Further criteria for the existence of steady line-driven winds

In an earlier paper we showed that steady line-driven disk wind solutions can exist by using simple'' models that mimic the disk environment. Here I extend the concepts introduced in the earlier paper and discuss many details of the analysis of the steady or unsteady nature of one-dimensional line-driven winds. This work confirms the results and conclusions of the earlier paper and is thus consistent with the steady nature of the one-dimensional streamline line-driven disk wind models of Murray and collaborators and the 2.5 dimensional line-driven disk wind models of Pereyra and collaborators. When including gas pressures effects, as is routinely done in time-dependent numerical models, I find that the spatial dependence of the nozzle function continues to play a key role in determining the steady or unsteady nature of supersonic line-driven wind solutions. I show here that the existence or nonexistence of local wind solutions can be proved through the nozzle function without integrating the equation of motion. This work sets a detailed framework with which we will analyze, in a following paper, more realistic models than the simple'' models of the earlier paper.