1. Global 3D MHD Simulations of Optically Thin Black Hole Accretion Disks
I would like to talk about thre reusults of global 3D MHD Simulations of …
Ryoji Matsumoto、
Mami Machida and Kenji Nakamura

2. Time Variabilities of Black Hole Candidates
The right panel shows the time variabilities of accretion rate obtained from numerical simulation. The time range is 0.7 seconds for 10 M_sun black hole. It shows sporadic time variations similar to that observed in Cyg X-1. In order to show it more quantitatively, we computed PSD from simulation results.
GRS
X-ray variability of Cyg X-1

3. Conventional Theory of Accretion Disks Introduces Viscosity Parameter α
Standard Accretion Disk Model (Shakura and Sunyaev 1973) : trf = aP
a = >>　Molecular Viscosity
MRI (Balbus and Hawley 1991) can generate magnetic turbulence and enhance the efficiency of angular momentum transport
Conventional theory of accretion disks introduced alpha to parametrize the mechanism of efficient angular momentum transport in accretion disks. The transition point and the time scale of transition depends on this parameter.

4. We study the time variabilities of black hole accretion flows by direct global 3D MHD simulations

5. Basic Equations .

6. Global Three-dimensional MHD Simulations of Black Hole Accretion Flows
(Machida and Matsumoto 2003 ApJ )
Gravitational potential 　：　 φ= - GM/(r-rg)
　Angular momentum　：　initially uniform
　at R=50rg
　Pgas/Pmag = β＝　１００
　Magnetic Reynolds Number
　Rm= 2000, (J/ρ-vc > 0)
250*64*192mesh 2
Anomalous Resistivity η= (1/Rm) max [(J/ρ) /vc– 1, 0.0]

7. Time Variation of Density Distribution

8. Equatorial Density and Magnetic Field Lines
These show the distribution of equatorial density and magnetic field lines.

9. Numerical Results Reproduce X-ray variability of Black Hole Candidates
The right panel shows the time variabilities of accretion rate obtained from numerical simulation. The time range is 0.7 seconds for 10 M_sun black hole. It shows sporadic time variations similar to that observed in Cyg X-1. In order to show it more quantitatively, we computed PSD from simulation results.
Numerical Results: Time Variation of Accretion Rate
X-ray Flux from Cyg X-1

10. Comparison of PSD Obtained by Observation and Numerical Simulation (see Machida’s poster)
-0.9
ＰＳＤ f
-1.5 f
This viewgraph compares PSD of time variation in Cyg X-1 and simulation results. The numerically obtained PSD of accretion rate has a break at 100Hz. Its slope changes from –1.5 to –2.5. The blue dots and red dots show results assuming equatorial symmetry and without assuming equatorial symmetry, respectively. For more details, please see the poster by Machida.
This break frequency corresponds to the epicyclic freqency at the innermost radius of black hole accretion flows and inversely proportional to the black hole mass. Numerical simulations successfully reproduced the slope of PSD between 1Hz and 100Hz.
Next, let us disuss the origin of low freqency part of PSD. It is related to the X-ray shots.
1Hz
100Hz
frequency
Power Spectral Density (PSD) of Time Variation in Cyg X-1
PSD of accretion rate obtained by Numerical Simulation

11. X-ray Shot of Cyg X-1 hard soft Negoro et al. 2001
Negoro et al. pointed out that the largest amplitude X-ray intensity peaks show typical interval of several seconds.
They call this as X-ray shots. The right panel shows the mean time profile of X-ray shot. It shows time symmetric profile
Distinct from the time profile of flares by magnetic reconnection. Manmoto et al. proposed that the symmetric profile is
Produced by the reflection of dense infalling blobs.
X-ray Intensity Variation in Cyg X-1 (Negoro 1995)
Manmoto et al. 1996

12. Time Variation of the Equatorial Density
3000　rg/c
In our smulations, we find infall of dense blobs from the outer torus. This viewgraph shows the isocontour of equatorial density. The horizontal axis is radius and vertical axis is time. The interval of infall is typically 0.3 seconds in our simulations, which corresponds to the Keplerian time scale of the torus.

