Simulations of Jets from
Black-Hole Accretion Disks
Chris Lindner
UT Austin
PI: P. Chris Fragile
College of Charleston
Collaborators: Peter Anninos, Jay
Salmonson
Relativistic Jets
•High Speed
•High Energy
•Observable in X-Ray and sometimes
even visible and radio spectrums
Images courtesy of NASA and ATNF
PKS 2356-61
NGC 4261
Radio and visible image
Radio and visible image
M87
Hubble Space Telescope
Visible
Relativistic Jets
Crab Nebula
Jet from a Neutron Star
Active Galaxy Centaurus A
Minkowski’s Object
Radio emissions overlaid in red
Jet from an AGN
Black Hole
• End of a star’s life
• Gravity bends light
around it
• It bends to the
point where no
light can escape!
• Can be found at
the center of almost
every galaxy
Accretion disks
• We can’t “see”
black holes…
• …but we can study
how their gravity
affects the objects
around them
Black Hole Accretion Disk
Systems
• X-ray binary star systems and galaxy nuclei
• 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
What is a
jet?
• Poynting Flux Jet – EM jet described by
Blandford-Znajek Mechanism located in
“evacuated funnel”
• Funnel Wall jet – gas-pressure launched
material jet surrounding the poyting flux
region
Hawley & Krolik, 2006
Total Pressure (gas plus magnetic)
The Magneto Rotational
Instability and Blandford-Znajek
Mechanism
• Positron-electron pair creation could
• Magnetic fields are enhanced via angular
momentum transport
• Leads to a strong polar magnetic field
create spark gaps in B fields, and
acceleration of these charges could
lead to observed emissions
Blandford and Znajek 1977
Jets: What we don’t know
What powers the jets?
What sets Jet orientation?
•Not all jets are perfectly linear
•Some form corkscrew patterns, indicating jet
precession
• Binary systems have been observed where jet
orientations don’t match the angular momentum of
the accreting object
How is the black hole oriented?
• Currently, this cannot be determined by
observation alone
Total intensity image at
4.85 GHz of SS433
Blundell, K. M. & Bowler, M. G., 2004, ApJ, 616, L159
Why do Computational Astrophysics?
• Tests the extremes
of space that cannot
be experimentally
recreated
• 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 – calculate
GRMHD Equations in Cosmos++
Extended Artificial Viscosity (eAV)
 
  S V 
 t D   i DV i
t S j

i
i
j

~
~
 t B j   i B jV i
~i
2
 t  ch  i B
mass conservation
 0
1
1

t  g B j B0 
i  g B j Bi
4
4
momentum conservation


S S
g   


B B  j g    g  j P  PB  Q 
0
 2S

8


~i
 B  iV j  g jk  k
induction
ch2
  2
“divergence cleanser”
cp




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, UT Lonestar, UT Ranger
Relativistic Jets in Simulation
• Angular momentum supported torus surrounding
a rotating black hole
• Weak seed dipole magnetic field (poloidal)
• Low density background
• Minor initial fluctuations to foster instabilities
• Mass disk << Mass BH
• Simulated for low number of orbital periods
Relativistic Jets in Simulation
Log Density
(~10 orders of magnitude between
dark red and blue)
McKinney 2005
Magnetic Field Geometry
Tilted
• Black holes spin
• Accretion Disks
Spin
• Do they have to
spin together?
• Could this explain
jet precession?
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
Initial tilted-disk simulations
[Show Movies]
Initial tilted-disk simulations
• Standing
shock along “line of nodes”
creates accretion streams
• Increase in accretion rate
• Observable precession
• No Bardeen-Petterson effect observed
Interesting physics.. but
No Jets!!!
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
Untilted Disk Jets
Magnetic
Field Lines
Unbound
Material
Untilted Disk Jets
(x10^6 – 6x10^6)
DeVilliers, Hawley & Krolik 2004
Scaled as 6 x (Mjet/Mtorus)
MassFluxRMax = Blue
UnboundMassFlux = Black
Possible Issues
• Unphysical or physical numerical reconnection
• Mass loading
• Lack of angular momentum conservation in
funnel region
•
… or maybe previous simulations are too symmetric?
Conclusions
• Two types of jets: Poynting flux and matter
(funnel wall)
• Jets do form in MHD simulations
– Do not require initial large-scale magnetic fields
• Further study is needed in the area of jet
orientation and eliminating symmetries (and
we’re working on it!)
Late time evolution of Gamma Ray
Bursts
• Light curve decays rapidly in
Gamma ray burst
• Is it a product of Central engine
activity?
• Is there enough material to feed
a jet?
Relativistic Jets in Simulation
Plasma β
Beckwith, Hawley, and Krolik 2008
Magnetosonic Mach Number
Hawley, and Krolik 2005
Untilted Disk Jets
Hawley & Krolik 2005
Magnetosonic Mach Number
“Late Time”
Hawley & Krolik 2005
“Late Time”