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Solar Physics DOI: 10.1007/·····-···-···-····-·

Present and Future Observing Trends in Atmospheric Magneto-seismology
D. Banerjee1 , R. ErdÈlyi2 , R. Oliver3 , E. O'Shea4
c Springer ····

Abstract With modern imaging and spectral instruments observing in the visible, EUV, X-ray and radio wavelengths, the detection of oscillations in the solar outer atmosphere has become a routine event. These oscillations are considered to be the signatures of a wave phenomenon and are generally interpreted in terms of magnetohydrodynamic (MHD) waves. With multi-wavelength observations from ground and space-based instruments, it has been possible to detect waves in a number of different wavelengths simultaneously and, consequently, to study their propagation properties. Observed MHD waves propagating from the lower solar atmosphere into the higher regions of the magnetized corona have the potential to provide an excellent insight into the physical processes at work at the coupling point between these different regions of the Sun. High-resolution wave observations combined with forward MHD modelling can give an unprecedented insight into the connectivity of the magnetized solar atmosphere, which further provides us with a realistic chance to reconstruct the structure of the magnetic field in the solar atmosphere. This type of solar exploration has been termed atmospheric magneto-seismology. In this review we will summarise some new trends in the observational study of waves and oscillations, discussing their origin, and their propagation through the atmosphere. In particular, we will focus on waves and oscillations in open (e.g., solar plumes) and closed (e.g., loops and prominences) magnetic structures, where there have been a number of observational highlights in the last few years. Furthermore, observations of waves in filament fibrils allied with a better characterization of their propagating and damping properties, the detection of prominence oscillations in UV lines, and the renewed interest in largeamplitude, quickly attenuated, prominence oscillations, caused by flare or explosive phenomena, will be addressed. Keywords: Coronal loops, MHD Waves, MHD Oscillations
Indian Institute of Astrophysics, Koramangala, Bangalore 560034 (e-mail: dipu@iiap.res.in) 2 Solar Physics and Space Plasma Research Centre (SP2 RC), Department of Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, (England) UK (e-mail: robertus@sheffield.ac.uk) 3 Departament de FÌsica, Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain (e-mail: ramon.oliver@uib.es) 4 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland (e-mail: eos@arm.ac.uk)
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1. Intro duction From Solar and Heliospheric Observatory (SOHO) and Transition Region And Coronal Explorer (TRACE) data, new results, that shed light onto dynamical events in the outer solar atmosphere, especially short time-scale variability and/or oscillations at EUV wavelengths, have emerged. The detection of waves in the outer solar atmosphere is made possible by the effect these waves have on the plasma. For example, the presence (or signature) of waves may be detected in the form of variations or oscillations in the radiant flux ("intensity"), due to changes in the plasma density, or in the line-of-sight velocities, due to motions in the plasma, both measurable from spectral lines. These periodic motions are generally interpreted in terms of magnetohydrodynamic (MHD) waves. They carry information from the emitting regions allowing a diagnosis of the frozen-in magnetic fields as well as the plasma contained in different magnetic structures, e.g., coronal loops. The wavelengths of these waves are often comparable to the characteristic sizes of coronal structures, their time scales are in the range of seconds to minutes and they are detectable from space and by ground-based instruments, e.g., the detection of EIT (or coronal Moreton) waves (Thompson et al., 1998), compressible waves in polar plumes (Ofman et al., 1997; DeForest and Gurman, 1998) or periodic phenomenon in the corona from ground-based observations (Aschwanden, 1987). Thus, imaging instruments (from space and ground) have uncovered a myriad of wave detections in the corona, which have been reviewed at length in Aschwanden (2003, 2004, 2006), De Moortel (2005, 2006), De Pontieu and ErdÈlyi 2006, ErdÈlyi, (2006a,b), Nakariakov and Roberts, (2003), Nakariakov and Verwichte, (2005), Nakariakov, (2006) and Wang, (2004). In this review we will report on current trends in the observational study of MHD waves. Summaries will be provided for imaging observations together with a slightly more detailed description of spectral methods as these have not been dealt with in previous reviews. It is not the purpose or intention of this review to make an exhaustive list of all observations. Instead, we seek to present a complementary view to those mentioned above by focusing on some recently reported observations of waves, particularly those related to spectroscopic and not imaging methods. We will also briefly address the status of prominence oscillations in a separate section, stressing their importance as a natural example and as a tool for studying wave signatures.

