MHD Simulations of Flares and Jets in the Sun, Stars, and

Accretion Disks

Kazunari ShibataKwasan and Hida Observatories

Kyoto University

East Asia Numerical Astrophysics Meeting Oct. 31, 2006 Taejeon, Korea 25min talk + 5min discussion

Contents

• Introduction

• Solar Flares and Jets

• （ Protostellar Flares and Jets)

• Jets from Accretion Disks

　　　　　　- With emphasis on magnetic reconnection

universe is full of flares

Solar flares

Protostellar flares

Gamma ray bursts

universe is full of jets and mass ejections

Solar jets

protostellar jets

Coronal mass ejectionsAGN (active galactic nuclei)

jets

Basic MHD processes in stars and disks

Solar Flares

various “flares” with different appearance

impulsive flares Long duration flares Giant arcade

microflares with jets

coronal mass ejections above giant arcades ~ 1011 cm

Plasmoid (flux rope) ejectionsare ubiquitous in flares

impulsive flares ~ 109 cm

Long Duration flares~ 1010 cm

Unified model

Plasmoid-Induced-Reconnection (Shibata 1999)

Unified model(plasmoid-induced reconnection

model: Shibata 1999)

(a,b) ： giant arcade,

long duration/ impulsive flare

(c,d) ： impulsive flares, microflares

　　　

Energy release rate＝ 22

222

410

4LV

BLV

B

dt

dEAin

What determines flare duration ?

Nishida et al. (2006a)

In preparation

Soft X-ray intensity of solar corona during a week (all bursts are flares)

What determines flare duration ?

L

BM

L

vM

L

v

L

AAAinflare

4

inflowoffieldmagnetic:

inflowofdensitymass:

ocityAlfven vel:

rateon reconnecti maximum:

velocityinflow:

regionon reconnectiofthickness:

B

v

M

v

L

A

A

in

After Plasmoid ejection

Field lines whch can be reconnected

Flare duration ~ reconnection time

Potential field (minimum energy state)Initial condition

Various cases with different size and field strength of reconnection region

II

III IV

Shiota et al. (2005)

Smallstrong

LargeWeak

I

Case of large reconnection region

• Color: gas pressure

• Contour: field lines

• Long duration

Case of small reconnection region

• Color: gas pressure

• Contour: field lines• Short duration

Reconnected flux as a function of time

• Duration become shorter when the reconnection size is small (and magnetic field strength is stronger)

t/tA

Re

conn

ected flu

x pe

r un

it time

Normalized reconnection rate

• Duration become shorter when the reconnection region is smaller

t/tA

No

rma

lized R

econ

nectio

n rate

Comparison with observations(Nagashima and Yokoyama 2006)

• Simulation data are plotted on Nagashima & Yokoyama (2006)’s figure

• Flare duration is different even when the flare loop lengths are similar

Flare loop

length

What determines reconnection rate

(energy release rate) ?Nishida et al. (2006b)

In preparation

Soft X-ray intensity of solar corona during a week (all bursts are flares)

Role of Plasmoid

plasmoid-induced-reconnectio

n(Shibata et al. 1

995, 1999,Shibata and Ta

numa 2001)

Model of impulsive flares

Nishida et al. 2006b in preparation

Two cases

• Case 1 : resistivity is changed

• Case 2:plasmoid velocity is changed (due to external force)

Case 1: resistivity is changed

Plasmoidvelocity

Rise velocity of Loop (Reconnection rate)

Case 2: plasmoid velocity is changed by external force

Reconnectionrate

Plasmoid velocity

Vloop (km/s)

Vej

e (k

m/s

)

×

(×)

△△

○

(□)

○

□ ： ～ 20”

○: 10-15”

△: 5-10”

×: < 5”

⊿ｈ

Observed correlation between Vloop and Veje 　(Shimizu et al. 2006 in preparation)

