Asteroseismology of RXJ 2117+3412, the hottest pulsating PG 1159 star

The pulsating PG 1159 planetary nebula central star RXJ 2117+3412 has been observed over three successive seasons of a multisite photometric campaign. The asteroseismological analysis of the data, based on the 37 identified $\ell=1$ modes among the 48 independent pulsation frequencies detected in the power spectrum, leads to the derivation of the rotational splitting, the period spacing and the mode trapping cycle and amplitude, from which a number of fundamental parameters can be deduced. The average rotation period is $1.16\pm 0.05$ days. The trend for the rotational splitting to decrease with increasing periods is incompatible with a solid body rotation. The total mass is 0.56 +0.02-0.04 $M_{\odot}$ and the He-rich envelope mass fraction is in the range 0.013-0.078 M*. The luminosity derived from asteroseismology is log( $L/L_{\odot})= 4.05$ +0.23-0.32 and the distance 760 +230-235 pc. At such a distance, the linear size of the planetary nebulae is $2.9\pm 0.9$ pc. The role of mass loss on the excitation mechanism and its consequence on the amplitude variations is discussed.