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Astron. Astrophys. 362, 1151-1157 (2000)

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1. Introduction

Magnetohydrodynamic waves are believed to play a very important role in the solar corona. In particular, the waves have been theoretically discussed for a couple of decades as a possible source for heating of the coronal plasma and acceleration of the solar wind. However, the main difficulty with testing of the theories has been connected with the lack of observational knowledge on the coronal wave activity. Before SOHO and TRACE, apart from the confident registration of oscillations in prominences (Oliver 1999), main information on coronal oscillations came from the radio band (e.g. see Aschwanden 1987 for a review) and there had only been a few observational reports of waves or oscillations of coronal structures: in coronal green line (Koutchmy et al. 1983), EUV (e.g. Chapman et al. 1972, Antonucci et al. 1984) and soft X-rays (Harrison 1987).

Only with SOHO/EIT and TRACE imaging telescopes, the direct detailed observation and investigation of coronal waves have become possible. Indeed, for the last few years, several types of coronal waves have been discovered. In particular, Thompson et al. (1999) have detected and investigated a global coronal wave generated by the coronal mass ejection or a flare and occupying a significant part of the solar disk. This wave has been called a coronal Moreton wave or EIT wave. This wave is propagating transversely to coronal structures, and is therefore most likely a fast magnetoacoustic wave. The coronal Moreton waves can interact with various coronal structures, generating secondary oscillations and waves in these structures, such as kink oscillations of coronal loops, detected with TRACE (Aschwanden et al. 1999a, Nakariakov et al. 1999).

Analyzing temporal and spatial variation of the emission intensity with SOHO/EIT, DeForest & Gurman (1998) have detected and investigated propagating disturbances of intensity emission at the 171 Å line, in polar plumes. These waves are observed at the distance of 1.01-1.2 [FORMULA] out of the limb. The quasi-periodic (with periods of about 10-15 min) groups of 3-10 periods, with the roughly balanced duty cycle are propagating outwardly with the speeds of about 75-150 km/s. The amplitude of the intensity perturbations is about 2% of the background. The ratio of the wave amplitude (in intensity) to the background value grows with height (Ofman et al. 1999). These propagating disturbances are probably connected with the periodic density fluctuations (periods [FORMULA] min), detected in coronal holes at 1.9[FORMULA] by Ofman et al. (1997, 1998, 2000) using white light channel of the SOHO/UVCS.

Taking into account these observational findings, the propagating compressive disturbances have been confidently interpreted as slow magnetoacoustic waves (Ofman, Nakariakov & Deforst 1999; Ofman, Nakariakov & Sehgal 2000). It has been understood that the main factors affecting the wave evolution are (a) gravitational stratification, leading to amplification of the relative amplitude of the wave, (b) dissipation, extracting the wave energy in the high wave number domain of the spectrum, and (c) nonlinearity, generating higher harmonics and responsible for the wave steepening and consequent enhanced dissipation. An evolutionary equation of the Burgers type, combining action of all of these three mechanisms, has been derived. Also, full MHD nonlinear numerical simulations of the slow wave dynamics have been undertaken. A perfect agreement of the numerical and analytical results, and a good qualitative agreement of the theoretical studies and observational finding have been found.

Investigating dynamics of on-disc coronal active regions, Berghmans & Clette (1999) and Robbrecht et al. (1999), using SOHO/EIT, have detected compressive disturbances propagating along coronal loops. This discovery has been confirmed by Berghmans et al. (1999) and De Moortel et al. (2000) with TRACE. The results turned out to be very similar to the polar plume waves discussed above. Here, there is a brief summary of the observational findings:

  1. Perturbations of the intensity (plasma density), propagating upwardly along long coronal loops have been detected at the EIT 195 Å (Berghmans & Clette 1999) and TRACE 171 Å (Berghmans et al. 1999, De Moortel et al. 2000) bandpasses.

  2. The projections of the propagation speeds are about 65-165 km s-1 (Berghmans & Clette 1999), or [FORMULA] km s-1 (De Moortel et al. 2000).

  3. Amplitude is [FORMULA]% in intensity ([FORMULA]% in density) in both 171 Å and 195 Å bandpasses.

  4. The periods are about 180-420 s (De Moortel et al. 2000). The periods are well below the acoustic cut-off period, which is about 87 min.

  5. The disturbances often show an exponential decay with the decay time of the order of 1.5-2 min (Robbrecht et al. 1999).

According to reports of both these groups, in most cases, only upwardly (from loop footpoints to loop apexes) propagating disturbances have been detected. A multi-wavelength analysis of the propagating disturbances observed simultaneously with EIT and TRACE has recently been undertaken by Robbrecht et al. (2000) and has strengthen the previous findings.

The obvious similarity of compressive propagating disturbances observed in coronal loops and in polar plumes, suggests that, as well as in the plume case, the perturbations of the loops are slow magnetoacoustic waves . To support this interpretation, it is necessary to develop a theoretical model for slow magnetoacoustic waves propagating along long loops, similar to the theory of slow waves in plumes developed by Ofman, Nakariakov & Deforest (1999) and Ofman, Nakariakov & Sehgal 2000). The difference in the geometry of the magnetic structures supporting the waves, (in the plume case, it is a radially divergent magnetic flux tube, which cannot be used to model a loop), requires a creation of theory for slow waves in coronal loops. This theory has to incorporate effects of the gravitational stratification, nonlinearity, dissipation and loop curvature. The theory has to explain the observed facts of the evolution of the compressive waves in loops. In particular, the theory has to provide us with an answer to why only the upwardly propagating waves are seen in most cases.

The paper is organized as follows: the model analyzed and governing equations applied are discussed in Sect. 2, an evolutionary equation is derived in Sect. 3 and analyzed in Sect. 4. The summary of results obtained and comparison of the theoretical results with observational findings is presented in Conclusions.

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 2000