GRMHD Astrophysics Simulations using Cosmos++
Joseph Niehaus, Chris Lindner, Chris Fragile
Why do Computational Astrophysics?
• Tests the extremes of space that cannot be simulated by conventional means
• Many vital parameters cannot be observed
• Many problems have no exploitable symmetry
Finite Volume Simulations• Divide the computational area into
zones• Each zone contains essential data
about the material contained inside
• The simulation is evolved in time through a series of time steps
• As the simulation progresses, cells communicate with each other
Highlights of Cosmos++
• Developers: P. Anninos, P. C. Fragile, J. Salmonson, & S. Murray– Anninos & Fragile (2003) ApJS, 144, 243– Anninos, Fragile, & Murray (2003) ApJS, 147, 177– Anninos, Fragile & Salmonson (2005) ApJ, 635, 723
• Multi-dimensional Arbitrary-Lagrange-Eulerian (ALE) fluid dynamics code– 1, 2, or 3D unstructured mesh
• Local Adaptive Mesh Refinement (Khokhlov 1998)
Highlights of Cosmos++• Multi-physics code for Astrophysics/Cosmology
– Newtonian & GR MHD– Arbitrary spacetime curvature (K. Camarda -> Evolving
GRMHD)– Relativistic scalar fields– Radiation transport (Flux-limited diffusion -> Monte Carlo)– Equilibrium & Non-Equilibrium Chemistry (30+ reactions)– Radiative Cooling– Newtonian external & Self-gravity
• Developed for large parallel computation– LLNL Thunder, NCSA Teragrid, NASA Columbia, JPL Cosmos,
BSC MareNostrum
Local Adaptive Mesh Refinement
GRMHD Equations in Cosmos++Extended Artificial Viscosity (eAV)
mass conservation
momentum conservation
induction
“divergence cleanser”
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Describing a Black Hole• Three possible intrinsic properties:
– Mass– Angular momentum (spin)– Electric charge
• Nothing else can be known about a black hole– “No hair” theorem
Astrophysically unlikely
Black Hole Accretion Disks• Often formed from binary star systems• Black hole accretes matter from donor star• Disk of plasma forms around black hole• Angular momentum is exchanged throughMagnetic fields• Magnetically dominated flux points away from black hole’s poles, forming jets
Accretion Disks: What we don’t knowJets•What powers jets?•What sets their orientation?•How is the black hole oriented?
Cooling and Heating•What type of radiative transport occurs in the disk?•How does this effect disk structure?•How does this effect what we observe?
QPOs•What is the source of these phenomena? Blundell, K. M. & Bowler, M. G., 2004, ApJ, 616, L159
Total intensity image at 4.85 GHz of SS433
What determines jet orientation in accretion disk systems?
We can answer this question by simulating systems where the angular momentum of the disk is not aligned with the angular momentum ofThe black hole
“Tilted accretion disks”(Fragile, Mathews, & Wilson, 2001, Astrophys. J., 553, 955)
•Can arise from asymmetric binary systems•Breaks the main degeneracy in the problem
Spherical-Polar Grid• Most commonly used type of
grid for accretion disk simulations– good angular momentum
conservation– easy to accommodate event
horizon• Not very good for simulating
jets in 3D– zones get very small along
pole forcing a very small integration timestep
– pole is a coordinate singularity
• creates problems, particularly for transport of fluid across the pole
Cubed-Sphere Grid• Common in atmospheric
codes• Not seen as often in
astrophysics• Adequate for simulating
disks– good angular momentum
conservation– easily accommodates event
horizon• Advantages for simulating
jets– nearly uniform zone sizing
over entire grid– no coordinate singularities
(except origin)
The Cubed Sphere
Each block has its own coordinate system
Six cubes are projected into segments of a sphere
Jet Orientation
Energy Equations in Cosmos++Extended Artificial Viscosity (eAV)
internal energy
total energy conservation
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Why Two Energy Equations?
• Tracked Simultaneously through code• Attempt to recapture as much heat as possible
– Attempting to counteract numerical diffusion• Used when total energy below error
– Both energies compared if both below error• Higher energy chosen
Heating Processes
• Magnetic– Magnetic Reconnection– Recaptured through total energy equation
• No explicit term
• Hydrodynamic– Shockwaves & Gas Compression– Handled directly by both energy equations
• Viscous– Internal heating due to fluid dynamics– Recaptured through total energy
Radiative Cooling Processes• Bremsstrahlung
– “Braking” cooling, emits radiation when decelerating
• Synchrotron– Relativistic electrons & positrons
• Inverse Compton– Electrons colliding with photons– Becomes prevalent as optical depth increases
Radiative Cooling Processes
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2.5D Simulations
• Initial stable solution for rotating torus
• Set up for MRI growth– Poloidal fields
• No mass or energy transported azimuthally– Vectors tracked numerically
2.5D Simulations
• 3 Scenarios for Comparison– M
• Similar to past runs• No heating or cooling
– Physical assumption
– TM• Heating included
– Total energy & Internal energy equations
– TMC• Heating and Cooling Processes• Total energy & Internal energy
2D Simulations - Resultstorus2d.m.h torus2d.tm.h torus2d.tmc.h
Conclusions
• Cosmos++• GR MHD• AMR• Radiative cooling
• Accretion Disks• Cooling/Heating• Jets/Tilted Disks• QPO’s
Untilted Disk Jets
MagneticField Lines
Unbound Material
15 Degree Tilt Jets
MagneticField Lines
Unbound Material
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