Diagnostics of the unstable envelopes of Wolf-Rayet stars

Context. The envelopes of stars near the Eddington limit are prone to various instabilities. A high Eddington factor in connection with the iron opacity peak leads to convective instability, and a corresponding envelope inflation may induce pulsational instability. Here, we investigate the occurrence and consequences of both instabilities in models of Wolf-Rayet stars. Aims. We determine the convective velocities in the sub-surface convective zones to estimate the amplitude of the turbulent velocity at the base of the wind that potentially leads to the formation of small-scale wind structures, as observed in several Wolf-Rayet stars. We also investigate the effect of stellar wind mass loss on the pulsations of our stellar models. Methods. We approximated solar metallicity Wolf-Rayet stars in the range 2-17 M-circle dot by models of mass-losing helium stars, computed with the Bonn stellar evolution code. We characterized the properties of convection in the envelope of these stars adopting the standard mixing length theory. Results. Our results show the occurrence of sub-surface convective regions in all studied models. Small (approximate to 1 km s(-1)) surface velocity amplitudes are predicted for models with masses below approximate to 10 M-circle dot. For models with M greater than or similar to 10 M-circle dot, the surface velocity amplitudes are of the order of 10 km s(-1). Moreover we find the occurrence of pulsations for stars in the mass range 9-14 M-circle dot, while mass loss appears to stabilize the more massive Wolf-Rayet stars. We confront our results with observationally derived line variabilities of 17 WN stars, of which we analysed eight here for the first time. The data suggest variability to occur for stars above 10 M-circle dot, which is increasing linearly with mass above this value, in agreement with our results. We further find our models in the mass range 9-14 M-circle dot to be unstable to radial pulsations, and predict local magnetic fields of the order of hundreds of gauss in Wolf-Rayet stars more massive than approximate to 10 M-circle dot. Conclusions. Our study relates the surface velocity fluctuations induced by sub-surface convection to the formation of clumping in the inner part of the wind. From this mechanism, we expect a stronger variability in more massive Wolf-Rayet stars, and a weaker variability in corresponding low metallicity Wolf-Rayet stars.