Waves and Currents in Coronal
Active Regions
Leon Ofman*
Catholic University of America
NASA Goddard Space Flight Center
*Visiting, Tel Aviv University
Overview
• Recent TRACE and Hinode observations show that some
coronal loop oscillations are associated with flows and jet
(Aschwanden et al 2002; Ofman and Wang 2008).
• The multi-stranded structure of loops suggested by the low
filling factors in past observations was confirmed in recent
high resolution observations.
• Linear models of waves in loops developed in the past are
limited to straight cylindrical loops, and to linear interaction
between the wave modes.
• Recently, oscillations of coronal loops were investigated
using 3D MHD model in straight and curved magnetic field
geometry (see, the review by Ofman 2009).
• The model allow studying nonlinear interactions of the
oscillation model in multi-stranded, the effect of realistic
geometry, and resistive dissipation.
3D MHD Equations and Model
 


    V  0,
t



V
G MS 1   

 V   V    p 
 J  B  Fv ,
2
r
c
 t


 

B
1  
 c  E , E   V  B   J ,
t
c
 4 
 B 
J,
c
 
T
 (  1)T   V  V  T  (  1)( H in  H loss )
t


In this study: using isothermal or polytropic energy equation.
Impact of the wave
Vy(x,z,0)=V0 0<t<dt
Impact from x-z boundary
Vx(0,y,z)=V0 0<t<dt
Impact from y-z boundary
Current and density
J2
n
0.01
Velocity at (0,0,1.5)
Temporal evolution at a point
V
V
0.005
V
y
z
0
-0.005
-0.01
0
50
100
150
Time
200
250
300
0
50
100
150
Time
200
250
300
-5
1.5 10
Ohmic Dissipation
x
-5
1 10
-6
5 10
0
CME/EIT wave in quadrature
with STEREO
(Patsourakos and Vourlidas 2009)
EIT waves animation
May 19, 2007 event
Schmidt & Ofman 2009
Model results
May 19, 2007 event
Schmidt & Ofman 2009
Spherical contour plots of plasma velocity Vpar parallel to the solar surface at a
heliocentric distance of 1.2 Rs. The EIT wave shows up as traveling velocity
enhancements in Vpar. The identified wave fronts (red bars) are centered around an
epicenter of the initial launching site of the CME above the active region.
Phase velocities of simulated EIT wave (II)
Point Angle
[degree]
Meas. Phase
Speed [km/s]
Sim. Phase Speed
[km/s]
Sim. Fast Mode
Speed [km/s]
1
30 ± 2
190 ± 40
152.2 ± 40
197 ± 40
2
40 ± 2
205 ± 40
249.4 ± 40
213 ± 40
3
55 ± 2
230 ± 40
267.0 ± 40
229 ± 40
4
80 ± 2
280 ± 40
296.0 ± 40
244 ± 40
This table shows our results for the simulated EIT wave phase speed in the fourth column
``Sim. Phase Speed’’. The angle is measured clockwise from the direction from the
coronal hole to the left of the images. ``Meas. Phase Speed’’ is the measured phase
speed of an observed EIT wave front propagating at about the same location. ``Sim. Fast
Mode Speed’’ is the simulated phase speed of a fast magneto acoustic wave.
Within the error limits we find a good agreement between our simulated EIT wave phase
speed, the measured EIT wave phase speed, and the simulated phase speed of a fast
magneto acoustic wave as well.
Evidence for waves in multithreaded loops
Hinode SOT
Cut 2
Ofman and Wang 2008
Cut 3
Cut 1
Mean for 6 measurements
P=113 ± 2 s
Td=560 ± 297 s
Am=0.67 ±0.12 Mm
=>Vm=Am*2/P=37±7 km/s
Cut 1
Cut 2
Cut 3
P=131 ± 14 s
P=115 ± 11 s
P=114 ± 25 s
Td=262 ± 457 s
Td=304 ± 540 s
Td=425 ± 2335 s
Am=1.02 Mm
Am=0.76 Mm
Am=0.57 Mm
MHD model of loops
•
•
•
•
•
3D Nonlinear, resistive MHD (Cartesian)
Background flow
No gravity
Isothermal energy equation
Boundary conditions:
– Line tied
– Applied twist
– Vx0=110 km/s (left foot), open (right foot)
• Initial Conditions:
–
–
–
–
Vx0=110 km/s
VA=627 km/s
Vm=36 km/s
Half wavelength (fundamental mode).
Multi threaded loop with twist
300x300x130
400x400x130
Currents in multithreaded loop
No twist
Twisted threads
z
x
Multi-threaded loop with twist
Density
Density
J2
y
y
x
x
Induced flows
Parallel threads
Twisted threads
y
y
x
x
Temporal evolution
X=-0.5
Previous 3D MHD Studies
(Ofman 2009)
Straight loops with flow and
externally excited oscillations:
Density
Flow Vz
Dipole field (curved) loop
without flow:
Current
(McLaughlin and Ofman 2008;
Selwa and Ofman 2009; 2010)
Jet: Boundary and Initial
conditions
Dipole field with gravitationally stratified density:
3D MHD model
Continuous flow injected at a loop’s
footpoint along the magnetic field:
2
2 2
 





