On the Dynamic Stability of Cool Supergiant Atmospheres

We have developed a new formalism to compute the thermodynamic coefficientGamma1 in the theory of stellar and atmospheric stability. We generalize theclassical derivation of the first adiabatic index, which is based on theassumption of thermal ionization and equilibrium between gas and radiationtemperature, towards an expression which incorporates photo-ionization due toradiation with a temperature T_rad different from the local kinetic gastemperature.Our formalism considers the important non-LTE conditions in theextended atmospheres of supergiant stars. An application to the Kurucz grid ofcool supergiant atmospheres demonstrates that models with T_rad =~ T_effbetween 6500 K and 7500 K become most unstable against dynamic perturbations,according to Ledoux' stability integral . This results from Gamma1 and acquiring very low values, below 4/3, throughout the entire stellaratmosphere, which causes very high gas compression ratios around theseeffective temperatures. Based on detailed NLTE-calculations, we discussatmospheric instability of pulsating massive yellow supergiants, like thehypergiant rho Cas (Ia+), which exist in the extension of the Cepheidinstability strip, near the Eddington luminosity limit.Comment: 54 pages including figures and the Appendix, 7 figures, Accepted for The Astrophysical Journal, Main Journal, 558, Sept. 200