Global MHD Simulations of Sawtooth-like Oscillations in Black Hole Accret

ion Disks

Ryoji Matsumoto (Chiba Univ.) Mami Machida (NAOJ)

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

Yohkoh Observations Confirmed Magnetic Reconnection in Solar Flares

Shibata and Yokoyama 1995

SOHO衛星観測

X-ray Flares in Protostars

Hayashi, Shibata and Matsumoto 1996Chandra observation

Numerical Simulation of the Magnetic Tower Jet

Kato, Hayashi, Matsumoto (2004)

Magnetorotational Instability in Accretion Disks

Angular momentum

MRI in accretion disks （ Balbus and Hawley 1991)

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

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

Formation of an Accretion Disk

Initial State t=26350rg/c

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

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

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

Time Evolution of Cooler Disk

Density distribution Toroidal magnetic field

Accumulation and Release of Magnetic Energy

Magnetic Energy

Joule Heating Rate

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

Similar Behaviors have been Observed in Resistive 3D Local

MHD Simulations

Sano and Inutsuka 2001

Growth and Disruption of m=1 Non-Axisymmetric Mode

Isosurface of Density Equatorial Density

Sawtooth-like Oscillations Accompany High Frequency QPOs

Sawtooth HFQPO

1Hz 10Hz 100HzRadial Dependence of PSD PSD of Luminosity

Dependence on the Azimuthal Resolution

32mesh 64mesh

Accretion rate

Joule Heating

Mass Outflow Rate also Shows QPOs

Log(Temperature) Density

Another Example: Double Periodic Oscillation

Density Distribution 250*64*384mesh

Time Evolution of Mass Accretion Rate and Joule Heating Rate

Mass accretion rate

Joule heating

Time Evolution of Mass Accretion Rate and Joule Heating Rate

Mass accretion rate

Joule heating

PDS of Mass Accretion Rate

Frequency (Hz)

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.

END