13. Magnetic Flare in the Innermost Region
Joule Heating
T=30590
Current density
Magnetic energy
T=30610
As dese blob infalls, it twists and stretches magnetic field lines and accumulates magnetic energy in the innermost region of the disk. The right panel shows the isocontours of current density and magnetic field lines projected on the equatorial plane.
We found that magnetic energy is released in the innnermost region of accretion disks. The right panel shows the
Curentdensity and magnetic field lines. In the innermost region, accreting matter produces large-scale current sheets.
Magnetic reconnection taking place in the current sheet converts the magnetic energy stored in the current sheet into
Thermal and kinetic energy. We found that current density well correlates with the accretion rate.
Accretion rate
T=30630
time
Current density and magnetic field lines

15. State Transition of Black Hole Accretion Flows Simulated by Global 3D MHD Simulations including Radiative Cooling

16. State Transition in Accretion Disks
Optically thick, geometrically thin disk (high/soft)
X-ray intensity
Qrad
Qvis =
energy
Optically thin disk （low/hard)
X-ray intensity
This viewgraph shows two states of black hole accretion flows. In high/soft state, accretion disk is optically thick and geometrically thin. In low/hard state the disk is optically thin and radial advection dominates the energy transport.
Qadv = Qvis
energy

17. Thermal Equilibrium Curve of Accretion Disks
Abramowicz et al. 1995
Accretion
Rate
Slim
ADAF
This viewgraph has been cited many times in this workshop. It shows the thermal equilibrium curve of black hole accretion disks.
The horizontal axis shows the surface density and the vertical axis shows the accretion rate. The upper left branch is the optically thin ADAF and the right branch is the optically thick disk. These curves were obtained by assuming the phenomenological viscosity parameter alpha.
SADM
Surface
Density
Optically thin
Optically thick

18. Correlation between Surface Density and Accretion Rate in Non-radiative Disk Simulation
ADAF Solution
This viewgraph plots the results of non-radiative disks simulations on surface density-accretion rate plane.
Red points denote the state at 2.5 and green points show those at 5.0. The solid curves are theoretical
ADAF solutions. The disk evolves along this ADAF curve.
r = 5.0 Σ

19. Numerical Simulation of Transition between Hard State to Soft State
Abramowicz et al. 1995
Accretion
Rate
Slim
ADAF
When we include radiative cooling, we expect that state transition takes place when the accretion rate gets larger than the critical value.
SADM
Surface
Density
Optically thin
Optically thick

20. We Included Optically Thin Radiative Cooling
Cooling term is switched on after the accretion flow becomes quasi-steady
We assume bremsstrahlung cooling
Qbrem ∝ ρ T
Cooling is not included in rarefied corona where ρ<ρcrit
1/2 2

21. Numerical Result
Hot
Cool

22. Summary of Numerical Results
Cool Down
ADAF
Low βdisk
This viewgraph summarizes the numerical result. As the disk is cooled down from outside, accretion rate decreases and the inner part is still in the ADAF blanch with smaller accretion rate. Since gas pressure decreases due to cooling, magnetic pressure dominates in the outer thin disk and becomes less turbulent. Mass accumulates in this region and surface density increases.
Mdot：decresase Σ：decrease
Mdot : decrease Σ： increase

23. Time Development in Σ：Mdot plane
This viewgraph sows evolution in the Sigma-Mdot plane. In the inner region, accretion rate increases and after the onset of the transition in the outer radius, accretion rate decreases. In the outer disk, after the onset of the transition, accretion rate decreases and surface density increases.

24. During the Transition from Low/hard State to High/soft state, Mdot Decreases
Abramowicz et al. 1995
Accretion
Rate
Slim
ADAF
In conclusion, the transition between ADAF and SADM follows this line. During this transition, X-ray luminosity
Incrases first, and decreases next.
SADM
Surface
Density
Optically thin
Optically thick

25. X-ray Light Curve of GRS1915+105
It may explain the peak of luminosity observed in GRS during the transition between low state to high state.

26. Summary
We carried out global 3D MHD simulations of radiatively inefficient black hole accretion flows without assuming the viscosity parameter α
Numerical results reproduce the time variabilities observed in X-ray hard states of black hole candidates
State transision from low/hard state to high/soft state is simulated by including optically thin radiative cooling
Next target is the global simulations of radiatively efficient disk