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Seismological observations with the Whole Earth Telescope (WET) allow thedetermination 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, whilethe cooler DB white dwarf GD 358 has a much thinner surface helium layer of10^-6 Msun. These results imply that either there is no evolutionary relationbetween these two stars, or that there is an unknown mass loss mechanism. Toinvestigate possible evolutionary links between these objects, we computedevolutionary sequences of white dwarf models including time-dependentdiffusion. Our initial model is based on the PG~1159 pulsational data, and hasa surface composition of 30% helium, 35% carbon, and 35% oxygen. Below this isa thin transition zone where the helium fraction falls to zero. As expected,diffusion caused a separation of the elements; a thickening surface layer ofnearly pure helium overlays a deepening transition zone where the compositionreturns to the original surface composition. When the model reached thetemperature range of GD~358 and the pulsating DB white dwarfs, this pure heliumsurface layer was 3x10^-6 stellar masses deep. The resulting evolved model isvery similar to the model used by Bradley and Winget (1994) to match thepulsation observations of GD 358. The pulsation periods of this model also showa good fit to the WET observations. These results demonstrate the plausibilityof a direct evolutionary path from PG 1159 stars to the much cooler DB whitedwarfs by inclusion of time-dependent diffusion. A problem still remains inthat our models have no hydrogen, and thus must retain their DB nature whiletheir surface tempeture drops from 45,000K to 30,000K. Since there are no knownDB stars in this range, we plan to address this problem in future calculations.Comment: LaTeX, 10 pages, using AAS Macros. 2 PostScript figures. Accepted for  publication in The Astrophysical Journal Letters

Thick to thin: The evolutionary connection between PG 1159 stars and the thin helium-enveloped pulsating white dwarf GD 358