general relativistic mhd simulations of black hole accretion
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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
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