Oscillations and waves in solar spicules
aa r X i v : . [ a s t r o - ph . S R ] J un Noname manuscript No. (will be inserted by the editor)
Oscillations and waves in solar spicules
T.V. Zaqarashvili · R. Erd´elyi
Received: date / Accepted: date
Abstract
Since their discovery, spicules have attracted increased attention as en-ergy/mass bridges between the dense and dynamic photosphere and the tenuous hotsolar corona. Mechanical energy of photospheric random and coherent motions can beguided by magnetic field lines, spanning from the interior to the upper parts of the solaratmosphere, in the form of waves and oscillations. Since spicules are one of the mostpronounced features of the chromosphere, the energy transport they participate in canbe traced by the observations of their oscillatory motions. Oscillations in spicules havebeen observed for a long time. However the recent high-resolutions and high-cadencespace and ground based facilities with superb spatial, temporal and spectral capacitiesbrought new aspects in the research of spicule dynamics. Here we review the progressmade in imaging and spectroscopic observations of waves and oscillations in spicules.The observations are accompanied by a discussion on theoretical modelling and inter-pretations of these oscillations. Finally, we embark on the recent developments madeon the presence and role of Alfv´en and kink waves in spicules. We also address the ex-tensive debate made on the Alfv´en versus kink waves in the context of the explanationof the observed transverse oscillations of spicule axes.
Keywords · · T.V. ZaqarashviliAbastumani Astrophysical Observatory at the Faculty of Physics and Mathematics, I.Chavchavadze State University, Chavchavadze Ave. 32, Tbilisi 0179, GeorgiaTel.: +995-32-294714Fax: +995-32-220009E-mail: [email protected]. Erd´elyiSolar Physics & Space Plasma Research Centre (SP RC)Department of Applied MathematicsUniversity of SheffieldSheffield S3 7RH, UKE-mail: robertus@sheffield.ac.uk
The rapid rise of plasma temperature up to 1 MK from the solar photosphere towardsthe corona is still an unresolved problem in solar physics. It is clear that the mechanicalenergy of sub-photospheric motions is transported somehow into the corona, where itmay be dissipated leading to the heating of the ambient plasma. A possible scenario ofenergy transport is that the convective motions and solar global oscillations may excitemagnetohydrodynamic (MHD) waves in the photosphere, which may then propagatethrough the chromosphere carrying relevant energy into the corona. It is of great desirethat the energy transport process(es) can be tracked by observational evidence of theoscillatory phenomena in the chromosphere. For a detailed discussion about MHDwave heating and heating diagnostics in the solar atmosphere see the recent work byTaroyan and Erd´elyi (2009).Much of the radiation from the upper chromosphere originates in spicules , which aregrass-like spiky features seen in chromospheric spectral lines at the solar limb (see Fig1). These abundant and spiky features in the chromosphere were discovered by Secchi(1877) and were named ”spicules” by Roberts (1945). Beckers (1968, 1972); Sterling(2000) dedicated excellent reviews to summarizing the observational and theoreticalviews about spicules at that time. Since these reviews, many observational reports of oscillatory phenomena in spicules appeared in the scientific literature. In particular,it is anticipated that signatures of the energy transport by MHD waves through thechromosphere may be detectable in the dynamics of spicules. A comprehensive reviewsummarizing the current views about the observed waves and oscillations in spicules, tothe best of our knowledge, is still lacking and such a summary has not been publishedyet in the literature. Here we aim to fill this gap.The goal of this review is to collect the reported observations about oscillationsand waves in spicules, so that an interested reader could have a general view of thecurrent standing of this problem. Here, we concentrate only on observed oscillatory andwave phenomena of spicules and their interpretations. We are not concerned about themodels of spicule generation mechanisms; the interested reader may find these lattertopics in the recent review by Sterling (2000) or in De Pontieu and Erd´elyi (2006).Section 2 is a short summary about the general properties of spicules, Section 3describes the oscillation events reported so far for solar limb spicules, Section 4 outlinesthe views and discussions about the interpretation of spicule oscillations and Section 5summarizes the main results and suggests future directions of research.
