1. Reconstructing Active Region Thermodynamics Loraine Lundquist Joint MURI Meeting Dec. 5, 2002

2. Motivation  Reconstructing an expected emission picture is an excellent way to compare with observations  Most current MHD models do not give a satisfactory treatment of the energy equation  Allows us to test assumptions about the coronal loop heating function  A temperature, density, and magnetic field vector map of the corona would allow us to model type II bursts, EIT and Moreton wave propagation, and shocks which may accelerate particles

3. Reconstruct temperature and density structure of active regions from first principles Magnetic field data (from Régnier FFF data or MHD) Integrate fieldlines Solve static energy equation along each fieldline, (with some simplifying assumptions) Assume a form for the loop heating function Interpolate to a regular grid Construct X-ray and EUV false images Compare with observations

4. Integrate fieldlines

5. Static Coronal Loop Model: Description Solve Static Energy Equation: E R = Energy losses due to radiation E H = Plasma heating function F C = Conductive heat flux along loop.

6. Heating Function Quiet Sun X-Ray Bright Points Solar Active Regions G, K, M dwarfs T-Tauri stars Solar Disc Averages Empirical relationship from Pevtsov et al. soft x-ray data.

7. Solve Static Energy Equation: Assumptions  Static (bulk plasma velocity vanishes) (bulk plasma velocity vanishes)  Thin straight loop (ignore area variations) (ignore area variations)  Uniform heating  Radiative losses approximated with a power law  No gravity  No losses through footpoints

8. Solve Static Energy Equation: Assumptions  Static (bulk plasma velocity vanishes) (bulk plasma velocity vanishes)  Straight (ignore curvature effects) (ignore curvature effects)  Uniform heating  Radiative losses approximated with a power law  No gravity  No losses through footpoints Delta function at base Look-up table or piecewise power law Add gravity

9. Construct False Images  Interpolate onto a regular grid. (This is easy in theory, but in practice, (This is easy in theory, but in practice, there are many difficulties, depending there are many difficulties, depending on the spatial coverage of the fieldlines.) on the spatial coverage of the fieldlines.)  Plot emissivity integrated along line of sight  If desired, integrate over known band passes to simulate pictures from Yohkoh, EIT, etc.

10. Preliminary Results Yohkoh SXT AR 8210 May 1, 1998 MURI case study 14:01 17:57 21:12 19:40 Reconstructed Active Region (emission integrated over line of sight)

11. Future Applications  Compare with results, and refine assumptions.  Do a statistical study to see which coronal heating functions give the best results over a broad range of data.  Create maps of the coronal Alfvén speeds and sound speeds for modeling EIT and Moreton waves, Type II bursts, and particle acceleration.