Three-dimensional MHD simulations of emerging flux and associated magnetic

reconnection

Hiroaki Isobe (DAMTP, Cambridge / Tokyo)Takehiro Miyagoshi, Kazunari Shibata (Kyoto)

Takaaki Yokoyama (Tokyo)

6th Solar-B Science Meeting, 8-11 November 2005, Kyoto

Outline• Theories of magnetic reconnection and its difficulties

– Huge magnetic Reynolds number– Scale gap

• Key observations and its implication to theory– fractal nature of current sheet– plasmoid ejection

• 3D MHD simulations of emerging flux and its reconnection with overlying coronal field– formation of filamentary structure– patchy reconnection– Observations by Solar-B

Theories of magnetic reconnection

€ VinVa=lL=Rm−1/2≈10−7

Sweet-Parker reconnection

Reconnection rate:

Parker 1957, Sweet 1958

€ VinVa∝lnRm≈0.01−0.1Petschek reconnection

Petschek 1964•MHD simulations: if resistivity is localized, Petschek-like reconnection (i.e., with slow shocks) occurs.

•Magnetosphere obs. and Lab experriments suggest that fast reconnection occurs when current sheet become as thin as ion Larmor radius or ion innertial length.

Fundamental problem in fast reconnection: huge scale gap

Ion inertia length 2/1611010100⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛≈=−KTGBcmeBvcmriLiIon Larmour radiuscmrflare910≈typical size of solar flare

•Laminar and steady reconnection with tiny diffusion region? Unlikely. •Mesoscale (MHD) structure?•Self-similar evolution in free space (Nitta P45)

2/1

310, 10300

−

− ⎟⎠

⎞⎜⎝

⎛≈=cmn

cmc

piionin ω

l

Fractal nature of current sheets

Hard X-ray emission(Ohki 1992)

Power spectrum of radio (610MHz) emission (Karlicky et al. 2005)

Fractal!

Fine spatial structure in reconnection events

Small kernels in flare ribbons(Fletcher, Pollock & Potts 2004)

aurora

Surges/jets

Supra-arcade downflows (McKenzie & Hudson 1999, Innes, McKenzie & Wang 2003, Asai et al. 2004 )

Plasmoid (flux rope) ejection

• Simultaneous acceleration of plasmoid and energy release • Slow rise and heating of plasmoid/flux rope prior to the hard X-ray burst

Ohyama & Shibata 1997

Zhang et al. 2001

Laboratory experiment

color: current densitysolid lines: magnetic field lines

Reconnection rate is enhanced when current sheet (plasmoid) is ejected (Ono et al. 1997).

Plasmoid-induced-reconnection (Shibata & Tanuma 2001)

Fractal current sheet with many islands?

Aschwanden 2002 Tajima & Shibata 1997

•Consistent with the fractal nature of flare emission•Natural connection between MHD and micro scales

S-P type reconnection with enhanced resistivity? Turbulence?

Statistical analysis of flares observed by Yohkoh/SXTPoster by Nagashima & Yokoyama, P43

Vin/VA Rm∝ -1/2Vin/VA Rm∝ -0.8

Laboratory experiment(Ji et al. 1998)

MHD turbulence in reconnecting current sheet

• Tearing instability (e.g., Furth et al. 1963, Shibata & Tanuma 2001...)

• Secondary kink of tearing-made flux rope (Dahlburg, Antiochos & Zang 1992)

• Kelvin-Helmholtz (Hirose et al. 2004)• Non-linear coupling of microinstabilities to macrosc

ale (e.g., Shinohara et al. 2001)

• Collision of reconnection jets (Watson & Craig 2003)

• Reconnection-driven filamentation (Karpen, Antiochos & DeVore 1997)

• Rayleigh-Taylor (indterchange) instability (Isobe et al. 2005)

Three-dimensional MHD simulation of emerging flux and reconnection with pre-existing coronal fie

ld

Isobe, Miyagoshi, Shibata & Yokoyama 2005, Nature,434, 478

Observation of emerging flux region: Halpha

Hα(Hida Obs.)

•H alpha(104K)-Arch filament connecting the sunspots.-Why filament? (magnetic field must fill the space in the lowβ corona!)