Spicules appear as grass-like, thin and elongated structures in images of the solar loweratmosphere and they are usually detected in chromospheric H α , D and Ca II H lines.These spiky dynamic jets are propelled upwards (at speeds of about 20 km s − ) fromthe solar surface (photosphere) into the magnetized low atmosphere of the Sun. Accord-ing to early, but still valid estimates by Withbroe (1983) spicules carry a mass flux ofabout two orders of magnitude that of the solar wind into the low solar corona. Withdiameters close to observational limits ( <
500 km), spicules have been largely unex-plained. The suggestion by De Pontieu et al. (2004) and De Pontieu and Erd´elyi (2006)of channeling photospheric motion, i.e. the superposition of solar global oscillations and convective turbulence, has opened new avenues in the interpretation of spicule dynamics
Fig. 1
High resolution image of spicules at the solar limb in Ca II H line taken by SolarOptical Telescope (SOT) on board of Hinode spacecraft (November 22, 2006). (see also Hansteen et al. (2006); De Pontieu et al. (2007c); Rouppe van der Voort et al.(2007); Heggland et al. (2007)). The real strength of the observations and the forwardmodelling by De Pontieu and Erd´elyi is that, as opposed to earlier existing models,they could account simultaneously for spicule ubiquity, evolution, energetics and therecently discovered periodicity (De Pontieu et al. (2003a,b)) of spicules.Excellent summaries about the general properties of spicule (labelled these days astype I spicules) have been presented almost forty years ago by Beckers (1968, 1972)and we broadly recall these findings here. Moreover, type II spicules were recentlydiscovered with Hinode and have very different properties from the classical spicules(De Pontieu et al. (2007b)).2.1 DiameterMeasured range of spicule diameter from ground based observations was ∼ α (Beckers (1972)). However, the unprecedentedly high spatialresolution of Solar Optical Telescope on board of Hinode spacecraft (0.05 arc sec forCa II H and 0.08 arc sec for H α ) revealed fine structure of spicules. Fig 1. showsthis fine structure of spicules in Ca II H line at the solar limb taken by Hinode/SOTon November 11, 2006. The type II spicules discovered by Hinode/SOT have smallerdiameters ( ≤
200 km) in Ca II H line (De Pontieu et al. (2007b)), while the diameterof spicules in H α line seems to be wider ∼ Fig. 2
High resolution image of spicules on solar disc taken by Swedish Solar Telescope (SST)in La Palma, adopted from De Pontieu et al. (2004). α (Beckers (1972)) and may reach to 7000-11000 km heightsfrom the limb when observing by ground based coronagraphs. On the other hand, thetype II spicules dominate in lower heights: they are tallest in coronal holes reachingheights of 5000 km or more, while in quiet Sun regions they reach lengths of orderseveral megameters and they are shorter in active regions (De Pontieu et al. (2007b)).Additionally, very long spicules, called as macrospicules by Bochlin et al. (1975) withtypical length of up to 40 Mm are frequently observed mostly near the polar regionsas reported by e.g. Pike and Harrison (1997); Pike and Mason (1998); Banerjee et al.(2000); Parenti et al. (2002); Yamauchi et al. (2005); Doyle et al. (2005); Madjarska et al.(2006); O’Shea et al. (2005); Scullion et al. (2009); Nishizuka et al. (2009).2.3 Temperature and DensitiesSpicules have the temperatures and densities typical to the values of the chromosphericplasmas. Table 1 summarizes the typical electron temperatures ( T e ) and number densi-ties ( n e ) of spicule values at different heights above the limb (Beckers (1968)). Cautionhas to be exercised as values at 2000 and 10000 km heights are unreliable because ofinsufficient data. Typical electron density at the heights, where spicules are observed, ismuch lower ∼ cm − (Aschwanden (2004), Fig 1.19 therein), therefore spicules are much denser than their surroundings. Matsuno and Hirayama (1988) estimated lowertemperatures ( ∼ Table 1
Electron temperatures and densities inferred from spicule emission, after Beckers(1968)h(km) T e ( K ) n e (cm − )2 000 17 000 22 × × × ×
