3.2 Non-TRACE observations

Kink modes of coronal loops - often erroneously called Alfvén waves (erroneously, because the true Alfvén waves guided by coronal loops are the torsional modes, see Section 8) - can also be observed through modulation of the broadband gyrosynchrotron emission by the periodic variation of the local magnetic field in flaring loops and through periodic variations of the Doppler shift. The optically thin gyrosynchrotron emission intensity $If$ at a frequency $f$ can be estimated with the use of (Dulk and Marsh, 1982 )’s approximated formula

where $N$ is the concentration of the nonthermal electrons with energies higher than $10 keV$ , $h$ is the angle between the magnetic field and the line-of-sight, $f B$ is the gyrofrequency and $d$ (usually $> 3- 5$ ) is the power law spectral index of the electrons. Transverse oscillations are accompanied by the changes of the angle $h$ and, consequently, modulate the gyrosynchrotron emission coming from the loop. This mechanism can be responsible for quasi-periodic pulsations with periods from several $s$ to several $min$ , abundantly present in the microwave emission coming from flaring loops.

However, confident identification of the kink mode requires observations with high spatial resolution. The pixel size should be smaller than the wave length of the mode. The first spatially resolved detection of microwave quasi-periodic pulsations, which could be associated with the fast kink mode, was performed by Asai et al. (2001 ) with the Nobeyama Radioheliograph (see Figure 11 ). The oscillation period was $6.6 s$ . They determined the number density in the loop to be $16 -3 4.5 × 10 m$ from filter ratios of soft X-ray images taken by SXT. The loop length was $16 Mm$ . The microwave pulsations had a less weaker modulated counterpart in hard X-ray emission observed by the HXT on Yohkoh. The modulation of the hard X-ray emission by the kink wave can be connected with modulation of the electron acceleration by the kink oscillation of the flaring loop, or with interaction of the flaring loop with another loop which performs kink oscillations. In both cases the reconnecting magnetic field is periodically fed to the reconnection site by the kink oscillation. As the thickness of the reconnection site is believed to be very small, even weak kink oscillations can produce the required modulation.

Figure 11:

Light curves of the second burst (scaled arbitrarily). From top to bottom: Radio brightness temperature observed at $17 GHz$ by NoRH (solid line) and hard X-ray count rate measured in the M2 band ( $3353 keV$ ; dash-dotted line) and M1 band ( $2333 keV$ ; dotted line) of Yohkoh/HXT. The vertical lines show the peak times of the microwave emission (from Asai et al., 2001

When the line of sight has a significant component parallel to the plane of the oscillations, the kink mode can be detected with spectral instruments through the periodically modulated Doppler shift. For example, $300 s$ , $80 s$ , and $43 s$ periodicities were found by Koutchmy et al. (1983

) in the Doppler shift of the green coronal line. In this event, no prominent intensity variations were observed. These oscillations were interpreted as standing kink waves by Roberts et al. (1984