Global MHD Simulations of Sawtooth-like Oscillations in Black Hole Accretion Disks
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Global MHD Simulations of Sawtooth-like Oscillations in Black Hole Accret
ion Disks
Ryoji Matsumoto (Chiba Univ.) Mami Machida (NAOJ)
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X-ray Flares in Black Hole Candidates
X-ray Flux (Negoro 1995)
PSD
Power Density Spectrum of Time Variation in Cyg X-1
f-0.9
f-1.5
1Hz 100HzX-ray shots
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Yohkoh Observations Confirmed Magnetic Reconnection in Solar Flares
Shibata and Yokoyama 1995
SOHO衛星観測
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X-ray Flares in Protostars
Hayashi, Shibata and Matsumoto 1996Chandra observation
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Numerical Simulation of the Magnetic Tower Jet
Kato, Hayashi, Matsumoto (2004)
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Magnetorotational Instability in Accretion Disks
Angular momentum
MRI in accretion disks ( Balbus and Hawley 1991)
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Basic Equations of Resistive MHD
radvisJ
2
QQ+Q=∇P+)ερ(∇+t∂
ερ∂
∇η+)×(×∇=t∂
∂
ρ+π4
×)×∇(+P∇=)∇•(ρ+
t∂
∂ρ
0=)(ρ∇+t∂
ρ∂
-
-
vv
BBvB
gBB
vvv
v
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Global Three-dimensional Resistive MHD Simulations of Black Hole Accretion Flows
Gravitational potential : φ= - GM/(r-rs)Initially constant angular momentum
Magnetic Field : purely azimuthal
Pgas/Pmag = β = 100 at 50r_s
Anomalous Resistivity
η= (1/Rm) max [(J/ρ) /vc– 1, 0.0] 2
(Machida and Matsumoto 2003 ApJ )
250*64*192mesh 250*32*384mesh
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Formation of an Accretion Disk
Initial State t=26350rg/c
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Magnetic Energy Release in Accretion Disks (Machida and Matsumoto 2003)
T=30590
T=30610
T=30630
Current Density and Magnetic Field Lines
time
Joule Heating
Magnetic Energy
Accretion Rate
Current density
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Black Hole Candidates Sometimes Show Quasi Periodic Oscillations
Pow
er D
ensi
ty
0.1 1 10 1000.01 Hz
GX 339-4
0.1 1 10 1000.01 Hz
XTE J1550-564
McClintock and Remillard 2004
LFQPO
LFQPO HFQPO
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HFQPOs Appear When a Hot Disk is Cooled Down (Mami’s talk)
Surface Surface DensityDensity
Accretion Accretion RateRate
Slim
Optically thickOptically thin
ADAF
Advection
Standard disk
Radiation
M = 10Msun, r =5, α= 0.1
Abramowicz et al. 1995
QPO
Hot disk
Cold disk
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Time Evolution of Cooler Disk
Density distribution Toroidal magnetic field
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Accumulation and Release of Magnetic Energy
Magnetic Energy
Joule Heating Rate
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Sawtooth Oscillation in Nonlinear Systems
• Sawtooth oscillation takes place when instability and dissipation coexists (e.g., Tokamak fusion reactors)
When dissipation is large
Growth of instability
Energy release
Sawtooth oscillationApproach to a quasi-steady state
When dissipation is small
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Similar Behaviors have been Observed in Resistive 3D Local
MHD Simulations
Sano and Inutsuka 2001
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Growth and Disruption of m=1 Non-Axisymmetric Mode
Isosurface of Density Equatorial Density
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Sawtooth-like Oscillations Accompany High Frequency QPOs
Sawtooth HFQPO
1Hz 10Hz 100HzRadial Dependence of PSD PSD of Luminosity
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Dependence on the Azimuthal Resolution
32mesh 64mesh
Accretion rate
Joule Heating
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Mass Outflow Rate also Shows QPOs
Log(Temperature) Density
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Another Example: Double Periodic Oscillation
Density Distribution 250*64*384mesh
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Time Evolution of Mass Accretion Rate and Joule Heating Rate
Mass accretion rate
Joule heating
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Time Evolution of Mass Accretion Rate and Joule Heating Rate
Mass accretion rate
Joule heating
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PDS of Mass Accretion Rate
Frequency (Hz)
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Summary
• Global 3D resistive MHD simulations of cool disks indicate that cool disks show sawtooth-like oscillations
• During the sawtooth oscillation, the disk repeats the amplification of magnetic energy and subsequent release of the energy by magnetic reconnection
• The sawtooth oscillation appears when m=1 one-armed density distribution develops in the inner torus
• The frequency of the sawtooth oscillation is typically 10Hz in stellar mass black holes.
• When sawtooth-like oscillation takes place, high frequency QPOs appear
• We need simulations including cooling.
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