2. MHD Waves in the Lower Solar Atmosphere The solar atmosphere from its visible lower boundary, the photosphere, through a transitional layer with sharp gradients, up to its open-ended magnetically dominated upper region, the corona, is magnetically coupled. This physical coupling is obvious when one overlays concurrently taken snapshots of the various solar atmospheric layers as a function of height and a magnetogram obtained at the same time at photospheric heights. A typical magnetic field concentration, e.g., an active region or an intense flux tube, will show up as a strong brightening at corresponding locations in the UV, EUV, and X-ray images indicating evidence in support of the coupling of the all pervasive magnetic field. Recent high-resolution satellite, and ground-based technology provides us with unprecedented fine-scale spatial and temporal resolution data of different magnetic

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structures in the solar atmosphere (e.g., plumes, coronal loops, arcades, and even dynamic features such as spicules) that support periodic motions (propagating waves or oscillations) on wide spatial and time scales. The large concentrated magnetic structures at photospheric to low-TR and coronal heights serve as excellent waveguides for the propagation of perturbations excited at footpoint locations. These observed oscillations within the magnetic structures, being intrinsically locked into them (in contrast to the acoustic solar global oscillations that are ubiquitous in the solar interior) provide us with the tools to diagnose the structures themselves. 2.1. Wave leakage from the photosphere As the acoustic wave frequency increases beyond 5.3 mHz, the upper boundary of subsurface cavities becomes increasingly transparent and the acoustic waves are able to propagate into the Sun's chromosphere. The high-frequency waves may therefore convey information about the properties of the chromosphere. Using time-distance analysis of solar acoustic waves with frequencies above the nominal atmospheric acoustic cutoff frequency (5.3 mHz) Jefferies et al., (1997) showed that the waves can be partially reflected at both the Sun's photosphere and a layer located higher in the atmosphere. From one dimensional spectroscopic observations, Baudin, Bocchialini and Koutchmy, (1996) showed for the first time that upward propagating five minute waves emerge from the deep chromospheric network. They suggested that the waves propagating in the open corona are reminiscent of photospheric oscillations transmitted by the magnetic field of the chromospheric network. Using the Magneto-Optical filters at Two Heights (MOTH) instrument, Finsterle et al., (2004) have recorded simultaneous dopplergrams at a high cadence (ten second sampling intervals) in two Fraunhofer lines formed at different heights in the solar atmosphere. They found evanescent-like waves at frequencies substantially above the acoustic cut-off frequency in regions of intermediate magnetic field. Furthermore, upwardlyand downwardly-propagating waves were detected in areas of strong magnetic field such as sunspots and plage: even at frequencies below the acoustic cut-off frequency. They conjectured that the interaction of the waves with the magnetic field must be a non-linear process depending on the field strength and/or inclination. Very recent observations of the transition region (hereafter, TR), in particular spicules and moss oscillations, detected by TRACE and by SUMER on board SOHO brings us closer to an understanding of the origin of running (propagating) waves in coronal loops. The correlations on arcsecond scales between chromospheric and transition region emission in active regions were studied in De Pontieu, Tarbell, and ErdÈlyi (2003). The discovery of active region moss (Berger et al., 1999), i.e., dynamic and bright upper transition region emission above active region (AR) plage, provides a powerful diagnostic tool to probe the structure, dynamics, energetics and coupling of the magnetized solar chromosphere and transition region. De Pontieu, Tarbell, and ErdÈlyi (2003) studied the possibility of the direct interaction of the chromosphere with the upper TR, by searching for correlations (or lack thereof ) between emission at varying temperatures using concurrently observed EUV lines emitted from the low chromosphere (Ca II K-line), the middle and upper chromosphere (H ), the low TR (C iv 1550 å at 0.1 MK), and from the upper TR (Fe ix/x 171 å at 1 MK and Fe xii 195 å at 1.5 MK). The relatively high cadence (24 to 42 second) data sets obtained with the Swedish Vacuum Solar Telescope (SSVT, La Palma) and TRACE allowed them to find a relationship between upper TR oscillations and low-lying

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Figure 1. Demonstrating the using wavelet power spectra for for TRACE 171 å (full, with tr Units of intensity are arbitrary

correlation between chromospheric and upper-TR oscillations TRACE 171 å, H - 350 må, H + 350 må and light curves iangles), H - 350 må (full blue) and H + 350 må (full red). (From De Pontieu, 2004).

