Extraction of synthetic data from model accretion streams in Polars.

Jennifer Cash, South Carolina State University


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.

Introduction to Polars:

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

schematic diagram

Stream Modeling:

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
top view of stream side view of stream

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
figure 3a
figure 3b
figure 3c

Radial Velocities:

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
figure 4a
figure 4b

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
Figure 5a
Figure 5b

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

figure 6

Observational Comparison:

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.

References and Resources:

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