Insert title here

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Computational Simulations of Relativistic Jets
using the Cubed Sphere Grid
Christopher C. Lindner, Dr. P. Chris Fragile,
Joseph D. Niehaus
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Relativistic Jets

• High Speed
• High Energy
• Observable in X-Ray and sometimeseven visible
  and radio spectrums

Images courtesy of NASA
Minkowskis Object Very Large ArrayRadio
emissions overlaid in red
M87Hubble Space Telescope Visible Wide Field
and Planetary Camera
Crab Nebula Chandra X-Ray Observatory
Jet from a Neutron Star
Jet from an AGN
Jet from AGN
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The Source Black Hole Accretion Disks

• Often formed from binary star systems orfound in
  galactic disks
• Black hole accretes matter from donor star
• Disk of plasma forms around black hole
• Angular momentum is given up to magneticfields
• Magnetically dominated flux points away from
  black holes poles, forming jets

Hawley, J. F. Krolik, J.H. 2006, ApJ, 641, 103
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Observational Peculiarities Precessing Jets and
Tilted Accretion disks

• Not all jets are perfectly linear form
• Some form corkscrew patterns, indicating jet
  precession
• Binary systems have been observed where jet
  orientationsdont match the angular momentum of
  the accreting object

Total intensity image at 4.85 GHz of SS433
Blundell, K. M. Bowler, M. G., 2004, ApJ, 616,
L159
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The Big Question What determines jet orientation
in accretion disk systems?

• Strong External Magnetic Fields?
• Angular momentum of the central
• object?
• Angular momentum of the disk?

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The Big Question What determines jet orientation
in accretion disk systems?

• Strong External Magnetic Fields?
• Angular momentum of the central
• object?
• Angular momentum of the disk?

But how do we decide which of these determines
jet orientation?
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The Big Question What determines jet orientation
in accretion disk systems?
We can answer this question by studying systems
where the angular momentum of the disk is not
aligned with the angular momentum of The black
hole
Video from Chandra resource library
chandra.harvard.edu

• Tilted accretion disks
• (Fragile, Mathews, Wilson, 2001, Astrophys. J.,
  553, 955)
• Can arise from asymmetric binarysystems
• Breaks the main degeneracy in the problem

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How can we Study This?

• The angular momentum of accretion disks is
  difficult to determine by observation
• Often derived from jet orientation
• These systems are highly time variable, and
  containno exploitable symmetry
• This makes it very difficult to derive an
  analyticmodel for the system
• Because of this, we perform numerical
  simulationsto model these systems

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How do we Simulate This?
Instead of simulating with individual pieces of
matter, we can divide the area around our black
hole Into a grid.
Each zone in the grid will contain
informationabout that space, including the mass
containedin it, the velocity and momentum of
that matter,and other important properties of
the simulation.

• This means that
• The more zones we have, the better resolved our
  simulation will be
• The more zones we have, the more computational
  power we require
• The size of our smallest zone will affect our
  overall simulation speed
• The structure of our grid will affect the
  accuracy of our results

So what coordinate system should we use?
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Coordinate Systems
Spherical Polar
Issues
Benefits

• Great angular momentumtransport
• Even distribution of cellsazimuthally
• Easy to accommodate forblack hole horizon in
  thecenter of the grid
• Most common grid forblack hole simulations

• Singularity along polaraxis
• Zones are very smallalong poles,
  requiringgreater computational power

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Coordinate Systems
Cartesian
Issues
Benefits

• Even distribution of zonesin all directions
• All zones are the same size

• Poor angular momentum transport
• Difficult to simulateblack hole frame dragging
• Requires high resolutionfor accuracy

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Coordinate Systems
Cubed Sphere
Issues
Benefits

• Even distribution of zonesin all directions
• Zone size is easier to manage
• Angular momentum transport is superior to
  Cartesian
• Easy to divide processing tasks
• Can be scaled down to 1, 2,or 4 block simulations

• Block boundaries cangenerate numericalerrors
• Each block has differentcoordinate systems

Koldoba, A. V., Romanova, M. M., Ustyugova, G.
V., Lovelace, R. V. E., 2002, ApJ, 576, L53
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The Cubed Sphere
Essentially a cubed projected onto a Sphere
The sphere is divided into six identical blocks
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The Cubed Sphere
Each block is given a dedicated processor
If more than six Processors are used, blocks
are radially subdivided
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The Cubed Sphere
The code can also be run with 1, 2, or 4 blocks
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Simulations on the Cubed Sphere
Sedov Blast Wave
Fluid Pulse
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Simulations on the Cubed Sphere
Accreting Torus
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Future Work

• Complete high-resolution runs of tilted disks
• Creating an expandable grid structure
• Test of 90 degree tilted disk case