Magnetic Fields and Jet Formation
John F. Hawley
University of Virginia
Workshop on MRI Turbulence
June 18th 2008
Collaborators :
Kris Beckwith (UVa)
Julian H. Krolik (JHU)
Scott Noble (JHU)
Jake Simon (UVa)
Jet Formation
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Young stellar objects
X-ray binaries – accreting NS or BH
Symbiotic stars – accreting WD
Supersoft X-ray sources – accreting WD
AGN – accreting supermassive BH
Gamma ray burst systems
The Ubiquity of Jets suggests that they are produced under general
conditions.
Gravity + Rotation (disk and/or central star) + Magnetic fields
Jet Theory
• Disk rotation + vertical field: Blandford-Payne type wind/jet
• Black Hole rotation + vertical field: Blandford-Znajek Poynting flux jet
• Past axisymmetric simulations with initial vertical fields have demonstrated
efficacy of these mechanisms.
• Under what circumstances will a large-scale poloidal field be present? Is
such a field always required for jet formation? Can such a field be
generated in the disk by a dynamo process, or is it brought in from outside?
Simulating Black Hole Accretion Disks
• Black hole accretion process
require us to describe the
behaviour of matter &
magnetic fields (& radiation!)
in strong gravity
• Solution of set of equations for
GRMHD necessary +
inversion method + scheme for
preserving divB=0
(constrained transport): see De
Villiers et al. (2003), Gammie
et al. (2004), Anninos (2005)
Advection:
Momentum:
Internal
Energy:
Induction:
Simulations of accretion into a Kerr hole
from an Initial Magnetized Gas Torus
Initial magnetic field
configurations: high b dipole and
quadrupole loops, toroidal field,
vertical field
Initial gas pressure supported
orbiting torus
Ensemble of black hole spins:
Colors indicate density
a/M = 0, 0.5, 0.9, -0.9, 0.93,
0.95, 0.99, 0.998
Limitations of Current Global Simulations
• Global problem difficult to
resolve spatially: turbulent scales
to parsecs – Need 3 spatial
dimensions
• Wide range of timescales
• Limited to simple equation of
state
• Dissipation, heating,
thermodynamics too limited
• No radiative losses; no global
radiative transfer
• System scales with M; density set
by assumed accretion rate
Side view: log density: a/M=0.9 model
Keplerian Dipole Disk Simulations
• Evolution:
– MRI acts on the initial field, leading to
large-amplitude MHD turbulence, which
drives the subsequent evolution of the
torus
• End of the simulation:
– Quasi-steady-state accretion disk,
surrounded by a hot corona
– Low density, hot funnel region filled with
(predominantly) radial field lines
– Material in this region is unbound and
with boost factor 2-10
– As black hole spin increases, Poynting
flux in jet increases due to dragging of
radial field lines anchored in black hole
event horizon by rotation of space time
Properties of the Accretion Disk
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Accretion disk angular momentum distribution near Keplerian
After several thousand M of time, models have come into approximate
steady state
Disk is MHD turbulent; internal stress due to the magnetorotational
instability
No abrupt changes at marginally stable orbit; density, velocity smooth &
continuous
Large scale fluctuations and low-m spiral features
No stress edge; evidence for transfer of angular momentum from hole to
disk
Implications for the equilibrium spin of the hole if it has grown from
accretion
What about the Poynting flux Jet?
Origin of the poloidal Funnel Field
From an initial dipole
2D Simulation – thick torus
Color: Plasma Beta
White field lines
Field Topologies
Dipole
Quadrupole
Multiple Loop
3D Simulations: Jet Properties
• Things in the disk seem pretty
much independent of field
topology
• Significant unbound Poynting
flux dominated outflow
(relativistic jet) present in the
dipole case
• Diagnostic: radial profiles of
shell integrated magnetic field
in unbound material
• Things here are very different.
Neither the toroidal nor
quadrupole fields produce
much of a jet
Magnetic Field Strength
dipole: black solid line
quadrupole: blue solid line
toroidal: purple solid line
dashed lines: +/- 1 std. dev.
Toroidal Field
• Generation of MHD turbulence from a toroidal field configuration relies on
non-axisymmetric modes, i.e. there’s no such thing as a 2D toroidal field
simulation
• No funnel field formation in this case
Jets: a summary
Large Scale poloidal field in the funnel can produce a jet
• Outflow throughout funnel, but only at funnel wall is there
significant mass flux
• Outgoing velocity ~0.4 - 0.6 c in funnel wall jet
• Poynting flux dominates within funnel
• Jet luminosity increases with hole spin – Poynting flux jet is
powered by the black hole
• Fraction of jet luminosity in Poynting flux increases with spin
• Both pressure and Lorentz forces important for acceleration
• Existence of funnel jet depends on establishing radial funnel field
– need to understand when this can happen
Field Topology
• Properties of magnetized black hole accretion disks seem to be remarkably
insensitive to magnetic field topology: the only dependence is in terms of the
magnetic field strength. Appearance of disk should be mostly independent of
magnetic field topology
• This is not true for the jet:
– Jet formation requires a consistent sense of vertical field to brought
down to the event horizon
– This occurs readily for dipole, less so for quadrupole, not at all for
toroidal initial field topologies
– Reconnection events between funnel and disk field determine the
variability of the jet
Origin of Large Scale Field
• Is net vertical flux required, or just large-scale poloidal field?
• Can significant large-scale poloidal field be generated with
MRI turbulent disks?
• Can net field be advected inward by MRI turbulent disks?
Balance magnetic diffusion/reconnection timescale against
accretion timescale
• How does the presence or absence of a jet relate to the overall
state of the disk and its magnetic field?
Conclusions
Global simulations are providing information about:
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Accretion disk structure
Accretion efficiency
Intrinsic variability
Spin of hole
Jet formation and power
But more work is needed to understand:
• Magnetic turbulence with non-ideal plasmas
• Thermodynamics and radiative properties of low density and
collisionless plasmas
• Large scale fields and dynamos in accretion systems
• Details of launching mechanisms for Astrophysical Jets