Evolution, Structure, and Seismology of Intermediate‐Mass Stars

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Abstract
The interior structure, the evolution, and the p-mode oscillation spectra of stellar models between 2.0 and 5 Mare presented. Interior details, including convective core and envelope growth and decay, the develop- ment of composition gradients, and the onset of hydrogen shell burning are shown to be testable by future asteroseismology observations. The stellar age and mass dependence of the large- and small-spacing oscilla- tion frequencies are discussed. The dependencies of the structure and the oscillation spectra on composition and mixing length are also discussed. A new oscillation diagnostic for stellar mass is introduced. Subject headings: stars: evolution — stars: interiors — stars: oscillations Numerical modeling of the equations of stellar structure and evolution, with the aid of sophisticated compilations of relevant opacities, the equation of state, and nuclear reac- tion rates, has successfully mapped out our understanding of the evolution of stars throughout the H-R diagram. Con- firmation of stellar evolution theory has come from the wonderful agreement between the predicted positions of stars in the H-R diagram and their observed positions, and the association of different phases of evolution with specific regions in the H-R diagram. The pulsation behavior of Cepheids and other nonlinear, radially oscillating stars has further confirmed stellar modeling for specific stars. Detailed confirmation of some of the physics of the stellar model has also come from the better than one part in one thousand agreement between the oscillation spectrum pre- dicted by the standard solar model and the observed solar p-mode oscillation spectrum. Additionally, and recently, is the conclusion from the Sudbury Solar Neutrino Observa- tory (SNO) collaboration (Ahmad, Allen, & Andersen 2001), using SNO (Boger et al. 2000) and Super- Kamiokande (Fukuda et al. 1998) data, that the electron neutrino has mass and hence oscillates, thus confirming that the nuclear physics of the solar model is correct, that is, spe- cifically, that both the p-p and CNO chains contribute to the solar luminosity. There remain many aspects of stellar theory that have not been observationally confirmed. The matching of theoreti- cal and observational H-R diagrams does not unambigu- ously confirm the interior structure predictions of the stellar models. With the exception of a few pulsating stars, our pic- ture of the stellar interior is derived exclusively from the physics of the stellar model, constrained by the observed surface boundary conditions. Although it is unlikely that the basic physics is in error, the opacities, the equation of state, the model of convection, and the atmosphere calcula- tion are uncertain to varying degrees. The uncertainties in the opacity and equation-of-state calculations are estimated to be approximately � 15% for conditions that exist in the deep interior of stars and as much as � 30% in the cooler outer layers. The mixing-length approximation, which has long been suspect, is now known to incorrectly specify the

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