RadiationDominated Accretion Disks

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Radiation-Dominated Accretion Disks

• Omer Blaes Shane Davis
• U.C. Santa Barbara

Jim Stone Princeton Julian Krolik JHU
Takayoshi Sano Osaka
Ari Socrates Princeton Mitch Begelman JILA
David Ballantyne CITA Andy Young MIT
Neal Turner Jet Propulsion Laboratory
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To Make Accreting Gas Shine

• Remove angular momentum
• Dissipate orbital kinetic energy
• Radiate photons

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Circinus X-1, artists impression
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Shakura-Sunyaev Picture Assumptions

• Hydrostatic equilibrium
• Stress aP
• Vertical thermal balance viscous
  heating diffusion cooling dissipation
  density
• Inflow equilibrium

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Innermost 300 RSchw
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• Innermost 300 RSchw
• Radiation Pressure gt Gas Pressure

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• Innermost 300 RSchw
• Radiation Pressure gt Gas Pressure
• Flat, thickness 2RSchw

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• Innermost 300 RSchw
• Radiation Pressure gt Gas Pressure
• Flat, thickness 2RSchw
• Uniform Density and Dissipation

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Instabilities of Shakura-Sunyaev model

• Convective
• Thermal
• Viscous

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Overview

• Shakura-Sunyaev Picture
• Radiation-MHD Equations
• Heating
• Cooling
• X-Ray Reflection
• Summary

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Equations of Radiation MHD
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3. Heating
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Balbus Hawley 1991
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To Black Hole
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100 RS
Density Fluctuations r / ltrgt
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1/10
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Flow is heated by

• Microscopic viscosity
• Magnetic dissipation
• Radiation damping

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Diffusion length
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Diffusion length
MRI wavelength
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Agol Krolik 1998
Radiation Damping
1. Magnetic fields squeeze gas
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Agol Krolik 1998
Radiation Damping
2. Gas radiates
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Magnetic Field Evolution
Height z / RS
Horizontally-averaged magnetic pressure
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0
-6
0
100
Time / orbits
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Gas and Radiation Pressures
Radiation
Magnetic
Accretion Stress
Gas
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Stability Against Convection
Radiation
Gas
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Compare Shakura-Sunyaev Model
Same surface mass density and flux
RMHD Calculation
a-model
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4. Cooling
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Radiation escapes by

• Vertical Diffusion
• Convection
• Photon Bubble Instability

Arons 1992 Gammie 1998
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Gravity
Strong Magnetic Field
Radiation Flux
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Gravity
Strong Magnetic Field
Extra Flux
Radiation Flux
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Gravity
Strong Magnetic Field
Time 1
Radiation Flux
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Gravity
Strong Magnetic Field
Time 2
Radiation Flux
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Gravity
Strong Magnetic Field
Radiation Flux
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Lengths and Speeds
Radiation sound speed
Isothermal gas sound speed
Radiation scale height
Gas scale height
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Blaes Socrates 2003
Domain Top
Center
2562
1282
Bottom
642
322
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Analytic Prediction
kz
kx
Growth Rate / W
-2.7
2.1
-0.3
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Numerical Results, 1282 Zones
kz
kx
Growth Rate / W
-2.7
2.1
-0.3
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1.6W
1.8
2.0
2.2
642
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Growth on Inclined Fields
180
5.0
qB
2.5
90
0.0
0
0
90
180
qk
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Begelman 2001
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Vertical Diffusion
Photon Bubbles
Convection
z
x
-8.2
log10 r g cm-3
-10.1
-12.0
Arrows B 6200 Gauss
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Vertical Diffusion
Convection
Photon Bubbles
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Photon Bubbles with MRI
z
R
-9.0
log10 r g cm-3
-10.0
-11.0
Arrows B 1500 Gauss
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Photon Bubbles with MRI
z
R
log10 r g cm-3
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Photon Bubbles with MRI
z
R
-7.2
log10 r g cm-3
-9.1
-11.0
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5. X-Ray Reflection
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Effects on X-Ray Reflection Spectrum
Ballantyne et al. 2004
Synthetic Spectrum
Best-Fit Uniform Slab Model
Residuals
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Effects on X-Ray Reflection Variability
Ballantyne et al. 2005
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Assumptions tested

• Hydrostatic equilibrium
• Stress aP
• Vertical thermal balance viscous
  heating diffusion cooling dissipation
  density
• Inflow equilibrium

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Summary

• Radiation-dominated disks are heated by magnetic
  dissipation and photon damping.
• Heating in low-density surface layers leads to
  convective stability and quick thermal evolution.
• Short-wavelength photon bubbles grow faster than
  W if magnetic pressure gt gas pressure.
• The bubbles become propagating shocks, and
  radiation escapes through the gaps between.

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Energy Flow
PHOTON BUBBLES