Three Dimensional Natures of Massive Star Envelopes

We review our current understanding on the outer envelope structures of massive stars based on three dimensional (3D) radiation hydrodynamic simulations. We briefly summarize the fundamental issues to construct hydrostatic one dimensional (1D) stellar evolution models when stellar luminosity approaches the Eddington value. Radiation hydrodynamic simulations in 3D covering the mass range from $13M_{\odot}$ to $80M_{\odot}$ always find a dynamic envelope structure with the time-averaged radial profiles matching 1D models with an adjusted mixing length parameter when convection is subsonic. Supersonic turbulence and episodic mass loss are generally found in 3D models when stellar luminosity is super-Eddington locally due to the opacity peaks and convection is inefficient. Turbulent pressure plays an important role in supporting the outer envelope, which makes the photosphere more extended than predictions from 1D models. Massive star lightcurves are always found to vary with a characteristic timescale consistent with the thermal time scale at the location of the iron opacity peak. The amplitude of the variability as well as the power spectrum can explain the commonly observed stochastic low frequency variability of mass stars observed by TESS over a wide range of parameters in the HR diagram. The 3D simulations can also explain the ubiquitous macro-turbulence that is needed for spectroscopic fitting in massive stars. Implications of the 3D simulations for improving 1D stellar evolution models are also discussed.