An Analytical Solution for “EIT Waves”

M. J. Wills-Davey, C. E. DeForest,Southwest Research Institute, Boulder, Colorado

and J. O. StenfloSouthwest Research Institute (on leave from Institute of

Astronomy, University of Zurich)

meredith@boulder.swri.edu

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. ThompsonEIT Event: 12 May 1997

TRACE Event: 13 June 1998

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.

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.

For the “EIT Wave Solution:”

cw2 =

[(1 – 3 )cs2 + (1 – 2 )vA

2]2

(cs2 + vA

2)[3( )2– 3 + 1) ρ1

ρ0 ρ1

ρ0 ρ1

ρ0

ρ1

ρ0 ρ1

ρ0

• cw2 depends on the initial conditions.

• For a range of ρ1/ρ0 01, cw2 < vA

2

Waves travel at observed velocities and with consistent density perturbations.

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.

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…