1. The Effect of Sub-surface Fields on the Dynamic Evolution of a Model Corona Goals :  To predict the onset of a CME based upon reliable measurements of photospheric magnetic field* * It may be possible to obtain a velocity field via LCT, “feature tracking”, * It may be possible to obtain a velocity field via LCT, “feature tracking”, or spectroscopic measurements or spectroscopic measurements  To model the evolution of the coronal magnetic field as eruptive events occur  To test reliability of the models by simulating known eruptive events and comparing model data with existing observational data* * MURI candidate event AR8210 May 1 1998 * MURI candidate event AR8210 May 1 1998

2. First Step:  Use dynamic sub-surface models of active region evolution to drive* the model corona. *Though it is possible to truly couple numerical models via a domain decomposition framework such as PARAMESH, we will not have the freedom to allow our coronal model to affect the observationally obtained photospheric boundary --- thus we must explore the consequences of driving a model corona without allowing “feedback” into the photospheric zones *Though it is possible to truly couple numerical models via a domain decomposition framework such as PARAMESH, we will not have the freedom to allow our coronal model to affect the observationally obtained photospheric boundary --- thus we must explore the consequences of driving a model corona without allowing “feedback” into the photospheric zones  A distinct advantage of this approach: Sub-surface code provides for self-consistent magnetic fields and flows throughout the boundary layers Sub-surface code provides for self-consistent magnetic fields and flows throughout the boundary layers eg. The induction equation is automatically satisfied throughout the eg. The induction equation is automatically satisfied throughout the boundary layers boundary layers

3. Approach:  Use a compressible MHD code (eg. Zeus3D, ZeusAMR, ARMS) to model the dynamic evolution of the magnetic field in the low-beta corona above an active region  Since vector magnetograms are measures of the magnetic field in the photosphere*, reliable models must: 1. Include in the computational domain the geometrically thin transition layers between the photosphere (where H p ~10 2 km, and the plasma beta is of order unity) along with the low-beta corona. 1. Include in the computational domain the geometrically thin transition layers between the photosphere (where H p ~10 2 km, and the plasma beta is of order unity) along with the low-beta corona. 2. Approximate (or treat exactly) the effects of optically thin radiative cooling, and thermal conduction in the transition layers so as to maintain a physical temperature and pressure stratification 2. Approximate (or treat exactly) the effects of optically thin radiative cooling, and thermal conduction in the transition layers so as to maintain a physical temperature and pressure stratification 3. Require that magnetic field is known along only a single slice in the photospheric layers of the simulation domain, and no additional sub-surface information is available 3. Require that magnetic field is known along only a single slice in the photospheric layers of the simulation domain, and no additional sub-surface information is available *some chromospheric measurements available *some chromospheric measurements available

4. Results 1 1. From Abbett & Fisher 2003 (Jan 1) ApJ (in press)

5. Results  The presence and distribution of boundary flows (particularly the component of the flow perpendicular to the boundary) are of great importance to the dynamic emergence process, since (in an ideal calculation) such a flow is necessary to transport magnetic field into the model corona while conserving flux.  As the apex of a (slightly) twisted Omega-loop emerges into the corona, the simulations suggest that in most regions surrounding the emerging structure, the field configuration differs from a force-free (or potential) configuration

6. Second Step: AR8210 (May 1 1998 19:40) A significant challenge:  Only the photospheric magnetic field is “known”. Since boundary flows are important to the dynamics of the coronal simulation, we must specify a self-consistent velocity field in the boundary layers that (at least) satisfies the vertical component of the induction equation  Options: 1. LCT (does NOT guarantee consistency) 1. LCT (does NOT guarantee consistency) 2. Feature tracking (does NOT guarantee consistency) 2. Feature tracking (does NOT guarantee consistency) 3. MEF method* (DOES guarantee consistency) 3. MEF method* (DOES guarantee consistency) *theoretical method that generates a velocity field given the vector magnetic field along a 2D slice with the constraint that kinetic energy is minimized --- does guarantee consistency, but the calculated flow field is part of a family of solutions and may not necessarily represent the true flows present in AR8210. *theoretical method that generates a velocity field given the vector magnetic field along a 2D slice with the constraint that kinetic energy is minimized --- does guarantee consistency, but the calculated flow field is part of a family of solutions and may not necessarily represent the true flows present in AR8210.

7. MEF method (D. Longcope)

8. AR8210  The initial atmosphere must be specified 1. Potential field extrapolation 1. Potential field extrapolation 2. Force-free model 2. Force-free model  Initial dynamic run --- uses MEF method at the photospheric boundary with an initial FFF atmosphere provided by S. Regnier:

9. Toward comparison with observational data --- Calculating temperatures and emissivities a posteriori along model coronal loops (L. Lundquist) Yohkoh SXT 01 May 1998 14:01 17:57 21:12 19:40