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photospheric oscillations. Figure 1 (from De Pontieu, 2004) shows a typical example demonstrating the correlation between chromospheric and upper-TR oscillations. The wavelet power spectra for TRACE 171 å (top panel), H ­ 350 må (second from top), H +350 må (third panel from top) and light-curves (bottom panel) for TRACE 171 å (full, with triangles), H ­ 350 må (full blue) and H + 350 må (full red), are quite similar, despite the atmospheric-seeing deformations the ground-based data suffer from. While there is generally a good correlation between the TRACE 171 å signal and the wings of H , there is often a delay between the H ­ 350 må and H + 350 må signals, usually of the order of 60 to 100 seconds. A simple estimate using this phase delay and the physical distance between the line formation of TRACE Fe IX/X 171 å lines has led to the possible conclusion of direct wave leakage. This correlation analysis provides clues to the understanding of the coupling between the different layers of the solar atmosphere. De Pontieu, ErdÈlyi, and de Wn (2003a) analysed intensity oscillations in the upper- TR above AR plage. They suggested the possible role of a direct photospheric driver in TR dynamics, e.g., in the appearance of moss (and spicule) oscillations. Wavelet analysis of the observations (by TRACE) found strong ( 5 ­ 15%) intensity oscillations in the upper TR footpoints of hot coronal loops. A range of periods from 200 to 600 seconds, typically persisting for about four to seven cycles was found. A comparison with photospheric vertical velocities (using the Michelson Doppler Imager onboard SOHO) revealed that some upper TR oscillations showed a significant correlation with solar global acoustic p-modes in the photosphere. In addition, the ma jority of the upper-TR oscillations were directly associated with upper chromospheric oscillations observed in H , i.e., periodic flows in spicular structures. The presence of such strong oscillations at low heights (of the order of 3 000 km) provides an ideal opportunity to study the direct propagation of oscillations from the photosphere and chromosphere into the TR (De Pontieu, ErdÈlyi, and James 2004) and low magnetic corona (see, for example, De Pontieu, ErdÈlyi, and De Moortel 2005). These type of measurements can also help us to (i) understand atmospheric magnetic connectivity, that is so crucial for diagnostic reconstruction in the chromosphere/TR, and shed light on the dynamics of the lower solar atmosphere, e.g., the source of chromospheric mass flows such as spicules (e.g., De Pontieu, ErdÈlyi, and James 2004); (ii) explore the dynamic and magnetised lower solar atmosphere using the method of seismology. This latter aspect is discussed in detail in recent review papers by e.g., De Pontieu and ErdÈlyi (2006) and ErdÈlyi (2006a). On the nature of oscillations in sunspots, Bogdan (2000) has summarized the observational and theoretical components of the sub ject in a coherent, common, and conceptual manner. We will not carry out a detailed review of this sub ject here but we would like to mention some recent developments. O'Shea, Muglach and Fleck (2002) reported oscillations within the umbra at different temperatures, from the temperature minimum as measured by TRACE 1700 å up to the upper corona as measured by CDS Fe xvi 335 å (log T = 6.4 K). Using cross-spectral analysis, time delays were found between low- and high-temperature emission suggesting the possibility of both upward and downward wave propagation. Earlier observations indicated that the waves responsible for these oscillations may not be reaching the corona. Based on a similar observing campaign as O'Shea, Muglach and Fleck (2002), and using TRACE and SOHO, Brynildsen et al., (2002) found that the oscillation amplitude above the umbra increases with increasing temperature, reaching a maximum for emission lines

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a b

Figure 2. Leakage of evanescent photospheric p-mode power into the chromosphere. Distribution of wavelet power (for cases a and b, respectively = 0 and 50 ), in arbitrary units, independent for each height as a function of wave period for different heights above the photosphere. Vertical flux tubes (a) allow minimal leakage of p modes with periods of 300 seconds (> Pc 220 seconds), so that only oscillations with lower periods (< 250 seconds) can propagate and grow with height to dominate chromospheric dynamics. Inclined flux tubes (b) show an increased acoustic cut-off period Pc , allowing enhanced leakage and propagation of normally evanescent p modes. Adapted from De Pontieu, Erd´lyi, and James (2004). e

