g-mode Pulsations in Doradus Stars: The Frozen-Flux Approximation and the Conservation of Energy

The first theoretical investigation of the suggested g-mode instability of Doradus stars based on a linear stability analysis carried out by Gautschy and Löffler (1996) revealed no unstable g modes at all and concluded that these g-mode pulsations can probably not be explained by the simple analysis of standard stellar models. More recently, Guzik et al. (2000) have claimed that the driving mechanism for the observed g modes is the so called “convective blocking” of the radiative energy transport due to long convective turn-over times in the stellar envelope and have even proposed a theoretical instability domain (Guzik et al., 2002). We have now investigated the stability of the first 100 g-mode overtones in a few carefully selected models using five different formulations for the neglection of the convective flux perturbation. Depending on which one of these so called frozen-flux variants we actually use, we find either strong evidence for “convective blocking” and many unstable modes or no “convective blocking” and no instability at all. After a closer look at the equation describing the linear perturbation of the energy conservation and the different approximations used to neglect the perturbation of the convective flux we have, however, some serious doubts that this proposed “convective blocking” is a real physical effect. We will show that, for the special case of an adiabatically convective stellar envelope, it is possible to construe a formal violation of the energy conservation for those frozen-flux approximations, which give rise to “convective blocking”, whereas the one formulation in agreement with the conservation of energy does not show any evidence of this this effect. Based on our results, we claim that the true destabilising mechanism of Gamma Doradus stars remains a mystery.

 
Print this abstract