1. GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK HOLE ACCRETION with: Kris Beckwith, Jean-Pierre De Villiers, John Hawley, Shigenobu Hirose, Scott Noble, and Jeremy Schnittman

2. Level of Contemporary Understanding of Accretion Physics: Like 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

3. Only Tool for Full-Scale MHD Turbulence: Numerical 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

4. 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

5. Status of Shearing-Box Studies Results (see Omer’s 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.

6. 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.

7. 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.

8. 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 Implications of the guessed boundary condition...

9. 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.

10. A Continuous Stress Profile Shell-integrated stress is the total rate of angular momentum outflow Time-averaged in the coordinate frame a/M=0 a/M=0.998 K., Hawley & Hirose 2005

11. In a fluid frame snapshot Vertically-integrated stressIntegrated stress in pressure units

12. A Smooth Surface Density Profile a/M=0a/M=0.998 K., Hawley & Hirose 2005

13. Spontaneously-Launched Poynting-Dominated Jets Cf. Blandford & Znajek 1976; McKinney & Gammie 2004 Hawley & K., 2006

14. Large-Scale Field Arises Spontaneously from Small-Scale Dipolar Field Hirose et al. 2004 McKinney & Gammie 2004

15. Significant Energy Efficiency for Rapid Spin a/M -0.90.0230.039 0.00.00030.057 0.50.00630.081 0.90.0460.16 0.930.0380.17 0.950.0720.18 0.990.210.26

16. But Non-dipolar Geometry Is Different Quadrupole topology: –2 loops located on opposite sides of equatorial plane –Opposite polarities –Everything else in torus is the same as dipole case Beckwith, Hawley & K. 2008

17. 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

18. Generic Broad-band Variability Orbital dynamics in the marginally stable region “turbocharges” the MRI; but accretion rate variations are translated into lightcurve fluctuations only after a filtration process Schnittman, K & Hawley 2007De Villiers et al. 2004

19. 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! r ¹ T ¹ º = ¡ L u º Principal modification to the equations:

20. Global efficiency defined by net binding energy passing through the event horizon: matter + electromagnetic per rest-mass accreted N-T = 0.155 accreted = 0.18 fully radiated = 0.23 a/M = 0.9; target H/R = 0.2 ´ = 1 + R H d ­T r t R H d ­ ½u r

21. 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