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3-D Visualization of
Cataclysmic Variables
With IDL
by:
Deidrick Capers
The focus of this summer's research was the modeling of magnetic cataclysmic
variables using Interactive Data Language(IDL) software. A basic IDL program
designed for this specific purpose was already in existence; created by Dr. Cash and
previous research students under her supervision. The ultimate goal of this summer's
work was to improve upon the already existing program and extend it to a point where it
could be efficiently used for other applications. In order to model or visualize
cataclysmic variables with the software or even mentally one must first have a firm grasp
of what cataclysmic variables are and the nature of their behavior.
Cataclysmic variables are just one of the many different types of binary star
systems that, together with other multiple star systems, make up more than half of all of
the stars found throughout our galaxy. Cataclysmic variables are composed of a single
red dwarf star and a collapsed white dwarf star. The two stars orbit each other once every
few hours and are extremely close to one another in distance. In fact they orbit one
another at such an extremely small distance that they might be mistaken for a single star
instead of the binary system that they actually are. The white dwarf star has a mass
approximately equal to that of the Sun contained in a volume approximately equal to that
of the Earth. The white dwarf is extremely high in temperature and very small in size in
comparison to other stars.
It is the small size of the white dwarf that is exactly the reason why it does
not give off much light. In contrast, the red dwarf is similar to our Sun but is much
redder in color and less massive. Because of the fact that the red dwarf and white dwarf
are orbiting so close to one another, gas is extracted from the red dwarf and is pulled in
toward the white dwarf. In some systems, especially those where the magnetic field of
the white dwarf is not very strong, the gas doesn’t actually fall directly into the white
dwarf but encircles it and forms a disc. This disc, known as an accretion disc with the
white dwarf serving as its center, usually gives off more visible light than the red dwarf
or the white dwarf.
The brightness of these star systems changes immensely when comparing them at
times when they are exchanging gases and when they are not. Some cataclysmic
variables, such as novae, have amplitude variations of 6 to 19 magnitudes, which
translates to factors of 100 to a few million in brightness. These changes in brightness
can take place over a period of months or even years. There are types of cataclysmic
variables that contain white dwarfs with extremely powerful magnetic fields and
obviously they quite behave differently than the nonmagnetic variety.
These particular types of magnetic CVs (cataclysmic variables) are known as a
polars. In these systems the gas that is pulled from the red dwarf down to the white
dwarf does not circle and form an accretion disc because of the strong magnetic field.
The particles within the accretion stream are partially ionized, and the strong magnetic
field near the white dwarf prevents the ionized gas particles from crossing the field lines.
Instead of forming accretion discs the gas is entwined along the field lines and pulled
directly to the magnetic poles of the white dwarf. In some systems the magnetic fields of
the white dwarf is so strong that it synchronizes its rotation with that of the whole binary
system thus creating the illusion that the stars are rotating as rigid bodies. To give an
example of the strength of the magnetic field of this type of white dwarf, it is
approximately 50 million times stronger than the magnetic field of the Earth.
Once the basic concepts of cataclysmic variables, polars in particular, are firmly
grasped the matter of modeling them in a 3-D environment becomes easier to visualize.
There are several different reasons for modeling polars in a 3-D environment. One of the
more, if not the most, important reasons is simply because they cannot be resolved as two
orbiting binary stars exchanging materials by any existing technology. Current
technology only allows for the changes in the amount of light given off by polars and the
spectrum of the light to be detectable. By modeling the stars, scientists can better
understand what is actually going on as far as the interactions of the binary stars go and
how it might appear if indeed it were resolvable.
Another important reason for modeling the system is to attempt to pinpoint the
positions of each star, in reference to each other and the stream in between them, at
different phases of their orbit. For example during a phase setting of 0.25 the two stars
and the stream appear in a straight horizontal line without any obstruction of view
whatsoever; shown in figure 1-1. This position in the model could possibly correlate
with the period of time in which the system giving off the most light. A phase setting
of 0.0 displays the red dwarf totally obstructing the view of the stream and the white
dwarf; shown in figure 1-2. This position may very well correlate to the period in time
when the system is giving off a smaller amount of light in relation to the previous phase
setting. As with all other models this model allows the user to manipulate the polars in
ways that are not possible in the real world making for an effective tool in the study of
polars.
The particular modeling software used in this work was Interactive Data
Language(IDL) utilized on a Linux operating system platform. The Linux operating
system was extremely useful and efficient because it allows secure transfers of data easily
and efficiently. Linux computers can effectively cooperate in the remote operation of
applications and graphical displays.
