Lecture 4 The Formation and Evolution of CMEs

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Lecture 4The Formation and Evolution of CMEs
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Coronal Mass Ejections (CMEs)

• Appear as loop like features that breakup helmet
  streamers in the corona.
• Three part structure
• Bright outer rim
• Dark cavity behind rim
• Bright inner core of erupted prominence material

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Scales of CMEs

• Gray areas are covered by codes
• Micro inertial length, Larmor radius
• As CME propagates out through the solar system
  both time and spatial scales increase (apparent
  shrinking is do to log log plot)

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Prominences

• Suspensions of cool (T104K), dense (n1010-1011
  cm-3) chromospheric material surrounded by the
  hot (T106K) and tenuous (n107-109 cm-3) corona

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Prominence Magnetic Field

• Magnetic field is found to be approximately
  aligned with the filament.
• Highly sheared field.
• Called a filament when viewed from above.
• Can be stable for days or weeks.

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Fundamental Questions

• How are CMEs initiated?
• Widely accepted that the energy of CMEs is stored
  in coronal magnetic fields the strongly sheared
  field of a filament (prominence) channel.
• The CME is thought to be the catastrophic
  disruption of the force balance between the
  upward magnetic pressure of the filament and the
  downward tension of the overlying field.
• How this disruption occurs is the main unanswered
  question in CME initiation.
• Flux cancellation models
• Breakout models
• Flux injection model

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Flux Cancellation Models

• Flux cancellation is the disappearance of
  magnetic fields of opposite polarity at the
  neutral line separating them.
• Flux cancellation at the neutral line of a
  sheared arcade causes the flux rope that supports
  prominence material.
• Equilibrium breaks down if flux cancellation
  continues after the flux rope is formed.
• A new equilibrium forms farther out.
• In reality the solar wind pulls the flux rope out
  and forms a current sheet at which reconnection
  occurs.

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A Simulation Study of the Eruption of a
CME(Linker et al., 2003)

• The initial configuration azimuthal symmetry
• Build a model of a helmet streamer
• Use a spherically symmetric MHD solar wind
  solution
• Use a potential magnetic field
• Integrate until an equilibrium results.
• To create a source of free magnetic energy put a
  shear flow near the neutral line of the streamer
  specify the tangential E field.

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Formation of a Flux Rope

• (top) Projected field lines (shading) and
  azimuthal field (color)
• (middle) Current density out of the plane.
• (bottom) Polarization brightness that a
  coronagraph would observe.
• Flux cancellation forms a stable flux rope within
  the helmet streamer (1350tA)
• Once the configuration is beyond a stability
  threshold halting the flux cancellation cannot
  stop the eruption (1390tA).
• Prominence formation is part of the flux
  cancellation mechanism.

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Change in Magnetic Energy and Kinetic Energy

• Magnetic energy closed flux (top-bottom), kinetic
  energy (bottom)
• During formation of helmet streamer B2/2µ0
  increases 15 (tlt600)
• Energization of streamer (600gttgt1300)
• Flux rope formation (1320)
• Eruption (1380)
• Energy of open flux (top-top) eruption occurs
  when closed energy open energy
• Half of energy goes into flux rope.

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Add azimuthal asymmetry

• Azimuthal models entire coronal field must be
  opened and flux rope is detached from the Sun.
• 3D model allows azimuthal asymmetry.
• Reduce magnetic flux only in one sector of Sun.
• Creation of flux rope and eruption occur as
  before.

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Structure of flux rope

• Isosurface of density
• Field lines in flux rope after it has propagated
  away from the Sun
• Note that both ends of the flux rope are attached
  to the Sun.

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The Breakout Model

• Reconnection occurs external to the filament
  channel quasi-potential overlying flux and
  neighboring flux systems.
• Axisymmetric system with two spatial dimensions
  and three velocity dimensions (MacNeice et al.,
  2004).
• Imposed shear flow at the equatorial neutral line
  generates a Bf which produces an upward
  magnetic pressure (50251s, 70680s)
• As fluxrope expands outward downward tension on
  overlying field lines increases stretch
  radially the field near the null.
• Reconnection begins at the top of the expanding
  rope (79008)
• Vertical current sheet forms deep inside (85185)
  reconnects.

