GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK HOLE

ACCRETION

with: Kris Beckwith, Jean-Pierre De Villiers, John Hawley, Shigenobu Hirose, Scott Noble, and Jeremy

Schnittman

Level of Contemporary Understanding of Accretion Physics:

Like Stellar Structure in the 1940s

Stellar StructureBasic problem: generation

of heat

Before 1939, no mechanism, reliance on scaling laws

After 1939, nuclear reactions + realistic opacities + numerical calculations

Complete solution

Accretion DisksBasic problem: removal of

angular momentum

Before 1991, no mechanism, reliance on scaling laws

Now, robust MHD instability + realistic opacities + numerical calculations

? Complete solution

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

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

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.

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.

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.

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...

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.

A Continuous Stress Profile

Shell-integrated stress is the total rate of angular momentum outflow

bound

rr uubbbgdd 2|| Time-averaged in the coordinate frame

a/M=0

a/M=0.998

K., Hawley & Hirose 2005

In a fluid frame snapshotVertically-integrated stress Integrated stress in pressure units

A Smooth Surface Density Profile

a/M=0a/M=0.998

K., Hawley & Hirose 2005

Spontaneously-Launched Poynting-Dominated Jets

Cf. Blandford & Znajek 1976;

McKinney & Gammie 2004

Hawley & K., 2006

Large-Scale Field Arises Spontaneously from Small-Scale Dipolar Field

Hirose et al. 2004McKinney & Gammie 2004

Significant Energy Efficiency for Rapid Spin

a/M

-0.9 0.023 0.039

0.0 0.0003 0.057

0.5 0.0063 0.081

0.9 0.046 0.16

0.93 0.038 0.17

0.95 0.072 0.18

0.99 0.21 0.26

EM NT..

/ accx ME

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

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

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 2007 De Villiers et al. 2004

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 ¹º = ¡ Luº

Principal modification to the equations:

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

Hd T r

tRH

d ½ur

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