# Spectrum formation in clumped stellar winds: consequences for the analyses of Wolf-Rayet spectra

### W.-R. Hamann and L. Koesterke

Inhomogeneous Wolf-Rayet type stellar winds are modeled in a first-order approximation, assuming that small-scale clumps are distributed with a constant volume filling factor within an interclump space which is void. Model calculations as well as analytical considerations show that the main spectral features, i.e. the strength of the emission lines, are approximately invariant if the enhanced density in the clump medium is compensated by a suitable scaling of the mass-loss rate. Hence, to the first order the mass-loss rate is the only empirical parameter which is affected by the application of clumped models for spectral analyses. In clumpy atmospheres the electron-scattering line wings become weaker than in homogeneous models. This effect can be used to determine the degree of clumping empirically. We select Wolf-Rayet stars of different spectral subclasses and compare their spectra with adequate models, varying the clumpiness. In all cases, the homogeneous model can be definitely ruled out because it predicts electron scattering wings that are significantly stronger than observed. If the clumps fill 1/4 of the volume, the line wings are in reasonable agreement, while for a filling factor of 1/16 the wings are possibly too shallow, but still compatible with the observation within the error margin. Adopting a filling factor of 1/4 (i.e. the density in the clumps is enhanced by a factor of four, compared to a smooth model with same mass-loss rate) as a typical value, the empirical mass-loss rates become smaller by a factor of two than obtained with homogeneous models.

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