Global Simulations of Turbulence
and Dynamos in Differentially
Rotating Astrophysical Plasmas

Ryoji Matsumoto (Chiba Univ.)
Collaborators: Minoru Tanaka (Chiba Univ.) andMami Machida (NAOJ)

Magnetic Activities of Astrophysical
PlasmaOptical image of sunspots by HINODE

X-ray Image by HINODE Satellite

Butterfly Diagram of Sunspots (NASA) 2

Filamentary Structure and Radio
Arc Near the Galactic Center

RaLosa et al (2000) VLA

Yusef-Zadeh and Morris 1987

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Accretion Disks and Jets

A Schematic Picture (NASA)

Protoplanetary Disk and Optical Jet(HST)4

Two Models of Magnetically Driven Jet

Magneto-centrifugally
driven jet

Magnetic tower jet

Blandford & Payne (1982)
Uchida and Shibata (1985)

Lynden-Bell & Boily (1994)
5
Kato et al. (2004)

Outline of This Talk
• Flows, Turbulence and Magnetic Field
Amplification in Astrophysical Rotating
Disks– Angular momentum transport in differentiallyrotating disks– Global 3D MHD Simulations of Accretion
Disks– Global 3D MHD Simulations of Galactic Gas
Disks
6Angular Momentum Transport inAccretion Disks

Plasma is confinedby gravity andcentrifugal force

Rotating gas should lose angular momentum to accreteStandard theory of accretion disk assume Trφ=αP• Interval of dwarf nova outbursts indicate α = 0.01 − 0.1• In hydrodynamical disks α = O(0.001)

too small !

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Theoretical Breakthrough:Magnetorotational Instability

Angularmomentum

Plasma element perturbed inward
loses angular momentum

MRI in differentially rotating disks (Balbus and Hawley 1991)8

Global Three-dimensional Resistive MHD
Simulations of Black Hole Accretion Flows(Machida and Matsumoto 2003 ApJ )Gravitational potential : φ = - GM/(r-rg)
Angular momentum : initially uniformMagnetic Field : purely azimuthal
Pgas/Pmag = β = 100 at 50r_g
Anomalous Resistivityη = (1/Rm) max [(J/ρ) /vc– 1, 0.0]

2250*64*192mesh
9Formation of an Accretion DiskMachida(2005)
Volume rendered image of density distribution
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Time Evolution of Magnetic
Energy and Maxwell Stress
Magnetic Energy

α = <BrBφ/4πP0>
α ~ 0.1

β = Pgas/Pmag~ 10time

TIME
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X-ray Shots in Black Hole Accretion Disks
Joule Heating
T=30590

Current Density

Magnetic Energy

T=30610

Current density(color)

Accretion Rate
T=30630

time

Time variabilities of Cyg X-1 12(Negoro 1995)

Sawtooth-like Oscillation
Magnetic energy

Joule Heating Rate

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Sawtooth-like Oscillation in NonlinearSystems• Sawtooth oscillation takes place when
instability and dissipation coexists
When dissipation is large

When dissipation is small
Growth of
instability

Approaches to a quasi-steady state

Energyrelease

Sawtooth oscillation

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Growth and Disruption of m=1
Non-axisymmetric Mode

We found that during the amplification of magnetic energy, m=1 nonaxisymmetric mode grows and deforms the disk to crescent shape.
15Why Sawtooth-like Oscillations
Appear in Low Temperature Disks ?
Machida andMatsumoto 2007
submitted to PASJ

Formation ot
the Inner
Torus isEssential for
sawtooth-likeoscillations
High temperature(HT) modelLow temperature (LT) model

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High Frequency Oscillations are Excitedduring Sawtooth-like Oscillation
LFQPO HFQPO

1Hz

10Hz

100Hz

Power spectrum ofluminosity variation

0.01 0.1

110100 HzXTE J1550-564
McClintock andRemillard 2004

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Magnetic Fields in Spiral Galaxies

Our
OurGalaxy
Galaxy(Han(Hanetetal.,al.,2002)
2002)

M51 (Berkhuijsen et al. 1997)

Our Galaxy (Han et al. 2002)

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How Galactic Magnetic Fields areAmplified and Maintained ?

reversalarc
Loop

Rotation

Magnetic Fields of Galactic Disk
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Simulation Model for a Galaxy
䠄Nishikori et al. 2006, ApJ 641,862)• Axisymmetric Gravitational Potential
Miyamoto et al. (1980)• Cylindrical Coordinate System• Simulation Region
0 <ϖ < 56kpc, 0 < z < 10kpc• Absorbing boundary at r=0.8kpc• Initally Weak Azimuthal Field– β = Pgas/Pmag = 100 −10000• Mesh points : 250 x 64 x 319
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Numerical Results (β =100)

2Gyr

3.5Gyrρ+B

t = 3.8Gyr21

Amplification and Saturation ofMagnetic Fields

β =100

Average in 2kpc < r < 5kpc and 0 < z < 1kpc
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Spacial and Temporal Reversal ofMagnetic Fields (β =1000)
after 2µG
1Gyr…

1Gyr

5Gyr
Time variation of mean
azimuthal magnetic fieldAt 5kpc < r < 6kpc
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Radial Reversal of Mean Magnetic
FieldsGalactic magnetic fieldobtained by Rotation Measure
Azimuthal field at t=3.8Gyr at z=0.25Kpc(Han et al. 2002)

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Summary• We carried out global 3D MHD simulations ofdifferentially rotating astrophysical plasmas suchas accretion disks and Galactic gas disks• In cool gas is supplied, sawtooth-like oscillation
is excited by the magnetic field amplification due
to MRI and magnetic energy release due tomagnetic reconnection• In Galactic disks, mean magnetic fields areamplified up to 1-2 micro Gauss• Azimuthal magnetic fields reverse their direction
both in space and in time. The period of fieldreversal is about 1Gyr in our Galaxy.
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