1. Global coronal seismology and EIT waves Istvan Ballai SP 2 RC, University of Sheffield, UK

2. Coronal seismology Local seismology: using waves propagating in magnetic structures (coronal loops, filaments, solar wind, etc) Global seismology: using waves propagating over very large distances in the quiet Sun, e.g. EIT waves and the connection between global and local waves Started with Roberts et al (1983), Aschwanden et al. 1999, Nakariakov et al. 1999; the development is accelerated and diversified by a large number of high- resolution observations Started with Meyer 1968, Uchida 1970, Ballai et al. 2005, Ballai 2007; is backed by observations og global waves by, e.g. SOHO, TRACE, STEREO

3. EIT waves Generated by sudden energy releases (flares, CMEs); very well correlated to CMEs, weakly to flares Observed to propagate over large distances, sometimes comparable to the solar radius; the shape is almost circular (in many cases) Large span of velocities (100-400 km/s) Able to carry information about the quiet Sun Problems with EIT waves  There is no unified concept about EIT waves  Most of observations during solar minima  Not properly observed (see, e.g. Wills-Davey, 2006)

4. Observation of EIT waves Although there is a very good correlation not every impulsive event is associated with an EIT wave Causes: 1. Observational SOHO/EUV  poor temporal resolution (1 frame/12-15 min)  not able to record EIT waves for flares/CMEs near the limb TRACE/EUV  Much better resolution but limited FOV (observation of EIT waves is merely a matter of luck)  Wave front too faint to be observed 2. Theoretical  If the idea of guided trapped waves is OK, waves become evanescent very quickly

5. EIT wave seen by SOHO/EIT (courtesy of M. Wills-Davey)

6. EIT wave seen by STEREO/EUVI (Courtesy of G. Attrill)Propagation speed: 288±55 km/s

7. TRACE 195 A (1.5 MK) The 13 June 1998 event (Wills-Davey and Thompson 1999, Ballai, Erdélyi and Pintér 2005) 15:25 UT– 15:44 UT EIT waves observed by TRACE/EUV Oscillatory motion with periods of about 400 seconds (Ballai, Erdélyi and Pintér 2005)

8. Generation of EIT waves For simplicity suppose a magnetic-free environment, and study the propagation of waves at a single spherical interface

9. Generation of EIT waves The difference in the pressure perturbation in the two regions could generate a siphon flow which drives much denser material in the outer region In the exterior (right hand side), the dimming propagates away from the source (as observed)

10. Sampling the magnetic field (vertical) Suppose that EIT waves are FMW propagating perpendicular to the ambient magnetic field c=(c S 2 +v A 2 ) 1/2 The propagation height of EIT waves is important since many physical parameters (temperature, density, pressure) have height-dependence Suppose a simple atmosphere such that (Sturrock et al. 1996) F 0 : inward heat flux (1.8×10 5 erg/cm 2 s) x: normalized height coordinate (=r/R ☼ ) T 0 : temperature at the base of the model (=1.3MK) κ: coefficient of thermal conductivity δ: a constant

11. Sampling the magnetic field (vertical) contd... With the sound speed and density calculated at each height, values of the magnetic field (via the Alfvén speed) are obtained to be xTncScS v A (1) B (1) v A (2) B (2) 1.001.303.601.721.811.573.613.13 1.021.413.301.801.731.443.572.97 1.041.503.101.851.671.343.542.85 1.061.582.951.901.611.273.512.76 1.081.642.831.941.571.213.492.69 1.101.702.731.971.521.153.472.63 [T]: MK [n]: 10 8 cm -3 [c S ],[v A ]: 10 7 cm/s [B]: G (a): c=250 km/s (b): c=400 km/s

12. Flare and magnetic field diagnostics EIT waves interact with loops transferring part of their energy to loops  loop oscillations Supposing that the entire energy of EIT waves is transferred to loops, the minimum energy of EIT waves is For the event on 13 June 1998, we obtain E=3.8×10 18 J, for the event on 14 July 1998 (Nakariakov et al. 1999) we obtain E=10 19 J. Since λ e -1 contains the Alfvén speed, it is possible to derive a formula giving the magnetic field in the oscillating loop provided the energy of the EIT wave can be measured.

13. Flare and magnetic field diagnostics Time L(Mm) R(Mm) n×10 8 (cm -3 ) E(J) 980714 1687.25.72.2x10 17 980714 2047.96.29.7x10 18 981123 19016.831.3x10 19 990704 25876.33.9x10 16 991025 1666.37.21.6x10 18 000323 1988.8175.2x10 16 000412786.86.92.5x10 16 010321 4069.26.27.4x10 16 010322 2606.23.21.9x10 16 010412 22674.41.4x10 18 010415 2568.55.11.4x10 16 010513 18211.442.2x10 18 010515 1926.92.71.6x10 19 010615 14615.83.21.1x10 17 Lengths, width and densities taken from Aschwanden et al. (2001) Time given in yymmdd format E: the minimum energy of EIT waves to generate the observed dislocation of loops No particular correlation between the energy and geometrical sizes of loops but a relative good agreement between energy and 1/n

14. Sampling the magnetic field (tangential) Magnetic map of the quiet Sun Magnetic tomography of the quiet Sun

15. Conclusions EIT waves are very good candidates for sampling the coronal magnetic field in the quiet Sun More observations are needed with higher resolution Since EIT waves relate flare/CMEs with oscillations in coronal loops, they are very useful tools to diagnose the magnetic field on a larger scale and connect CMEs and loop oscillations After all, the magnitude of the magnetic field is not the most important factor, instead the of structure (sub-structure) of the magnetic field could be more interesting and important