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

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 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

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

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

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

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

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.


General relativistic mhd simulations of black hole accretion

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

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

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


General relativistic mhd simulations of black hole accretion

In a fluid frame snapshot

Vertically-integrated stress

Integrated stress in pressure units


A smooth surface density profile

A Smooth Surface Density Profile

K., Hawley & Hirose 2005

a/M=0.998

a/M=0


Spontaneously launched poynting dominated jets

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

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

Hirose et al. 2004

McKinney & Gammie 2004


Significant energy efficiency for rapid spin

Significant Energy Efficiency for Rapid Spin


But non dipolar geometry is different

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

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

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


What is the radiative efficiency

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:


General relativistic mhd simulations of black hole accretion

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

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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