Turbulent Pressure in the Envelopes of Yellow Hypergiants and Luminous Blue Variables

Abstract

The manner in which turbulence (especially turbulent pressure) affects the structure and stability of luminous post-red-supergiant stars is critically evaluated by calculating both realistic and one-zone models of the convective envelopes. In these stars, the remnant outer envelope closely approaches the Eddington limit, with the result that the local gas densities are driven down. Such a tenuous environment promotes high turbulent velocities in the marginally convective layers of the outer envelope. In the hydrogen and helium convection zones, however, the velocities, even though high, fall well below sound velocity, and the temperature gradient there is essentially radiative, making both the turbulent pressure and the turbulent kinetic energy flux structurally unimportant. Instability is tested for by assuming that turbulence adapts either slowly or rapidly to small perturbations, depending on the magnitude of the turbulent velocity. Although the adiabatically stratified iron convection zone lies too deep below the surface to influence the formal dynamical stability or instability of the outer envelope, radiative instability in this zone is increased if supersonic turbulence occurs and generates energetic shocks or if convection is unable to transport all of the super-Eddington luminous flux. It is concluded that turbulent pressure has no significant effect on the formal dynamical instability of the outer envelope in yellow hypergiant stars and luminous blue variables (LBVs), but it may significantly ease the requirement for radiative instability in the brightest and hottest LBVs and in their close relatives, the hydrogen-poor WN stars. Since both dynamical instability and radiative instability lead to a strong dynamical outflow of matter, the unresolved complications arising from supersonic turbulence and from the consequent inapplicability of mixing-length theory render uncertain the predicted domains of instability for the brightest and hottest stars.