We now have a good measurement of the cooling rate of G117-B15A. In the near future, we will have equally well determined cooling rates for other pulsating white dwarfs, including R548. The ability to measure their cooling rates offers us a unique way to study weakly interacting particles that would contribute to their cooling. Working toward that goal, we perform a careful asteroseismological analysis of G117-B15A and R548. We study them side by side because they have similar observed properties. We carry out a systematic, fine grid search for best fit models to the observed period spectra of those stars. We freely vary 4 parameters: the effective temperature, the stellar mass, the helium layer mass, and the hydrogen layer mass. We identify and quantify a number of uncertainties associated with our models. Based on the results of that analysis and fits to the periods observed in R548 and G117-B15A, we clearly define the regions of the 4 dimensional parameter space ocuppied by the best fit models.
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