formed close to 1 ­ 2â105 K, and decreasing for higher temperatures. Furthermore, they report that three minute oscillations fill the sunspot umbra in the transition region, while in the corona the oscillations are concentrated in smaller regions that appear to coincide with the endpoints of sunspot coronal loops. This suggests that wave propagation along the magnetic field makes it possible for oscillations to reach the corona. However, it must be pointed out that Doyle, DzifÀkovÀ, and Madjarska (2003) discussed the possibility that the observed oscillations seen in TRACE 171 å by Brynildsen et al., (2002) and Mg ix 368 å (and other coronal lines) by O'Shea, Muglach and Fleck (2002) may not actually be coronal in origin due to the effect of non-Maxwellian contributions. 2.2. The Source of Propagating Waves In order to answer the question of where propagating coronal waves originate from, and, inspired by the observational findings of similarities between photospheric and TR oscillations, De Pontieu, ErdÈlyi, and James (2004) developed the general framework of how photospheric oscillations can leak into the atmosphere along inclined magnetic-flux tubes. In a non-magnetic atmosphere p modes are evanescent and cannot propagate upwards through the temperature minimum barrier since their period P ( 200 ­ 450 seconds) is above the local acoustic cut-off period Pc 200 seconds. However, in a magnetically structured atmosphere, where the field lines have some natural inclination (), where is measured between the magnetic guide channelling he oscillations and the vertical, the acoustic cut-off period takes the t form Pc T / cos with the temperature T . This inclination will allow some nonpropagating evanescent wave energy to tunnel through the temperature minimum into the hot chromosphere of the waveguide, where propagation is once again possible because of higher temperatures (Pc > 300 seconds). The authors have shown that the inclination of magnetic flux tubes (applicable, e.g., to plage regions) can

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Figure 3. Wavelet power of loop intensity oscillations as a function of time and wave period, as observed with TRACE (top panel, case 16a of De Moortel et al., (2002a)) and for simulations (bottom panel) driven by MDI velocities at the loop footpoint region. Middle panel shows the running difference (I ) of loop intensity at one location (relative to total intensity I ) as a function of time for observations (full line, diamonds) and simulations (dashed). The area contained between the horizontal axis and cone of influence is free of edge effects introduced by the wavelet analysis. Adapted from De Pontieu, Erd´lyi, and De Moortel (2005). e

dramatically increase tunnelling, and may even lead to direct propagation of p-modes along inclined field lines, as plotted in Figure. 2. McIntosh and Jefferies (2006) have demonstrated observationally that the acoustic cutoff frequency in the lower solar chromosphere can be modified by changing the inclination of the magnetic field in the lower solar chromosphere. Though they have demonstrated this effect from a study of a sunspot with TRACE, they expect a similar modification of cutoff frequency to occur whenever plasma conditions permit (low- , high-inclination magnetic fields) elsewhere on the Sun, in particular in magnetically- intense network bright points anchored in super-granular boundaries. A natural generalisation of the above idea was put forward by De Pontieu, ErdÈlyi, and De Moortel (2005) who proposed that a consequence of the leakage of photospheric oscillations is that spicule driven quasiperiodic shocks propagate into the low corona, where they may lead to density, and thus intensity oscillations with properties similar to those observed by TRACE in one MK coronal loops. In other words, the origin of the propagating slow MHD waves detected in coronal loops (see a recent review on their properties by, e.g., De Moortel, 2006) is linked to wave energy leakage of solar global standing oscillations. De Pontieu, ErdÈlyi, and De Moortel (2005) highlighted that oscillations along coronal loops associated with AR plage have many properties that are similar to those of moss oscillations: (i) the range of periods is from 200 to 600 seconds, with an average of 350 ± 60 seconds and 321 ± 74 seconds, for moss and coronal oscillations, respectively; (ii) the spatial extent for coherent moss oscillations is about 1 ­ 2 ,

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whereas for coronal waves, the spatial coherence is limited to 2 in the direction perpendicular to that of wave propagation. They also point out that, although the oscillations in moss and corona have similar origins, they are the result of different physical mechanisms: moss oscillations occur because of periodic obscuration by spicules, and coronal oscillations arise from density changes associated with the propagating magneto-acoustic shocks that drive the periodic spicules. A typical example of a comparison of the observed properties of coronal intensity oscillations with synthesized observations is shown in Figure. 3.

