The US-Russia Plasma Astrophysics Collaboration is the first research team to calculate the complicated flows of the ionized matter drawn into rotating magnetized stars. Dr. Marina Romanova, Senior Research Associate, of the Cornell University Department of Astronomy, and Professor Richard Lovelace, of the Cornell University Departments of Astronomy and Applied and Engineering Physics, led the team that developed the theory and methods for solving this problem. Their work marks the first major step toward providing numerical understanding of the dynamics (and associated variability) of matter flow around rotating magnetized stars. Their model and the results of simulations run on the parallel Windows-based Velocity Cluster at the Cornell Theory Center (CTC) are published in the October 1 issue of The Astrophysical Journal. The Collaboration investigates astrophysical phenomena that can not be resolved by today’s best telescopes but can be modeled, “observed,” and studied through numerical experiments using computer simulations. The group of scientists working on this simulation includes Dr. Koldoba, from the Institute of Mathematical Modelling, Moscow, and Dr. Ustyugova, from the Keldysh Institute of Applied Mathematics, Moscow, who created the three-dimensional code for numerical modeling of this problem, and Justin Wick, Cornell Applied and Engineering Physics ’04, who developed the MPI version of this code for use on the Velocity Cluster. A large volume of observational data on the radio, optical, and X-ray emissions exists for the class of astrophysical objects studied by the Collaboration. However, until recently scientists have not studied the three-dimensional magnetized flows of the ionized matter in and around these objects using numerical simulations. The Collaboration’s recent three-dimensional simulations pertain to stars with dipole magnetic fields, specifically young, newly-formed stars, which rotate slowly (typically a period of 10 days) and very old stars, neutron stars, which rotate with periods ranging from milliseconds to tens of seconds. A young star is formed when a cloud of gas collapses in on itself due to its gravity. After the collapse, the star is usually surrounded by a disk of gaseous matter, the accretion disk, that slowly falls into the star. As the ionized matter in the disk approaches the star, the star's magnetic field modifies the motion of the charged matter, and the matter is drawn toward the magnetic poles during its descent. The oldest stars, white dwarfs and neutron stars, also have dipole type magnetic fields and accretion disks. However, their disks are created from the matter lost from a companion star. The simulations done by the US-Russia Collaboration apply to both the young and old stars. These flow simulations are complicated by the fact that the axis of the magnetic poles is tilted relative to the disk's rotation axis, making the model inherently three-dimensional. To solve this problem, the Collaboration used a system of eight partial differential equations, consisting of three vectors of velocity, three vectors of magnetic field, a variable for density, and a variable for energy-density. A special “cubed sphere” numerical grid was developed along with specific finite difference numerical code for the model. Assuming that the rotation axis of the star is the same as the rotation axis of the accretion disk, Romanova and Lovelace simulate the flow of matter around a star at different inclination angles. Even the fastest desktop workstation would take three months to solve just one case, and it would take years to complete all of the necessary simulations for this project. To help speed up their calculations, Romanova and Lovelace approached the Cornell Theory Center. The group now uses CTC's Dell/Windows Velocity V+ Cluster, typically employing 24 or 48 processors per simulation. With this increase in computing power, Romanova and Lovelace are able to run a case in a mere one to five days. The group conducts simulations that run for five to twelve rotations of the disk, sufficient to show the physics of the process, as the flow was shown to settle after approximately one rotation. Romanova and Lovelace were able to efficiently calculate for the first time the complicated flow of ionized matter around magnetized stars using the high-speed parallel processing power of CTC’s Velocity Clusters. Based on the results of their simulations, the group found that the flow of matter around a star takes on different shapes depending on the inclination of the magnetic axis relative to the rotational axis of the disk. Currently, the group is conducting detailed comparisons of their results with observational data, including records of variability from different young stars. The US-Russia Plasma Astrophysics Collaboration investigates numerically different astrophysical objects, including the formation of magnetically driven jets and outflows from the accretion disks, propagation of magnetized neutron stars through the interstellar medium, and other topics (see http://www.astro.cornell.edu/us-rus).
The magnetic field of young stars is typically a thousand times larger than that of the sun, so that the disk is disrupted by the magnetic field of the star at several stellar radii, and matter spirals up above the disk along the magnetosphere and then down to the stellar surface in the area close to magnetic poles, forming hot spots. At a relatively small inclination angle (15°) matter accretes in two streams which form two hot spots at the surface of the star.
At the medium inclination angle (45°) the accretion stream has a complicated shape, while the hot spots split into two spots. At a very large inclination angle (75°) matter again flows in two streams, but the streams are located almost in the plane of the disk. This behavior was not expected from the simple theoretical models and will greatly help to untangle the complicated light curves observed from these stars. It is interesting, that at small densities, the matter blankets a disk across the entire magnetosphere, whereas at higher densities matter accretes in streams.
