Asteroseismological measurements on PG 1159−035, the prototype of the GW Vir variable stars

Aims. An asteroseismological study of PG 1159−035, the prototype of the GW Vir variable stars, has been performed on the basis of detailed and full PG1159 evolutionary models presented by Miller Bertolami & Althaus (2006). Methods. We carried out extensive computations of adiabatic g-mode pulsation periods on PG1159 evolutionary models with stellar masses spanning the range 0.530 to 0.741M⊙. These models were derived from the complete evolution of progenitor stars, including the thermally pulsing AGB phase and the born-again episode. We constrained the stellar mass of PG 1159−035 by comparing the observed period spacing with the asymptotic period spacing and with the average of the computed period spacings. We also employed the individual observed periods reported by Costa et al. (2007) to find a representative seismological model for PG 1159−035. Results. We derive a stellar mass in the range 0.56 − 0.59M⊙ from the period-spacing data alone. We also find, on the basis of a period-fit procedure, an asteroseismological model representative of PG 1159−035 that reproduces the observed period pattern with an average of the period differences of δΠi = 0.64 − 1.03 s, consistent with the expected model uncertainties. The model has an effective temperature Teff = 128 000 +8 600 −2 600 K, a stellar mass M∗ = 0.565 +0.025 −0.009M⊙, a surface gravity log g = 7.42 −0.12 , a stellar luminosity and radius of log(L∗/L⊙) = 2.15 ± 0.08 and log(R∗/R⊙) = −1.62 −0.09 , and a He-rich envelope thickness of Menv = 0.017M⊙ . The results of the period-fit analysis carried out in this work suggest that the surface gravity of PG 1159−035 would be 1σ larger than the spectroscopically inferred gravity. For our best-fit model of PG 1159−035, all of the pulsation modes are characterized by positive rates of period changes, at odds with the measurements by Costa & Kepler (2007).