3. Propagating Waves into the Corona In the pre-SOHO/TRACE era, the first observations of MHD waves in the corona were reported by Chapman et al., (1972) with the GSFC extreme-ultraviolet spectroheliograph on OSO-7 (the spatial resolution was a few arcsec, the cadence time was 5.14 seconds). In Mg vii, Mg ix and He ii emission intensity periodicity of about 262 seconds was detected. The importance of this early work is that within the range of low-frequencies, an analogy to photospheric and chromospheric oscillations was found and, it was further speculated that the photospheric and chromospheric evanescent waves become vertically propagating, gravity-modified acoustic waves at a height in the chromosphere where a temperature rise admits propagation again. Antonucci, Gabriel, and Patchett (1984) using the Harvard College Observatory EUV spectroheliometer on Skylab detected oscillations in the C ii, O iv, and Mg x emission intensity with periods of 117 seconds and 141 seconds. They suggested that the intensity fluctuation of the EUV lines was caused by small amplitude waves, propagating in the plasma confined in the magnetic loop, and that the size of the loop might be important in determining its preferential heating in the active region. A final example from that era, though at much shorter wavelengths, is the observation by Harrison (1987), who detected, with the Hard X-ray Imaging Spectrometer onboard SMM, soft X-ray (3.5 ­ 5.5 keV) pulsations of 24 minute period lasting for six hours. The periodicity was thought to be produced by a standing wave or a travelling wave packet which existed within the observed loop. It was concluded that the candidates for the wave were either fast- or AlfvÈn- MHD modes of AlfvÈnic surface waves. Since the launches of SOHO and TRACE, and the abundant evidence that has emerged for MHD phenomena and, in particular, propagating waves, our views have changed considerably. However, the source of propagating waves still remains a puzzle. 3.1. Waves in Open Structures Propagating waves may propagate in open (e.g., plumes) and closed (e.g., loops) coronal magnetic structures. The first undoubted detection of propagating slow MHD waves was made by the Ultraviolet Coronagraph Spectrometer (UVCS/SOHO). Detection of slow waves in an open magnetic structure high above the limb of coronal holes was reported by Ofman et al., (1997, 2000a). DeForest and Gurman (1998), analysing Extreme-ultraviolet Imaging Telescope (EIT/SOHO) data of polar plumes, detected similar compressive disturbances with linear amplitudes of the order of 10 ­ 20% and periods of 10 ­ 15 minutes. Ofman, Nakariakov, and DeForest (1999)

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Observing Trends in Atmospheric Magneto-seismology Table 1. Overview of the periodicities and propagation speeds of propagating slow MHD waves detected in coronal structures. Authors Berghmans and Clette (1999) Nightingale, Aschwanden, and Hurlburt (1999) Schrver et al. (1999) Banerjee, O'shea, and Doyle (2000) Banerjee et al., (2001a) Banerjee et al., (2001b) De Moortel, Ireland, and Walsh (2000) Robbrecht et al., (2001) Berghmans, McKenzie, and Clette (2001) De Moortel et al., (2002a) De Moortel et al., (2002b) Sakurai et al., (2002) King et al., (2003) Popescu et al., (2005) O'Shea, Banerjee, and Doyle (2006) O'Shea, Banerjee, and Doyle (2007) Perio d (s) 600 ­ 300 600 ­ 1200 (plume) 1200 ­ 1800 (inter-plume) 600 ­ 1200 (coronal hole) 180 ­ 420 (282 ± 93) 172 ± 32 (sunspot) 321 ± 74 (plage) 180 ­ 600 120 ­ 180 & 300 ­ 480 600 ­ 5400 & 10200 (off-limb) 300 ­ 1000(off-limb) 300 ­ 1000(coronal hole) Speed (km/s) 75 ­ 200 130 ­ 190 70 ­ 100 70 ­ 165 65 ­ 150 300 122 ± 43 100 ­ 200 25 ­ 40 ­ 150 ­ 170 50 ­ 70 Wavelength 195 171 & 195 195 629 629 629 171 171 & 195 SXT 171 171 171 5303 171 & 195 SUMER CD S CD S

