What determines the reconnection speed? The role of plasmoid ejection and

turbulence

Naoto Nishizuka

Kwasan and Hida Observatories

Kyoto University

２００９ / １１ / ３　 Taiyoh Zasshi-kai

MR2009 Oct 3-5 @ Wisconsin university

Remaining puzzles on flares/CMEs

• Energy storage mechanism ?

• Triggering mechanism ?

• What determines the speed of reconnection (energy release rate) ?

• What fraction of released energy goes to nonthermal particle energies ?

Fundamental puzzle inherent tosolar reconnection

• microscopic plasma scale (ion Larmor radius or ion inertial length = 10 – 100 cm) is much smaller than the size of a flare (= 10^9 cm)

• So even if micro-scale plasma physics is solved, there remains fundamental puzzle how to connect micro and macro scale physics to explain solar flares

MHD simulations show plasmoid-induced reconnection

in a fractal current sheet(Tanuma et al. 2001, Shibata and Tanuma 2001)

Tanuma et al. (2001)

Vin/VA

plasmoid

Reconnection rate

time

Scenario of fast

reconnection (Shibata and

Tanuma 2001)

Cf ） Hoshino et al. 1994 Lee-Fu 1986 Kitabata, Hayashi, Sato 1995

Observation of hard X-rays and microwave emissions show fractal-like time variability, which

may be a result of fractal plasmoid ejections

(Ohki 1992)

(Tajima-Shibata 1997)

Benz and Aschwanden 1989Zelenyi 1996, Karlicky 2004 Aschwanden 2002

This fractal structure enable to connect micro and macro scale structures and dynamics

Fractal current sheet

Turbulent (fractal) current sheet in magnetotail (A.A.Petrukovich & L.M.Zelenyi 2006 STP11 talk)

cf) Hoshino et al. (1994) Chang, T. (1999)

Particle acceleration in a collapsing plasmoid

(Drake et al. 2006, Nature, 443, 553)

Interaction of particles and plasmoid dynamics may be a keyTo solve particle acceleration mechanism

Chromospheric reconnection may suggest that fast reconnection is occurring in the solar chromosphere such as weakly ionized collisional

plasma. This means not only microphysics (e.g. resistivity ) but also the dynamics of the reconnection are important.

Giant chromospheric jet and MHD reconnection model

What enables the fast reconnection?: Dynamics of the reconnection

Anomalous resistivity ---- Hall effects

--- Ambipolar effects

Plasmoid ejection

Turbulence

* Plasmoid-induced reconnection model

*Turbulence reconnection (Strauss 1988, Lazarian & Vishniac 1999)

* Fractal model (Shibata and Tanuma 2001)

Current sheet thinning

(Sweet-Parker → Petchek)

Samtaney et al. 2009, PRL, 103, 105004“Formation of Plasmoid chain in Magnetic

Reconnection”

• High Lundquist-number reconnection

104 < S <108 　　　 : S=LVA/η

• Large-aspect-ratio Sweet-Parker current sheets are shown to be unstable to super-Alfvenically fast formation of plasmoid chain.

• The plasmoid number scales as S3/8 and the instability growth rate in the linear stage as S1/4, in agreement with the theory by Loureiro et al. (2007)

Reynolds number and Reconnection (Lundquist number)

Biskamp 1986, Bulanov et al. 1979

τrec ~ τA S1/2 : S = LvA/η >>1 L/δSP ~ S1/2 δSP = LS-1/2 = (Lη/vA)1/2 …SP current layer

vin = vAS-1/2 = (vAη/L)1/2

Loureiro et al. 2007 a Linear thepry of the instability of large-aspect-ratio current sheets : emerges

from a controlled asymptotic expansion in large S.

tearing instability: δinner ~ S-1/8 δSP, maximum growth rate scaling: γτA ~ S1/4, The number of plasmoids formed along the current scales: S3/8

Simulation model

• Compressible resistive MHD equations in an elongated 2D box [-Lx, Lx] x [-Ly, Ly]

• (the adiabatic index 5/3, viscosity and thermal conductivity are ignored)

• 512x8192, Lx=δSP =(Lη/vA)1/2

• Upstream boundary

By(x=±Lx, y)=±Bin, vx(x=±Lx, y)=±vinx(-1)

• Dowstream boundary

Free outflow boundary

Time evolution of an SP current sheet for S~108, t/tA=0.20, 0.40, 0.45, 0.50 (S=108)

Current density for S=104, 105, 106, and 107

Relation between Lundquist number and Growth rate of tearing instability

The instability growth rate in the linear stage as S1/4

non linear

Linear

δinner

δSP

The muximum number of plasmoids in the central part of the sheet

plasmoid number scales as S3/8

Plasmoid-dominated current layers are inevitable, and they may be key to attaining fast reconnection, both in collisional and collisionless systems.

Kowal, Lazarian, Vishniac & Otmianowska-Mazur 2009, ApJ, 700, 63 “Numerical Tests of Fast

reconnection in weakly stockastic magnetic field”

[ Lazarian, Vishniac (1999) ]

Simulation model

256x512x256, grid size=0.004

Sweet-Parker reconnection stage

Turbulent reconnection

Time variation of total Mass, Magnetic/Kinetic energy

& reconnection rate for the stage with turbulence

Period of turbulence injection

Total mass, Magnetic/Kinetic energies are conserved.

Reconnection speed Vrec with different power of turbulence Pinj

• Reconnection speed Vrec ~ Pinj1/2 ~ Vl

2

Reconnection speed with different injection scale linj

• Reconnection speed Vrec ~ linj3/4

Reconnectin speed with different uniform (Ohmic) resistivity ηu

• Reconnection speed does not depend on the uniform resistivity in turbulence reconnection → 　 fast reconnection (?)

Reconnection speed with different anomalous resistivity / guide field

• Reconnection speed does not depend on neither anomalous resistivity nor guide field

Comparison of the reconnection rate Vrec in two initial conditions with antiparallel and

Uniform B.

• Turbulence structure cannot enhance reconnection rate by itself. We also need antiparallel B configuration.

Summary (1)

• Reconnection speed Vrec ~ Pinj1/2 ~ Vl

2

• Reconnection speed Vrec ~ linj3/4

• Reconnection speed does not depend on the uniform resistivity in turbulence reconnection →　 fast reconnection (?)

• no depence on neither anomalous resistivity nor the guide field.

• Turbulence structure cannot enhance reconnection rate by itself. We also need antiparallel B configuration.

Summary (2)

• While in the absence of turbulence we successfully reproduce the Sweet-Parker scaling of reconnection, in the presence of turbulence we do not observe any dependence on Ohmic resistivity, confirming that the reconnection of the weakly stochastic field is fast.

• We do not observe a dependence on anomalous resistivity, which suggests that the presence of anomalous effects, e.g. Hall effects, may be irrelevant for astrophysical systems with weakly stochastic magnetic fields.