The Magnetic Nature of Coronal Mass Ejections

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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 under sponsorship of the National
Science Foundation. An Equal Opportunity/Affirmati
ve Action Employer.
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The Solar Corona

• Hot, tenuous, fully ionized, highly conducting
  plasma

Yohkoh SXT May 11, 2000
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• 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
• Ohms law
• the perfect gas law
• equations of mass continuity, motion, and energy.

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Evolution of the large scale coronal magnetic
field

• The MHD induction equation

• 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.

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Evolution of the large scale coronal magnetic
field

• The Lorentz force

force due to tension
force due to pressure

• In the lower solar corona, ,
  magnetic energy dominates and the magnetic field
  is very close to being a force-free field

• Minimum energy state a potential field

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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.

• 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.

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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
  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.

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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.

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Prominences/Filaments

• Dense, cool plasma suspended in the much hotter
  and rarer corona

• 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.

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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)
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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.
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• Sigmoid shaped filaments in association with
  X-ray sigmoids

Gibson et al. 2002
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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)

Pevtsov, Canfield, Latushko (2001)
203 regions in cycle 22
263 regions in cycle 23
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• 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)
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Observational properties of CMEs

• CMEs are large-scale ejections of mass and
  magnetic flux from the lower corona into
  interplanetary space
• Energetics

Three-part structure of a CME in white light
Yohkoh SXT, Mar. 8, 1999
For a fast and large CME
Estimates of coronal energy sources
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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
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Observational properties of CMEs

• Sigmoid ? Cusp ? Sigmoid recurring eruptions

Gibson et al. (2002)
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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)
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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)
• 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)
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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.

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Resistive models
Mikic and Linker (1994)
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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.

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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.

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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 t112
Case A emergence stopped at t118
Flux emergence stops at t118
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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
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Ideal resistive hybrid models
Fan and Gibson (2007) eruption of 3D line-tied
flux rope due to the helical kink instability
Loss of equilibrium
Confined flux rope
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• kink motions in eruptions

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• Formation of sigmoid shaped current sheet during
  eruption

Fan and Gibson (2007)
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• post-eruption state

Case T t136
Case K t135
Fan and Gibson (2007)
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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).