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GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK HOLE ACCRETION

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GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK HOLE ACCRETION

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

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

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

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

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.

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.

- 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.

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

- 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.

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

In a fluid frame snapshot

Vertically-integrated stress

Integrated stress in pressure units

K., Hawley & Hirose 2005

a/M=0.998

a/M=0

Cf. Blandford & Znajek 1976;

McKinney & Gammie 2004

Hawley & K., 2006

Hirose et al. 2004

McKinney & Gammie 2004

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

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

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

¹

r

T

L

¡

u

=

¹

º

º

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:

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

- 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