Simulating the Extreme Environment Near Luminous Black Hole Sources Omer Blaes University 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 -2  v

Black hole accretion is a POWERFUL source of energy! ISCO

-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 State Luminosity Maximum Temperature Implies that there is a fixed emitting area, because of the ISCO???

LMC X-3 in the thermal dominant state BeppoSAXRXTE -Davis, Done, & Blaes (2006) Such detailed spectral fits can potentially constrain the spin of the black hole, thereby completely determining the spacetime. But there are uncertainties…

Accretion power is fundamentally the release of gravitational binding energy, which can only take place in a disk if fluid 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 is the cause of the anomalous stress (“viscosity”) responsible for outward angular momentum transport. Shakura & Sunyaev (1973) 3075 citations and counting…

Magnetorotational Instability (MRI) -Balbus & Hawley 1991, 1998

Magnetorotational Instability (MRI)   B B rotates faster rotates slower Magnetic fields in a conducting, rotating plasma behave EXACTLY like springs!

Snapshot of angular momentum per unit mass in MRI turbulence. -Hawley & Balbus (1992)

-Hawley & Balbus (2002) Structure of (Non-Radiative) Accretion Flows From Simulation

There Are MAJOR Uncertainties in the Inner, Most Luminous Regions, Which are Dominated by Radiation Pressure Chief among these is the prediction of standard (Shakura & Sunyaev) models that the disk is thermally unstable when radiation pressure dominates gas pressure. IF  r   P rad, then dissipation is proportional to T 8, while cooling is proportional to T 4, implying a thermal instability. But does the turbulent stress really work this way? People have tried all sorts of choices when building models:  r   P rad  r   P gas  r   P gas P rad ) 1/2 How does MRI turbulence behave in this regime?

- Belloni et al. (2000) GRS Evidence for Thermal Instability?

Subsonic fluid motions are generally incompressible: if fluid is slowly squeezed in one direction, pressure has time to force it to expand in another direction, so density remains approximately constant. Radiation Pressure Dominated Plasma Is Fragile

Suppose now that we squeeze the fluid slowly enough that photons can diffuse out of the region faster than the squeezing is taking place. Then radiation pressure will NOT build up. If motions are subsonic, but supersonic with respect to the much smaller gas sound speed, then considerable compression can occur. Radiation pressure can’t build up because of diffusion, and gas pressure does not have time to 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 at center 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 simulations of MRI turbulence in vertically stratified shearing boxes have been done: Turner (2004): prad>>pgas Hirose et al. (2006): prad<<pgas Krolik et al. (2007), Blaes et al. (2007): prad~pgas

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

Radiation Gas Magnetic times 10

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

Complex Structure of Surface Layers Photosphere Thermalization Photosphere

Dynamical Support Against Gravity Radiation pressure, Gas pressure, Magnetic forces, Gravity

Upward pressure Downward tension Magnetic Pressure vs. Magnetic Tension

Parker Instability g B

Red=fluid velocityBlack=magnetic field

Heavy regions associated with upward tension. Light regions associated with downward tension.

3D visualization of tension/density fluctuation correlation.

Strong Density Fluctuations - NOT Because of Radiative Diffusion, 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):

Overall Vertical Structure of Disk with P rad ~P gas MRI - the source of accretion power Photosphere Parker Unstable Regions Parker Unstable Regions P mag >P rad ~P gas P rad ~P gas >P mag -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 Gravity Total

-Blaes et al. (2006) i=55  CVI K-edge

-Blaes et al. (2006) No magnetic fields With magnetic fields

-Davis et al. (2004) Blackbody Modified blackbody Density fluctuations help thermalize the spectrum. Density scale height may also decrease as flux is able to escape through 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

CVI K-edge

-Turner et al. (2005) B F g “Photon Bubble Instability”