論文紹介 “Proton acceleration during coalescence of two parallel current loops in solar flares”, J.I.Sakai & K.Shimada 2004, A&A, 426, S.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 Microwave at 17Ghz The 1980 Jun 7 flare Hard X-ray at keV X-ray at keV Gamma-ray lines at MeV The 1980 Nov 26 flare Microwave at 17Ghz Heights of two microwave sources See also Nakajima et al (left fig) Time

Coalescence of Two Flux Tubes Sakai et al. 2002b; Tajima et al 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 D particle simulation of coalescence Time B^2/8πkT Electrostatic energy E^2/8πkT Ion temperature in x-direction Fluid (kinetic) energy Reconnected magnetic flux Time

Multiple Coalescence Tajima et al Multiple coalescence could explain more realistic pattern of quasi-periodic oscillation x y T=7.2/ΩiT=9.6/Ωi B lines Electron density Electric field 2D distribution in x-y plain B^2/8πkT Electrostatic energy E^2/8πkT Ion temperature in x-direction

Gamma-ray Observation by RHESSI Hurford et al 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 arcsec from that of 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 Coalescence 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 Conditions We examine the reconnection and coalescence between two flux tubes. Ny=100, Nx=Nz=300 Radius a=30 Plasmaβ=0.06 at center |B0i|=1 Twist parameter: qi=1 y x z Bx= qi By (z-zci) / a Bz=-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 caseCounter-helicity case By EyBy Ey T=3.8TA T=4.7TA T=6.6TA Coalescence of two flux tubes Nishikawa 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)^1/2 A=VA/c=1/300 R=VA/(ωci a)=10^-8

Proton Velocity Distribution Function Vx Vy Vz Dot-dashed line: the initial proton velocity distribution Doted line: counter-helicity case Solid line: co-helicity case Va=c/300=1000 km/s Cs=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 5MeV7MeV 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 5MeV7MeV 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

3. Discussion

Anisotropic Proton Acceleration The anisotropic proton acceleration along the loop 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 acceleration 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 z x Ey Proton Velocity and Vy z x Ey

Mori et al Proton density Magnetic field vectors

Hurford et al. 2003