Theoretical wind clumping predictions of OB supergiants from line-driven instability simulations across the bi-stability jump

Context. The behaviour of mass loss across the so-called bi-stability jump, where iron recombines from Fe IV to Fe III, is a key uncertainty in models of massive stars. Specifically, while an increase in mass loss is theoretically predicted, this has not yet been observationally confirmed. However, radiation-driven winds of hot massive stars are known to exhibit clumpy structures triggered by the line-deshadowing instability (LDI). This wind clumping severely affects empirical mass-loss rates inferred from rho(2)-dependent spectral diagnostics. Thus, if clumping properties differ significantly for O and B supergiants across the bi-stability jump, this may help alleviate current discrepancies between theory and observations. Aims. We investigated with analytical and numerical tools how the onset of clumpy structures behave in the winds of O supergiants (OSG) and B supergiants (BSG) across the bi-stability jump. Methods. We derived a scaling relation for the linear growth rate of the LDI for a single optically thick line and applied it in the OSG and BSG regime. We ran 1D time-dependent line-driven instability simulations to study the non-linear evolution of the LDI in clumpy OSG and BSG winds. Results. Linear perturbation analysis for a single line shows that the LDI linear growth rate Omega scales strongly with stellar effective temperature and terminal wind speed: Omega proportional to nu(2)(infinity) T-eff(4). This implies significantly lower growth rates for (the cooler and 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 towards explaining the general lack of observed intrinsic X-ray emission in single B-star winds.