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6.3 Propagating slow waves as a tool for coronal seismology

According to the previous sections, slow magnetoacoustic waves follow magnetic field lines and propagate at the local sound speed. Because of the high coronal thermal conduction along the field, the equilibrium temperature does not experience significant changes in this direction, at least at the distances comparable with the detection distance of the slow waves. As the sound speed is proportional to the temperature squared, the propagation speed should be constant along the structure, and the speed measured observationally would contain information about the temperature and about the value of the adiabatic index g. However, such a measurement is impossible at the moment, because the observations with the single line of sight provide us with the apparent speed only, which is affected by the projection effect. Possibly, future 3D observations of the propagating slow waves with STEREO will make such an estimation possible.
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Figure 18: Simultaneous time-distance plots of propagating EUV disturbances observed by TRACE in the 171 Å and 195 Å bandpasses along a slit. The distance along the slit is shown in opposite directions to demonstrate that the disturbances observed in different bandpasses form a “fishbone” structure (from King et al., 2003Jump To The Next Citation Point).
Another interesting possibility arises when the waves are observed simultaneously in different bandpasses which correspond to different temperatures of the emitting plasma. First such observation was done by Robbrecht et al. (2001) with SOHO/EIT 195 Å filter and TRACE 171 Å filter. It was found that wave propagating along the same coronal structure was detected in both bandpasses. The big difference in spatial resolution of EIT and TRACE imagers (2.5” vs 0.5”) did not allow to study the correlation in detail. Later on, King et al. (2003Jump To The Next Citation Point) analysed slow waves observed in 171 Å and 195 Å with TRACE, confirming the correlation (see Figure 18View Image). Figure 19View Image shows the evolution of the correlation coefficient of the perturbations observed in the different bandpasses with distance along the loop. There is a systematic decrease of the correlation coefficient which may be caused by the different propagating speed of the disturbances observed in different bandpasses. This may be interpreted as an indication to the sub-resolution structuring of the analysed active region: The observed loop can be either a bundle of magnetic threads of varying temperature, or have a transverse temperature profile. The further development of this study seems to be promising.
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Figure 19: Six upper panels (loops A - F): Evolution of correlation coefficients of propagating disturbances observed simultaneously in 171 Å and 195 Å bandpasses with the distance along six different slits. The solid lines show the correlation of unfiltered data while the dashed lines show the correlation of the signals after subtraction of slower variation. The dotted lines are the best-fitted straight lines. Two lower panels: Evolution of correlation coefficients of simulated signals. The left panel shows the correlation for the same angle with the line of sight, but for different temperatures T171 = 1.05, 1.15, and 1.2 MK and T195 = 1.55, 1.55, and 1.45 MK for the solid, dotted and the dashed line, respectively. The right panel shows varying angle o h171 = 15 and o h195 = 15, 14.5o, and 14o for the solid, dotted and dashed lines, respectively, while keeping the temperature the same. The dash-dotted lines in both panels are the correlation of the simulated signals with amplitude noise added (from King et al., 2003).

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