Wind inhomogeneities in Wolf-Rayet stars. II. Investigation of emission-line profile variations

We present high-resolution spectroscopic monitoring of the line-profile var iations (LPVs) in the He II lambda 5411 emission line of four Wolf-Rayet (W R) stars of the WN sequence (HD 96548, HD 191765, HD 192163, and HD 193077) and in the C III lambda 5696 emission line of five WR stars of the WC sequ ence (HD 164270, HD 165763, HD 192103, HD 192641, and HD 193793). The LPVs are shown to present systematic patterns: they all consist of a number of r elatively narrow emission subpeaks that tend to move from the line centers toward the line edges. We introduce a phenomenological model that depicts W R winds as being made up of a large number of randomly distributed, radiall y propagating, discrete wind emission elements (DWEEs). This working model is used to simulate LPV patterns in emission lines from a clumped wind. Gen eral properties of the LPV patterns are analyzed with the help of novel num erical tools (based on multiscale, wavelet analysis), and simulations are c ompared to the data. We investigate the effects on the LPVs of local veloci ty gradients, optical depths, various numbers of discrete wind elements, an d a statistical distribution in the line flux from individual elements. We also investigate how the LPV patterns are affected by the velocity structur e of the wind and by the extension of the line-emission region (LER). Eight of the stars in our sample are shown to possess strong similarities in the ir LPV patterns, which can all be explained in terms of our simple model of local wind inhomogeneities. We find, however, that a very large number (gr eater than or similar to 10(4)) of DWEEs must be used to account for the LP V. Large velocity dispersions must occur within DWEEs, which give rise to t he <(sigma(xi))over bar> similar to 100 km s(-1) line-of-sight velocity dis persions. We find evidence for anisotropy in the velocity dispersion within DWEEs with sigma(upsilon r) similar to 4 sigma(upsilon theta), where sigma (upsilon r) and sigma(upsilon theta) are the velocity dispersions in the ra dial and azimuthal directions, respectively. We find marginal evidence for optical depth effects within inhomogeneous features, with the escape probab ility being slightly smaller in the radial direction. The kinematics of the variable features reveals lower than expected radial accelerations, with 2 0 < beta R-*(R.) < 80, where beta and R-* are parameters of the commonly us ed velocity law upsilon(r) = upsilon(infinity)(1 - R(*)r(-1))(beta), with u psilon(infinity) the terminal wind velocity. The mean duration of subpeak e vents, interpreted as the crossing time of DWEEs through the LER, is found to be consistent with a relatively thin LER. As a consequence, the large em ission-line broadening cannot be accounted for by the systematic radial vel ocity gradient from the accelerating wind. Rather, emission-line broadening must be dominated by the large "turbulent" velocity dispersion sigma(upsil on r) suggested by the LPV patterns. The remaining WR star in our sample (H D 191765) is shown to present significant differences from the others in it s LPV pattern. In particular, the associated mean velocity dispersion is fo und to be especially large (<(sigma(xi))over bar> similar to 350 km s(-1), compared to <(sigma(xi))over bar> similar to 100 km s(-1) in other stars). Accordingly, the LPV patterns in HD 191765 cannot be satisfactorily account ed for with our model, requiring a different origin.