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 Image provided by B. J. Thompson EIT Event: 12 May 1997

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 = ρ 0 + ρ 1 sech 2 [x-c w t/L w ] Solutions with constant c w, no dispersion are possible.

6. For the “EIT Wave Solution:” c w 2 = [(1 – 3 )c s 2 + (1 – 2 )v A 2 ] 2 (c s 2 + v A 2 )[3( ) 2 – 3 + 1) ρ1ρ0ρ1ρ0 ρ1ρ0ρ1ρ0 ρ1ρ0ρ1ρ0 ρ1ρ0ρ1ρ0 ρ1ρ0ρ1ρ0 c w 2 depends on the initial conditions. For a range of ρ 1 /ρ 0 0  1, c w 2 < v A 2 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 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 Solitons provide a simple, non-linear solution consistent with observations. Where to go now…