1. Extrapolation vs. MHD modeling Hardi Peter Kiepenheuer-Institut Freiburg, Germany Contribution to the discussions at the SDO workshop / Monterey Feb 2006

2.  3D MHD model for the corona: 50 x 50 x 30 Mm Box ( 150 3 ) – fully compressible; high order – non-uniform mesh  full energy equation (heat conduction, rad. losses)  starting with scaled-down MDI magnetogram – no emerging flux  photospheric driver: foot-point shuffled by convection  braiding of magnetic fields (Galsgaard, Nordlund 1995; JGR 101, 13445)  heating: DC current dissipation (Parker 1972; ApJ 174, 499)  heating rate  j 2 ~ exp(- z/H )  loop-structured 10 6 K corona Gudiksen & Nordlund (2002) ApJ 572, L113 (2005) ApJ 618, 1020 & 1031 Bingert, Peter, Gudiksen & Nordlund (2005) 3D MHD coronal modeling horizontal x [ Mm] horizontal y [ Mm] MDI magnetogram vertical z [ Mm] current log 10 J 2 mean B 2 mean J 2 histogram of currents Gudiksen & Nordlund (2002) ApJ 572, L113 010 20 3040 10 20 horizontal X [Mm] vertical Z [Mm] Bingert et al. (2005) “emission” @ 10 6 K

3. Coronal emission and plasma–   atmosphere is mostly in low–  state,  numerous  >1 regions even at high  (but mostly at low density)  source region of coronal emission: 90% of emission from log I/  I  > 0  there ~5% of volume at  >1  corona is not in a pure low–  state: plasma able to distort magnetic field to some extent Peter, Gudiksen & Nordlund (2006) ApJ 638

4. Coronal emission and magnetic field lines I The "usual" paradigm: The coronal emission is aligned with the magnetic field emission synthesized from a 3D coronal model side view / at the limb Peter, Gudiksen & Nordlund (2004) ApJ 618

5. Coronal emission and magnetic field lines II Not all emission we see in EUV / X-rays outlines field lines !!! synthesized emission top view / at the limb potential field extrapolation Peter, Gudiksen & Nordlund (2004) ApJ 618 Gudiksen & Nordlund (2002)

6. Conclusions  field extrapolations (NLFF): – possible to match photospheric B boundary conditions very well – time evolution through sequence of equilibria – do we really "see" field lines in EUV ?  MHD coronal models – proper time evolution – not easy to match observed B at photosphere (all 3 components) – proper interaction of B and plasma – emission properties through forward modeling  One needs both: MHD models and field extrapolations !