SIMBAD references

The goal of this paper is to study instability regions in the HR diagram, through a calculation of the atmospheric accelerations for spherically symmetric stars, in dynamic equilibrium, without using detailed atmospheric models. The input data are five primary data, viz.: the stellar luminosity L, the effective temperature T_eff, the mass M, the rate of mass loss {dot}(M), and the microturbulent velocity component ζ_µ, while we assume the temperature for a reference atmospheric layer, an assumption that appears not to be critical. An iterative solution of the momentum equation, simultaneous with some other equations, yields values for the various accelerations acting on a stellar atmosphere and their algebraic sum g_eff', the predicted effective acceleration. In the first part of the paper we compare this latter quantity with the g_eff-value derived observationally from spectral studies of nine program stars and we find overall fair agreement. This supports the method as well as the values of the five input data. In part 2 we determine g'_eff in same way for the whole upper part of the Hertzsprung-Russell diagram by using statistical primary data on the mass (based on evolutionary calculations), on mass-loss and on microturbulence (shockstrengths). We find as a fairly general rule that, as stars move along their evolutionary track, and for time scales longer than the dynamic time scale of the atmosphere, the atmosphere continuously adapts to the new (L,T_eff)-values and essentially remains stable. Current practice of determining the stability limit of stellar atmospheres by extrapolating hydrostatic models to the Eddington limit is not justified by this study. There is one exception: we find a small area around T_eff=8300K and log(L/L_☉)=5.7, where no solution is possible for evolved stars on their blueward evolutionary track; the stars in this area have in any case effective accelerations <1mm/s²: the "Yellow Evolutionary Void". In the third part we estimate approximately the pulsational (in-)stability of stars in the upper part of the Hertzsprung-Russell diagram, by comparing the g'_eff values determined in part 2 with the average outward pulsational acceleration. We thus confirm the 'Yellow Evolutionary Void' for blueward evolving stars, and also find an instability region for blueward evolving stars in the area occupied by the Wolf-Rayet stars. This seems to agree with the observations that the low-temperature boundary of the Yellow Evolutionary Void appears to coincide with the region where the yellow hypergiants are clustering. The yellow hypergiants are therefore interpreted as blueward moving stars with ZAMS masses of about 25-40M_☉, and actual masses between 15 and 25M_☉. For our galaxy it is found that only a few stars are situated within the 'Yellow Evolutionary Void', in accordance with our expectation.