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0
50251s
70680s
79008s
85185s
95020s
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Mass Density and Radial Velocity of Flux Rope
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The Breakout Model and Observations

• The main feature of the breakout model
• Flare reconnection does not initiate the
  eruption,
• Multipolar pre-eruption topology
• Density difference shows changes in density.
• The three part structure seen in coronagraph
  images is found in the simulations.

Lynch et al., 2004
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Energetics of the Breakout Model

• Azimuthal magnetic energy solid line
• Azimuthal magnetic energy below 1.5RS
  dashed-dotted line
• Change in non-azimuthal energy dashed line
• The kinetic energy dotted line with triangles.
• Initially about half of the azimuthal magnetic
  energy is converted into kinetic energy. By the
  end of the simulation all magnetic energy about
  1.5RS has been converted.

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Flux Injection Model (Chen, 1989, 1996)

• The underlying magnetic field of a CME is that of
  a three-dimensional flux rope.
• While all models end up with flux ropes this one
  starts with them.
• The flux rope is determined by the Lorentz force,
  pressure gradients and drag on the coronal
  plasma.
• It is difficult to distinguish between the flux
  cancellation models and the flux injection model
  since they evolve in the same way once the flux
  rope emerges.

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CME Evolution and Propagation (Forbes et al.,
2006)

• A CME propagates through the interplanetary
  medium as an ICME.
• Assume a flux tube (the CME) circles the Sun like
  in the symmetric simulation.
• Under excess internal pressure the flux tube
  expands that expansion is resisted by the
  inertial reaction of the medium into which it
  expands.
• The excess total pressure (particle plus
  magnetic) causes the flux tube to accelerate into
  the medium over coming gravity and drag.

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Basic Interaction

• The interaction can be written in words
• Expansion
• (Ambient mass density) X (Rate of expansion)2
  Delta Pressure (inside outside)
• Acceleration
• (Mass of CME Virtual mass) X Acceleration
  Force of gravity Delta (outside magnetic and
  particle pressure on lower surface area outside
  magnetic and particle pressure on upper surface
  area) Drag
• Virtual mass allows us to correct for the force
  necessary to move all the ambient medium away
  volume of cylinder time the mass density of the
  ambient medium.
• Problem is in turning this into equations.
• Standard drag term CDA? abs (VCME Vsw) (VCME
  Vsw) where CD is a drag coefficient, and
  (VCME Vsw) is relative velocities of CME and
  solar wind.
• How to do it is controversial.

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MHD simulation of CME propagation in the
heliosphere (Riley et al., 2003)

• Combined a CME eruption model (flux cancellation)
  with a solar wind model.
• Flux cancellation model was used as input to
  solar wind model.
• Flux cancellation model assumes g1.05 to mimic
  near-isothermal corona.
• Solar wind model has g5/3.
• Discontinuity at interface is harmless
  affecting only temperature slightly.
• Corotation enforced at the boundary between the
  models
• Plasma and magnetic field parameters were set at
  the outer boundary of the heliospheric simulation

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Evolution of the CME out to 0.5AU

• Number density black Vr color contours
  Magnetic field lines blue
• White line is boundary between solutions.
• Flux rope becomes circular and then pancake
  shaped kinematic expansion as ejecta expands
  and then collision with surrounding material.
• Shock and flux rope develop concave deformations.

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Evolution of CME out to 5AU

• Density red, field lines black and velocity
  shading.
• Ejecta becomes more distorted with distance.
• Acceleration related to post eruption
  reconnection.

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Comparison with spacecraft observations

• Ejecta was traveling faster than ambient solar
  wind shock (both)
• Speed profiles are similar
• Simulated B does not have peak in sheath (ACE))
• Magnetic discontinuity not found in simulation
  (Ulysses)
• B modeled better at Ulysses.
• Strong magnetic structure at Ulysses but not at
  ACE Ulysses passed near center of flux rope
  ACE near the flank