While unstable growth rates for both the limiting regimes of short-scale perturbations, , and very long-scale perturbations, , were formerly discussed using simplifying assumptions (i.e.: optically thin perturbations, resp. lowest order Sobolev approximation), we have found that the physically most interesting regime of moderate long-scale perturbations, , which was hitherto only treated within the elaborate analyses of OR and Lucy (1984), is also accessible to a simplified approach using second order Sobolev approximation.
While the standard, first order approach demonstrates the existence of so-called radiative-acoustic waves, the second order treatment shows the inward branch of these waves to be unstable: accidental, positive perturbations in the velocity field of the wind imply larger absolute curvatures; this reduces the optical depth, raises the line force, and consequently leads to a further acceleration.
Somewhat astonishingly therefore, the radiative-acoustic waves according to Abbott (1980) and the line-driven instability seem to have a similar basis, stemming respectively from first and second-order Sobolev approximation. On the other hand, Owocki & Rybicki (1986) showed by using a Green's function analysis that the true signal propagation speed in an unstable wind which is driven by pure absorption lines is the ordinary sound speed. Future work has to clarify this dichotomy.
Our analysis allows one to abandon the usual WKB approximation, and to account for wave stretching. We hope that the simplicity of this approach also leads to an applicability in cases of, e.g., more complex flow geometries, as may occur in line-driven winds from accretion disks in quasars or cataclysmic variables.
© European Southern Observatory (ESO) 1998
Online publication: March 10, 1998