Simulating the Extreme EnvironmentNear Luminous Black Hole Sources

Omer BlaesUniversity of California, Santa Barbara

Collaborators

Spectral calculations: Shane Davis, Ivan Hubeny, Julian Krolik

Simulations: Shigenobu Hirose, Julian Krolik, Jim Stone, Neal Turner

Observers: Chris Done

Outline

• Observational Context - Black Hole X-ray Binaries

• Physical Ingredient 1: Magnetorotational Turbulence

• Physical Ingredient 2: Radiative Diffusion

• The Most Recent Thermodynamically Consistent Stratified Shearing Box Simulation

• Implications and Future Work

-figure from

Orosz

-Charles &Coe (2003)

v

-2v

Black hole accretion is a POWERFUL source of energy!

ISCO

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L ≈GM ˙ M

2rin

≈ (0.04 − 0.42) ˙ M c 2

-Remillard (2005)

- jet always present

-no jet whatsoever

Thermal State

Hard State?

Steep Power Law State???

-Gierlinski & Done (2004)

Luminosity vs. Temperature in the Thermal Dominant StateLu

min

osity

Maximum Temperature

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L∝Tmax4

Implies thatthere is a fixedemitting area,because of theISCO???

LMC X-3 in the thermal dominant state

BeppoSAX RXTE

-Davis, Done, & Blaes (2006)

Such detailed spectral fits can potentially constrain the spin ofthe black hole, thereby completely determining the spacetime.But there are uncertainties…

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˙ M

€

˙ J

Accretion power is fundamentally the release of gravitationalbinding energy, which can only take place in a disk iffluid elements can give up their angular momentum:

Accretion Disk Theory is Undergoing a (Slow) Revolution

Mantra in the 70’s and 80’s: the biggest uncertainty isthe cause of the anomalous stress (“viscosity”) responsiblefor outward angular momentum transport.

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τRφ = αP Shakura & Sunyaev (1973)

3075 citationsand counting…

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Magnetorotational Instability (MRI)

-Balbus & Hawley1991, 1998

Magnetorotational Instability (MRI)

B Brotates faster

rotates slower

Magnetic fields in a conducting, rotating plasma behaveEXACTLY like springs!

Snapshot ofangular momentumper unit mass inMRI turbulence.

-Hawley & Balbus (1992)

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τRφ = ρ < vRvφ − BR Bφ /(4πρ) >

-Hawley & Balbus (2002)

Structure of (Non-Radiative) Accretion Flows From Simulation

There Are MAJOR Uncertainties in the Inner, Most LuminousRegions, Which are Dominated by Radiation Pressure

• Chief among these is the prediction of standard (Shakura& Sunyaev) models that the disk is thermally unstable whenradiation pressure dominates gas pressure.

IF τrPrad, then dissipation is proportional to T8, whilecooling is proportional to T4, implying a thermal instability.

But does the turbulent stress really work this way? Peoplehave tried all sorts of choices when building models:

τrPrad τrPgas τrPgasPrad)1/2

How does MRI turbulence behave in this regime?

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- Belloni et al. (2000)

GRS 1915+105 - Evidence for Thermal Instability?

Subsonic fluid motionsare generally incompressible:if fluid is slowly squeezed inone direction, pressure hastime to force it to expand inanother direction, so densityremains approximatelyconstant.

Radiation Pressure Dominated PlasmaIs Fragile

Suppose now that we squeezethe fluid slowly enough thatphotons can diffuse out of theregion faster than the squeezingis taking place. Then radiationpressure will NOT build up.

If motions are subsonic, butsupersonic with respect to themuch smaller gas sound speed,then considerable compressioncan occur. Radiation pressure can’tbuild up because of diffusion, andgas pressure does not have timeto act.