In addition to remote access another important feature of the Linux operating
system was bash shell scripting. Bash shell scripting is a cross between command line
and an actual computer programming language. The scripting allows for a series of
commands to be inputted inside of a text file, whose name is the calling method,
formatted in such a way that it can be called simply by inputting the name of the file.
Once the name is inputted on the command line the commands contained within the file
are executed in sequential order as if it were a stand alone computer program. Bash shell
scripting was utilized, in this work, to extract input files of a specified format from
existing file lists so that they could accessed quickly and efficiently for analyzing.
Although Linux and bash shell scripts were vital components, the main
component was IDL. IDL is an immensely powerful software in the realm of 3-D
visualization and image analysis. Currently it is being used in the medical industry to
produce 3-D images of organs such as the heart or brain. The simple fact that this
software can to be used to visualize the human body and celestial bodies is a testament to
its enormous capabilities. The precision with which it can manipulate images makes it an
extremely useful tool when analyzing topographical or contour maps also. The main
parts of IDL used in this work was its 3-D object creation and placement capabilities.
The actual IDL program that is the center of the research conducted this summer
is a collection of 3-D objects placed on an three dimensional axis. From first glance at
the program one might be led to believe that it is merely a collection of orbs on a grid but
it is much more than that. While the placement of the orbs may appear to be a simple
aesthetic treatment with the larger orb representing the red dwarf, the small blue orb
representing the white dwarf, and the string of orbs in between them representing the
flow of materials, their placements are actually scientifically accurate. The input files,
mentioned earlier, that were extracted by the bash shell scripts contain the data which
describes the placement of the flow of particles between the two stars.
The input files are actually output files from scientific codes that solve for the
position of the particles in the stream. These files, which are retrieved by the bash shell
scripts mentioned above, are used to test the models. These particular models are first
run on non-interactive direct graphic programs. There are two separate direct programs
designed to display a snapshot of the stream from an x-axis vs. y-axis and an x-axis vs. zaxis perspective. Both programs take the files as input and uses the numerical arrays
contained within them to create a 2-D scatter plot as illustrated in figures 1-3 and 1-4.
The stream appears on the plot as a series of colored points that flow with some degree of
uniformity.
The direct graphics programs serve as a manner of testing the models in order to
decide which ones are accurate and usable and which ones are not. The models that are
deemed accurate move on to become part of the 3-D model program. After the positions
of the particles are determined from the direct graphics program, orbs are created at these
positions on the program's grid forming the stream between to the two stars. It is this
scientific and mathematic method that makes it possible to depict the positions of the
stars and the stream accurately and not just as conveniently placed orbs that resemble
preceding models of polars.
Along with displaying the system the program allows the user to adjust not only
the phase, as mentioned earlier, but the inclination making it possible to view the system
from many different angles. After modifications made this summer, a zoom feature was
added along with an output that displays the updated phase and inclination when the
program is executing automotion. In addition to this feature the user may also transfer a
snapshot to a TIF file or create MPEGs. The automotion feature, when selected, allows
for a perpetual rotation of the system at a designated phase and inclination and for
MPEGs to be created from this motion. These features are important because they allow
the model results to be shared which enables others to view and possibly perform analysis
in addition to the user of the program. Figure 1-5 illustrates the newly modified
program's GUI.
As with most working projects new improvements and innovations are constantly
sought after. There are a few major ones involving this project that are being explored
presently. The first is the exporting of the program to other computers that don't
necessarily have IDL software on them. This feature would allow for a seemingly
unrestricted distribution of the program to many different users and increase the size of
the audience capable of viewing the program. Potentially it could mean that anyone with
an interest in polars or cataclysmic variables and a computer could have access to a
program that allows them to see the systems and manipulate them in a 3-D environment.
Another possible improvement on the program is an increase in the amount of
detail in which it depicts the cataclysmic variables. IDL has the capability to render
surfaces and contours with an enormous amount of detail. In the future it will be possible
to render the program in such a way that it resembles currently existing images of stars.
This will not only improve the visualization process but it will allow for a much more
scientifically accurate program in general.
This summer has provided an immeasurable amount of quality learning
experience. Whether it was computer science concepts, astronomical concepts, or even a
new problem solving technique, the research done this summer was truly a quality work
experience. As stated earlier this is a working project that will continue to become more
extensive. As time goes on there will be aspects about the program and the research that
will change but the goal will remain the same; to analyze, visualize and understand polars
in order to expand upon the already vast knowledge of the universe.
FIGURE 1-1
FIGURE 1-2
FIGURE 1-3
X vs Y Plot
FIGURE 1-4
X vs Z Plot
FIGURE 1-5
GUI