GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK HOLE ACCRETION

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. 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 Level of Contemporary Understanding of Accretion Physics:Like Stellar Structure in the 1940s

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. Implications of the guessed boundary condition... 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

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

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

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

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

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

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

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

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

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