1. Simulations of Emerging Magnetic Flux in Active Regions W. P. Abbett Space Sciences Laboratory University of California, Berkeley

2. 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?

3. 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)

4. Modeling the Interior  The Thin Flux Tube Approximation: Assumptions: Assumptions: Active region fields behave as distinct, tube-like entities Active region fields behave as distinct, tube-like entities embedded in a field-free plasma. The flux tube diameter embedded 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 1D One 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.

5. Modeling the Interior  The 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).

6. 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.

7. Modeling Flux Ropes in the interior 3D vs 2D axisymmetric (Abbett et al. 2000,2001)

8. 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).

9. 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?

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

11. 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 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 employing transition region / low corona employing an approximate treatment of the energy equation an approximate treatment of the energy equation (Fan 2001, Magara & Longcope 2001) (Fan 2001, Magara & Longcope 2001)

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

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

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

15. 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).

16. 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

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

18. Example of driving a ZeusAMR coronal simulation with an ANMHD generated lower boundary. True “code coupling” can be achieved using the PARAMESH framework achieved using the PARAMESH framework.

19. 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. -- 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.