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)

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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