Kepler and TESS Observations of PG 1159-035

PG 1159-035 is the prototype of the PG 1159 hot (pre-)white dwarf pulsators. This important object was observed during the Kepler satellite K2 mission for 69 days in 59 s cadence mode and by the TESS satellite for 25 days in 20 s cadence mode. We present a detailed asteroseismic analysis of those data. We identify a total of 107 frequencies representing 32 1= 1 modes, 27 frequencies representing 12 1=2 modes, and eight combination frequencies. The combination frequencies and the modes with very high k values represent new detections. The multiplet structure reveals an average splitting of 4.0 +/- 0.4 mu Hz for l = 1 and 6.8 +/- 0.2 mu Hz fort= 2, indicating a rotation period of 1.4 +/- 0.1 days in the region of period formation. In the Fourier transform of the light curve, we find a significant peak at 8.904 +/- 0.003 mu Hz suggesting a surface rotation period of 1.299 +/- 0.002 days. We also present evidence that the observed periods change on timescales shorter than those predicted by current evolutionary models. Our asteroseismic analysis finds an average period spacing for 1= 1 of 21.28 +/- 0.02 s. The 1= 2 modes have a mean spacing of 12.97 +/- 0.4 s. We performed a detailed asteroseismic fit by comparing the observed periods with those of evolutionary models. The best-fit model has T-eff =129, 600 +/- 11 100 K, M-* = 0.565 +/- 0.024M(circle dot), and log g = 7.41(-0.54)(+0.38) within the uncertainties of the spectroscopic determinations. We argue for future improvements in the current models, e.g., on the overshooting in the He-burning stage, as the bestfit model does not predict excitation for all of the pulsations detected in PG 1159-035.