final equilibrium state, as predicted by previous analytic calculations for stationary flows, is followed. It is shown that some of the predicted discontinuous equilibrium states are not physically accessible, while the attainment of the remaining equilibrium states depends on both the temporal and the spatial parameters characterizing the perturbation. The results are derived for solar conditions, but in fact can be applied to outflows in other astrophysical systems. In particular, applications to the solar wind and flows in astrophysical jets are discussed.