z - Nobeyama Solar Radio Observatory

Internal Shocks
in the Reconnection Jet
in Solar Flares
Turbulence
Dissipation
Shocks region
Shocks Turbulence
S.Tanuma
(Kwasan Observatory, Kyoto University)
Outline
1. Introduction: Tearing Instability
2. MHD Simulations and Results
–
–
–
Model A: Internal Shocks in Reconnection Jet
Model B1: Oblique Shocks in Reconnection Jet
Model B2: Propagation of Bow Shocks
3. Discussion
4. Conclusions and Summary
Internal Shocks in Reconnection Jet
• We suggest that the internal shocks could be created in the
reconnection jet by the secondary tearing instability.
• We also suggest that the energetic electrons could be
accelerated in the internal shocks.
Observations
• If the internal shocks could be created by the
ejection of plamoids, we could explain
– the “slowly drifting structures” (Karlicky 2003) and
– “narrowband dm-spikes” (Barta & Karlicky 2001) in
the upward jet, observed in radio.
• We could also explain
– the origin of energetic electrons (Masuda et al.
1994)
– nonsteady plasmoid-ejection (Asai et al. 2004;
McKenzie & Hudson 1999)
– oscillation in the downflow (e.g., observed by
TRACE on Apr.21, 2002).
Basic Problems of Reconnection
In the solar corona,
2
• Ion Lamor radius: 10 cm
8
• Initial current sheet thickness: 10 cm
Originally, we started simulations to know
• How does the fast reconnection occur (i.e., How
does the current sheet becomes very thin)?
• What determines the reconnection rate?
(Tanuma et al. 1999, PASJ, 51, 161;
Tanuma et al. 2001, ApJ, 551, 312;
Shibata & Tanuma 2001, Eearth, Planets & Space, 53, 473)
Tearing Instability
1. Initial current sheet
linit
The sheet is torn by a resistivity (0 )
2. LinearNonlinear
init
 tearing
 ( Ainit dinit )1/ 2
1/ 2
 linit 

 
init 
 0 v A 
3
tearing  10  20linit
3. NonlinearPlasmoid-ejection
The sheet becomes much thin by the
secondary tearing instability so that
an nomalous resistivity is enhanced
and the fast reconnection starts.
(Furth et al. 1964)
(Tanuma et al. 1999, 2001; Shibata & Tanuma 2001)。
2. MHD Simulations and Results
Model A: Internal Shocks Created by
the Secondary Tearing Instability
z
Initial Condition
•Bx=Bo tanh(z/D), Bz=By=0
•Gas pressure + magnetic pressure：Uniform
z
•Temperature：Uniform
(“Harris”-like sheet)
B
Gravity: g=0
160 points
Specific heat
ratio: g5/3
Plasma b=0.2
Jy
x
B
•Grid size (uniform): (dx, dz)=(0.013D, 0.013D)
•Grid number:
(Nx, Nz)=(16000, 1600)
•Simulation region size:(Lx, Lz)=(210D, 21D)
(Tanuma et al., in prep.)
Anomalous Resistivity Model
• The electric resistivity is difined by
(vd  vc )
  0
2
(vd  vc )
  0   (vd / vc  1)
where 0  0.005, max  1,   10.0
vd  Jy /  ：drift velocity
vc  20 ：threshold of onset
 0 is assumed to be much larger than “numerical
resistivity” due to numerical noise (0  num )
•Magnetic Reynolds (Lunquist) number
Rm  v A Lx / 0  2.45 169 / 0.005  82810
Gas Pressure at Reconnection Region
The electric resistivity is enhanced
only at the central region for a short time.
z
B//(1,0)
Initial Current Sheet
B//(-1,0)
x
Only central region (12.5x2.5) is shown.
The current sheet becomes thin via the secondary
tearing instability, and fast reconnection starts.
Simulation Results
(Flowchart)
*The current sheet becomes thin by the
tearing instability.
*Sweet-Parker-like reconnection starts.
*The sheet becomes much thinner by
the secondary tearing instability.
*The anomalous resistivity is
enhanced and Petschek-like
reconnection starts.
*The secondary tearing instability
continues in the diffusion region where
the anomalous resistivity is enhanced.
*Mutiple fast shocks are created by the
secondary tearing instability.
Time Variation of
Current Sheet Thickness
Tearing instability
Onset of secondary
tearing instability
The results are explained
by the analytic solution
(l=0.3) of the thickness of
current sheet collapsed by
the tearing instability
Onset of the
anomalous resistivity
Fast reconnection
• The current sheet becomes thin gradually by the tearing
instability and secondary tearing instability.
• Then, anomalous resistivity are enhanced and the
Petschek-like reconnection starts.
Creation of Plasmoids
• Many plasmoids are created by the secondary tearing
instability in the diffusion region.
• The interval of plasmoids is 0.54. It is much consistent
with the wavelength of secondary tearing instability
(0.58 in analytic solution).
• Each plasmoids are resolved with 0.54/0.013=42 grids.
z
0.58
Time Variation of Reconnection Rate
Vin|(x,z)=(0, 2)
Vin|(x,z)=(0,-2)
• The inflow velocity to
diffusion region (Vin)
and reconnection rate
(Vin/VA) vary with time.
• It is due to the
plasmoid-ejection and
plasmoid-formation
(Tanuma et al. 1999, 0.1
2001; Shibata &
Tanuma 2001).
(Vin/VA)
0.1
Oscillation
Results of Model A
• The current sheet becomes very thin via the
secondary tearing instability so that the fast
reconnection starts.
• During Petschek reconnection, the reconnection
rate is determined by plamoid-ejection.
• We also find that many plasmoids are created by
the secondary tearing instability and ejected, so
that the multiple fast shocks are created in the
reconnection jet.
Model B1: Oblique Shocks
in the Reconnection Jet
• We examine the dependence of results on resistivity
model and grid size.
• In some cases, we find that oblique shocks are created in
the reconnection jet.
• They could be created by Kelvin-Helmholtz instability
(we are now examining it).
Tanuma & Shibata 2003, ICRC 2003
—The 28th International. Cosmic Ray Conf. 2003, p2277;
Tanuma & Shibata 2003, ICRC 2003
—The 28th International. Cosmic Ray Conf. 2003, p3351;
Tanuma, S. & Shibata, K. 2003, in IAU 8th Asian-Pacific
Regional Meeting, Vol II, ASP Conf. Ser., 289, p469
Gas Pressure at Reconnection Region
The electric resistivity is enhanced
only at the central region for a short
time.]
z
B//(1,0)
電流シート
B//(-1,0)
x
• Only central region (60x5) is shown.
• Large plasmoids are created and ejected.
• The reconnection jet oscillates by K-H instability(?).
Profiles of Reconnection Jet
Dissipation region
Turbulence
Pg
Pg
z=0.0
Vx
Multiple fast shocks
(oblique shocks) created
by the secondary tearing
instability
Vz
z=0.2
Multiple fast shocks created by the Kelvin-Helmholtz(like) instability (we are examining it now.)
The oblique shocks and turbulence can play an important role in
the particle acceleration if they are created in the actual flares.
Model B2: Propagation of Bow Shock
The electric resistivity is enhanced
only at the central region for a short time.
z
B//(1,0)
Initial Current Sheet
B//(-1,0)
x
• Only central region (12.5x2.5) is shown.
• Large plasmoids (O-points) are created and ejected.
• Bow shocks propagate along the current sheet. It is also
possible site for particle acceleration.
3. Discussion
Number of Accelerated Electrons
D  10
• Even if multiple fast
shocks could be created
near the dissipation
region, the electron flux
to the shocks could be:
dN / dt  nV AW ' D
 1034 /s
• It could explain the
impulsive flares
(Masuda et al 1994):
(dN / dt ) obs  103435 /s
width
L  1010 cm
9
cm
W  109 cm
L'  109 cm
Internal shocks
107 cm
W '  108 cm
n  109 /cm 3 , VA  108 cm/s
(Tanuma & Shibata in prep.; See Tsuneta & Naito 1998)
Radio Emission
• We apply the simulation results to the “slowly
drifting structures” (Karlicky 2003), and
“narrowband dm-spikes” (Barta & Karlicky 2001)
in the upward jet observed with the radio.
• Time scale of these phenomena is
well consistent with it of the
secondary tearing instability
(Karlicky 2004):
 ldiss 
tearing
 2 nd _ t  30 5

 10 cm 
3/ 2
vA


 8
-1 
 10 cm s 
1 / 2
( ldiss : dissipation region thickness)
 T 
 6 
 10 K 
3/ 4
s
(Fig: Karlicky 2004)
Other Applications
• The interval of the nonsteady plasmoid-ejection
(Asai et al. 2004; McKenzie & Hudson 1999)
could be also consistent with the time scale of the
secondary tearing instability.
• The oscillation in the downflow observed by
TRACE on Apr.21, 2002 could be explained by
Kelvin-Helmholtz instability in the reconnection
jet.
4. Conclusions and Summary
• We perform MHD simulations of magnetic
reconnection with a highly spatial resolution to
remove the numerical resistivity.
• As the results, we find that many plasmoids are
created by the secondary tearing instability. They
are ejected, and the multiple fast shocks are created.
• We also find that the oblique shocks and bow
shocks are also created in some cases.
• The internal shocks are possible sites of the particle
acceleration in the solar flares.
References
[1] Tanuma, S. et al. 1999, Publication of Astronomical Society of Japan
(PASJ), 51, p161
[2] Tanuma, S. et al. 2001, Astrophysical Journal (ApJ), 551, p312
[3] Shibata, K. & Tanuma, S. 2001, Earth, Planet and Space (EPS), 53, p473
[4] Tanuma et al. 2003, Astrophysical Journal (ApJ), 582, p215
[5] Tanuma & Shibata 2003, ICRC 2003—The 28th International. Cosmic Ray
Conf. 2003, ed. T. Kajita et al. (Universal Academy Press: Tokyo) , p2277
[6] Tanuma & Shibata 2003, ICRC 2003—The 28th International. Cosmic Ray
Conf. 2003, ed. T. Kajita et al. (Universal Academy Press: Tokyo) , p3351
[7] Tanuma, S. & Shibata, K. 2003, in IAU 8th Asian-Pacific Regional
Meeting, Vol II, ed. S. Ikeuchi, J. Hearnshaw, & T. Hanawa, ASP Conf. Ser.
(Astronomical Society of Japan: Tokyo), 289, p469
[8] Tanuma, S. & Shibata, K. 2003, in Stars as Suns, IAU Symp., ed. A. Benz,
ASP Conference Series (IAU), in press
[9] Tanuma & Shibata in prep. 2004
Observations
• If the internal shocks could be created by the ejection
of plamoids, we could explain
– the “slowly drifting structures” (Karlicky 2003) and
– “narrowband dm-spikes” (Barta & Karlicky 2001) in the
upward jet, and
– “quasi-periodic pulsation (oscillation)” (Asai et al. 2001;
Kamio’s talk) observed in radio.
• We could also explain
– the origin of energetic electrons (Masuda et al. 1994)
– nonsteady plasmoid-ejection (Asai et al. 2004; McKenzie &
Hudson 1999)
– oscillation in the downflow (e.g., observed by TRACE on
Apr.20, 2002).
この研究で新しいこと
• メッシュサイズに由来する数値ノイズが「数値的
電気抵抗」として働く。
• そこで、細かいメッシュと異常抵抗モデルに含ま
れる一様なバック・グラウンド抵抗を仮定した。
• その結果、「数値的電気抵抗」を消した。
• そして、セカンダリー・テアリング不安定性が発生
と(Tanuma et al. 2004)、その後のペチェック・リコ
ネクション時の、異常抵抗が効いた散逸領域中
のセカンダリー・テアリング不安定性を分解した。
リコネクション領域の電流分布
初期摂動として抵抗を強める
z
B//(1,0)
電流シート
B//(-1,0)
x
計算領域のうち中心部分(12.5x2.5) を表示
Secondary Tearing Instability
(Anomalous Resistivity is Enhanced)
1) The current sheet is collapsed by the secondary tearing instability.
tearing
ltearing  0.15
ltearing
tearing  25
2) The secondary tearing instability occurs. Grid size: dx=dz=0.013
3) The secondary tearing instability continues
after the anomalous resistivity sets in.
2 nd _ t*  0.58
This explains the
simulation results well.
リコネクション・
ジェットの断面図
Dissipation region
• 0<x<6.5にプラズモイド
（ショック）が12個ある。
• 波長は、
2 nd _ t*  6.5 / 12  0.54
• セカンダリー・テアリング
不安定性の波長と一致。
• ランキン・ユゴニオと
96%以上一致。
6.5
リコネクション領域の電流分布
初期摂動として抵抗を強める
z
B//(1,0)
電流シート
B//(-1,0)
x
計算領域のうち中心部分(60x10) を表示
アニメーションはメッシュの粗い場合の結果
ガス圧分布（多重衝撃波の発生）
テアリング不安定性
→遅いリコネクション
→セカンダリー・テアリ
ング不安定性
→速い(Petschek)リコ
ネクションが発生
(a)セカンダリー・テアリ
ング不安定性に伴う多
重衝撃波
(b)ジェットの振動に伴
う多重衝撃波（注）
(Arzner & Scholer
2001;
(Tanuma et al. in prep.)
Time=30
Time=35
(a)
(a)
Time=40
乱流
(a)
(b)
(b) (a)
乱流
テアリング不安定性
初期条件：β=0.2；初期の電流シートの厚み： linit  1,
v init
A  2.45, 0  0.005
1/ 2
3

linit 
init
init init 1/ 2
 tearing  ( A  d )   init 
0 v A 

init
v
init
A linit
m, z 
 500
0
9
tearing
ltearing
アスペクト比=84
l  25
テアリング不安定性 tearing  5.6
tearing1 / 2
電気抵抗の効果で電流
ltearing  (tearing / 2) m
 0.15
init 1 / 4
m, z
init
シートが契れるようになり、
プラズモイドができる現象
(Tanuma et al. 2001;
Magara & Shibata 1997)
tearing

m
(tearing / 2)v init
A
0
 6000
セカンダリー・テアリング不安定性
（異常抵抗あり）
散逸領域では異常抵抗が働く。散逸領域の厚みが l  l2 nd _ t  ltearing
の時に   max  1.0 になるとすると、
1/ 2
2 nd _ t *
 tearing
 ltearing3 


init
 max v A 


 0.0014
ジェット
2nd _ t*  5
tearing*1/ 4
m, z
tearing
2nd _ t*  b
l
7 / 64
 0.58
衝撃波
衝撃波

プラズマβにはあまり依存しない。異常抵抗が入るのが
l2 nd _ t  ltearingの時だとしても、あまり依存はしない。
Other Observations
• Nonsteady plasmoid-ejection (Asai et al. 2004;
McKenzie & Hudson 1999) and oscillation in the
downflow (2002.4.20) observed by TRACE.
• Time scale of these phenomena is also well
consistent with the time scale of the secondary
tearing instability.
*“Quasi-periodic pulsation (QPP)” (5-16sec) (Asai
et al. 2001; Kamio’s talk) (Alfven transition and
fast sausage instability are also possible candidates
[see Asai’ talk and Kamio’s talk])
Results(Gas Pressure)
z
Parallel Magnetic Field
Point Explosion
B
Current Sheet
B
Parallel Magnetic Field
x
The central region (50x10) is shown:
The simulation region is (140x230).
(movie--hyperlink)
(Tanuma et al 1999, 2001)

Download Report