The Magnetic Nature of Coronal Mass
Ejections
High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR)
The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research
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The Solar Corona
•
Hot, tenuous, fully ionized, highly conducting plasma:
Parameter
photosphere
Inner corona
Outer corona
Electron density (cm-3)
21017
1 10 9
1 10 7
Temperature (K)
5 103
1000
2106
1 10 6
10
0.1
3
0.07
7
Magnetic Field (G)
Plasma
  p /( B 2 / 8 )
Yohkoh SXT May 11, 2000
• The macroscopic behavior of the solar atmosphere
as a continuous ionized gas (or plasma) can be well
described by the theory of magneto-hydrodynamics
(MHD):
• a simplified form of the Maxwell equations in
the non-relativistic limit
• Ohm’s law
• the perfect gas law
• equations of mass continuity, motion, and
energy.
Evolution of the large scale coronal magnetic field
• The MHD induction equation:
V ~ 100km/s, L ~ 100 Mm,  ~ 1 m 2 /s,  Rm ~ 1013 !
• The perfectly conducting limit or the large length scale limit: ignore the diffusive term
– frozen-in evolution: magnetic field lines behave as if frozen into the plasma and are
carried along with it.
– Conservation of magnetic helicity:
linkage of magnetic flux in a closed field
is conserved.
H m  21 2
Evolution of the large scale coronal magnetic field
• The Lorentz force:
force due to tension
force due to pressure
• In the lower solar corona,   1 , magnetic energy dominates and the magnetic field is
very close to being a force-free field:
J  B  0  J is parallel to B, or   B   B
• Minimum energy state: a potential field
  B  0, or B   and  2  0
Evolution of the large scale coronal magnetic field
• The coronal magnetic field evolves quasi-statically through force-free equilibria as it is
driven at the foot points by continual motions and flux emergence at the photosphere.
 ph  1,
 cor  1
 ph ~ 10 9  cor
C ph , V Ap h ~ 10  2 V Aco r
– in the photosphere, pressure dominates, plasma moves magnetic field; in the corona,
magnetic field dominates and tries to relax to a force free state
– photosphere is much heavier and has a much longer dynamic time scale compared to
the corona. Thus coronal magnetic field can adjust quickly to new force-free
equilibria in response to the slow perturbations on the photosphere.
– For fast dynamic evolution of magnetic fields in the corona, photosphere acts as an
inertially line-tying lower boundary.
– force-free evolution while preserving the frozen-in constraint often leads to the
formation of magnetic tangential discontinuities or current sheets in the corona.
Magnetic current sheet and magnetic reconnection
Priest (1982)
• A current sheet is a magnetic tangential discontinuity across which total pressure is continuous.
• Frozen-in evolution outside, inside current sheet, magnetic diffusion becomes important and magnetic
energy is dissipated.
• A steady state is established with Vi   / l , the magnetic field being brought towards the current sheet
reconnects at the central current sheet and the plasma along with a weaker reconnected field are
ejected from the two ends of the sheet.
Spontaneous formation of current sheets
Low and Wolfson
(1988)
• A coronal potential field (a) is subject to a converging displacement of its foot-points on the
photosphere and the new potential field it tries to relax to is (c), which is not accessible due
to the frozen-in constraint. Instead it evolves to the field (b) in which a current sheet is
formed. Reconnection in the current sheet then allows the transition to the (c) field.
Prominences/Filaments
• Dense, cool plasma suspended in the much hotter and rarer corona:
11
-3
• T ~ 8000K, n ~ 10 cm , B ~ 10 G
• Supported by magnetic field against
gravity.
• Form along polarity inversion lines with
magnetic field direction having a small
angle relative to the PIL.
• Active prominences: form in active regions;
higher field strength, temperature and
density, shorter life time
• Quiescent prominences: in decaying active
regions or boundaries between decaying
active regions, can be extremely long and
extremely long lived.
Three-part structure of coronal helmet streamers
• The flux rope model: the cavity in the helmet corresponds
to the cross-section of a magnetic flux rope containing
helical field lines with a strong axial field component whose
magnetic pressure supports the low density cavity, and the
filament mass is supported in the lower dipped portion of
the helical field lines.
from Low (2001)
Hemispheric dependence of magnetic twist
• Coronal soft X-ray observations: soft X-ray images of solar active regions sometimes show
hot plasma of S or inverse-S morphology called “sigmoids”,with the northern hemisphere
preferentially showing inverse-S shapes and the southern hemisphere preferentially showing
forward-S shapes:
Pevtsov, Canfield, & Latushko (2001)
Soft-x ray observation from Yohkoh
Canfield et al. (1999)
Active regions are
significantly more likely to
produce flares or CMEs if
they are associated with
sigmoid structures.
