GRMHD Astrophysics Simulations using Cosmos++

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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  WT ,  , h, B     internal energy

    V 
 t      i
              i
                      i F 0i  0  WT ,  , 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



   1010 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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