Simulations of Emerging Magnetic Flux in Active Regions

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Simulations of Emerging Magnetic Flux in Active
Regions

• W. P. Abbett
• Space Sciences Laboratory
• University of California, Berkeley

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Toward a Global View of Emergence

• Interior Modeling Evolution of flux ropes deep
  in the Convection Zone
• Surface Layers Modeling the evolution of
  magnetic features at the solar surface
• The Local Corona Evolution of the coronal
  field in response to magnetic flux emerging
  through the photosphere
• Global models of the solar corona
• Coupled models Can we achieve a more holistic
  picture?

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Interior Modeling
The Flux Tube Picture Toroidal flux layer near
the tachocline succumbs to an instability, and
creates a buoyant flux rope that ascends through
the CZ as an Omega-loop. The loop emerges
through the photosphere, and is observed as a
magnetic bipole.
(Cauzzi et al. 1996)
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• Modeling the Interior
• The Thin Flux Tube Approximation
• Assumptions
• Active region fields behave as distinct,
  tube-like entities
• embedded in a field-free plasma. The flux
  tube diameter
• is small compared with all other relevant
  length scales,
• and pressure balance exists across the tube
  at all times.
• Advantages
• One can derive a simplified equation of
  motion for a 1D
• tube moving within a 3D model of the solar
  interior.

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• Modeling the Interior
• The Thin Flux Tube Approximation
• Successes
• Certain observational properties of active
  regions can
• be addressed for example, distribution of
  active region
• tilt angles (Longcope Fisher 1996), and
  asymmetric
• spot motions and morphologies (Caligari et
  al. 1995,
• Fan Fisher, 1996).

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• Modeling Flux Ropes in the CZ
• 3D local MHD in the anelastic approximation
• Assumptions
• Approximation results from a scaled variable
  expansion of
• the 3D MHD equations about a zero-th order,
  stratified
• reference state. This approximation is valid in
  the high beta,
• gravitationally stratified plasma of the solar
  convection zone
• below the photosphere.
• Advantages
• Fast-moving acoustic waves are effectively
  filtered out of the
• simulations. Time steps are less restrictive,
  and a large
• amount of parameter space can be explored.

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Modeling Flux Ropes in the interior
3D vs 2D axisymmetric (Abbett et al. 2000,2001)
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Of interest Highly twisted, knotted
configurations (Linton, Fan, Fisher)
Kink unstable magnetic flux tube rising through a
stratified model CZ (LHS using ANMHD Fan et al.
1999) and evolving in a non-stratified domain
using the periodic spectral code, CRUNCH-3D (RHS
Linton et al. 1999).
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Delta Spot Active Regions modeled as buoyant,
initially kink-unstable flux tubes that emerge
through CZ
Q Is emerging flux (especially in highly
sheared configurations) an important component of
the CME initiation process?
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ANMHD Examples LHS --- magneto-convection and
the local solar dynamo RHS --- emerging
magnetic flux (Abbett, Fan Fisher 2002 in prep).
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Surface Layers

• A fully compressible treatment is required.
• Two approaches for modeling magnetic fields at or
  near the solar surface
• 1. Realistic radiative-magnetoconvection over
  
• small spatial scales (Stein Nordlund
  2001,
• Bercik 2002, Gudiksen et al. 2002)
• 2. 3D MHD simulation of the local photosphere
  /
• transition region / low corona employing
• an approximate treatment of the energy
  equation
• (Fan 2001, Magara Longcope 2001)

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Surface Layers

• Granular-scale surface magneto-convection
• (Bercik 2002)
• Computationally expensive calculation
• thus, the domain size is restricted.

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Surface Layers Modeling Large-scale Flux
Emergence into the Corona

• Zeus3D fully-compressible
• 3D ideal MHD (Fan 2001)
• Calculations of this
• type are important to
• test theoretical models
• of CME initiation.
• Do flux ropes exist in
• the corona, and can they
• be formed self-consistently
• through emergence of a
• twisted magnetic structure
• from below?
• Are multipolar magnetic
• configurations necessary
• prerequisites for an
• eruptive event?

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Surface Layers Modeling Large-scale Flux
Emergence into the Corona
Fully-compressible 3D ideal MHD (Magara
Longcope 2001)
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2.5-D simulation of how a layer of magnetic field
can spontaneously shear as a result of a
mixed-mode buoyancy instability (Manchester 2001).
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Toward Coupled models of Flux Emergence

• PARAMESH A domain decomposition, adaptive
  mesh refinement (AMR) framework developed by
  MacNeice et al. 2000 and distributed by GSFC
• Zeus3D A staggered mesh finite-difference
  (non-relativistic) MHD code originally developed
  by Stone Norman 1992, and publicly distributed
  by NCSA
• ZeusAMR A fully compressible 3D MHD code with
  AMR which resulted from a merge of PARAMESH with
  a modified version of Zeus3D

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Toward Coupled Models of Flux Emergence

• ANMHD Interior model
• drives the lower boundary
• of a Zeus3D model
• corona (Abbett in prep
• 2002).
• Code coupling Does
• the corona significantly
• affect the sub-surface
• calculation (Welsch
• Longcope 2000)
• How important are
• treatments of the
• energy equation in
• the transition layers
• and corona (Mikic,
• Linker, Lionello, Mok
• 2002)?

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Example of driving a ZeusAMR coronal simulation
with an ANMHD generated lower boundary. True
code coupling can be achieved using the
PARAMESH framework.
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Toward Coupled Models of Flux Emergence Summary

• Existing code coupling frameworks have the
  potential to provide a straightforward way to
  self-consistently connect existing numerical
  treatments of local flux emergence into
  large-scale models of global phenomena.
• Though, the devil is in the details
• -- Different numerical algorithms,
  boundary treatments, and physical conditions
  between individual models of different regimes
  make the task of transferring information back
  and forth between codes in a suitably efficient,
  yet physically consistent manner, a non-trivial
  task.