The temporal changes of the pulsational periods of the pre-white dwarf PG 1159-035

Abstract

Context. PG 1159-035, a pre-white dwarf with Teff -~ 140 000 K, is the prototype of the PG 1159 spectroscopic class and the DOV pulsating class. Pulsating pre-white dwarf stars evolve rapidly: the effective surface temperature decreases rapidly, the envelope contracts and the inner structure experiences stratification due to gravitational settling. These changes in the star generate variations in its oscillation periods. The measurement of temporal change in the oscillation periods, ˙P, allows us to estimate directly rates of stellar evolutionary changes, such as the cooling rate and the envelope contraction rate, providing a way to test and refine evolutionary models for pre-white dwarf pulsating stars. Aims. Previously, only two pulsation modes of the highest amplitudes for PG 1159-035 have had their ˙P measured: the 516.0 s and the 539.3 s modes. We measured the ˙P of a larger number of pulsation modes, increasing the number of constraints for evolutionary studies of PG 1159-035. We attempted to use the secular variations in the periods of multiplets to calculate the variation in the rotational period, the envelope contraction rate, and the cooling rate of the star. Methods. The period variations were measured directly from the PG 1159-035 observational data and refined by the (O–C) method. Results. We measured 27 pulsation mode period changes. The periods varied at rates of between 1 and 100 ms/yr, and several can be directly measured with a relative standard uncertainty below 10%. For the 516.0 s mode (the highest in amplitude) in particular, not only the value of ˙P can be measured directly with a relative standard uncertainty of 2%, but the second order period change, ¨P, can also be calculated reliably. By using the (O–C) method, we refined the ˙Ps and estimated the ¨Ps for six other pulsation periods. As a first application, we calculated the change in the PG 1559-035 rotation period, ˙Prot = (−2.13 ± 0.05) × 10−6 ss-ˡ, the envelope contraction rate ˙R = (−2.2 ± 0.5) × 10−13 R s−1, and the cooling rate T˙ = −1.42 × 10−3 Ks-ˡ.