White dwarf Asteroseismology.

Morten Andersen & Rimas Liubertas

ABSTRACT

One DA white dwarf PG 1159-03 has been observed twice with the Whole Earth Telescope (WET). We analysed the second run obtained by WET in 1993, and compared the results with the first one (Winget et al APJ 378,326,1991.) We have reviewed what changes have occurred.

1.WET program and data

Because of the change between night and day, continuous observations of a given astronomical object from a single site are impossible. In order to avoid aliases in the Fourier Transform of the light curve, a complete light curve is needed. In order to obtain this complete coverage in the time domain, the WET program was initiated. The idea is that object is observed from different places on the Earth so that the object can be observed 24 hours a day. This idea have been realized on several occasions in order to observe variable objects like DA WD's which have oscillation modes excited. Since these modes will be completely swamped by a too broad window function or a window function with large sidelobes, the only hope to observe the oscillations from the ground is by mean of the WET program. Beside WD's, also cataclysmic variables have been observed in case of possible short periods and other variable stars like delta scuti stars have been observed.

The WET has some problems though. In order to get 5-10 observatories too agree on doing the observations so in order to create a good light curve a lot of planning is needed. Of course, good or at least reasonable weather is required at most observing sites. Also, in order to make things easier, the observers should agree on the observation methods.

2. Reduction

Observations from 6 observatories of the DA WD PG1159-03 around the world have been joined to a single light curve that is almost continuos. The observations were obtained between 18 of March 1993 and 26 of April 1993. A subset of the complete sample have been reduced by us and analyzed to see whether the light curve have changed since the last WET run in 1989. We chose the best covered time interval from 19 of March to 25 of March. Even though we only considered a small part of the entire light curve was it our hope that our window function would be sufficient narrow to identify and separate individual peaks. The data was a mixture of 2 and 3 channel photometer data. The removal of "bad points" was done in the package Quilt. Because of the short time available, we did not correct properly for clouds, so the data affected by clouds was simply excluded. Some problems with synchronization of the data files from different observatories resulted in the exclusion of some of our observations by the Quilt package. The removal of bad data points and Quilt's exclusion of some of the observations meant that even though we started with an almost continuous light curve, we had some gaps in the reduced light curve. This, as we shall see later, had some implications for the Window function. The data was then collected in one data file and the total light curve was the Fourier transformed in order to obtain the power spectrum. Figure 1 shows the time coverage of the observations. The Fourier transform done is a simple one, where FFT is done on each data set separately and the different power spectra are then collected to one final power spectrum. In the following we only consider the FT in the frequency range 1750 to 2350 micro Hertz

3. Results

Figure 2a shows the obtained power spectrum. Several peaks are immediately evident. Figure 3 shows the window function. In order to see whether a peak is due to a real oscillation or is an artifact of the window function the most prominent peaks were removed. After removal, the most prominent peak is then removed and so on. After removal of a given number of peaks, all that is left should noise. Figure 2b show the whitened power spectrum. The noise is approximately 0.2 (mili mag squared). No peaks are above ten standard deviations. Since we only analyzed a subset of the data, we tried to look at the total FT of the time series reduced by other people. The power spectrum can be seen at figure 4.

The general features is the same, but the noise is apparently much larger. This is probably because of the window function. The window function from different peaks will interact and it will look like noise in the pre whitened spectrum. If the spectrum is cleaned for large peaks, this noise will probably be reduced significantly and should be smaller than the noise in our sub sample. Because of lack of time this has not been done. We have identified the following oscillations in our sub sample.

muHz1787.191790.311854.231858.051929.391933.631937.552024.992205.362210.662214.16
ump3.552.7957.758.656.3519.0532.556.103.1612.2911.51
rad0.27-0.39-0.732.38-2.66-0.49-0.84-0.613.331.73-0.55

4. Comparison with results obtained in 1989

All the peaks found in our sub sample have been observed in the 89 run as well. However, more peaks are seen in the 89 sample. Some of these peaks are because of better time sampling. What is more interesting is that some of the oscillations with significant power have either vanished or have become weak compared to the neighbor peaks. Also, the power within a triplet does not seem to be conserved with time. This consideration is build upon the triplet identification made in the 89 run. Some of these identifications were only tentative and the result obtainable from the whole light curve from 93 might change some of these identifications. Especially the triplet with the m=0 oscillation at 1790 micro Hertz has changed dramatically during the 4 years between the runs. The oscillation with most power has apparently vanished and the total power is definitely not conserved. The reason for the relative changes of the modes in not apparent but it is probably an evolutionary effect of the WD. The evolution effects can be changes in the stratifying layers or maybe changes in the convective zone or evolution in the size of the convective zone. In the case of time dependant analyses it might be possible to see whether variation happens during the observation run.

One of the conclusions of the 89 run was that the rotation axis of the WD was inclined 60° derived from the figure by Pesnell 85. This is based on the fact that we see both the m=+1 and the m=-1 in the l=1 triplets. If the angle were 0° then, because we can not resolve the disk, the 2 modes would cancel. The ratio of the m=0 mode and the average the m=+1 and the m=-1 mode gives an estimate of the inclination angle. We only have on triplet with all three modes observed (around 1933 micro Hertz) and we find the ratio to be 2. The 89 run found 1.9, so the results are compatible.

It is interesting that the three lines we see now at 2205-2215 micro Hertz previously was separated into a triplet and quadruplet, that might be a l=2 multiplet, Now it seems to only be a triplet since we do not see the other lines in our sub sample. They might show up in the total light curve though.

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