Asteroseismology of the DOV star PG 1159-035

Abstract

Grids of DOV star models are evolved by \texttt{WDEC} with fixed atmospheric constituent to the spectral values of $X_{C}/X_{He}/X_{O}$ = 50/33/17. The core compositions are from white dwarf models at highest $T_{eff}$ evolved by \texttt{MESA}. The eigenfrequencies are calculated and used to fit the observed modes. Based on 264.1 hours of photometric observations on PG 1159-035, Winget et al. identified 125 individual frequencies. Costa et al. identified 198 pulsation modes for PG 1159-035 according to the WET photometric data from 1983, 1985, 1989, and 2002. Both of them derived frequency splitting values of $\delta\sigma_{l=1}$ $\sim$ 4.2\,$\mu$Hz and $\delta\sigma_{l=2}$ $\sim$ 6.9\,$\mu$Hz. According to the values of $\delta\sigma_{l=1}$ and $\delta\sigma_{l=2}$, 20 triplets and 9 quintuplets are selected and used to constrain the fitting models. Our optimal model has $T_{eff}$ = 129000\,K, $M_{*}$ = 0.63\,$M_{\odot}$, log$g$ = 7.59, log($M_{\rm env}/M_{*}$) = -5.0, and $\sigma_{RMS}$ = 1.97\,s. The values of $T_{eff}$ and log$g$ are consistent with that values of C\'orsico et al.. The calculated modes of minimum rate of period change correspond to modes with maximum kinetic energy distributed in the envelope. The observed rates of period change with positive and negative values can also be partially reproduced. In particular, there are negative rates of period change for the calculated modes from our optimal model, which is not found in previous work.