10 000 15 000 3.5 × Oscillations in solar limb spicules can be detected either by imaging or spectroscopic ob-servations. Imaging observations may reveal the oscillations in spicule intensity and thevisual periodic displacement of their axes. Imaging observations became especially im-portant after the recently launched Hinode spacecraft. SOT (Solar Optical Telescope)on board of Hinode gives unprecedented high spatial resolution images of chromosphere(see Fig. 1). On the other hand, the spectroscopic observations may give valuable in-formation about spicules through the variation of line profile. Variations in Doppler shift of spectral lines can provide information about the line-of-sight velocity. Throughspectral line broadening it is possible to estimate the non-thermal rotational veloci-ties leading to the indirect observations of e.g. torsional Alfv´en waves as suggested byErd´elyi and Fedun (2007), and reported recently by Jess et al. (2009) in the context ofa flux tube connecting the photosphere and the chromosphere. Jess et al. used the tech-nique of analysing Doppler-shift variations of spectral lines, based on the optically thickH α line for which a straightforward interpretation of linewidth changes and intensitychanges in terms of velocity and density are sometimes very difficult and appropriatecaution has to be exercised, and detected oscillatory phenomena associated with a largebright point group, located near solar disk centre. Wavelet analysis reveals full-widthhalf-maximum oscillations with periodicities ranging from 126 to 700 s originatingabove the bright point, with significance levels exceeding 99%. These oscillations, 2.7km s − in amplitude, are coupled with chromospheric line-of-sight Doppler velocitieswith an average blue-shift of 23 km s − . The lack of co-spatial intensity oscillationsand transversal displacements rule out the presence of magneto-acoustic wave modes.The oscillations are interpreted as a signature of torsional Alfv´en waves, produced bya torsional twist of ±
25 degrees. A phase shift of 180 degrees across the diameter ofthe bright point suggests these Alfv´en oscillations are induced globally throughout theentire brightening. The estimated energy flux associated with this wave mode seemsto be sufficient for the heating of the solar corona, once dissipated. The question self-evidently emerges: Could spicules guide similar (torsional) Alfv´en waves and leak themto the upper solar atmosphere?Let us return to the possibility of intensity variations of spicules. Variation of lineintensity indicates the propagation of compressible waves. And finally, the visible dis-placement of spicule axis may reveal the transverse waves and oscillations in spicules.Note that ground based coronagraphs can play an especially important role in spec-troscopic observations. Spatial resolutions of ground based coronagraphs reach to ∼ α line were obtained with the coronagraphof the Institute of Terrestrial Magnetism (Russia) on 1 August 1964. The H α profilesand radial velocities of 11 different spicules were successfully derived from successiveH α line spectra formed at a height of ∼ α line for 10 different spicules. Fig. 3
Temporal variations in radial velocities (solid curves) and half widths (dotted curves)of 10 individual H α spicules, adapted from Nikolsky and Sazanov (1967). Quasi-periodic oscillations are clearly seen. The authors concluded that the radialvelocities vary randomly with time with a mean period of ∼ α line profile also tendsto oscillate with a period similar to the mean period of ∼ Fig. 4
Temporal variation of Doppler velocities in H-line of Ca II from Pasachoff et al. (1968).
H-line was 13 s and the spatial resolution was less than 2 arc sec. Pasachoff et al. (1968)were searching for the sign reversal of Doppler velocities in order to determine the ris-ing/falling stages of spicule evolution. Indeed, some features show the sign reversal, butthe common property is the clear quasi-periodic temporal variation of Doppler veloci-ties with periods of 3-7 min. The amplitudes of oscillations are rather high, though stillbeing within the range of 10-20 km/s. Pasachoff et al. (1968) interpreted the detectedtemporal variation as motion along the spicule axis, but transverse oscillations alsocannot be ruled out.3.3 Weart (1970)Observations have been carried out with the Mount Wilson Solar Tower Telescopeduring the period of 10 September - 13 October, 1967. Time sequences of H α spectrawith time lapse rates of 5 to 15 s have been obtained corresponding to height 5000-6000km height above the solar limb.The author reported that, both Doppler velocity and horizontal motion of spiculesas a whole have significant input into spicule dynamics. In at least two cases, the authorfound that the combined motion indicate movement of a gas in an arc of a horizontalcircle, firstly towards the observer, followed by sideways, finally away. Weart concludedthat only true transverse motion could explain the observed pattern of motion.The power spectrum of temporal variations resembled the familiar 1/frequencycurve, typical to many types of random motions. Substantial power was found to beconcentrated at periods of 1, 2.5 and 10 minutes. However, no statistically significantpeaks were observed. Therefore, it was concluded that spicules move horizontally atrandom. α spectrograms of the chromosphere were obtained during about a 21minute observing campaign at the height of 4200 km. The time interval between suc-cessive frames varied from 14 to 100 s being on the average about 30 s. The spatialresolution of observations was ∼ Fig. 5