Plasmoid-induced reconnectionin a fractual current sheet

(Tanuma et al. 2001, Shibata and Tanuma 2001)

Tanuma et al. (2001)

Vin/VA

plasmoid

Reconnection rate

time

Simulations of smaller flares - reconnection driven by emerging

flux (Parker instability)

Shimizu et al. (2006) In preparationIsobe et al., (2005) NatureIsobe et al. (2006) PASJ

Reconnection driven by emerging flux

Solar jet

Model of solar jet (Shimizu et al. 2006, in preparation)Same as Yokoyama and Shibata (1995)But with CIP scheme (200x110)

This model is useful as model of generation of Alfven waves, which accelerate high speed Solar wind (Parker 1991, Axford and McKenzie 1996, cf) Kudoh and Shibata 1999, Suzuki and Inutsuka 2005)

Reconnection driven by emerging flux : case of vertical field (Shimizu et al. 2006)

3D-MHD modeling of emerging flux using the Earth simulator (Isobe et al., 2005, Nature 434, 476)

800x400x600blue ： iso-magnetic field strength surface 、 side ： temperature

z

y

x t=50 t=70

t=90

Comparison with observed H alpha arch filament (Isobe et al. Nature 2005)

Hα （ Hida ） Density isosurface

density~1012/cc, temperature~10000K　Length~10000km, width~1000km

3D structure as a result of Rayleigh-Taylor instability

(Isobe et al. Nature 2005, Isobe et al. PASJ 2006)

Density

•Top of emerging flux becomes top-heavy, so that Rayleigh-Taylor instability occurs.• As a result, filamentary structures along magnetic field lines are created 　　• mushroom type vortex motions (due to KH instability) are seen • 3D patchy reconnection occurs

xzy

Filamentary jet produced by 3D patchy reconnection

(Isobe et al. 2005 Nature)

simulation

observations

EUVTRACE

HalphaHIda

Reported in Newspapers …

Jets and flares in accretion disks

3D structure of jets from disks(Kigure and Shibata 2005)

Model R6Non-axisymmetric structure appeared in a diskAnd propagate into jets

Very weak field case:Magnetic buoyancy driven outflow

(Kigure and Shibata 2006 in prep)

Magnetic buoyancy is a main force of acceleration !

Do jets and disks reach steady state ?

No !!, because Magnetorotational Instability is so powerful (Balbus and Hawley 1991)

Disks arefull of reconnectionevents

Kudoh et al2002Sato et al.2005Ibrahim et al.2005

Long term simulations of jets from accretion

disks (Ibrahim and Shibata 2006, see poster)

Region size in previous simulations(Kudoh et al. 1998, 2002, KatoS et al. 2004)

Quasi-periodic ejections of jets(see Ibrahim’s poster)

Period is roughly determined byAlfven time

General relativistic jets from Kerr hole (Koide et al. 2006 Phys Rev, listen to his talk)

Summary

• Reconnection model of solar flares has been developed significantly in these 10 years owing to rapid progress of space observations and supercomputer, though key puzzles remained: triggering mechanism, coronal heating, micro-macro coupling.

• MHD simulations of astrophysical jets have also been developed significantly, including general relativistic model. Remaning important questions are: collimation, 3D stability of jets, and production of ultra relativistic jets (Lorentz factor > 10).

• jets and disks never reach steady state, and are full of reconnection events

I hope more and more astrophysicists will join this exciting field “astrophysical reconnection” !

Protostellar flares and jets

Uehara et al. (2006) in preparation

Kawamiti and Shibata (2006) in preparation

reconnection modelof protostellar flare

and jets（ Hayashi, Shibata, Matsu

moto 1996)

Many reconnection events (flares)(Uehara et al. 2006 in preparation)

Emg = 2x10^{-5}

Global and long term simulations(Uehara et al 2006 in prep)

Global simulation(Uehara et al. 2006 in preparation)

Protostellar jets