GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK HOLE ACCRETION

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GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK
HOLE ACCRETION

• with Kris Beckwith, Jean-Pierre De Villiers,
  John Hawley, Shigenobu Hirose, Scott Noble, and
  Jeremy Schnittman

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Level of Contemporary Understanding of Accretion
PhysicsLike Stellar Structure in the 1940s

• Stellar Structure
• Basic problem generation of heat
• Before 1939, no mechanism, reliance on scaling
  laws
• After 1939, nuclear reactions realistic
  opacities numerical calculations
• Complete solution

• Accretion Disks
• Basic problem removal of angular momentum
• Before 1991, no mechanism, reliance on scaling
  laws
• Now, robust MHD instability realistic opacities
  numerical calculations
• ? Complete solution

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Only Tool for Full-Scale MHD TurbulenceNumerical
Simulation
Hawley, Stone, Gammie .
Shearing-box simulations focus on wide dynamic
range studies of turbulent cascade, vertical
structure and thermodynamics
Global simulations study inflow dynamics, stress
profile, non-local effects, surface density
profile, identify typical structures
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State-of-the-art Simulation Physics
Shearing box simulations (Hirose et al.)---
3-d Newtonian MHD including radiation forces
total energy equation flux-limited
diffusion (thermal)
Global simulations (De Villiers Hawley
Beckwith Gammie, McKinney Toth Noble)---
3-d MHD in Kerr metric internal (or total)
energy equation So far, (almost always)
zero net magnetic flux, no radiation
but see update in about 30 minutes
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Status of Shearing-Box Studies

• Results (see Omers talk to follow)
• Vertical profiles of density, dissipation
• Magnetic support in upper layers
• Thermal stability (!)

• Questions
• Prandtl number dependence?
• Resolution to see photon bubbles?
• Box size?
• Connection to inflow dynamics

Foreseeable future Possibly all three technical
questions, but probably not the fourth issue
anytime soon.
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Global Disk Results Overview

• Results
• Continuity of stress, surface density throughout
  marginally stable region
• Spontaneous jet-launching (for right field
  geometry)
• Strong noise source, suitable for driving
  fluctuating lightcurves

Big picture for all three notable results
magnetic connections between the stretched
horizon and the accretion flow are
central---another manifestation of
Blandford-Znajek mechanics.
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The Traditional Framework the Novikov-Thorne
model

• Content
• Axisymmetric, time-steady, zero radial velocity,
  thin enough for vertical integration
• Energy and angular momentum conservation in GR
  setting
• Determines radial profiles of stress,
  dissipation rate.
• Forms are generic at large radius,
• But guessed inner boundary condition required,
• which strongly affects profiles at
  small radius.

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Implications of the guessed boundary condition...
Zero stress at the marginally stable orbit means
Free-fall within the plunging region i.e., a
trajectory conserving energy and angular momentum
So the zero-stress B.C. determines the energy and
angular momentum left behind in the disk
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Novikov-Thorne Limitations

• No relation between stress and local conditions,
  so no surface density profile proportional to
  pressure?
• Vertically-integrated, so no internal structure
• No variability
• No motion out of equatorial plane
• Profiles in inner disk, net radiative efficiency
  are functions of guessed boundary condition
  surface density at ISCO goes abruptly to zero.

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A Continuous Stress Profile
K., Hawley Hirose 2005
a/M0.998
Shell-integrated stress is the total rate of
angular momentum outflow
a/M0
Time-averaged in the coordinate frame
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In a fluid frame snapshot
Vertically-integrated stress
Integrated stress in pressure units
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A Smooth Surface Density Profile
K., Hawley Hirose 2005
a/M0
a/M0.998
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Spontaneously-Launched Poynting-Dominated Jets
Cf. Blandford Znajek 1976 McKinney Gammie
2004
Hawley K., 2006
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Large-Scale Field Arises Spontaneously from
Small-Scale Dipolar Field
Hirose et al. 2004
McKinney Gammie 2004
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Significant Energy Efficiency for Rapid Spin
a/M
-0.9 0.023 0.039
0.0 0.0003 0.057
0.5 0.0063 0.081
0.9 0.046 0.16
0.93 0.038 0.17
0.95 0.072 0.18
0.99 0.21 0.26
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But Non-dipolar Geometry Is Different
Beckwith, Hawley K. 2008

• Quadrupole topology
• 2 loops located on opposite sides of equatorial
  plane
• Opposite polarities
• Everything else in torus is the same as dipole
  case

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Quadrupole Geometry Permits Reconnection,Makes
Jet Weaker and Episodic
Small dipole loops lead to similar results
toroidal field makes no jet at all.
Rule-of-thumb vertical field must retain a
consistent sign for at least 1500M to drive a
strong jet
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Generic Broad-band Variability
Schnittman, K Hawley 2007
De Villiers et al. 2004
Orbital dynamics in the marginally stable region
turbocharges the MRI but accretion rate
variations are translated into lightcurve
fluctuations only after a filtration process
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What Is the Radiative Efficiency?
Previous simulations have either been 3-d and
non-conservative (GRMHD) or 2-d and conservative,
but without radiation losses (HARM). But Scott
Noble has just built HARM 3-d with optically-thin
cooling!
Principal modification to the equations
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Global efficiency defined by net binding energy
passing through the event horizon matter
electromagnetic per rest-mass accreted
a/M 0.9 target H/R 0.2
fully radiated 0.23
accreted 0.18
N-T 0.155
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Next Questions to Answer

• Effects of large-scale magnetic field?
• Aspect ratio dependence?
• Oblique orbital plane/Bardeen-Petterson
• Jet mass-loading
• More realistic equation of state
• Thermal emissivity/radiation transfer
  (diffusion?)
• Radiation pressure
• Non-LTE cooling physics in corona