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

We present high-resolution spectroscopic monitoring of the line-profile variations (LPVs) in the He II lambda 5411 emission line of four Wolf-Rayet (WR) 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 sequence (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 relatively narrow emission subpeaks that tend to move from the line centers toward the line edges. We introduce a phenomenological model that depicts WR winds as being made up of a large number of randomly distributed, radially propagating, discrete wind emission elements (DWEEs). This working model is used to simulate LPV patterns in emission lines from a clumped wind. General properties of the LPV patterns are analyzed with the help of novel numerical tools (based on multiscale, wavelet analysis), and simulations are compared to the data. We investigate the effects on the LPVs of local velocity gradients, optical depths, various numbers of discrete wind elements, and a statistical distribution in the line flux from individual elements. We also investigate how the LPV patterns are affected by the velocity structure 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 their 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 (greater than or similar to 10(4)) of DWEEs must be used to account for the LPV. Large velocity dispersions must occur within DWEEs, which give rise to the <(sigma(xi))over bar> similar to 100 km s(-1) line-of-sight velocity dispersions. 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 radial and azimuthal directions, respectively. We find marginal evidence for optical depth effects within inhomogeneous features, with the escape probability being slightly smaller in the radial direction. The kinematics of the variable features reveals lower than expected radial accelerations, with 20 < beta R-*(R.) < 80, where beta and R-* are parameters of the commonly used velocity law upsilon(r) = upsilon(infinity)(1 - R(*)r(-1))(beta), with upsilon(infinity) the terminal wind velocity. The mean duration of subpeak events, 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 emission-line broadening cannot be accounted for by the systematic radial velocity gradient from the accelerating wind. Rather, emission-line broadening must be dominated by the large "turbulent" velocity dispersion sigma(upsilon r) suggested by the LPV patterns. The remaining WR star in our sample (HD 191765) is shown to present significant differences from the others in its LPV pattern. In particular, the associated mean velocity dispersion is found 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 accounted for with our model, requiring a different origin.