Left: temporal variation of spicule positions along the solar limb, fromNikolsky and Platova (1971). Points denote the different positions of spicules during time se-ries. I and II are the ”bench-mark” spicules. Right: distribution of periods of spicule oscillationsalong the solar limb. in almost all frames, were chosen as reference ones. Then, the variation of other spiculesalong the limb with respect to these ”bench-mark” spicules were determined. Fig. 5 (leftpanel) shows the position of several spicules vs time with respect to the ”bench-mark”spicules. There is evidence of oscillations of spicule position along the limb.The distribution of periods of spicule oscillations along the limb is shown on theright panel of Fig. 5. The most probable period lies between 50-70 s and the authorsconcluded that spicules undergo transversal oscillations with a period of ∼ − . The observationshave been performed at the height, where the type II spicules may reach, therefore itis possible that observed temporal variations here are connected to their activity. Fig. 6
Distribution of periods of Doppler velocity V r , intensity W and full-width at half-maximum ∆λ , adapted from Kulidzanishvili and Nikolsky (1978). vs the observed periods of oscillation in line-of-sight velocity, line width and intensity.About 70% of the observed periods of Doppler shift oscillations are within 3-7 min.The same per cent of observed periods lies within 4-9 min in the spicule intensity and80% of observed periods of line width oscillations are within 3-7 min.3.6 Gadzhiev and Nikolsky (1982)Observations were also carried out with the 53 cm Lyot coronagraph at ShemakhaAstrophysical Observatory resulting in H α time series corresponding to a height of 4Mm above the solar limb. 26 spectrograms have been taken over an 8-min intervalwhich gives ∼
20 s between consecutive frames. A total number of 15 spicules wereinvestigated in details. Gadzhiev and Nikolsky analysed variations in Doppler velocityas well as in the tangential velocity, i.e. reflecting the visible displacement of spiculeaxes along the solar limb.The authors found that the spicules oscillate with typical periods of 3-6 mins, bothin line-of-sight and tangential directions. Fig. 7 shows the time variation of line-of-sight and tangential velocities in one of the spicules. The periodicity in both velocitycomponents is clearly visible. Gadzhiev and Nikolsky also constructed the trajectoriesof spicule motion by putting together both velocity components. They concluded thatspicules undergo a cyclic motion as a whole on an ellipse with an average period of 4mins. The average amplitude of this cyclic motion was 11 km s − . Fig. 7
Time variation of the radial and tangential velocities V r , V t and the modulus V of thevelocity vector for a spicule, adapted from Gadzhiev and Nikolsky (1982). α line, was analyzedfor a total number of 25 spicules. The statistically significant period of oscillations inintensity, line width and line-of-sight velocity was found to be ∼ α spectra corresponding tofive slit positions above the solar limb were recorded every 8 s in order to investigatethe temporal variations of spicules. The spatial resolution of these observations wasbetter than 2 arcsec.Hasan and Keil detected the temporal variations of the line-of-sight velocity attwo different heights for two spicules. The fine time resolution allowed them to discernsmall amplitude fluctuations with periods of about 2-3 mins.3.9 Papushev and Salakhutdinov (1994)Observations were carried out with the 53 Lyot coronagraph of Sayan Observatorylocated near Irkutsk (Russia). The spectroscopic time series in different spectral linesvaried from several minutes to hours with an excellent temporal resolution of 10-20 s.The spatial resolution of observations was better than 1 arcsec. The spectra weresimultaneously registered at three different heights (5000 -8000 km above the limb)above the limb with a three-level image slicer. Fig. 8
