Thick to Thin: The Evolutionary Connection Between PG 1159 Stars and the Thin Helium-Enveloped Pulsating White Dwarf GD 358

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Abstract
Seismological observations with the Whole Earth Telescope (WET) allow the determination of the subsurface compositional structure of white dwarf stars. The hot DO PG 1159 has a helium surface layer with a mass of 0.001 Msun, while the cooler DB white dwarf GD 358 has a much thinner surface helium layer of 10^-6 Msun. These results imply that either there is no evolutionary relation between these two stars, or that there is an unknown mass loss mechanism. To investigate possible evolutionary links between these objects, we computed evolutionary sequences of white dwarf models including time-dependent diffusion. Our initial model is based on the PG~1159 pulsational data, and has a surface composition of 30% helium, 35% carbon, and 35% oxygen. Below this is a thin transition zone where the helium fraction falls to zero. As expected, diffusion caused a separation of the elements; a thickening surface layer of nearly pure helium overlays a deepening transition zone where the composition returns to the original surface composition. When the model reached the temperature range of GD~358 and the pulsating DB white dwarfs, this pure helium surface layer was 3x10^-6 stellar masses deep. The resulting evolved model is very similar to the model used by Bradley and Winget (1994) to match the pulsation observations of GD 358. The pulsation periods of this model also show a good fit to the WET observations. These results demonstrate the plausibility of a direct evolutionary path from PG 1159 stars to the much cooler DB white dwarfs by inclusion of time-dependent diffusion. A problem still remains in that our models have no hydrogen, and thus must retain their DB nature while their surface tempeture drops from 45,000K to 30,000K. Since there are no known DB stars in this range, we plan to address this problem in future calculations.

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