Connecting Accretion Disk Simulations with Observations: Part I

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Connecting Accretion Disk Simulations with
Observations Part I

• Jason Dexter
• 9/18/2008

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Accreting Systems

• Accreting systems are everywhere
• Planetary disks
• Compact binaries
• SMBHs, AGN
• Supernovae, GRBs

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Accreting Black Hole Systems

• Types
• Stellar mass
• Supermassive (106-109 Msun)
• No hard surface
• Energy lost to black hole
• Inner accretion flow probes strong field GR
• Astronomy?Physics

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Exciting Observations Sgr A

• Galactic center black hole (candidate)
• SMBH with largest angular size
• Microarcseconds baby penguin on moon.
• VLBI
• High resolution ?/D
• Sub-mm scattering?2

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Exciting Observations Sgr A

• Doeleman et al, Nature, 2008
• Detections of Sgr A at 1.3mm using an
  Arizona-Hawaii baseline.
• Size 4 Rs

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Exciting Observations Sgr A

• Flares in many wavebands
• Eckert et al (2008), Yusef-Zadeh et al (2008),
  Marrone et al (2008)
• NIR, x-ray, radio polarized flares
• Position wander
• Reid et al (2008)
• Limits on astrometric motion of centroid

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Exciting Observations

• AGN
• Relativistically broadened iron lines
• Size of emission regions from microlensing
• Black hole binaries (x-ray)
• Quasi-periodic oscillations with integer
  frequency ratios (e.g., 32)
• ? Plenty of problems for theorists!

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Accretion Theory

• Spherical Accretion
• Bondi (1952), relativistic Michel (1972), Shapiro
  (1973)
• Thin Disk Accretion (standard, alpha)
• Shakura Sunyaev (1973), relativistic Page
  Thorne (1974)
• ADAF, RIAF
• Narayan Yi (1995), Yuan et al (2003)

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The Alpha Parameter

• How does matter lose angular momentum?
• Torque due to viscosity
• Molecular viscosity is many orders of magnitude
  too weak
• Parameterize unknown mechanism via a parameter, 0
  lt a 1
• Model sounds primitive, but highly predictive.
  Still used regularly.

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Magnetic Fields

• Mentioned, but ignored in early papers
• Spherical accretion assumed collisional despite
  large mean free path.
• Balbus Hawley (1991) (Re-)discovery of the MRI
• Nonlinear shear instability?outward transport of
  angular momentum, accretion!

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The MRI

• Magnetic terms in MHD include a pressure and a
  tension force.
• In perfect MHD, field lines tied to fluid.
• Infinite conductivity, no E.
• MHD with a weak radial magnetic field,
  Keplarian-like velocity profile?MRI.

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Toy Model of the MRI

• Radially separated fluid elements differentially
  rotate.
• Spring stretches, slows down inner element and
  accelerates outer.
• Inner element loses angular momentum and falls
  inward. Outer element moves outward.
• Differential rotation is enhanced and process
  repeats.
• ?Strong magnetic field growth, turbulence

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State of Affairs Post-MRI

• Pros
• Accretion mechanism is known. Can include much
  more realistic physics (no ad-hoc alpha
  prescription).
• Cons
• MRI is nonlinear, leads to fully developed
  turbulence. No simple model. Computationally
  expensive numerical simulations.

De Villiers et al (2003)
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Contemporary Simulations

• Types Global vs. Local, 2d vs. 3d, GR vs.
  Paczynski-Wiita potential

Stone et al (1996)
De Villiers et al (2003)
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GRMHD Simulations

• Includes the most physics
• 3D, global, fully relativistic
• MRI, turbulence produced organically
• Extremely difficult computationally
• Can only evolve for short times
• Need to check convergence
• Dependence on initial conditions, disk
  boundaries, resolution.

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Connecting Theory and Observation

• Most observational work fits results with
  simplified analytic model.
• GRMHD only tracks basic fluid variables.
• Ignores radiation
• Simple thermodynamics
• May not even conserve energy
• Results are pretty, but coordinate dependent!

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Coordinate Dependent Results

• Font et al (1999)
• Comparison of two common coordinate systems for
  relativistic wind accretion onto an extreme Kerr
  BH.