Simulations of Emerging Simulations of Emerging Magnetic Flux in Active RegionsMagnetic Flux in Active Regions

W. P. AbbettW. P. AbbettSpace Sciences LaboratorySpace Sciences Laboratory

University of California, BerkeleyUniversity of California, Berkeley

Toward a Global View of “Emergence”Toward a Global View of “Emergence”

Interior ModelingInterior Modeling: Evolution of flux ropes deep : Evolution of flux ropes deep in the Convection Zonein the Convection Zone

Surface LayersSurface Layers: Modeling the evolution of : Modeling the evolution of magnetic features at the solar surfacemagnetic features at the solar surface

The “Local” CoronaThe “Local” Corona: Evolution of the coronal : Evolution of the coronal field in response to magnetic flux emerging field in response to magnetic flux emerging through the photosphere through the photosphere

Global modelsGlobal models of the solar corona of the solar corona Coupled modelsCoupled models: Can we achieve a more : Can we achieve a more

holistic picture?holistic picture?

Interior ModelingInterior ModelingThe Flux Tube Picture: Toroidal flux layer near the tachocline succumbsto 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)

Modeling the InteriorModeling the Interior

The Thin Flux Tube ApproximationThe Thin Flux Tube Approximation: : Assumptions:Assumptions: Active region fields behave as distinct, tube-like entitiesActive region fields behave as distinct, tube-like entities embedded in a field-free plasma. The flux tube diameterembedded in a field-free plasma. The flux tube diameter is small compared with all other relevant length scales,is small compared with all other relevant length scales, and pressure balance exists across the tube at all times.and pressure balance exists across the tube at all times.

Advantages:Advantages: One can derive a simplified equation of motion for a 1DOne can derive a simplified equation of motion for a 1D tube moving within a 3D model of the solar interior.tube moving within a 3D model of the solar interior.

Modeling the InteriorModeling the Interior The Thin Flux Tube ApproximationThe Thin Flux Tube Approximation: :

Successes:Successes: Certain observational properties of active regions can Certain observational properties of active regions can be addressed; for example, distribution of active region be addressed; for example, distribution of active region tilt angles (Longcope & Fisher 1996), and asymmetric tilt angles (Longcope & Fisher 1996), and asymmetric spot motions and morphologies (Caligari et al. 1995,spot motions and morphologies (Caligari et al. 1995, Fan & Fisher, 1996). Fan & Fisher, 1996).

Modeling Flux Ropes in the CZModeling Flux Ropes in the CZ

3D local MHD in the anelastic approximation:3D local MHD in the anelastic approximation:

Assumptions:Assumptions: Approximation results from a scaled variable expansion of Approximation results from a scaled variable expansion of the 3D MHD equations about a zero-th order, stratifiedthe 3D MHD equations about a zero-th order, stratifiedreference state. This approximation is valid in the high beta,reference state. This approximation is valid in the high beta,gravitationally stratified plasma of the solar convection zone gravitationally stratified plasma of the solar convection zone below the photosphere. below the photosphere.

Advantages:Advantages: Fast-moving acoustic waves are effectively filtered out of the Fast-moving acoustic waves are effectively filtered out of the simulations. Time steps are less restrictive, and a large simulations. Time steps are less restrictive, and a large amount of parameter space can be explored. amount of parameter space can be explored.

Modeling Flux RopesModeling Flux Ropesin the interiorin the interior

3D vs 2D axisymmetric3D vs 2D axisymmetric(Abbett et al. 2000,2001)(Abbett et al. 2000,2001)

Of interest: Highly twisted, knotted Of interest: Highly twisted, knotted configurations (Linton, Fan, Fisher)configurations (Linton, Fan, Fisher)

Kink unstable magnetic flux tube rising through a stratified model CZ (LHS using 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 ANMHD – Fan et al. 1999) and evolving in a non-stratified domain using the periodic spectral code, CRUNCH-3D (RHS – Linton et al. 1999).spectral code, CRUNCH-3D (RHS – Linton et al. 1999).

Delta Spot Active Regions modeled as Delta Spot Active Regions modeled as buoyant, initially kink-unstable flux tubes buoyant, initially kink-unstable flux tubes that emerge through CZ:that emerge through CZ:

Q: Is emerging flux (especially in highly sheared configurations)Q: Is emerging flux (especially in highly sheared configurations)an important component of the CME initiation process?an important component of the CME initiation process?

ANMHD Examples: LHS --- magneto-convection and the local solar dynamo;ANMHD Examples: LHS --- magneto-convection and the local solar dynamo;RHS --- emerging magnetic flux (Abbett, Fan & Fisher 2002 in prep).RHS --- emerging magnetic flux (Abbett, Fan & Fisher 2002 in prep).

Surface LayersSurface Layers A fully compressible treatment is required.A fully compressible treatment is required.

