Asteroseismological constraints on the pulsating planetary nebula nucleus (PG 1159-type) RX J2117.1+3412

Aims. We present asteroseismological inferences on RXJ2117.1+3412, the hottest known pulsating PG1159 star. Our results are based on full PG1159 evolutionary models recently presented by Miller Bertolami & Althaus (2006). Methods. We performed extensive computations of adiabatic g-mode pulsation periods on PG1159 evolutionary models with stellar masses ranging from 0.530 to 0.741M⊙. PG1159 stellar models are extracted from the complete evolution of progenitor stars started from the ZAMS, through the thermally pulsing AGB and born-again phases to the domain of the PG1159 stars. We constrained the stellar mass of RXJ2117.1+3412 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 to find a representative seismological model for RXJ2117.1+3412. Results. We derive a stellar mass M∗ � 0.56 0.57M⊙ from the period spacing data alone. In addition, we found a best-fit model representative for RXJ2117.1+3412 with an effective temperature Teff = 163400 K, a stellar mass M∗ = 0.565M⊙, and a surface gravity log g = 6.61. The derived stellar luminosity and radius are log(L∗/L⊙) = 3.36 and log(R∗/R⊙) = 1.23, respectively, and the He-rich envelope thickness is Menv = 0.02M⊙. We derive a seismic distance d � 452 pc and a linear size of the planetary nebula DPN � 1.72 pc. These inferences seem to solve the discrepancy between the RXJ2117.1+3412 evolutionary timescale and the size of the nebula. All of the seismological tools we use concur to the conclusion that RXJ2117.1+3412 must have a stellar mass M∗ � 0.565M⊙, much in agreement with recent asteroseismology studies and in clear conflict with the predictions of spectroscopy plus evolutionary tracks.