-Turner, Stone, & Sano (2003)

-Turner et al. (2005)

F

g

“Photon Bubble Instability”

The Stratified Shearing Box

x (radial)

y (azimuthal)

z (vertical)Cartesian box corotating with fluid atcenter of box. Boundary conditions are periodic in y, shearing periodic in x, outflow in z.

Equations of Radiation Magnetohydrodynamics

Flux-Limited Diffusion

Three thermodynamically consistent, radiation MHD simulationsof MRI turbulence in vertically stratified shearing boxes havebeen done:

Turner (2004): prad>>pgasHirose et al. (2006): prad<<pgasKrolik et al. (2007), Blaes et al. (2007): prad~pgas

-Blaes, Hirose, Krolik, & Stone (2007)

Radiation

Gas

Magnetictimes 10

Expect strong (but marginally stable) thermal fluctuations atlow energy and stable (damped) fluctuations at high energy.

Complex Structure of Surface Layers

Photosphere

ThermalizationPhotosphere

Dynamical Support Against Gravity

Radiation pressure,Gas pressure,Magnetic forces,Gravity

Upwardpressure

Downwardtension

Magnetic Pressure vs. Magnetic Tension

Parker Instability

gB

Red=fluid velocity Black=magnetic field

Heavy regionsassociated withupward tension.

Light regionsassociated withdownward tension.

3D visualization oftension/densityfluctuationcorrelation.

Strong Density Fluctuations - NOT Because of RadiativeDiffusion, but Because of Strong Magnetic Forces

Spectral Consequences

• Magnetically supported upper layers decrease density at effective photosphere, resulting in increased ionization and a hardening of the spectrum.• Strong (up to factor 100) irregular density inhomogeneities exist well beneath photosphere of horizontally averaged structure. They will soften the spectrum.• Actual photosphere is therefore complex and irregular, which will reduce intrinsic polarization of emerging photons (Coleman & Shields 1990). Magnetic fields may also Faraday depolarize the photons (Gnedin & Silant’ev 1978):

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θ ≈0.8τ T

Pmag

Prad

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

≈ 2 radians

Overall Vertical Structure of Disk with Prad~Pgas

MRI - the source ofaccretion power

Photosphere

Photosphere

Parker UnstableRegions

Parker UnstableRegions

Pmag>Prad~Pgas

Pmag>Prad~Pgas

Prad~Pgas>Pmag

-Blaes, Hirose, Krolik, & Stone (2007)

Conclusions• Radiation MHD simulations are beginning to handle not only the dynamics, but the thermodynamics of accretion disks. Theory can now begin to make contact with observations of photon spectra.

• Annulus is thermally stable at this level of radiation pressure.

• Upper layers are supported by magnetic fields. No photon bubbles seen. Parker instability dominates, and drives strong density fluctuations.

• Unclear what this means for spectra and black hole spin measurements - magnetic field support will harden spectra, density fluctuations will soften spectra.

Work in Progress• Monte Carlo radiative transfer calculation of emergent spectra from simulation. This will also test flux-limited diffusion used by the code.

• Linear instability analysis of atmospheres supported by both radiation and magnetic fields - are photon bubbles suppressed somehow?

• Radiation pressure dominated simulation is running now.

• Further work also needed on the regime examined in current simulation - unstable Parker wavelengths barely fit inside the box!!!

Gas

Radiation

Magnetic

GravityTotal

-Blaes et al. (2006)i=55C

VI K

-ed

ge

C

VI K

-ed

ge

-Blaes et al. (2006)

No magneticfields

With magneticfields

-Davis et al. (2004)

Blackbody

Modifiedblackbody

Density fluctuations help thermalize the spectrum.

Density scale height may also decrease as flux is able to escapethrough low density channels - this will also soften the spectrum.

-Gierlinski & Done (2003)

Steep power law

Thermal

Hard

-dF/dm

Turner 04

Hirose et al. 05

CV

I K-e

dg

e

-Turner et al. (2005)

B

F

g

“Photon Bubble Instability”