Structure formation in the envelopes of massive stars

Excessive supersonic broadening of photospheric lines of massive stars indicates the presence of a very turbulent outer stellar envelope. Radiation-hydrodynamical models of massive stars (Jiang et al., 2015; Moens et al., 2022; Debnath et al., 2024) indeed show large structures being formed in the sub-surface layers, which may impact the energy transport and stellar structure just below the photosphere as well as observable properties. Therefore, it is very important to understand the origin and properties of this subsurface turbulence. In this talk, we investigate the physical origin of the predicted structures in the outer layers of massive stars, and we attempt to characterize the resulting non-linear turbulent properties. Following Blaes & Socrates (2003), who performed a linear stability analysis to predict multiple instabilities originating from the iron opacity bump, we study the linear growth phase of the structures in the Wolf-Rayet (WR) star models by Moens et al. (2022) and the O-star models by Debnath et al. (2024) and compare our results to theoretical predictions. Furthermore, we consider the fully developed non-linear turbulence and compute energy power spectra which we then compare to classical Kolmogorov theory. In particular, we study how the optically thick and optically thin winds of these WR stars and O-stars, respectively, can impact the emergent turbulent properties, both in the linear stage and in the non-linear stage.