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The Vertical Structure of Radiation Dominated Accretion Disks. Omer Blaes. with Shigenobu Hirose and Julian Krolik. Huge Theoretical Uncertainties Have Plagued Us for Years - Even In the Standard Geometrically Thin, Optically Thick Disk Model.

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slide1

The Vertical Structure

of Radiation Dominated

Accretion Disks

Omer Blaes

with

Shigenobu Hirose

and

Julian Krolik

slide2

Huge Theoretical Uncertainties Have Plagued Us for Years - Even

In the Standard Geometrically Thin, Optically Thick Disk Model

  • How is (turbulent!) dissipation distributed vertically?
  • What role (if any) do convection and Poynting flux play
  • in the vertical transport of energy?
  • Are thermal (and “viscous”) instabilities in the radiation
  • dominated regime real, or are they merely artifacts of
  • a bad choice of stress prescription?
  • How big are fluctuations about equilibrium?
  • Do magnetic forces play any role in hydrostatic support?
slide3

Expectations in Radiation-Dominated Regime

Hydrostatic equilibrium:

A radially constant disk half-thickness:

slide4

Expectations in Radiation-Dominated Regime

Radiative equilibrium:

A vertically constant dissipation

rate per unit volume:

After vertical and time-averaging, this must be given

by turbulent stress times rate of strain:

(Shakura & Sunyaev 1976)

slide5

IF we choose the dissipation per unit MASS

to be spatially constant as well, then the density must

be constant.

Ad Hoc Prescription I: The Density Profile

The vertical density profile is completely unconstrained!

Convective instability!

(Bisnovatyi-Kogan & Blinnikov 1977)

But perhaps the dissipation per unit mass is not constant???

slide6

Ad Hoc Prescription II: The Stress/Pressure Relation

The radial midplane temperature and surface density profiles

are completely unconstrained unless we adopt, e.g., an alpha

prescription for the vertically averaged stress.

If we choose , then the disk is thermally and

“viscously” unstable if .

or

But other choices are possible, e.g.

(Sakimoto & Coroniti 1981, …, Merloni & Fabian 2002, …)

Or perhaps much of the accretion power is dissipated in

a corona above the disk? (Svensson & Zdziarski 1994)

slide7

No Observational Evidence for

Radiation Pressure Thermal/“Viscous” Instabilities

- Except Perhaps in GRS 1915+105

-Belloni et al. (1997)

slide8

MRI Turbulence Can be Highly Compressible

in Radiation Dominated Regime

-Turner et al. (2003)

Silk damping of turbulence may be important.

(Agol & Krolik 1998)

slide9

“Photon Bubble Instability”

F

g

-Turner et al. (2005)

slide10

z (vertical)

y (azimuthal)

x (radial)

Stratified Shearing Box Simulations

of MRI Turbulence

Cartesian box corotating with fluid at

center of box. Boundary conditions are

shearing periodic in x,

periodic in y,

outflow in z.

slide11

Altitude

Time

Miller & Stone (2000)

25% of magnetic energy generated in turbulence buoyantly

rises and dissipates in outer layers. Does this produce a

hot corona?

Uncertain, as simulation was isothermal.

slide12

Thermodynamically consistent, radiation MHD

simulations in vertically stratified shearing boxes:

slide13

z (vertical)

y (azimuthal)

x (radial)

The Simulation Domain

Lx=0.45H, 48 zones

Ly=1.8H, 96 zones

Lz=8.4H, 896 zones

(Apologies to Arthur

C. Clarke and Stanley

Kubrick)

slide14

Energy Balance - NO Thermal Instability!

Heating

vs.

Cooling

Radiation,

Gas Internal,

Magnetic,

and

Turbulent

Kinetic

Energies

slide15

Heating

vs.

Cooling

Radiation,

Gas Internal,

Magnetic,

and

Turbulent

Kinetic

Energies

slide16

Time-Averaged Vertical Dissipation Profile

Most of the dissipation is concentrated near midplane.

slide17

Turbulence near Midplane is Incompressible

-----Silk Damping is Negligible

slide19

Density is far from constant with height.

Density profile

at 200 orbits.

Time-averaged

density profile.

slide21

r/Pgas

r/(PtotPgas)1/2

r/Ptot

slide28

Large Density Fluctuations at Effective

and Scattering Photospheres

-upper effective photosphere

at t=200 orbits

slide29

Photospheric Density Fluctuations

Strong density fluctuations,

at both scattering and

effective photospheres.

Strong fluctuations also

seen at effective

Photosphere in previous

simulations with Prad>>Pgas

and Prad~Pgas.

slide30

Overall Vertical Structure for all Prad/Pgas Regimes

Photospheres

Pmag>Prad, Pgas

Parker Unstable

Regions

Prad, Pgas>Pmag

MRI - the source of

accretion power

Parker Unstable

Regions

Pmag>Prad, Pgas

Photospheres

slide31

Conclusions

  • No evidence for radiation pressure driven thermal instability,
  • despite fact that turbulent stresses may be tracking total
  • pressure (causal direction is OTHER way around, though!).
  • Dissipation is concentrated near disk midplane, with no
  • energetically significant corona.
  • Upper layers are always supported by magnetic fields, even
  • well beneath the photospheres. (Reflection modelers beware!)
  • Parker instability dominates, and drives strong density
  • fluctuations in all radiation/gas pressure regimes. Photon
  • bubble instability is unresolved in this simulation.
  • Spectra and color correction factors: magnetic field support
  • should harden spectra, density fluctuations should soften
  • spectra. Which dominates?
slide32

Caveats and Uncertainties

  • Simulations are expensive, and much more work needs to be
  • done to address the following issues:
  • Numerical convergence with increased resolution and box
  • size in all three directions (particularly radial and azimuthal).
  • How does initial magnetic field topology affect things? (We
  • start with a twisted azimuthal flux tube with net azimuthal
  • flux, but no net poloidal flux.)
  • Most of our dissipation is numerical and is captured at the
  • grid scale. Viscous and resistive scales are therefore
  • identical (i.e. Prandtl number is unity). Simulations in
  • non-stratified shearing boxes show that this might matter.
slide33

More Details on the (Time-Averaged) Energy Balance

Stress

Dissipation Rate

Divergences of

Poynting flux,

Gas energy advection,

Radiation energy advection,

and Radiative diffusion,

Total of last three matches

dissipation rate.

slide34

Flux from top

Flux from bottom