Magnetic Fields and Jet Formation

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Magnetic Fields and Jet Formation

• John F. Hawley
• University of Virginia
• Workshop on MRI Turbulence
• June 18th 2008

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Collaborators

• Kris Beckwith (UVa)
• Julian H. Krolik (JHU)
• Scott Noble (JHU)
• Jake Simon (UVa)

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Jet Formation

• 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
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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?

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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 divB0
  (constrained transport) see De Villiers et al.
  (2003), Gammie et al. (2004), Anninos (2005)

Advection
Momentum
Internal Energy
Induction
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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 a/M 0, 0.5, 0.9,
-0.9, 0.93, 0.95, 0.99, 0.998
Colors indicate density
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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

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Side view log density a/M0.9 model
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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

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Properties of the Accretion Disk

• 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

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What about the Poynting flux Jet?
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Origin of the poloidal Funnel Field From an
initial dipole 2D Simulation thick torus Color
Plasma Beta White field lines
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Field Topologies
Dipole
Quadrupole
Multiple Loop
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3D Simulations Jet Properties
Magnetic Field Strength

• 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

dipole black solid line quadrupole blue solid
line toroidal purple solid line dashed lines
/- 1 std. dev.
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Toroidal Field

• Generation of MHD turbulence from a toroidal
  field configuration relies on non-axisymmetric
  modes, i.e. theres no such thing as a 2D
  toroidal field simulation
• No funnel field formation in this case

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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

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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

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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?

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Conclusions
Global simulations are providing information
about

• 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