White dwarf asteroseismology offers the opportunity to probe the structure and composition of stellar objects governed by relatively simple physical principles. The observational requirements of asteroseismology have been addressed by the development of the Whole Earth Telescope, but the analysis procedures still need to be refined before this technique can yield the complete physical insight that the data can provide. We have applied an optimization method utilizing a genetic algorithm to the problem of fitting white dwarf pulsation models to the observed frequencies of the most thoroughly characterized helium-atmosphere pulsator, GD 358. The free parameters in this initial study included the stellar mass, the effective temperature, the surface helium layer mass, the core composition, and the internal chemical profile.
For many years, astronomers have promised that the study of pulsating white dwarfs would ultimately lead to useful information about the physics of matter under extreme conditions of temperature and pressure. The optimization approach developed in this dissertation has allowed us to finally make good on that promise by exploiting the sensitivity of our models to the core composition. We empirically determine that the central oxygen abundance in GD 358 is 84 ± 3 percent. We use this value to place a preliminary constraint on the 12C (,)16O nuclear reaction cross-section of S300 = 295 ± 15 keV barns.
We find a thick helium-layer solution for GD 358 that provides a better match to the data than previous fits, and helps to resolve a problem with the evolutionary connection between PG 1159 stars and DBVs. We show that the pulsation modes of our best-fit model probe down to the inner few percent of the stellar mass. We demonstrate the feasibility of reconstructing the internal chemical profiles of white dwarfs from asteroseismological data, and we find an oxygen profile for GD 358 that is qualitatively similar to recent theoretical calculations. This method promises to serve as a powerful diagnostic that will eventually allow us to test theories of convective overshooting and stellar crystallization.