Sawtooth-like Oscillations of Black Hole Accretion Disks

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

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

Let’s Show How QPOs are Excited by Global 3D MHD Simulations of Black Hole Accre

tion Flows

Gravitational potential 　：　 φ= - GM/(r-rg)Magnetic Field : purely azimuthal Pgas/Pmag =100 at r = r0

Anomalous Resistivity

= (1/Rm) max [(J /vc– 1, 0.0] 2

250*32*384mesh250*64*384mesh

rg=3.0 x 106(M/10Msun) cm

t0=rg/c=10-4(M/10Msun) sec

Unit

Basic Equations of Resistive MHD

radvisJ QQQPρt

ρ

t

ρπ

Pρt

ρ

t

－

－

vv

BBvB

gBB

vvv

v

∇)ε(∇∂

ε∂

∇η)(∇∂

∂

4

)∇(∇)∇(

∂

∂

0)(ρ∇∂

ρ∂

2

Numerical Results for Radiatively Inefficient Hot Disk

Power Spectral Density of time variation of accretion rate

QPOs Appear When a Hot Disk is Cooled Down

Surface Surface DensityDensity

Accretion Accretion RateRate

Slim

Optically thickOptically thin

ADAF

Advection

Standard disk

Radiation

Abramowicz et al. 1995

QPO

Hot disk

Cold disk

Time Evolution of Cooler Disk

Density distribution Azimuthal magnetic field

Magnetic Reconnection in Accretion Disks

Dense blob accretes

Current Sheet is Formed

Magnetic Reconnection Takes Place

Machida and Matsumoto 2003

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

Growth and Disruption of m=1 Non-Axisymmetric Mode

Isosurface of Density Equatorial Density

Sawtooth-like Oscillations Excite High Frequency QPOs

Sawtooth HFQPO

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

Another Example: Double Periodic Oscillation

Density Distribution

Time Evolution of Mass Accretion Rate and Joule Heating Rate

Mass accretion rate

Joule heating

PSD of Mass Accretion Rate

Frequency (Hz)

Mass Outflow Rate also Shows QPOs(Machida’s poster)

Log(Temperature) Density

Summary

• Global 3D resistive MHD simulations of cool disks indicate that cool disks show sawtooth-like oscillations

• During the sawtooth oscillation, amplification of magnetic energy and subsequent release of the magnetic energy repeats

• The sawtooth oscillation appears when one-armed density distribution develops in the inner torus

• The frequency of the sawtooth oscillation is several times of the rotation period of the torus, and typically 5-10Hz in stellar mass black holes. This frequency agrees with that of low frequency QPOs in galactic black hole candidates

• The sawtooth-like oscillation excites high frequency QPOs

END

Similar Behaviors have been Observed in Resistive 3D Local

MHD Simulations

Sano and Inutsuka 2001