An Analytical Solution for “EIT Waves”

1. An Analytical Solution for “EIT Waves” M. J. Wills-Davey, C. E. DeForest, Southwest Research Institute, Boulder, Colorado and J. O. Stenflo Southwest Research Institute (on leave from Institute of Astronomy, University of Zurich) meredith@boulder.swri.edu

2. Observed Properties of “EIT Waves” • Large, single-pulse fronts • Intensity-enhancements (compressional MHD waves) • Travel global distances through QS • Tend to travel much more slowly than the Alfvén or fast-mode speeds (~300 km/s vs. ~600-1000 km/s) • Often instigate loop oscillations EIT Event: 12 May 1997 Image provided by B. J. Thompson

3. TRACE Event: 13 June 1998

4. Certain properties of EIT waves have been difficult to model. If you use plane waves, it’s hard to: • make ubiquitous waves move slowly. • create a long-lived, coherent single pulse. • Dispersion should show periodicity. • instigate loop oscillations with a plane wave.

5. A Soliton Solution • Non-linear • Matches observations • Assume a simple MHD environment • No boundaries • v B Density: ρ = ρ0 + ρ1sech2[x-cwt/Lw] Solutions with constant cw, no dispersion are possible.

6. [(1 – 3 )cs2 + (1 – 2 )vA2]2 ρ1 ρ0 ρ1 ρ0 ρ1 ρ0 ρ1 ρ0 (cs2 + vA2)[3( )2– 3 + 1) ρ1 ρ0 For the “EIT Wave Solution:” cw2 = • cw2 depends on the initial conditions. • For a range of ρ1/ρ0 01, cw2 < vA2 Waves travel at observed velocities and with consistent density perturbations.

7. Instigating Loop Oscillations • Unlike plane waves, solitons do not return things to IC • Shifts about pulse width • Consistent with observations Solitons must generate loop displacement.

8. Conclusion Solitons provide a simple, non-linear solution consistent with observations. • Relation to CMEs • Large events ideal non-linear wave generator • Better geometry, boundary conditions • Gravity, surface curvature, more-D propagation • Now may be useful for coronal seismology Where to go now…