Computational Simulations of Relativistic Jets using Computational Simulations of Relativistic Jets using the Cubed Sphere Gridthe Cubed Sphere Grid

Computational Simulations of Relativistic Jets using Computational Simulations of Relativistic Jets using the Cubed Sphere Gridthe Cubed Sphere Grid

Previous Grid ConstructionsPrevious Grid Constructions

The objective of our study is to The objective of our study is to determine what establishes the jet determine what establishes the jet orientation in black hole accretion disk orientation in black hole accretion disk systems. Unfortunately, fundamental systems. Unfortunately, fundamental parameters like angular momentum are parameters like angular momentum are not directly observable, and analytic not directly observable, and analytic models are difficult to develop. For models are difficult to develop. For these reasons, we use numerical models these reasons, we use numerical models to study these systems.to study these systems.

Current grid constructions are Current grid constructions are inadequate for simultaneously inadequate for simultaneously simulating disks and jets. In order to simulating disks and jets. In order to do so, we must develop a new grid do so, we must develop a new grid system.system.

Christopher C. Lindner, P. Chris FragileChristopher C. Lindner, P. Chris FragileAbstractAbstract

Relativistic Jets are Relativistic Jets are streams of plasma streams of plasma moving throughout the moving throughout the universe at speeds up universe at speeds up to 99% the speed of to 99% the speed of light. They produce light. They produce high-energy X-ray, high-energy X-ray, radio, and visible radio, and visible radiation that are radiation that are observable from great observable from great distances across the distances across the universe.universe.

Many of these jets have Many of these jets have been attributed to been attributed to black hole accretion black hole accretion disk systems. In these disk systems. In these systems, a disk of systems, a disk of material surrounds a material surrounds a black hole, black hole, andand through through magnetic processes the magnetic processes the material accretes onto material accretes onto the black hole.the black hole.

Relativistic jets Relativistic jets originating from the originating from the Crab Nebula (above) Crab Nebula (above) and the galaxy M87 and the galaxy M87 (below)(below)

Accretion disk simulations Accretion disk simulations can be run in two or three can be run in two or three dimensions. In two dimensions. In two dimensional simulations, dimensional simulations, we consider a “slice” of we consider a “slice” of the disk, and can treat it the disk, and can treat it as an azimuthal average as an azimuthal average of the entire disk. of the entire disk.

However, in studies of However, in studies of systems where the systems where the angular momentum of the angular momentum of the disk is not aligned with disk is not aligned with the angular momentum of the angular momentum of the black hole, our the black hole, our symmetry is broken, and symmetry is broken, and we must study our we must study our problem in three problem in three dimensions.dimensions.

The cubed sphere grid structure is essentially 6 The cubed sphere grid structure is essentially 6 cubes that together are morphed in a sphere. The cubes that together are morphed in a sphere. The resulting domain features no poles and has an even resulting domain features no poles and has an even distribution of zones in each of the six domains.distribution of zones in each of the six domains.

Our code is designed Our code is designed to dedicate each to dedicate each block to one block to one processor. If more processor. If more processors are used, processors are used, each block can be each block can be radially subdivided.radially subdivided.

For simulations where For simulations where the polar region is not the polar region is not being studied, we can being studied, we can restrict our simulation restrict our simulation to 1, 2, or 4 blocks to to 1, 2, or 4 blocks to limit the computational limit the computational expense.expense.

The Cubed SphereThe Cubed Sphere

Traditionally we have used the spherical polar Traditionally we have used the spherical polar coordinate grid for studying this type of coordinate grid for studying this type of problem. Though this is sufficient for problem. Though this is sufficient for studying the disk itself, the spherical polar studying the disk itself, the spherical polar mesh is flawed in that it features two poles mesh is flawed in that it features two poles which create numerical irregularities in these which create numerical irregularities in these regions. This makes it virtually impossible to regions. This makes it virtually impossible to conclusively study flows near the poles, conclusively study flows near the poles, including jets.including jets.

If we wish to study jets in these systems, we If we wish to study jets in these systems, we must implement a new coordinate system must implement a new coordinate system that both adequately conserves angular that both adequately conserves angular momentum and is well defined along the momentum and is well defined along the poles.poles.

Current and future work on the Current and future work on the Cubed SphereCubed Sphere

Thus far we have run several test problems to Thus far we have run several test problems to determine the effectiveness of the cubed sphere determine the effectiveness of the cubed sphere grid including rotating fluids around the grid, grid including rotating fluids around the grid, relativistic jet simulations, and black hole torus relativistic jet simulations, and black hole torus accretion simulations.accretion simulations.

In the future we plan to run full, high-In the future we plan to run full, high-resolution simulations of the black resolution simulations of the black hole accretion disk problem and hole accretion disk problem and develop analysis tools to allow us to develop analysis tools to allow us to further study relativistic jet further study relativistic jet production and orientation in black production and orientation in black hole accretion disk systems.hole accretion disk systems.

Simulations run on the cubed sphere grid: a pulse of Simulations run on the cubed sphere grid: a pulse of liquid circles the grid (left), an adaptation of the Sedov liquid circles the grid (left), an adaptation of the Sedov Blast Wave to simulate relativistic jets (center), and an Blast Wave to simulate relativistic jets (center), and an accretion disk falling into a black hole (right)accretion disk falling into a black hole (right)

We gratefully acknowledge the We gratefully acknowledge the support of Faculty R&D and SURF support of Faculty R&D and SURF grants from the College of grants from the College of Charleston and a REAP Grant Charleston and a REAP Grant from the South Carolina Space from the South Carolina Space Grant Consortium.Grant Consortium.

AcknowledgementAcknowledgementss