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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
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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
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TRACE Event: 13 June 1998
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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.
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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.
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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.
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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.
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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…
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