On the Dynamic Stability of Cool Supergiant Atmospheres

We have developed a new formalism to compute the thermodynamic coefficient Γ1 in the theory of stellar and atmospheric stability. We generalize the classical derivation of the first adiabatic index, which is based on the assumption of thermal ionization and equilibrium between gas and radiation temperature, towards an expression which incorporates photo-ionization due to radiation with a temperature Trad different from the local kinetic gas temperature. Our formalism considers the important non-LTE conditions in the extended atmospheres of supergiant stars. An application to the Kurucz grid of cool supergiant atmospheres demonstrates that models with Trad'Teff between 6500 K and 7500 K become most unstable against dynamic perturbations, according to Ledoux’ stability integral <Γ1>. This results from Γ1 and <Γ1> acquiring very low values, below 4/3, throughout the entire stellar atmosphere, which causes very high gas compression ratios around these effective temperatures. Based on detailed NLTE-calculations, we discuss atmospheric instability of pulsating massive yellow supergiants, like the hypergiant ρ Cas (Ia), which exist in the extension of the Cepheid instability strip, near the Eddington luminosity limit. Subject headings: instabilities — stars: atmospheres — stellar dynamics — pulsations — supergiants — stars: variables: hypergiants — Cepheids