Matsumoto et al. 1993

Observation of emerging flux region: EUV

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ǙDZÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

•EUV-Hot (T=106K) loops and cold (T=104K) loops exist alternatively- Intermittent coronal heating. - Jets and flares... reconnection.

TRACE EUV

2D MHD simulation(Yokoyama & Shibata 1995)

Parker instability => emergence of loop in the corona => reconnection with pre-existing coronal field => jet

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Simulation model

•3D extension of Yokoyama & Shibata (2005)

•anomalous resistivity

vd=J/ρ： ion-electron drift velocity

•Upper convection zone - photosphere/chromosphere - corona

•Horizontal magnetic sheet in the convection zon＋ uniform background field.•Grid: 800x400x620. Calculation was carried out using 160 processors of the Earth Simulator (about 8 hours for 50000 steps).

Result: overview

•Basically similar evolution to 2D simulation.

Magnetic field lines

Magnetic field lines + isosurface of |B| + temperature

Filamentary structure from the magnetic Rayleigh-Taylor instability

•The top of the emerging flux becomes top-heavy ＝＞ unstable to the Rayleigh-Tyalor instability

•Bending of magnetic field is stabilized ＝＞ Filamentary structure

x

zy

Color: mass density

Isosurface of mass density

Hαimage of arch filaments

Why top-heavy?Nonlinear evolution of Parker instability is approximately self-similar (Shibata et

al. 1990).

simulation self-similar solution

density at middle

Field lines at different time

•The outermost part deviates from self-similar solution.

Why top-heavy?

The outermost field lines undergo:

• Compression between coronal pressure above and magnetic pressure below.

• Larger curvature radius => smaller gravity along B => less evacuation.

divvpara

divvperp

Evolution of the Rayleigh-Taylor instabilityDensity at the y-z plane

t=70

t=81t=78

t=76

• Small wavelength modes grow first (larger linear growth rate)• Larger scales from inverse cascade• Scale (width of filaments) may change with the presence of shear€

γ= kyg(ρ 2 − ρ1) / (ρ 2 + ρ1)

Fourier modes of Vz

Linear growth rate

Observational signature

• Rayleigh-Taylor instability– Rising loops and (relatively) sinking loops exist alternatively.– Sinking loops are denser and probably colder– Spectroscopy in H-alpha and/or EUV

• When the emerging loops become coronal temperature?– time scale of indivisual loop emergence 〜 1000 s– For EIS observations, time cadence is more important

• Vortex excited by secondary Kelvin-Helmholtz instability– Tortional Alfven wave – Small scale twist in individual filaments– Chromospheric magnetic field measurement

Formation of filamentary current sheets

Mass density isosurface (gray)Current density distribution (color)

Mass density (contour) and current density (color) at the y-z cross section

•Deformation of magnetic field by the Rayleigh-Taylor instability =>current formation in the periphery of the dense filaments•Dissipation of these current sheets may result in intermittent heating, leading to the formation of the hot/cold loops system.

xz

y

Reconnectin in the interchanging current sheet

•Larger current density and smaller mass density in the rising part of the R-T instability

•anomalous resistivity sets in locally•fast reconnection occurs in spatially intermittent way

•Reconnection inflow enhance the nonlinear evolution of the R-T instability => nonlinear instability

Anomalous resistivityB×

・

Intermittent, patchy reconnection

Isosurfaces of velocity.

•Fast reconnection occurs in spatially intermittent way after the ejections of plasmoids.•Many narrow reconnection jets from initially laminar current sheet.

Isosurfaces of gas preasure+ magnetic field line

Many small plasmoids in the intialy laminar current sheet.

Supra-arcade downflows = reconnection jets?

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Conjecture•R-T instability can occur if there is density jump across the current sheet and effective acceleration (in suitable direction).•Effective acceleration is likely to exist in dynamically evolving system (like eruptive flares, CMEs, solarwind-magnetosphere) and in driven reconnections.

•RT instability is ideal instability, hence no restriction from large Reynolds number.

