4. Short-scale vs. long-scale perturbations
Carlberg (1980) pointed out that the growth of optically thin, short-scale perturbations (OR) should saturate at small velocity amplitudes of a few thermal speeds. By then, the perturbed gas is essentially shifted into the unshadowed continuum, and any further velocity shift does not provide more flux or force.
In contrast, the long-scale perturbations analysed in the previous section can grow to much larger amplitudes before they become optically thin.
This suggests that the fast-growing, short-scale perturbations can be considered as noise superimposed on the process of a slow and coherent tilt of the thermal band over large distances, as induced by perturbations with . This view is supported by numerical simulations of O supergiant winds where a spectrum of base frequencies is injected into the flow (Feldmeier et al. 1997). Here, the longest waves grow into saturation, giving rise to shocks with velocity jumps of up to .
Obviously, one has to ensure that the growth time of such long-scale perturbations is still short as compared to the flow time. For O star winds, the longest base perturbations which can still grow into saturation give typical distances between subsequent, strong reverse shocks of at distances from the star where the wind has essentially reached its terminal speed (note: wavelength stretching). On the other hand, optically thin perturbations which grow at maximum rate give structural length scales in the outer wind of shorter than .
Furthermore, it is presently not clear whether velocity amplitudes are the most relevant measure of importance of the wind structure, e.g., because only a very small amount of wind material is actually involved in such large velocity amplitudes (Owocki et al. 1988). Thus other measures, for example dissipation of wind kinetic energy, might be more strongly influenced by the structure at smaller scale.
© European Southern Observatory (ESO) 1998
Online publication: March 10, 1998