x

x
y

y
0
0

  
  
V0  AvVA0 exp  
   r0   r0   
 
 

V  ( Bx , By , Bz )V0 / B
Z=1 plane: Outside 2r0 use V0=0; linetied boundary conditions.
Other boundaries: open
Resolution: 2583 (previous runs: 1303)
Plasma injected at the footpoint
Numerical Results: loop formation
Density isosurface
Density cut
Inflow at Xp0=0.7
z
x
Inflow at Xp0=0.7; V0=0.11VA
Temporal evolution of jet induced
loop oscillations
V0=0.11VA
D
D
V0=0.055VA
‘Long’ magnetic loop
Density isosurface
Density cut
z
x
Inflow at Xp0=1.2; V0=0.11VA
D
Temporal evolution in ‘long’ loop
Magnetic field lines
Inflow at Xp0=0.7
Inflow at Xp0=1.2
Coronal Seismology of a loop
•The Alfvén speed for the transverse wave in the loop can be
estimated using (Nakariakov et al 1999; Roberts 2000;
Nakariakov & Ofman 2001):
VA 
2L

P
B
4
•Where L is the loop length, and P=1/f is the period, B is the
magnetic field and  is the density.
•Thus, we can determine the magnetic field from
observations:
L, PVA B
•Effects of flow must be included for V0 ~ VA:
 V0 
f  f 0 1  
 VA 
   y  y 2   z  z 2  p 
0
0
 
 i   e d exp  
 
w
 
 

McLaughlin and Ofman 2008
Selwa and Ofman 2009, 2010
Slow standing waves: 3D model
Selwa, Ofman (2009)
  x  x0 2     y  y0 2 
Vz  AVA exp 

 for 5  t  7 A
2
2
w
w



Duration of the pulse << wave-period,
not sensitive to the spatial/temporal shape
(contr. Taroyan, Erdélyi, Doyle, Bradshaw 2005)
Propagating wave
Slow standing waves: 3D model and
observations
Selwa, Ofman (2009)
Slow standing waves: 3D model
2D
1D
tex  4 P tex  1.6 P
SOHO/SUMER
Wang et al 2003
 / P  5  / P  1.44
tex  1P 3D
 / P ~ 0.6
Selwa, Ofman (2009)
Loop geometry vs. coronal seismology
Height/radius of a loop
Closed geometry
Open geometry
Loop geometry vs. coronal seismology
Direction of Lorentz force
Doppler shift oscillations
3D kink oscillations: damping (tunneling)
Leakage (tunneling) mainly in horizontal direction
AR topology and its impact on oscillations
Selwa, Ofman (2010)
Summary and Conclusions
• High resolution observations indicate that coronal Active
Regions contain oscillating loops associated with flares,
and jets of heated plasma.
• We use 3D MHD model to study the excitation of various
modes of oscillations in coronal loops by different forms of
excitation, and the effect of magnetic topology.
• We find that the inflow leads to formation of low-beta loops
with higher density than the surroundings, and excites
coupled transverse and longitudinal oscillations.
• The properties of the oscillations (wavelength, damping
rate), depend on loop length, structure, and curvature can
be used for coronal seismology.
• We conclude that the excitation of loop oscillation observed
with TRACE and Hinode are due to impulsive events at
footpoints of loops.
• The inflow of hot material is responsible for loop formation,
as seen in observations and in our model.