and Ofman, Nakariakov, and Seghal (2000b) identified the observed compressive longitudinal disturbances as propagating slow MHD waves. We have summarized the main features of the observed oscillations following De Moortel (2006) in Table 1. A number of studies using the CDS and SUMER spectrographs on SOHO have reported oscillations in plumes, interplumes and coronal holes in the polar regions of the Sun (e.g., Banerjee, O'shea, and Doyle 2000; 2001a,b, O'Shea, Banerjee, and Doyle , 2006; 2007). All of these studies point to the presence of compressional waves, thought to be slow magnetoacoustic waves as found by DeForest and Gurman (1998). The detected damping of slow propagating waves was attributed to compressive viscosity. Up to now evidence for the fast magnetoacoustic wave modes in these same regions has been absent, even though recent results by Verwichte, Nakariakov, and Cooper (2005) have shown that propagating fast magnetoacoustic waves can be present in open magnetic field structures, albeit in this instance, in a post-flare supra-arcade. For the fast mode the wavelengths of the propagating wave should be much shorter than the size of the structure guiding the wave. Shorter wavelength implies shorter period, thus it demands high cadence observations. TRACE can work on 20 ­ 30 second cadence, allowing us to detect a wave with a 40 ­ 60 second periodicity at

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best. Thus it is difficult to detect smaller periodicity with the present space-based instruments, whereas ground-based coronagraphs and radioheliographs have much better time resolution and have been used for the detection of short-period waves. 3.2. Waves in Closed Structures Koutchmy, Zhugzhda, and Locans (1983) devoted an experiment to the search for short period coronal waves using the green coronal line 5303 å of Fe xiv. Their power spectra showed evidence of Doppler-velocity oscillations with periods near 300 seconds, 80 seconds, and, especially, 43 seconds. However no prominent intensity fluctuations were reported. Though Koutchmy considered that their oscillations were due to resonant AlfvÈn oscillations viewed at a low level through several legs of coronal arches, later these data were re-interpreted as standing kink waves by Roberts, Edwin, and Benz (1984). The first detection of microwave quasi periodic pulsations, with a periodicity of 6.6 seconds, which could be associated with the fast kink mode was performed by Asai et al., (2001) with the Nobeyama radioheliograph. Four bursts were observed with the hard X-ray telescope onboard YOHKOH and the Nobeyama Radioheliograph during the impulsive phase of the flare. Williams et al., (2001, 2002) and Katsiyannis et al., (2003) reported on the presence of high-frequency MHD waves in coronal loops observed during a total solar eclipse with the SECIS instrument. The detections lie in the frequency range 0.15 ­ 0.25 Hz (4 ­ 7 seconds), last for at least 3 periods at a confidence level of more than 99%, and arise just outside known coronal loops. This led them to suggest that they occur in low emission-measure or different temperature loops associated with active regions. Madjarska et al., (2003), using a number of different transition region and coronal lines from SUMER on SOHO, were the first to report oscillations in coronal bright points, finding a periodicity of six minutes Ugarte-Urra et al., (2004), using data from CDS on SOHO, found evidence of oscillations occurring with periods between 420 ­ 650 seconds in a number of TR lines (O v and O iii) but none in the coronal line of Mg ix. They also report on a separate measurement of an oscillation with a period of 491 second period observed with the transition region line of S iv of SUMER in a bright point. Using EIT/SOHO, Berghmans and Clette (1999) were the first to report on slow modes in closed loop structures. Following the success of SOHO, observers using TRACE also searched successfully for quasi-periodic disturbances in coronal loops (e.g., Schrver et al., 1999; Nightingale, Aschwanden, and Hurlburt 1999; De Moortel, Ireland, and Walsh 2000). A detailed overview of the observed properties of these propagating intensity perturbations is given by De Moortel et al., (2002a, b). From a ground-based coronagraphic observation at the Norikura Solar Observatory, Sakurai et al., (2002) have reported on the detection of coronal waves from Doppler velocity data. The propagation speed of the waves was estimated by correlation analysis. The line intensity and line width did not show clear oscillations, but their phase relationship with the Doppler velocity indicated propagating waves rather than standing waves. In all of the reported cases, the phase speed is of the order of the coronal sound speed. In TRACE observations the propagating waves are observed as intensity oscillations, hence they are likely to be candidates for compressive disturbances. No significant acceleration or deceleration was observed. The combination of all of

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these facts leads to the most plausible conclusion that the observed propagating waves are indeed slow MHD waves. 3.3. Detection of Waves Through Statistical Methods Most of the aforementioned detection was restricted to a few specific case studies. A new approach has been taken up by O'Shea et al., (2001), where wavelets were used to measure oscillations in a statistical manner. A novel randomisation method was used to test their significance. This form of statistical testing is us