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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) t D i DV i 0 mass conservation t S j S V i j i 1 4 t g B j B0 1 4 i g B j Bi momentum conservation S S g B B j g g j P PB Q 2S 0 8 ~ ~ t B j i B jV i ~i B iV j g jk k induction 2 ~i ch t ch i B 2 2 “divergence cleanser” cp Active Galaxy Centaurus A Describing a Black Hole • Three possible intrinsic properties: – Mass – Angular momentum (spin) – Electric charge Astrophysically unlikely • Nothing else can be known about a black hole – “No hair” theorem 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 through Magnetic fields • Magnetically dominated flux points away from black hole’s poles, forming jets Accretion Disks: What we don’t know Jets •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 Total intensity image at 4.85 GHz of SS433 •What is the source of these phenomena? Blundell, K. M. & Bowler, M. G., 2004, ApJ, 616, L159 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 of The 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 Six cubes are projected into segments of a sphere Each block has its own coordinate system Jet Orientation Energy Equations in Cosmos++ Extended Artificial Viscosity (eAV) t E i EV i P tW P Q i WV i WT , , h, B internal energy V t i i i F 0i 0 WT , , h, B total energy conservation 0 gT 0 F 0i 0j g g g V P PB j Q j 00 j i i 1 0 i 4 B B B 0 B 0V i 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 1010 g/cm3 B 8380 G H 2.7 107 cm 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 - Results torus2d.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 Magnetic Unbound Field Lines Material 15 Degree Tilt Jets Magnetic Unbound Field Lines Material

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posted: | 4/19/2013 |

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