The standard theory of pulsations deals with the frequencies and growth rates of infinitesimal perturbations in a stellar model. Modes which are calculated to be linearly driven should increase their amplitudes exponentially with time; the fact that
nearly constant amplitudes are usually observed is evidence that nonlinear mechanisms inhibit the growth of finite amplitude pulsations. Models predict that the mass of convection zones in pulsating hydrogen-atmosphere (DAV) white dwarfs is very sensitive to temperature (i.e., $M_{rm CZ} propto T_{rm eff}^{-90}$), leading to the possibility that even low-amplitude pulsators may experience significant nonlinear effects. In particular, the outer turning point of finite-amplitude g-mode pulsations can vary with the local surface temperature, producing a reflected wave that is out of phase with what is required for a standing wave. This can lead to a lack of coherence of the mode and a reduction in its global amplitude. In this paper we show that: (1) whether a mode is calculated to propagate to the base of the convection zone is an accurate predictor of its width in the Fourier spectrum, (2) the phase shifts produced by reflection from the outer turning point are large enough to produce significant damping, and (3) amplitudes and periods are predicted to increase from the blue edge to the middle of the instability strip, and subsequently decrease as the red edge is approached. This amplitude decrease is in agreement with the observational data while the period decrease has not yet been systematically studied.
We present limits on planetary companions to pulsating white dwarf stars. A subset of these stars exhibit extreme stability in the period and phase of some of their pulsation modes; a planet can be detected around such a star by searching for periodi
c variations in the arrival time of these pulsations. We present limits on companions greater than a few Jupiter masses around a sample of 15 white dwarf stars as part of an on-going survey. One star shows a variation in arrival time consistent with a 2 M_J planet in a 4.5 year orbit. We discuss other possible explanations for the observed signal and conclude that a planet is the most plausible explanation based on the data available.
PG 1159-035, a pre-white dwarf with T_eff=140,000 K, is the prototype of both two classes: the PG1159 spectroscopic class and the DOV pulsating class. Previous studies of PG 1159-035 photometric data obtained with the Whole Earth Telescope (WET) show
ed a rich frequency spectrum allowing the identification of 122 pulsation modes. In this work, we used all available WET photometric data from 1983, 1985, 1989, 1993 and 2002 to identify the pulsation periods and identified 76 additional pulsation modes, increasing to 198 the number of known pulsation modes in PG 1159-035, the largest number of modes detected in any star besides the Sun. From the period spacing we estimated a mass M = 0.59 +/- 0.02 solar masses for PG 1159-035, with the uncertainty dominated by the models, not the observation. Deviations in the regular period spacing suggest that some of the pulsation modes are trapped, even though the star is a pre-white dwarf and the gravitational settling is ongoing. The position of the transition zone that causes the mode trapping was calculated at r_c = 0.83 +/- 0.05 stellar radius. From the multiplet splitting, we calculated the rotational period P_rot = 1.3920 +/- 0.0008 days and an upper limit for the magnetic field, B < 2000 G. The total power of the pulsation modes at the stellar surface changed less than 30% for l=1 modes and less than 50% for l=2 modes. We find no evidence of linear combinations between the 198 pulsation mode frequencies. PG 1159-035 models have not significative convection zones, supporting the hypothesis that nonlinearity arises in the convection zones in cooler pulsating white dwarf stars.
We report 323 hours of nearly uninterrupted time series photometric observations of the DBV star GD 358 acquired with the Whole Earth Telescope (WET) during May 23rd to June 8th, 2000. We acquired more than 232 000 independent measurements. We also r
eport on 48 hours of time-series photometric observations in Aug 1996. We detected the non-radial g-modes consistent with degree l=1 and radial order 8 to 20 and their linear combinations up to 6th order.We also detect, for the first time, a high amplitude l=2 mode, with a period of 796s. In the 2000 WET data, the largest amplitude modes are similar to those detected with the WET observations of 1990 and 1994, but the highest combination order previously detected was 4th order. At one point during the 1996 observations, most of the pulsation energy was transferred into the radial order k=8 mode, which displayed a sinusoidal pulse shape in spite of the large amplitude. The multiplet structure of the individual modes changes from year to year, and during the 2000 observations only the k=9 mode displays clear normal triplet structure. Even though the pulsation amplitudes change on timescales of days and years, the eigenfrequencies remain essentially the same, showing the stellar structure is not changing on any dynamical timescale.
The white dwarfs are promising laboratories for the study of cosmochronology and stellar evolution. Through observations of the pulsating white dwarfs, we can measure their internal structures and compositions, critical to understanding post main seq
uence evolution, along with their cooling rates, allowing us to calibrate their ages directly. The most important set of white dwarf variables to measure are the oldest of the pulsators, the cool DAVs, which have not previously been explored through asteroseismology due to their complexity and instability. Through a time-series photometry data set spanning ten years, we explore the pulsation spectrum of the cool DAV, G29-38 and find an underlying structure of 19 (not including multiplet components) normal-mode, probably l=1 pulsations amidst an abundance of time variability and linear combination modes. Modelling results are incomplete, but we suggest possible starting directions and discuss probable values for the stellar mass and hydrogen layer size. For the first time, we have made sense out of the complicated power spectra of a large-amplitude DA pulsator. We have shown its seemingly erratic set of observed frequencies can be understood in terms of a recurring set of normal-mode pulsations and their linear combinations. With this result, we have opened the interior secrets of the DAVs to future asteroseismological modelling, thereby joining the rest of the known white dwarf pulsators.
