Modeling the Accretion Stream in Polars

Abstract

I present a summary of my dissertation research into a method of modeling the accretion stream in magnetic cataclysmic variables known as polars. Polars are interacting binary stars in which the primary star is a magnetic white dwarf with a surface field strength 10 MG. Material is accreted from a low-mass main-sequence secondary star and funneled by the magnetic field onto the white dwarf surface. The standard, simple picture of the accretion stream has two regions: the ballistic path where the magnetic forces are negligible and the magnetically controlled path where the material is forced to flow along the magnetic field lines onto the white dwarf surface. The “coupling” point is located where the gas stream transitions from the ballistic path to the magnetically controlled path. The stream is assumed to be a thin tube with a cylindrically symmetric density distribution. This simple picture, however, is unable to explain the complex features often seen in polar observations. In order to develop a better understanding of the complex accretion streams, a more detailed model is needed. My models solve for the three-dimensional stream geometry and provide the density distribution and gas velocity throughout the stream from the L1 point to the white dwarf surface. In order to solve for the detailed stream structure without resorting to simplified geometries, we must employ computationally intensive algorithms such as smoothed particle hydrodynamics (SPH). SPH treats a continuous gas as a superposition of extended segments of the gas, referred to as particles. The hydrodynamic equations can then be approximated by summations over the particles. In my SPH models, the gas particles are released from the L1 boundary and then allowed to flow under the influence of the gravitational, rotational, and thermodynamic forces. These initial models use the common assumption that the magnetic pressure is negligible as long as the ram pressure of the gas is higher. Once the magnetic pressure on a particle exceeds the ram pressure, the particle “couples” and is forced to flow along the magnetic field lines. The SPH method has been applied to a “reference system” that has system parameters typical of what is found in known polars. The reference system results are in general agreement with the standard, simplified model of the accretion stream but show considerably more detail. Interesting features include the coupling region and the impact region on the white dwarf surface. The coupling region is significantly extended, approximately 11 white dwarf radii long. The low-density edges of the stream couple to the field lines first, while the higher density core of the stream is able to penetrate farther into the magnetosphere of the white dwarf. In addition, because of the orientation of the magnetic dipole axis to the stream, the edge of the stream closest to the dipole will begin to couple before the far edge. The resulting shape is an asymmetric cone. The basic structure in the coupling region is projected down to the white dwarf surface at the impact region. Material from the stream impacts the surface in an arc shape offset from the dipole axis. One end of the arc, corresponding to the material that coupled from the core of the stream, has a much higher density than material impacting along the remainder of the arc. The arc is more accurately described as a V shape with two wings extending out from the high-density core region. The impacting density drops off along these wings, which are also asymmetric. In addition to the stream geometry described above, the reference SPH model reveals another feature not seen in the standard simple accretion-stream model. While the vast majority of the gas in the stream flows away from the L1 point along the ballistic stream, a small fraction of the material is predicted to be controlled by the magnetic field immediately and couple to the lines directly at the L1 point. This small amount of material would flow along a distinct path and impact the white dwarf away from the main arc-shaped impact region. The initial reference model work was supplemented with additional SPH models that explore the effects of various system parameters on the accretion stream. In particular, the magnetic field strength, mass-transfer rate, dipole orientation, and stream temperature were varied. As expected, the coupling position depends upon the mass-transfer rate and magnetic field strength. The stream temperature, which is assumed to be isothermal, does not significantly affect the coupling position but does affect the width of the accretion stream. The dipole orientation naturally affects the geometry of the magnetically confined path and impact location on the white dwarf but shows