Pulsating White Dwarfs
A Paper Written for the
Iowa State University Summer 2000 REU Program
By Drew Goettler
Abstract
Pulsating white dwarf stars are a special subclass of white dwarfs, and they are
very useful tools for studying the interiors of stars. As the interior of the white dwarf
changes and oscillates, the light signal from the star will pulsate at numerous frequencies.
By determining the frequencies at which the star pulsates and using these as boundary
conditions in stellar models, astronomers can determine the interior properties of white
dwarfs. This summer I was involved in using data from the Whole Earth Telescope and
CCD images to determine the frequencies at which two different white dwarf stars
pulsate.
Background on Pulsating White Dwarfs
A white dwarf star is the final resting stage of 98 % of all stars (Kawaler A 1).
The size of a white dwarf is comparable to Earth, but its mass is on the same order as the
Sun. To keep such a dense star from collapsing, the core of the star, which is composed
of carbon and oxygen, becomes electron degenerate. Surrounding the core is a thin layer
of helium and hydrogen. This outer layer contains about .01% of the white dwarf’s mass,
and it extends about 30 miles below the surface (Kawaler B 133). Without the thin
“blanket” of hydrogen and helium, the white dwarf would cool very rapidly.
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As the white dwarf cools, the release of heat is comparable to a pot of boiling
water with a lid on it. As steam tries to escape, it causes the lid on the pot to move up
and down. Instead of the outer layer of the star moving up and down, the outer layer will
vary in luminosity due to nonradial pulsations/oscillations in the interior of the star. The
changes in luminosity are on the order of millimagnitudes (11 millimagnitudes equals a
1% change in brightness), but the oscillations are observable. These observable
oscillations are due to g-modes, which are modes produced by the restoring force of
buoyancy (Winget 216). Not all white dwarfs pulsate, though. Astronomers have
determined four locations on the white dwarf branch of the H-R diagram where white
dwarfs pulsate (Figure 1) (Nather 374).
When looking at pulsating white dwarf, longer is better. As the star pulsates, the
brightness of the star plotted versus time creates a graph that looks sinusoidal, and the
graph is called a light curve. The top of figure 2 shows an example light curve. Looking
at a pulsating star from a single location can only yield a light curve that is at most about
8 hours long, but this is not long enough to resolve a light curve from a star into all of its
components. In order to get a light curve long enough, astronomers make use of the
Whole Earth Telescope (WET).
WET is a collaboration of many observatories from
around the world, and it allows astronomers to get light curves that are days long, not just
hours long. Figure 3 shows a map of participating WET sites. As a star sets on one
observatory, another observatory to the west begins to track the star. Once a site has
completed a night of observation, the site sends its data to the headquarters of WET
located at ISU. At the headquarters each set of data, or run, is processed right away. Due
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to the huge collaboration needed to do a WET run, runs are only made once or twice a
year. The data collected, however, is worth the effort.
Why Study Pulsating White Dwarfs
By studying pulsating white dwarfs, astronomers can determine what the interior
of a white dwarf actually looks like. Once they know what the inside looks like,
astronomers have a better idea of how the stars cool. By knowing how the star cools,
astronomers can get better estimates of the ages of white dwarfs. As mentioned before,
98% of all stars will eventually become white dwarfs, including our Sun.
There are two main reasons why pulsating white dwarfs are very useful to look at.
One reason they are useful to look at is the number of modes at which they pulsate: white
dwarf stars pulsate at more frequencies than other types of pulsating stars. Also, the
structure of a white dwarf is much simpler than other stars. A cooling lump of gas is a lot
easier to model than a fusion reaction. Think of a white dwarf as a piano with only 3
strings and 100 constraints on how to tune it, and then think a star fusing material as a
piano with 100 strings and only 3 constraints. It is be much easier for a piano tuner to
tune the 3-stringed piano than the other type.
Astronomers who study pulsating white dwarfs could also be considered star
pathologists. Instead of an astronomer looking at a dead body to determine the lifestyle
of the person and the cause of death, an astronomer looks at a “dead” star. Based on what
the make-up of a star was before it died the composition of its corpse (a pulsating white
dwarf) will tell astronomers what the star was like when it was fusing material.
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What I Did
The data I looked at this summer was taken from a pulsating white dwarf star with
a helium rich outer layer called EC20058-5234, and it has a visual magnitude of 15.6.
Figure 4 shows a finder chart for EC20058. The data was acquired between June 30,
1997 and July 13, 1997 on the WET run called XCov 15. To reduce the data taken with
the Whole Earth Telescope, I used a program call QED. With this program, I looked at
each individual run, and on some nights there was more than one run. Each run contained
two light curves: a light curve of the target star and light curve of a comparison star. To
get the two light curves for the individual runs, a 2-channel photometer was used. The top
of figure 2 shows a sample light curve with the target star above the light curve of the
comparison star. The first procedure I did involved taking out garbage points from each
curve. By marking points as garbage, they are taken out of the light curve and are not
used in determining the Fourier transform of the light curve. Points can be labeled as
garbage due to guide or aperture checks, clouds coming between the telescope and the
stars being observed, or if an observer bangs his/her head on the telescope while
observing. Basically, garbage points are points that should not be associated with the
actual light curve from the star.
