Title: GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK HOLE ACCRETION
1GENERAL RELATIVISTIC MHD SIMULATIONS OF BLACK
HOLE ACCRETION
- with Kris Beckwith, Jean-Pierre De Villiers,
John Hawley, Shigenobu Hirose, Scott Noble, and
Jeremy Schnittman
2Level of Contemporary Understanding of Accretion
PhysicsLike 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
3Only Tool for Full-Scale MHD TurbulenceNumerical
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
4State-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
5Status of Shearing-Box Studies
- Results (see Omers 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.
6Global 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.
7The 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.
8Implications 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
9Novikov-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.
10A Continuous Stress Profile
K., Hawley Hirose 2005
a/M0.998
Shell-integrated stress is the total rate of
angular momentum outflow
a/M0
Time-averaged in the coordinate frame
11In a fluid frame snapshot
Vertically-integrated stress
Integrated stress in pressure units
12A Smooth Surface Density Profile
K., Hawley Hirose 2005
a/M0
a/M0.998
13Spontaneously-Launched Poynting-Dominated Jets
Cf. Blandford Znajek 1976 McKinney Gammie
2004
Hawley K., 2006
14Large-Scale Field Arises Spontaneously from
Small-Scale Dipolar Field
Hirose et al. 2004
McKinney Gammie 2004
15Significant 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
16But 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
17Quadrupole 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
18Generic 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
19What 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
20Global 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
21Next 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