Temporal variations of H α line profile parameters and the line-of-sight velocity ofspicules at different heights, adapted from Papushev and Salakhutdinov (1994). The solid linecorresponds to the height of 5 Mm and the dashed line to 8 Mm above the solar limb, respec-tively. Temporal variations of H α line profile parameters and line-of-sight velocity for oneof spicules at two different heights are shown on Fig.8. The quasi periodic fluctuationsare clearly seen. Papushev and Salakhutdinov found that the oscillation periods laybetween 80-120 sec.3.10 Xia et al. (2005)Xia et al. analyzed the time series of EUV spicules in two polar coronal holes ob-tained by the SUMER (Solar Ultraviolet Measurements of Emitted Radiation) cameraon-board the SOHO (SOlar and Heliospheric Observatory) spacecraft. The spatial res-olution of the observations was 1 arcsec and the exposure time for different data setsvaried as 15, 30 and 60 s. Fig. 9 shows Dopplergrams and radiance map for the C III 977˚A line (left panel). The right panel shows the relative Doppler shifts at four differentlocations above the solar limb. The Doppler velocity and radiance indicate evidence of ∼ α are 0.04 ˚A and 1 ˚A/mm correspondingly) at the solar limb. Thescanning of height series began at the height of 3800 km measured from the photo-sphere, and continued upwards (Khutsishvili (1986)). The chromospheric H α line wasused again to observe solar limb spicules at 8 different heights. The distance betweenneighbouring heights was 1 ′′ (which was the spatial resolution of observations), thusthe distance of ∼ α height series. Nearly 20% of the measured height series showeda periodic spatial distributions in the Doppler velocities. A typical Doppler velocity Fig. 9
Time series Dopplergram and radiance map for the C III 977 ˚A line showing levelsof radiance in logarithmic scale (adapted from Xia et al. (2005)). The right panel shows therelative Doppler shift at four location above the limb. −2 −1.5 −1 −0.5 0 0.5 1 1.5 23000400050006000700080009000 velocity (km/s) h e i gh t ( k m ) Fig. 10
The Doppler velocity spatial distributions for one of the height series fromKukhianidze et al. (2006). The marked dots indicate the observed heights. spatial distributions for one of the height series is shown in Fig. 10, which shows aperiodic behavior. The authors suggested that the spatial distribution was caused bytransverse kink waves. The wavelength was estimated to be ∼ α spectra with aninterval of ∼ D opp l e r v e l o c i t y ( k m / s ) Height 5900km0 100 200 300 400 500 6000510152025 time (s) D opp l e r v e l o c i t y ( k m / s ) Height 5200km −1 )Height 5900 km P o w e r ( k m / s ) −1 )Height 5200 km P o w e r ( k m / s ) Fig. 11
Left: Doppler velocity time series at the heights of 5200 and 5900 km in one ofthe spicules, adapted from Zaqarashvili et al. (2007). The time interval between consecutivemeasurements is ∼ shows the Doppler velocity time series at two different heights above the solar limbin one of the spicules (left panel). The time series show the evidence of quasi-periodicoscillations in line-of-sight velocity. The power spectra resulted from Discrete FourierTransform (DFT) analyses of the time series are presented in the right panel. The mostpronounced periods at both heights are 180 and 30 s. The oscillation with the periodof 90 s is also seen but preferably at higher heights (note the small peak at the lowerheight as well).The power spectra of Doppler velocity oscillations in two other spicules at theheights of 5200 km (lower panels) and 5900 km (upper panels) are plotted on Figure 12.One of the spicules (left panels) shows the two clear oscillation periods of 120 and 80s at both heights. Both periods are above the 98% confidence level. Another spiculeundergoes oscillations with periods ∼
110 and ∼
40 s, respectively.Zaqarashvili et al. also presented the results of DFT for 32 different time series as ahistogram of all the oscillation periods above the 95.5% confidence level (see Figure 13).Almost half of the oscillatory periods are located in the period range of 18-55 s. Anotherinteresting range of oscillatory periods is at 75-110 s, with a clear peak at the periodof 90 s. Note that there is a further interesting period peak at 178 s as well, which isinterpreted as a clear evidence of the well-known 3 min oscillations ubiquitous in thelower solar atmosphere. −1 )Height 5900 km P o w e r ( k m / s ) −1 )Height 5200 km P o w e r ( k m / s ) −1 )Height 5900 km P o w e r ( k m / s ) −1 )Height 5200 km P o w e r ( k m / s ) Fig. 12
Power spectra of Doppler velocity oscillations in another two spicules at the heightsof 5200 and 5900 km (Zaqarashvili et al. (2007)). The dotted lines in both plots show 95.5%and 98% confidence levels.
18 26 34 42 50 58 66 74 82 90 98 106 114 122 130 138 146 154 162 170 17802468 periods (s)
Fig. 13
Histogram of all oscillation periods that are above 95.5% confidence level, adaptedfrom Zaqarashvili et al. (2007). The horizontal axis shows the oscillation periods in seconds,while the vertical axis shows the number of corresponding periods. ∼ Fig. 14
An example of the transversal motion of a spicule obtained with Hinode/SOT byDe Pontieu et al. (2007a). Panel A shows the intensity as a function of time along the spatialcut indicated by a white line on panels B-G. