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Three-Dimensional Filament Eruption driven by a Emerging Flux
Tube in the Sun S.Notoya T.Yokoyama (University of Tokyo)
K.Kusano,T.Sakurai,T.Miyagoshi,H.Isobe,T.Yamamoto
Abstract
Coronal Mass ejections(CMEs) are one of the most dynamical phenomena and have been studied theoretically and observationally. But their origins are still unknown. From
theoretical views(Kusano, Devore), CMEs have been considered to occur owing to an instability or a loss of a equilibrium of the coronal magnetic field since the coronal gas
pressure and the gravity is much lower than the magnetic force. As a process of losing a equilibrium, magnetic arcade which has a large shear and with a converging motion is
widely studied. Observations(Feynman & Martin) suggest that the emerging flux has a strong connection with CMEs. As a interpretation to understand both of the results of the
theories and the observations, we suggest that the dynamical motion such as a conversing one may be due to the emergence of the flux tube. The aim of our paper is to
understand the basic mechanism by which the emerging flux can trigger the filament eruption, which can be a source of CMEs. For this purpose, we performed threedimensional simulations of the filament eruption caused by the emergence of the magnetic flux tube from the convective zone into the coronal region. Our simulations show that
when emerging flux appears near the outer edge of the arcade field, the arcade is deformed strongly by the high magnetic pressure of the flux tube. At the height of the lower
corona, where the magnetic force is much higher than the other forces, the distance between the opposite polarity regions of the arcade becomes smaller because the emerging
flux push the one of the polarity region to the other. Then the current sheet is made inside the arcade, and the reconnection process starts, which leads to the eruption of the
arcade field. These results of our simulations suggest that the emerging flux can be a cause of the CMEs.
The Model of the Simulation
the model of the flux tube
xˆ  b( z  z 0 )yˆ  b( y  y 0 )zˆ
B  B0
(force  free)
2
1  (br )
B 0  30 b  0.5 y 0  0 z 0  14 r0  4
Ｚ
Ｙ
twisted in a right handed way
the model of the arcade field
Y
X
・3D resistive MHD equations
(no radiation and conduction)
・the anormalous resistivity model
・the initial perturbation at central part
of the flux tube
・units
H p  310 [ km] C sp  12 [ km / s ]
L 2 0.5
y  z / a
Bx  (1  ( ) ) Barc sin
e
a
L
L
y  z / a
By 
Barc sin
e
a
L
y  z / a
Bz  Barc cos e
(force  free)
L
Barc  0.05 L  80 a  100
Hp
C sp
 26 [ s ] (Pp ) 0.5  480 [ gauss ] Ppho  2.3  10 5 [ergs / cm 3 ]
The temporal evolution of magnetic field
t=0
Ｚ
6*10^4 km
Te
200
Ｙ
0
t=140
Te
200
t=140
10^5 km
Z
X
t=170
0
t=170
Te
200
0
cross sections at x=0
It can be seen from these figures that the structure of the arcade is deformed by the
magnetic pressure of the emerging flux during its expansion in the corona, and the
collapsed arcade gains upward velocity in the process of the magnetic reconnection.
In the right panel, the blue plus red line shows the reconnected field line, and the
yellow, green lines are un-reconnected lines.
Time profile of the Energy
of the Erupting Arcade
ΔE
Poynting Flux
kinetic
t=166
The upward forces inside
the region of the plasmoid
thermal+potential+magnetic
1.*10^(-6.)
3
t=166
1
200
total force
0
(ｘ
25s)
t
(ｘ12 km/s)
Vz
by the expansion
of the emerging flux
the eruption
of the arcade
(ｘ25s)
t
the upward velocity at o-point in the filament
The results of the simulation of the
case of the wider arcade (twice as
large as the former case).
80
With the expansion of the emerging flux,
the magnetic energy is stored in the arcade
field and released in the process of the
magnetic reconnection. The released energy
is converted to the thermal, potential, and
kinetic energy, and the newly reconnected
field lines have upward velocities.
Z
200
In the process of the magnetic reconnection,
the arcade field collapses and becomes the
filamentary structure, and then goes upward
because the magnetic energy of the emerging
flux is continuously released below the
filament. The main upward force is the
magnetic pressure, and the downward tension
force exists around the o-point inside the
filament owing to the unreconnected field
lines.
t=166
Summary & Discussion
thermal+potential+magnetic
ΔE
by the expansion
of the emerging flux
Poynting Flux
kinetic
1.5
magnetic
Vz
(ｘ12 km/s)
no eruption
of the arcade
0.3
Te
200
t
(ｘ
25s)
the energy differences from the initial state
Em(t=0)=6.9,Eth(t=0)=15.0,Epot(t=0)=17.1
t=166
Te
200
plasmoid
-1.*10^(-6.)
the energy differences from the initial states
Em(t=0)=6.9,Eth(t=0)=15.0,Epot(t=0)=17.1
t=0
0
g
O point
magnetic
Te
0
 Pm  Pg Tm
t
(ｘ
25s)
the upward velocity at o-point
in the filament
In the case of the wider arcade (the density of the magnetic energy is
same as the former case), the filament eruption des not occur.
Although the arcade is deformed, it does not collapse completely
since the arcade itself has more energy than the former case and the
reconnection process does not proceed effectively. In other words, the
emerging flux has not enough energy to make the arcade collapse, and
can not trigger the filament eruption.
･We studied the process that the emerging flux triggers
the filament eruption, which can be a source of CMEs.
･It was found that the arcade was deformed by the high
magnetic pressure of the emerging flux, making the
current sheet inside the arcade.
･Through the reconnection process, the field lines of
the filamentary structure were made from the collapsed
arcade, and had upward velocities by the released energy
of the emerging flux.
･These results of our simulations suggest that the
converging motion which can destabilize the sheared
arcade field may be due to the flux emergence which has
been observed so far, and the reconnection process can
be thought to be a key process for the eruptions.
References
•Kusano & Maeshiro 2004,APJ,610,537
•DeVore 2000,APJ,539,954
•Feynman & Martin 1995,JGR,100,3355