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

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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

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


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.


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


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

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


A Smooth Surface Density Profile

K., Hawley & Hirose 2005

a/M=0.998

a/M=0


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. 2004

McKinney & Gammie 2004


Significant Energy Efficiency for Rapid Spin


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


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

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

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:


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


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


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