• Sigmoid shaped filaments in association with X-ray sigmoids:
Gibson et al. 2002
Hemispheric dependence of magnetic twist
• Solar Active Regions: Vector magnetic field observations show that solar active
regions on the photosphere show a small but statistically significant trend for left
handed twist in the northern hemisphere and right handed twist in the southern
hemisphere (Pevtsov et al. 1994, 1995, 2001):
  J z / Bz
Pevtsov, Canfield, & Latushko (2001)
203 regions in cycle 22
263 regions in cycle 23
• Twisted magnetic flux ropes as CME precursors:
– contain free magnetic energy
– dipped field lines support prominence material against gravity
– current sheet formation along the “bald-patch” separatrix surface (BPSS) of a
line-tied flux rope  X-ray sigmoids (Titov & Demoulin 1999; Low and
Berger 2003; Fan & Gibson 2004; Gibson et al. 2004):
Gibson et al. (2004)
Observational properties of CMEs
• CMEs are large-scale ejections of mass and magnetic flux from the lower corona into
interplanetary space:
Three-part structure of a CME in white light
Yohkoh SXT, Mar. 8, 1999
• Energetics:
For a fast and large CME
Estimates of coronal energy sources
mass ~ 1016 g, speed ~ 1000 km/s
kinetic energy ~ 1032 erg
kinetic (m p nV 2 / 2) : ~ 10-5 erg/cm 3
work done against gravity ~ 1031 erg
thermal (nkT ) : ~ 0.1 erg/cm 3
heating and radiation ~ 1032 erg
gravitatio nal (m p ngh) : ~ 50 erg/cm 3 in prominence s
volume of source region ~ 1030 cm 3
magnetic ( B 2 / 8 ) : ~ 400 erg/cm 3
energy density ~ 100 erg/cm 3
Observational properties of CMEs
• Sigmoid  Cusp  Sigmoid: recurring eruptions
Yohkoh SXT images from June 6 through June 7, 2000
From http://solar.physics.montana.edu/nuggets/2000/000609/000609.html
Observational properties of CMEs
• Sigmoid  Cusp  Sigmoid: recurring eruptions
Gibson et al. (2002)
A unified picture for solar eruptions
• CMEs, prominence eruptions, and large
two-ribbon flares are closely related and
may in fact be different manifestations of a
single physical process, the disruption of a
large-scale coronal magnetic field
structure.
• The eruptions are caused by a loss of
stability or equilibrium of the coronal
magnetic field which contains free
magnetic energy that has been built up over
time through continual emergence of new
flux and shuffling of field-line foot-points
at the photosphere.
Forbes (2000)
The Aly-Sturrock constraint
•
The magnetic energy of a force-free magnetic field with
all its field lines anchored to the boundary cannot exceed
the energy of the fully open magnetic field (Aly 1984;
Sturrock 1991; Low & Smith 1993):
Em  Eopen
•
Ways around the constraint:
– CMEs do not open all the field lines
– An ideal eruptive process causes the formation of a current
sheet where magnetic reconnection allows the ejection of a
magnetic flux rope.
– Presence of detached magnetic flux rope
– Non-force free field: the weight of cold prominence mass
Low (2000)
Some representative models
• All models are based on the principle that CMEs are driven by the
sudden release of the free magnetic energy stored in pre-eruptive
coronal magnetic fields.
– Resistive MHD models: where magnetic reconnection in a current sheet
plays an important role in triggering the CME onset and in sustaining the
eruption.
– Ideal resistive hybrid: where eruption is triggered by an ideal loss of
equilibrium of the magnetic field but that subsequent formation of a current
sheet and magnetic reconnection is crucial for sustaining the eruption and
allowing a magnetic flux rope to escape.
– Non-force free models: the weight of the prominence mass plays a
important role in building up the magnetic energy to exceed that of the
open-field limit, and that a sudden drop of the prominence weight triggers
the eruption.
Resistive models
Mikic and Linker (1994)
Resistive models
Antiochos et al. (1994): the break out model
• During the initial quasi-static evolution, the gradual shearing of the inner arcade field and its
confinement by the overlying un-sheared arcade build up free magnetic energy.
• Reconnection at the current sheet weakens the confinement such that a run-away expansion of the
central sheared field takes place. The end state is a partially open field where the sheared arcade field
expands to infinity while the overlying un-sheared field moves out of the way by reconnection and
remains closed.
Ideal resistive hybrid models
Lin et al. (1998): loss of equilibrium of a twisted flux rope
• Initial force-free equilibrium: a flux rope suspended in the corona confined by an external dipole field
• As the strength of the dipole field is reduced, there exists a sequence of force-free equilibria with
increasing height of the flux rope until the nose point, where the force balance can no-longer be
maintained and the flux rope jumps to an equilibrium at a higher height of lower magnetic energy, and
containing a current sheet.
• Subsequent reconnection in the current sheet at a sufficiently fast rate is then necessary to sustain a
smooth escape of the flux rope.
Ideal resistive hybrid models
Fan and Gibson (2006): 2D axisymmetric MHD simulations of loss of equilibrium of coronal flux rope
Case C: emergence stopped at t=112
Case A: emergence stopped at t=118
Flux emergence
stops at t=118
Ideal resistive hybrid models
Fan and Gibson (2007): eruption of 3D line-tied flux rope due to the torus instability
Confined flux rope
Loss of equilibrium
Ideal resistive hybrid models
Fan and Gibson (2007): eruption of 3D line-tied flux rope due to the helical kink instability
Confined flux rope
Loss of equilibrium
• kink motions in eruptions:
• Formation of sigmoid shaped current sheet during eruption
Fan and Gibson (2007)
• post-eruption state:
Case T: t=136
Case K: t=135
Fan and Gibson (2007)
Summary
• It is fairly certain that CMEs are driven by the free magnetic energy stored in the twisted
magnetic fields (with field aligned current) in the corona. However the detailed form of
the twisted fields for CME precursor structures and the triggering mechanisms for CME
onset are not clear.
• Models and simulations of CMEs are still using highly idealized field structures and
invoking very artificial lower boundary conditions to represent the driving perturbations
on the photosphere. Also simulations of the dynamic evolutions are critically effected by
the process of magnetic reconnection whose physics are not well represented in current
numerical simulations.
• New observations from Hinode, STEREO, and upcoming new instruments that directly
measures the coronal magnetic fields will provide important input for constraining and
distinguishing between models.
• It has been argued that CMEs are an inevitable consequence of the accumulation of
magnetic helicity on the Sun, and they are means by which helicity can be removed, which
may have important implications for the working of the solar dynamo (e.g. Zhang and
Low 2005).