Measurement of the Reconnection Rate in Solar Flares

H. Isobe 2004/12/6 Taiyo-Zasshikai

• Chromospheric brightenings during solar flares are

• Observation of

Reconnection rateMagnetic flux reconnected per unit time is given by BVin = E (Electric field)or in dimensionless form, Vinflow/VA

The electric field E can be inferred from the motion of flare footpoint emission (flare ribbons) and magnetograms.

“Mortion of Flare Footpoint Emission and Inferred Electric Field in Reconnecting Current Sheet” Qui, J., Lee, J., Gary, D. E., Wang, H. (2002, ApJ, 56

5, 1335)

C9.0 flare on 2000 Mar. 16 (NOAA8906)

Ha (BBSO)HXR (Yohkoh)

Qui et al. 2002

• E=VxB=9000 V/m (maximum)• Temporal correlation with HXR• 2D approximation seems bad.

“Study of Ribbon Separation of a Flare Associated with a Quiescent Filament Eruption” Wang, H., Qui, J., Jing, J. & Zhang, H

(2003, ApJ, 593, 564)

M1 flare2000 Sep. 12Quiet region

E=100 V/m (10 V/m in decay phase)

H alpha image from Kanzelhohe Solar Observatory

Wang et al. 2003

Good correlation with ribbon separation and filament/CME acceleration.

“Magnetic Reconnection and Mass Acceleration in Flare-Coronal Mass Ejection Event” Qui, Wang,

Cheng, & Gary (2004, ApJ, 604, 900)

X1.6 flare 2001 Oct. 19NOAA 9661E=580 V/m

M1.0 flare2000 Sep. 12Decaying ARE=50 V/m

Qui et al. 2004

Good correlation with filament/CME acceleration and the reconnection rate (E)

“Tracking of TRACE Ultraviolet Flare Footpoints”Fletcher, Pollock, & Potts (2004, Sol. Phys., 222,

279)

M8.5 flare 2002 Jul. 17

•Focus on the fine structure of the ribbon and motion of each kernel.•Found evidence that UKV kernels move along the boundary of granules.

How to calculate the reconnection rate

(Isobe et al. 2002, ApJ, 566, 528)

H: heating rate (erg/s), Vin: inflow velocity, Bc: magnetic field strength in the corona. Ly, Lz: size of the reconnection region ~ size of the flare arcade

• Energy release rate by reconnection is given by the Poynting flux into the reconnection region;

• Conservation of the magnetic flux;

Ly

Lz

Bfoot: magnetic field strength at the photosphereVfoot: separation velocity of the flare ribbons

Energy release rate H•Temperature and emission measure (and hence density, with assumption of the line-of-sight depth) calculated from Yohkoh/SXT data using filter ratio method.•To estimate the cooling terms Isobe et al. (2002) used following approximate forms:

Radiative cooling

Conductive cooling

Possible errors: (1) conduction may be overestimated, (2) enthalpy flux from chromospheric evaporation not considered.

=>we carried out 1D numerical simulation of a flare loop.

Numerical simulation of 1D flare loop

•1D hydrodynamical simulations•Flare energy injected at loop top •Nonlinear (Spitzer) heat conduction, radiative cooling, chromospheric evaporation

Pseudo observation of the simulation result1.From the temperature and density (emission measure) obtained from simulations, soft X-ray emissions detected by the bandpass filters of Yohkoh/SXT are calculated.2. From the spatially integrated SXT count rates of the simulation result for Be and Thick Al. filters, temperature, emission measure, and hence thermal energy are calculated.3. The rate of thermal energy increase during the impulsive phase is compared with the energy injection rate in the simulation.

Scaling law of the dEth/dt and energy release rate

•A series of simulations with different loop length and flare energy allows us to derive a scaling law that gives the ratio of thermal energy that would be observed by SXT to the real energy release rate.

•The ratio is 0.3〜 0.8 depending on loop length and input heat flux.

Ratio

to in

put e

nerg

y fu

x

EventsX2.3 class 2000/11/24

M3.7 class 2000/07/14

C8.9 class 2000/11/16

GOESX-raylight curve

TRACE 1600 A image

Data analyses 1. Vfoot and Bfoot

Time slice of the flare ribbons => VfootCoalignment with magnetogram => Bfoot

TRACE 1600 A image

SOHO/MDI

Data analyses 2. Energy release rate

• Energy release rate H is calculated from Eth obtained from SXT data and the scaling law.

SXT count rates Eth

Thick Al.

Be

Results 1. Reconnection Rate

GOES class

Heating rate (erg/s)

Bfoot (G)

Vfoot (km/s)

Bcorona (G)

V inflow (km/s)

Reconnection Rate

X2.3 4.6e28 613 10 54 110 0.03

M3.7 6.4e27 165 3.3 96 5.6 0.003

C8.9 1.1e27 76 10 11 67 0.08

Results 2. Electric fieldGOES class

Heating rate (erg/s)

Bfoot (G)

Vfoot (km/s)

vxB Electric field (V/m)

HXT Lband count (CTS/s/sc)

HXT M1band count (CTS/s/sc)

X2.3 4.6e28 613 10 613 2800 1300

M3.7 6.4e27 165 3.3 54 50 40

C8.9 1.1e27 76 10 76 3 0

Ratio 28:4:1 8:2.2:1 1:0.3:1 8:0.7:1 933:16:1 32:1:---

•Electric field in the current sheet is larger in C class than in M class.•The length along the flare ribbon is nearly the same in these flares. Therefore the total voltage drop along the current sheet is also smaller in the M class flare.•Acceleration is not by direct electric field?

Summary• We propose an indirect method to determine the inflow velocity,

coronal magnetic field, and hence reconnection rate from observational data.

• Applying the method to three two-ribbon flares, we found that reconnection rate is 0.003-0.08. These values are consistent with previous studies.

• The macroscopic electric field in the reconnecting current sheet inferred from separation velocity of the flare ribbons shows no correlation with hard X-ray count rate, though data samples are too few.

• It is likely that the macroscopic electric field influences the spectrum of the high energy particles. Statistical study using RHESSI data may answer the question.

Asai et al. 2003, 2004

• 1230 Gauss, 63km/s, 7.7 kV/s• GOES X2.3 HXT Hband 80/s/sc (only aft

er peak)• Measure vfBf and vfBf^2 (proxy of Poynti

ng flux in the corona). Their difference along the ribbon is large enough to explain the localization of HXR source.

Electric Field vs GOES class

SXR flux (GOES)

Electric field (V/m)

Results from Isobe, Takasaki, Shibata in prep, Qui et al. 2002, 2004, Wang et al. 2003, Asai et al. 2003