Two approaches for modeling magnetic Two approaches for modeling magnetic fields at or near the solar surface:fields at or near the solar surface:

1. Realistic radiative-magnetoconvection over 1. Realistic radiative-magnetoconvection over

small spatial scales (Stein & Nordlund 2001, small spatial scales (Stein & Nordlund 2001,

Bercik 2002, Gudiksen et al. 2002)Bercik 2002, Gudiksen et al. 2002)

2. 3D MHD simulation of the local photosphere /2. 3D MHD simulation of the local photosphere /

transition region / low corona employingtransition region / low corona employing

an approximate treatment of the energy equationan approximate treatment of the energy equation

(Fan 2001, Magara & Longcope 2001)(Fan 2001, Magara & Longcope 2001)

Granular-scale surface magneto-convectionGranular-scale surface magneto-convection(Bercik 2002)(Bercik 2002)

• Computationally expensive calculation;Computationally expensive calculation; thus, the domain size is restricted.thus, the domain size is restricted.

SurfaceSurface LayersLayers

Zeus3D fully-compressibleZeus3D fully-compressible3D ideal MHD (Fan 2001)3D ideal MHD (Fan 2001)

• Calculations of thisCalculations of this type are important totype are important to test theoretical modelstest theoretical models of CME initiation.of CME initiation.

• Do flux ropes exist inDo flux ropes exist in the corona, and can they the corona, and can they be formed self-consistentlybe formed self-consistently through emergence of a through emergence of a twisted magnetic structuretwisted magnetic structure from below? from below?

• Are multipolar magnetic Are multipolar magnetic configurations necessaryconfigurations necessary prerequisites for an prerequisites for an eruptive event?eruptive event?

Surface Layers: Modeling Large-scale Flux Emergence into the Corona Surface Layers: Modeling Large-scale Flux Emergence into the Corona

Surface Layers: Modeling Large-scale Flux Emergence into the CoronaSurface Layers: Modeling Large-scale Flux Emergence into the Corona

Fully-compressible 3D ideal MHD (Magara & Longcope 2001)Fully-compressible 3D ideal MHD (Magara & Longcope 2001)

2.5-D simulation of how a 2.5-D simulation of how a layer of magnetic field can layer of magnetic field can spontaneously shear as a spontaneously shear as a result of a mixed-mode result of a mixed-mode buoyancy instability buoyancy instability (Manchester 2001).(Manchester 2001).

Toward Coupled models of Flux EmergenceToward Coupled models of Flux Emergence

PARAMESHPARAMESH: A domain decomposition, : A domain decomposition, adaptive mesh refinement (AMR) framework adaptive mesh refinement (AMR) framework developed by MacNeice et al. 2000 and developed by MacNeice et al. 2000 and distributed by GSFCdistributed by GSFC

Zeus3DZeus3D: A staggered mesh finite-difference : A staggered mesh finite-difference (non-relativistic) MHD code originally developed (non-relativistic) MHD code originally developed by Stone & Norman 1992, and publicly by Stone & Norman 1992, and publicly distributed by NCSAdistributed by NCSA

ZeusAMRZeusAMR: A fully compressible 3D MHD code : A fully compressible 3D MHD code with AMR which resulted from a merge of with AMR which resulted from a merge of PARAMESH with a modified version of Zeus3DPARAMESH with a modified version of Zeus3D

ANMHD Interior modelANMHD Interior modeldrives the lower boundarydrives the lower boundaryof a Zeus3D modelof a Zeus3D modelcorona (Abbett in prepcorona (Abbett in prep2002).2002).

• Code coupling: DoesCode coupling: Does the corona significantlythe corona significantly affect the sub-surfaceaffect the sub-surface calculation (Welsch &calculation (Welsch & Longcope 2000)Longcope 2000)

• How important are How important are treatments of thetreatments of the energy equation in energy equation in the transition layersthe transition layers and corona (Mikic,and corona (Mikic, Linker, Lionello, MokLinker, Lionello, Mok 2002)?2002)?

Toward Coupled Models of Flux Emergence:Toward Coupled Models of Flux Emergence:

Example of driving a ZeusAMR coronalExample of driving a ZeusAMR coronalsimulation with an ANMHD generated lowersimulation with an ANMHD generated lowerboundary. True “code coupling” can be boundary. True “code coupling” can be achieved using the PARAMESH frameworkachieved using the PARAMESH framework.

Toward Coupled Models of Flux Emergence: Toward Coupled Models of Flux Emergence: SummarySummary

Existing code coupling frameworks have the Existing code coupling frameworks have the potential to provide a straightforward way to potential to provide a straightforward way to self-consistently connect existing numerical self-consistently connect existing numerical treatments of local flux emergence into large-treatments of local flux emergence into large-scale models of global phenomena. scale models of global phenomena.

Though, the devil is in the details:Though, the devil is in the details:

-- Different numerical algorithms, boundary treatments, -- Different numerical algorithms, boundary treatments, and physical conditions between individual models of and physical conditions between individual models of different regimes make the task of transferring different regimes make the task of transferring information back and forth between codes in a suitably information back and forth between codes in a suitably efficient, yet physically consistent manner, a non-trivial efficient, yet physically consistent manner, a non-trivial task.task.