6.1 Observational results

One of the most wide-spread examples of the coronal wave activity is the slow propagating intensity disturbances observed with imaging telescopes in both open and closed coronal magnetic structures. The standard detection technique is the use of the stroboscopic method: the emission intensities along a chosen path, taken in different instants of time are laid side-by-side to form a time-distance map. Diagonal stripes on these maps exhibit disturbances which change their position in time and, consequently, propagate along the path. This method allows the determination of periods (or wavelengths), relative amplitudes and projected propagation speeds. Usually these waves are observed propagating along the assumed coronal magnetic structures and, thus, along the magnetic field. Their speeds are usually much slower than the expected coronal Alfvén speed which leads to their interpretation as longitudinally propagating slow magnetoacoustic (aka acoustic or longitudinal) waves. The first observational detection of longitudinal waves came from analysing the polarised brightness (density) fluctuations. The fluctuations with periods of about $9 min$ , were detected in coronal holes at a height of about $1.9Ro .$ by Ofman et al. (1997 , 1998b ) using the white light channel of SOHO/UVCS. Developing this study and analysing several other UVSC data sequences with a $75- 125 s$ cadence time, Ofman et al. (2000b ) determined the fluctuation periods in the range of $7- 10 min$ . The propagation speeds of the fluctuations indicated values in the range of $-1 160 -260 km s$ at $2Ro .$ . This value of the speed is slightly below the estimated value of the sound speed. Possibly, a similar phenomenon was observed by Marsh et al. (2002 ), who detected quasi-periodic variability of coronal EUV emission lines covering a temperature range of $log T = 5.3-6.1 K e$ with SOHO/CDS. Statistically significant periods were found within the range $100 -900 s$ and $1500 s$ , also short wavepackets with periods of the order $50 -100 s$ with durations of $2- 5$ cycles were reported.

DeForest and Gurman (1998 ), using EIT 171 Å data confirmed this discovery: Outwardly propagating perturbations of the intensity were observed at distances of $1.01- 1.2Ro .$ , gathered in quasi-periodic groups of $3 -10$ periods, with periods of about $10- 15 min$ , The projected speeds are about $75 -150 km s-1$ and the relative amplitude (in density) was about $2- 4 %$ .

A similar phenomenon was observed near the footpoints of coronal loops, with EIT (Berghmans and Clette, 1999 ) and TRACE (Nightingale et al., 1999 ; De Moortel et al., 2000 , 2002a ,b ) imagers as near-isothermal EUV intensity disturbances, which start near the loop footpoints and propagate along the loops at the apparent speed lower than the sound speed. Multi-wavelength observations have been performed by Robbrecht et al. (2001 ) combining TRACE 171 Å and EIT 195 Å and by King et al. (2003 ) with TRACE 171 Å and 195 Å. Robbrecht et al. (2001 ) found the projected propagation speeds to vary roughly between $65$ and $150 km s- 1$ for both instruments, which is close to and below the expected sound speed in the coronal loops, respectively. King et al. (2003 ) pointed out the high correlation of the disturbances observed in the different bandpasses. Also, recently, a coordinated observation of this phenomenon with SOHO/CDS and TRACE instruments has been carried out Marsh et al. (2003 ). A propagating oscillation with a period of about $300 s$ , observed by TRACE in the 171 Å bandpass, was also observed in He I, O V and Mg IX emission lines with CDS, corresponding to the chromospheric, transition region, and coronal temperatures, respectively. This is consistent with about $5 min$ oscillations observed by O’Shea et al. (2001 ) with CDS in both velocity and intensity time series associated with the coronal lines Mg IX and Fe XVI, as well as in O V.

A comprehensive overview of observational properties of the longitudinal oscillations, based upon the analysis of $38$ examples, is given in De Moortel et al. (2002a ), and a more recent one in Nakariakov (2003 ). The properties of propagating EUV disturbances may be summarised as follows: the projected propagation speed is $35 - 165 km s-1$ ; the amplitudes are always less than $10 %$ in intensity (less than $5 %$ in density); the disturbances are quasi-periodic with the periods about $140 -420 s$ . In most cases, only upwards propagating disturbances have been detected (from the footpoints to the apex of the loop). Sometimes, the waves can be present for several consecutive hours with, more or less, constant period. It is possible that the disturbances with shorter, about $3 min$ , periods are situated above sunspot regions, whereas disturbances propagating along the loops which are not associated with sunspots have longer periodicity, of about $5 min$ (De Moortel et al., 2002c ). However, King et al. (2003 ) showed that both $3 min$ and $5 min$ perturbations can coexist in the same coronal structure, at least in the analysed example, so the question still remains open.

The propagation direction and speed, together with the fact that the observed waves are compressible suggest their interpretation as slow magnetoacoustic waves. Slow waves of the observed periodicities (shorter than $20 min$ ) can propagate without reflection in the $1.0- 2.0 MK$ corona, as the acoustic cut-off period is about $70 min$ . According to this interpretation, the waves propagate at about the sound speed in the loop. The observed speed of the waves is reduced by line-of-sight projection.

Waves were also recently detected in the Doppler velocity data in the $1 -3 mHz$ and $5- 7 mHz$ ranges by Sakurai et al. (2002 ). The line intensity and line width did not show clear oscillations, but their phase relationship with the Doppler velocity indicates propagating waves rather than standing waves. These waves were interpreted as superposition of propagating slow and Alfvén waves.