論文紹介“ Proton acceleration during coalescence of two parallel current loops in solar flare

s”,J.I.Sakai & K.Shimada 2004,

A&A, 426, 333-341S.Tanuma

(Kwasan Observatory)

Abstract

• We investigate the plasma dynamics during coalescence of two parallel current loops in solar flares by performing a resistive 3D MHD simulations.

• As the results, we find the most effective electromagnetic fields for the production of high-energy protons.

• Next we investigate the orbit of many protons (test particles) in the electromagnetic fields obtained by the MHD simulations.

1. Introduction

• Observations

• Coalescence

• Recent papers on simulations

Characteristic Current Loop Coalescence and Related Solar Flares

• Quasi-periodic energy release and high-energy particle acceleration: 1980 Jun 7 flare and 1982 Nov 26 flare (Sakai & Ohsawa 1987)

• Plasma jet formation driven by tilting motion and shock formation: 1980 May 26 flare (coronal explosion) (Sakai & de Jager 1989a)

• 3D point-like explosion following strong magnetic collapse and shock formation: 1994 May 21 flare (Sakai & de Jager 1989b)

Sakai & de Jager 1991

Both flares show quasi-periodic amplitude oscillations with double sub-peak structure in both hard X-ray and microwave time profiles.

Quasi-Periodic Oscillation

Tajima et al. 1987

Microwave at 17Ghz

The 1980 Jun 7 flare

Hard X-ray at 40-140 keV

X-ray at 300-350 keV

Gamma-ray lines at 4.1-6.4 MeV

The 1980 Nov 26 flare

Microwave at 17Ghz

Heights of two microwave sources

See also Nakajima et al. 1983 (left fig)

Time

Time

Coalescence of Two Flux Tubes

Sakai et al. 2002b; Tajima et al. 1987

Coalescence of two flux tubes→Energy release and quasi-periodic amplitude oscillation (QPO)

(???) unconsistent with Asai et al (2001) and Kamio et al. in press., who explain the QPO(QPP) by the Alfven transit time (I.e., sausage or kink instability ).But physical meaning is same with these instabilities.

Quasi-Periodic Oscillation by Coalescence

Tajima et al. 1987

2.5D particle simulation of coalescence

TimeTime

B^2/8πkT

Electrostatic energyE^2/8πkT

Ion temperature in x-direction

Fluid (kinetic) energy

Reconnected magnetic flux

Time

Multiple Coalescence

Tajima et al. 1987

Multiple coalescence could explain more realistic pattern of quasi-periodic oscillation

x

y T=7.2/Ωi T=9.6/Ωi

B lines

Electron density

Electric field

2D distribution in x-y plain

B^2/8πkT

Electrostatic energyE^2/8πkT

Ion temperature in x-direction

Gamma-ray Observation by RHESSI

Hurford et al. 2003

The X4.8 flare of 2002 Jul 23

The observation could be explained by anisotropic proton acceleration.In this paper, we calculate the motion of protons (test particles).

The center of 2.223MeV emission is displaced by 20+-6 arcsec from that of 0.3-0.5 emission.

See also Heerikhuisen et al. (2002), Craig et al. (2001), Takasaki et al. in prep.

3D Particle Simulations of Two Tubes

Nishikawa et al. 1994Coalescence of two twisted flux tubes

3D MHD Simulations of Two Tubes

between almost parallel twisted flux tubes (Linton et al. 2001)

between untwisted flux tubes (Linton & Priest 2003)

MHD simulations of the interaction (reconnection and tearing instability)..…

Some of Recent Papers on Flux Tubes by Sakai Group

• One flux tube:– Sakai & Kakimoto 2004, ApJ, 425, 333 (test particle)– Sakai et al. 2003, ApJ, 584, 1095 (MHD)– Sakai et al. 2002, ApJ, 576, 1018 (MHD)– Sakai et al. 2002, ApJ, 576, 519 (MHD)– Sakai et al. 2000, ApJ, 544, 1108 (MHD)

• Two flux tubes: – Sakai & Shimada 2004, A&A, 426, 333 (test particle)– Saito & Sakai 2004, ApJ, 604, L133 (particle)– Sakai et al. 2002, ApJ, 576, 1018 (MHD)– Sakai et al. 2001, ApJ, 556, 905 (MHD)

2. Simulations and Results

Models

Sakai et al. 2002b

• We investigate two cases of the coalescence process between two parallel flux tubes:

• (1) “co-helicity reconnection” where only the poloidal magnetic field produced from the axial currents dissipates

• (2) “counter-helicity reconnection” where both poloidal and axial magnetic fields dissipates.