Once the garbage points were marked, I then marked sky points. Sky points are
parts of the light curve where the observer checked the sky’s brightness. Once all of the
sky points are marked, QED linearly connects all of the sky points to produce a curve that
will eventually be subtracted from the light curves of the target and comparison stars.
To aid me in determining garbage and sky points, each observer kept a log for each
individual run.
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After I had marked garbage and sky points, I ran a number of commands that
corrected for dead time, extracted the sky readings, prepared the sky channel for
subtraction, subtracted the sky from each channel, and corrected for extinction. I also ran
commands called bridging and function fitting on each of the runs. By bridging a run,
gaps in the light curve were linearly connected with artificial data points (The question of
whether or not to bridge is debatable. By bridging a run, you are creating points on the
light curve that did not originate from the star and possibly creating false periods in the
star’s light curve). With the function fitting command, a low order polynomial is divided
out of the light curve. The removal of a low order polynomial from the light curve is
done to remove low level fluctuations that other commands such as extinction might have
missed. By doing all of this data reduction, I was trying to reproduce what the light curve
looked like before entering our atmosphere.
During the next step of the data reduction process, I used a program called qplot
to plot both of the light curves and also produce a fast Fourier transform for each run.
The bottom of figure 2 shows the Fourier transforms of the two light curves at the top of
figure 2. This allowed me to see if I had missed any garbage or sky points or if the curve
needed to smoothed out more. Once all of the runs had been individually reduced, they
needed to be fit all together.
When putting together 27 different runs from 13 different nights, time becomes a
crucial element. Due to the Earth’s constant movement through the solar system, the
center of the solar system was used as the point of reference for time. This time
correction is referred to as the bari-centric time correction, and it removes any time
aliases due to the movement of Earth.
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Once all of the runs were combined, I used a program called pspec to create a
Fourier transform of the entire Xcov 15 run (Figure 5). From this point on, my goal was
to distinguish real peaks from false peaks in the Fourier transform. First, I removed the
largest peak in terms of amplitude from the Fourier transform. I then performed a least
squares fit on the peak. Next, I removed that peak and any of its aliases from the original
Fourier transform, and I also removed its period from the light curve. With that period
removed I ran a Fourier transform on the new light curve, and I took out the next highest
peak. I repeated this process until the graph of the Fourier transform was nothing but
noise. With this process I marked sixteen peaks, or frequencies, in the Fourier transform.
Figure 6 shows a Fourier transform with the 16 peaks marked. Using these sixteen peaks,
I looked for any linear combinations of the frequencies. “Does the frequency of peak A
plus the frequency of peak B equal the frequency of peak C?” Once the true peaks had
been identified, my job was done. It is then left up to someone else to use fit these
frequencies to a stellar model.
CCD Experiment
For part of the summer I was involved with testing the performance of a CCD
camera used in high-speed photometry. The camera was mounted on the 26-inch
telescope at Fick Observatory. Between the 6th and 10th of July, over 1300 images of the
pulsating sub-dwarf star KPD1930 were taken, and each image had an exposure time of
five seconds. My job was to reduce the CCD images and extract the light curve, which
was then used for time series analysis.
To reduce the CCD images, I used a program called IRAF. Most of the images
were of the target star and its surroundings (figure 7), but flat field and dark field images
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were also taken periodically. Dark fields are images taken with the shutter of the camera
closed, and they show any electronic noise on the CCD camera and also any hotspots.
The flat field images are images of an equally lit out of focus area, and the images show
obstructions such as dirt on the CCD lens cover and mirrors.
From the dark fields and flat fields, I created one dark field image and one flat
field image. I then subtracted the dark field from each of the images and divided out the
flat field for each image. Once the images had been corrected using the darks and flats, I
began to extract data. From each image I extracted flux, sky reading, and total counts for
the target star and eight comparison stars. The data I extracted is currently being used for
pulsation analysis.
Results
The results of my research are shown in Tables 1-5. Table 1 lists in increasing
frequency the 16 frequencies I took out of the Fourier transform of the light curve from
EC20058. Tables 2 and 3 list what peaks from the Fourier transform are combinations of
other peaks. Table 3 also lists a triplet in the Fourier transform. Table 4 lists two
possible families of peaks. They are listed as families because those groups of peaks
appeared to combine together only with others in their family. Table 6 is a list of all the
independent frequencies. These are the frequencies that would be used as constraints in a
stellar model.
Conclusion
The goals for this summer were to perform data reduction on light curves of
pulsating white dwarfs and to gain research experience. Over the course of the summer, I
was successful in reducing the data of a pulsating white dwarf taken with WET because I
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had found the independent frequencies at which the star pulsates. Besides being
successful in find the independent frequencies, I also gained experience doing data
reduction of light curves taken by WET and also CCD images. In the future, my
experience may even allow me to take part of the next WET run.
Works Cited
Kawaler, Steven D. and Winget, Donald E. “White Dwarfs: Fossil Stars.” Sky and
Telescope. August 1987.
Kawaler, Steven D. and Dahlstrom, Michael. “White Dwarf Stars.” American Scientist.
In press 2000.
Nather, Edward R. and Winget, Donald E. “Taking the Pulse of White Dwarfs.” Sky and
Telescope. April 1992.
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