PRECISION ASTEROSEISMOLOGY OF PULSATING PG-1159 STARS

Observations of the pulsation spectrum of the hot white dwarf PG 1159- 035 with the Whole Earth Telescope provide rich detail on the normal m ode spectrum of nonradial g-modes in this star. We present a grid of e volutionary models appropriate for PG 1159 stars in an effort to model the details of their observed pulsation spectra. We can match the obs erved pulsation frequencies to remarkable precision using models deriv ed from standard post-asymptotic giant branch (AGB) stellar models. A grid of post-AGB models with systematically varied stellar mass, effec tive temperature, surface helium layer thickness, and helium abundance is used to explore how the pulsation properties depend on these quant ities. The models show that the mean spacing between consecutive overt one g-mode periods is a direct probe of the total stellar mass. Regula r departures from uniform period spacing result from resonant mode tra pping by the sharp composition gradient at the base of the He-rich sur face layer. The depth of the He/C + O composition transition region go verns the periods of maximum departure from uniform spacing while the steepness of the composition gradient affects the amount of departure. While most modes show periods that increase with time, some trapped m odes show periods that decrease with time because trapped modes are mu ch more sensitive to the contraction of the outer nondegenerate layers than nontrapped modes. Comparison with the observed periods in PG 115 9-035 yields a best fit with a mass of 0.59 +/- 0.01 M., an effective temperature of almost-equal-to 136,000 K, and a He-rich layer of appro ximately 0.004M with Y(surf) almost-equal-to 0.27. This fit is in ver y good agreement with prior pulsational and spectroscopic studies of t his star. The mode nearest 516 s is almost a trapped mode in the best- fit model. We therefore interpret the observed negative value of the p eriod derivative as resulting from mode trapping. The 539 s mode in PG 1159-035 is a trapped mode in our models and shows a negative dP/dt, so we suggest that observational determination of dP/dt for this mode will show a larger negative value than seen in the 516 s mode. We disc uss the applications of our model grid to other pulsating PG 1159 star s, and implications of our results for PG 1159 on models of white dwar f formation and chemical evolution.