Initial ConditionsWe examine the reconnection and coalescence between two flux tubes.

Ny=100, Nx=Nz=300Radius a=30Plasmaβ=0.06 at center|B0i|=1Twist parameter: qi=1

y

x

z

Bx= qi By (z-zci) / aBz=-qi By (x-xci) /a

Magnetic field and gas pressure:

Schematic illustration of two parallel current loops and the coordinate system.

Normalization Unit

• N=10^8 cc

• Va=c/300=1000 km/s

• Cs=0.4Va=400 km/s

• kT=1.6 keV (ambient ions): which is acceptable for a well-developed flare in the pre-flare phase.

• L=100 km (radius a=30)

• Rm=1300

Basic Equations

Results (2D distributions in y=50)Co-helicity case Counter-helicity case

By Ey By Ey

T=3.8TA

T=4.7TA

T=6.6TA

Coalescence of two flux tubesNishikawa et al. 1984

Simulation of Proton Dynamics

• The motions of test particles are calculated by the following normalized relativistic equations of the motion of a proton:

Parameters: γ=(1+A^2u^2)^1/2A=VA/c=1/300R=VA/(ωci a)=10^-8

Proton Velocity Distribution FunctionVx

Vy

Vz

Dot-dashed line: the initial proton velocity distributionDoted line: counter-helicity caseSolid line: co-helicity case

Va=c/300=1000 km/sCs=0.4Va=400 km/s～ 1.6 keV ambient ions

1.6 keV ions can be accelerated to 7 MeV (co-helicity cases) and 5 MeV (counter-helicity cases)

Proton Energy Spectra

Ωci t=1500

Ωci t=2000

Ωci t=2500

The solid and dodded lines show the co-helicity and counter-helicity case, respectivity.

E=(Vx^2+Vy^2+Vz^2)/Va^2

•We found a “bump-on-tail” distribution in the same direction as the original loop current for both the cases of co-helicity and counter-helicity.

1000Eo=1.6MeV

1MeV

5MeV 7MeV

Ωci t=100 is 0.1 sec if B=100G.

Proton Energy Spectra

Ωci t=1500

Ωci t=2000

Ωci t=2500

The solid and dodded lines show the co-helicity and counter-helicity case, respectivity.

E=(Vx^2+Vy^2+Vz^2)/Va^2

1000Eo=1.6MeV

1MeV

5MeV 7MeV

• The maximum proton energy exceeds the energy (2.223 MeV) of the observed prompt nuclear de-excitation lines of gamma-ray.

• The proton energy spectrum is neither a pure power-law type nor a pure exponential type.

Energy Spectrum• As the results of investigation of complicated

structure of electromagnetic fields in the coalescence process, we found that the energy spectrum is neither purely exponential nor purely power-law, in contrast to the result by Mori et al. (1998) (fig: power-law).

Mori et al. (1998) examined the proton acceleration near X-type magnetic reconnection. As the results, they found the spectrum is in a power-law with index of 2.0-2.2.

3. Discussion

Anisotropic Proton Acceleration• The anisotropic proton acceleration along the loo

p can be realized both for co-helicity and counter-helicity reconnection during two parallel coalescence.

•This result is important to understand gamma-ray observation by RHESSI (Hurford et al. 2003) (fig).

Proton Acceleration

• The proton-associated gamma-ray source does not coincide with the electron-bremsstrahlung sources.

• It suggests that the protons are accelerated in one direction by the DC electric field and could subsequently interact in spatially separated sources.

A Scenario of Proton Acceleration• A possible scenario: • The single loop (with β=0.

5) disrupted by kink instability (Sakai et al. 2002a) (fig).

• The disrupted part (with high energy protons and hot thermalized protons) could move up and interact with the overlying other loop.

Further Acceleration by Reconnection

• The interaction between the ascending magnetized plasma blobs and the other loop can lead to magnetic reconnection in the interaction region (see Linton et al. 2001, Linton & Priest 2003).

• The proton could be accelerated further by the inductive electric field associated with the magnetic reconnection mostly in one direction along the guiding magnetic fields.

4. Conclusion• We may conclude that anisotropic proton acceler

ation along the loop can be realized both for co-helicity and counter-helicity reconnection during the coalescence of two parallel loops.

Ωci=2500

Counter-helicityCo-helicity

Vy

Vy

z

x

Ey

Proton Velocity and

Vy

Vy

z

x

Ey

Mori et al. 1998

Proton densityMagnetic field vectors

Hurford et al. 2003