The Emergence of a Twisted Flux Tube into the solar atmosphere: Sunspot Rotations and the formation

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The Emergence of a Twisted Flux Tube into the
solar atmosphere Sunspot Rotations and the
formation of a Coronal Flux Rope

• Yuhong Fan
• High Altitude Observatory
• Earth and Sun Systems Laboratory
• National Center for Atmospheric Research
• Boulder, CO

March 20, 2009
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Simulation set up

• An initial twisted flux tube placed at z
  -2.1Mm, with its middle portion made buoyant.

• Numerically solve the ideal compressible MHD
  equations
  
• Staggered finite difference
• A modified 2nd order Lax-Friedrichs scheme
  (Rempel et al. 2009) with significantly reduced
  numerical diffusion
  
• Constrained transport scheme for solving the
  induction equation (Stone and Norman 1992)

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3D emerging field in the atmosphere
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Evolution in the central vertical plane of x0
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• Critical condition for emergence into the stable
  atmosphere through onset of magnetic buoyancy
  instability (Archontis et al. 2004, Murray et al.
  2006)

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Evolution in the central vertical plane of x0
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How emerged field lines rotate due to vortical
motions at the foot-points
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Vortical motions of the two polarities
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Helicity flux into the solar atmosphere

• Relative magnetic helicity in the atmosphere
  above the photosphere of z 0 (Finn and Antonsen
  1985)

where is the reference potential field having
the same normal flux distribution at the lower
boundary, and is the vector potential of .

• Helicity flux through the photosphere (Berger
  and Field 1984)

where is the vector potential of the
potential magnetic field satisfying
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• Vortical motions of the two polarities are
  manifestations of non-linear torsional Alfven
  waves propagating along the flux tube

• The net axial torque exterted on a thin flux
  tube segment is (Longcope and
  Welsch 2000)

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Current sheet and sigmoid loops
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Summary

• Through 3D MHD simulations of the emergence of a
  twisted flux tube from the solar interior into
  the solar atmosphere, it is found
  
• Flux emergence into the atmosphere is initiated
  by the onset of the magnetic buoyancy
  instability.
  
• Soon after the two polarity flux concentrations
  of the emerging region become separated, a
  prominent rotational motion sets in within each
  polarity, reminiscent of sunspot rotations. The
  rotational motions become the dominant source of
  helicity flux into the atmosphere.
• A twisted subsurface flux tube does not emerge as
  a whole into the atmosphere due to the heavy
  plasma trapped at the bottom concave portions of
  the helical field lines. However, subsequent
  shear and rotational motions of the two
  polarities twist up the inner emerged field
  lines, driving the formation and rise of a
  coronal flux rope with sigmoid-shaped, dipped
  core fields.
• A current sheet form in the lower atmosphere,
  extending up to the base of the corona. Field
  lines going through the current sheet all show a
  sigmoid shape and may correspond to the observed
  X-ray sigmoid loops.
• The rotational motion centered on each polarity
  flux concentration is a manifestations of
  non-linear torsional Alfven waves propagating
  along the emerging flux tube, transporting twist
  from its interior portion towards the expanded
  coronal portion. This may be a major mechanism
  that drives the formation of coronal flux ropes
  in solar active regions as the precursor
  structures for solar eruptions.

Fan (2009, ApJ in press)