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(Abridged) The behaviour of mass loss across bi-stability jump is a key uncertainty in models of massive stars. While an increase in mass loss is theoretically predicted, this has so far not been observationally confirmed. However, radiation-driven winds of massive stars are known to exhibit clumpy structures triggered by the line-deshadowing instability (LDI). Wind clumping affects empirical mass-loss rates inferred from density square-dependent spectral diagnostics. If clumping properties differ significantly for O and B supergiants across the bi-stability jump, this may help alleviate discrepancies between theory and observations. We investigate with analytical and numerical tools how the onset of clumpy structures behaves in the winds of O supergiants (OSG) and B supergiants (BSG) across the bi-stability jump. We derive a scaling relation for the linear growth rate of the LDI for a single optically thick line and apply it in both regimes. We run 1D time-dependent line-driven instability simulations to study the non-linear evolution of the LDI in clumpy OSG and BSG winds. Linear perturbation analysis for a single line shows that the LDI linear growth rate scales strongly with stellar effective temperature and terminal wind speed. This implies significantly lower growth rates for (cooler, slower) BSG winds than for OSG winds. This is confirmed by the non-linear simulations, which show significant differences in OSG and BSG wind structure formation, with the latter characterized by significantly weaker clumping factors and lower velocity dispersions. This suggests that lower correction factors due to clumping should be employed when deriving empirical mass-loss rates for BSGs on the cool side of the bi-stability jump. Moreover, the non-linear simulations provide a theoretical background toward explaining the general lack of observed intrinsic X-ray emission in (single) B star winds.
The influence of the wind to the total continuum of OB supergiants is discussed. For wind velocity distributions with beta > 1.0, the wind can have strong influence to the total continuum emission, even at optical wavelengths. Comparing the continuum
We investigate the effects of stellar limb-darkening and photospheric perturbations for the onset of wind structure arising from the strong, intrinsic line-deshadowing instability (LDI) of a line-driven stellar wind. A linear perturbation analysis sh
Mass-loss rates and terminal wind velocities are key parameters that determine the kinetic wind energy and momenta of massive stars. Furthermore, accurate mass-loss rates determine the mass and rotational velocity evolution of mass stars, and their f
We study the origin of the observed bi-stability jump in the terminal velocity of the winds of supergiants near spectral type B1. To this purpose, we have calculated a grid of wind models and mass-loss rates for these stars. The models show that the
We probe the radial clumping stratification of OB stars in the intermediate and outer wind regions (r>~2 R*) to derive upper limits for mass-loss rates, and compare to current mass-loss implementation. Together with archival multi-wavelength data, ou