•Possible scenario may be...•Small scale turbulence grows by R-T instability (and couple with micro-scales) •tearing occurs in small scale•formation of large plasmoids (flux ropes) by coallescense => fast reconnection in global scale

Observation of reconnection signatures by Solar-B

• Few spectroscopic detection of reconnection inflows/outflows (Innes et. al. 1997, Lin et al. 1995).

=>EIS– Precise determination of the reconnection rate.– Slow shock? (Shiota et al. 2003)

• Turbulent broadening Vturb ≈VA in hottemperature lines such as FeXXIV(10MK) if reconnection is fractal, i.e., many small reconnection.

FeasibilityTemperature: T ≈ 5-20MK. FeXXIV(192.08) is suitable?.

Time scale: t ≈ 10-100 (s).

If turbulent-enhanced Sweet-Parker, the width of current sheet w is:w = MAL ≈ 10 - 1000 km.

Assuming the (pre-flare) density of 109 cm-3, EM ≈ 1024-26 cm-5.

For FeXXIV(192.028), several photons /s/pixel ... not easy but possible.(Thanks: Helen Mason)

Same figure with isosurface of current density

3D structure of reconnectionMagnetic field line + current density distribution

• Petschek-like slow shocks

Reconnection inflow/outflow in 3D

Isosurface of |V| Velocity and current density on the x-z cross section

Velocity on the y-z cross section in the outflow region. Contour is velocity perpendicular to the figure.Diverging

•Outflow in diverging = more effective in plasma expelling. => faster than 2D reconnection?

x

zy

Velocity on the y-z cross section in the outflow region.Converging

Comparison of the reconnection rate with 2D case

•Locally, 3D reconnection is faster and more bursty than 2D reconnection.•The spatial average is comparable with 2D.•Rayleigh-Taylor does not occur in 2D... so the local condition near the reconnection point is not the same.

Reconnection rate measured by maximumηJ in the y-z cross section.

Preliminaly.

Summary

• Filamentary structure spontaneously arises due to the magnetic Rayleigh-Taylor instability in the emerging flux.

• Current sheets are formed in the periphery of arch filaments due to the R-T instability. Intermittent heating.

• Magnetic reconnection becomes patchy, due to the interchanging of the current sheet.

• Fine structure and dynamics in EFR filaments/loops (SOT/EIS/XRT)

• Detection of reconnection inflows/outflows (EIS/XRT)• Turbulence in the current sheet (EIS)• EFR is suitable to target to catch the reconnection event (ev

en in solar minimum).

Why top-heavy?Density in 2D simulations

with coronal field

without coronal field

•Vertical distribution of density (color symbols) and Bx(solid) at the mid-point of the emerging flux.•Color indicates the Lagrangean trace of the fluid elements (i.e. same color indicates the same field lines.)

Divergence of the velocity components parallel and perpendicular to B

divV

divVpara

divVperp

　•Top-heavy sheath locates at orange-magenta boundary.

•Divergence of V (especially Vperp) changes the sign at this point. => convergence.

Deviation from self-similar solution (Shibata et a. 1990)

•The outermost part of emerging flux deviate from self-similar solution.•Compressed beteen coronal pressure and upward magnetic pressure from below (divVperp<0)•Outerfield lines have larger curvature radius and hence smaller effective gravity along B. (effect of divVpara ）

simulation self-similar solution Density at the midpoint of the emerging flux.

Density@midpoint t=10 t=80

t=84 t=88 t=92

t=96 t=104 t=112

Helical flux rope

Helical structure erupting after a prominence eruption (TRACE/EUV; Liu & Kurokawa 2004)

•With the presence of the guide field (By), helical flux rope is formed.

(This calculation is still preliminary)

The Earth Simulator•A parallel vector computer system installed at the Earth Simulator Centre, in Yokohama, Japan.•Fastest computer in the world since 2002 until September 2004.

↓Tokyo↑Yokohama

Kyoto↓

The Earth Simulator: hardware and software

•640 Processor Nodes (PNs)•One PN consists of 8 vector-type arithmetic processors (APs) and 16 GB shared memory..

•In total, 5120 APs and 10TB memory (distributed).•40Tflops at peak, 35.86Tflops for Linpack Benchmark