Asteroseismological Constraints on the Structure of the ZZ Ceti Stars G117‐B15A and R548

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Abstract
This study compares the theoretical pulsation periods from a new grid of evolutionary DA white dwarf models to the observed periods of the ZZ Ceti white dwarfs G117-B15A and R548 (≡ ZZ Ceti) in order to constrain their internal structure. Assuming that the similar periods of the two stars is the result of their having nearly identical internal structures, then they must have a hydrogen layer mass of ~10-7M or greater. If we follow Clemens's work and identify the period near 215 s as the ℓ=1, k = 2 mode, then the hydrogen layer mass is close to 10-4M, quite close to the maximum hydrogen layer mass allowed by stellar evolution theory. Based on this analysis, G117-B15A and R548 probably have masses near 0.60 M☉ and MH ~ 10-4M, and R548 is about 0.04 M☉ less massive than G117-B15A. Alternatively, if 215 s is the k = 1 mode, then the hydrogen layer mass decreases to about 10-7M, but the stellar mass remains near 0.60 M☉. In all cases, the helium layer mass is near 10-2M, and the C/O core of both stars is oxygen rich. The existence of the 304 s mode of G117-B15A strongly restricts the allowable core structure. At 0.60 M☉, the core is either 50:50 C/O to 0.75M or 20:80 C/O to 0.83M. The fine-structure splitting of R548 is due to slow rotation, and we can duplicate the observed splitting trend and periods if the 213 s mode is k = 2, the model mass is near 0.54 M☉, and the hydrogen layer mass is near 1.5 × 10-4M.