On the steady nature of line-driven disk winds

We perform an analytic investigation of the steady nature of line-driven disk winds, independent of hydrodynamic simulations. Our motive is to determine whether line-driven disk winds can account for the wide/broad UV resonance absorption lines seen in cataclysmic variables (CVs) and quasi-stellar objects (QSOs). In both CVs and QSOs, observations generally indicate that the absorption arising in the outflowing winds has a steady velocity structure on timescales exceeding years ( for CVs) and decades ( for QSOs). However, published results from hydrodynamic simulations of line-driven disk winds are mixed, with some researchers claiming that the models are inherently unsteady, while other models produce steady winds. The analytic investigation presented here shows that the line-driven disk winds can be steady if the accretion disk is steady and capable of locally supplying the corresponding mass flow. In particular, we show that a gravitational force initially increasing along the wind streamline, which is characteristic of disk winds, does not imply an unsteady wind. The steady nature of line-driven disk winds is consistent with the one-dimensional streamline disk wind models of Murray and collaborators and the 2.5-dimensional time-dependent models of Pereyra and collaborators. This paper emphasizes the underlying physics behind the steady nature of line-driven disk winds using mathematically simple models that mimic the disk environment.