I
will present the current results of my on-going efforts to accurately
model the accretion streams in the magnetic cataclysmic variable
stars known as Polars. I have developed a computational code that
uses SPH as a basis for tackling the extremely complex physics
involved in the accretion stream. The current version of the
computational models include an improved treatment of the motion
along the magnetically confined portion of the accretion stream which
allows the extraction of synthetic radial velocity data and phase
information for stream eclipses. I am currently developing a
secondary analysis code that will automatically extract radial
velocity data positions along the entire stream from any specified
inclination and phase. The progress and initial results of the
extraction code and observational comparisons at the time of the
conference are presented.
The term Cataclysmic Variable (CV)
defines a class of binary systems composed of a white dwarf primary and
a low-mass, main sequence secondary star. In these binary systems, some
material is pulled off of the secondary star and onto the white dwarf
in a process called accretion. Polars are a subset of CVs which are
distinguished by the strong magnetic field of the white dwarf primary,
typically > 10 MG. This magnetic field acts to synchronize the
rotation of the primary to the secondary orbital period as well as
significantly affecting the accretion process.
In non-magnetic CVs the accretion material forms an accretion disk
around the white dwarf which is fed by a thin ballistic accretion
stream from the L1 point on the secondary star to the edge of the
accretion disk. In contrast the accretion stream in polars is diverted
by the magnetic field of the white dwarf before an accretion disk can
form. Once diverted the accretion stream flows along the magnetic field
lines directly onto the white dwarf surface. The synchronous rotation
and the diverted stream result in a relatively stable accretion
geometry containing a ballistic stream in the orbital plane and a
magnetic stream out of the orbital plane. (See Figure 1 for a schematic diagram of
a typical polar.)
This highly simplified view of the
accretion stream is commonly used and seems to represent the major
features of polars, but the simple models are inadequate to fully
represent the complicated structure that most likely exists in these
systems.
Figure
1: schematic diagram of a typical polar
The goal of this project is to create a detailed, coherent model of the accretion stream in polars from the L1 point to the white dwarf surface that is not constrained by the major simplifying assumptions of the standard model. In order to create detailed models of the accretion stream, we must make use of computationally intensive algorithms such as smoothed particle hydrodynamics (SPH).
In our model, the particles enter the
stream at the L1 point as ballistic stream particles. The number of
particles entering the stream depends on the mass transfer rate and can
be time dependant. Within the ballistic stream, the motion of the gas
is influenced by gravity, the rotation of the binary system, and the
thermal pressure gradients within the stream. SPH calculates the
density and pressure gradients and adds that to the acceleration due to
any other external forces. At each time step, the condition for
coupling to the magnetic field is checked. When the magnetic pressure
due to the white dwarf first exceeds the ram pressure of the gas, the
particles are flagged as coupled.
Once coupled, the magnetically confined
stream particles move along the dipole field lines according to the
conservation of energy equations. The total mechanical energy at
coupling is calculated by the sum of the gravitational potential energy
and kinetic energy. The code allows the full kinetic energy to be
conserved during the coupling process or a portion of that kinetic
energy can be transferred into thermal energy. Once the magnetically
confined particles reach the surface of the white dwarf (impact) they
are “recycled” to the secondary star to re-enter the stream.
Figure 2a and 2b show the top and side view of the full
accretion stream. The ballistic stream particles are show in green
while the magnetic stream particles are red. The white dwarf is
indicated in blue, and the secondary star lies just off the right side
of the plot.
As predicted in earlier models there is some coupling of material
directly from L1 as well as the main coupling region further
downstream. The improvements in the latest modeling code concerning
information about the positions of particles along the magnetic streams
clearly show that the portion of the magnetically confined stream
starting directly at L1 has a much lower density than the main confined
stream.
| Figure 2a: top view of accretion stream model click on image for enlarged view |
Figure 2b: side view of accretion stream model click on image for enlarged view |
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We have also developed a new
visualization tools that allows us to view the stream as it would
appear from any inclination and phase. Figures 3a,
3b, and 3c
show visualizations of the stream at various phases. The IDL
visualization program can also create animations showing the binary
rotating through all phases. These visualizations aid in the
understanding of the phase and inclination dependency of the system
geometry in both eclipsing and non-eclipsing systems. (Animation not available on the poster at AAS)
| Figure 3a: 3-D view of a model stream phase = 0, inclination = 55 click on image for enlarged view |
Figure 3b: 3-D view of a model stream phase = 0.15, inclination = 55 click on image for enlarged view |
Figure 3b: 3-D view of a model stream phase = 0.70, inclination = 55 click on image for enlarged view |
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In addition to the geometric results,
the new models results can be easily analyzed to provide information on
the velocities within both the ballistic and magnetic portions of the
accretion stream. The same basic equations used for the 3D
visualization are used to convert the velocities into phase and
inclination dependant radial velocities.
Looking at the velocity for every
particle in the stream would provide too much information to analyze.
Therefore, we extract the average density and velocity across a grid of
points laid over the stream. Figure 4a and 4b shows the grid overlaid on top of the stream
particles. Also labeled in these figures are 7 points within the stream
that will be examined in more detail.
| Figure 4a: top view of accretion stream model overlaid with grid points in green click on image for enlarged view |
Figure 4b: side view of accretion stream model overlaid with grid points in green click on image for enlarged view |
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Figures 5a
and 5b show the radial velocities for each
grid point at the phase and inclinations used in the figure 3b and 3c
visualizations. The grid points cover a wide range of radial velocities
and the three structural components of the stream can be easily
separated (click here for a version of
figure 5a that includes labels for the components). The diagrams
also show the great variation of radial velocities at different phases.
| Figure 5a: radial velocities for stream particles phase = 0.15, inclination = 55 click on image for enlarged view |
Figure 5b: radial velocities for stream particles phase = 0.70, inclination = 55 click on image for enlarged view |
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Figure 6
shows the radial velocity over the entire range of phases for each of
the seven extraction points indicated in figure 4. You can easily see
the great range in radial velocities especially for points in the
magnetically confined stream near the white dwarf. It is also
noticeable that the radial velocity peak occurs at different phases for
different points in the stream.
Figure 6: radial velocity curves for
selected locations in the stream
click on image for enlarged view
Now that the models are producing data
for the line of sight geometry and radial velocity, we can use the
model results for observational comparisons. To build a model of a
polar, we need good constraints on the system parameters input into the
SPH code. Then we need observational data that show a clear signature
of the accretion stream such as trailed spectrograms of emission lines
thought to originate in the stream or eclipse timings of the accretion
hot spot by the accretion stream.
By comparing the model results and
observations, we will be able to correlate observational features with
the geometrical locations in the accretion stream and possibly
constrain system parameters by model fitting.
Cash, J., 2002, “Modeling the Accretion Stream in Polars”, PhD Thesis,
University of Wyoming.
Cash, J., and Howell, S., 2005, “Modeling the Accretion Stream in
Polars”, ApJ, in prep.
For further information see:
My website at http://physics.scsu.edu/~jcash/research/
This work was supported by NASA/OSS NNG04GD62G NASA/MU-SPIN NNG04GC40A,
NASA/URC NCCW-0085 and NASA/PAIR NCC 5-454.
This work was possible through the use
of the following software packages:
PGI
CDK
http://www.pgroup.com/
IDL
http://www.rsinc.com/idl/
I would like to acknowledge the
following students for their contributions this research project:
Deidrick Capers, Alexander Alexandrov, Sarah Constantine, and Patrick
Michael
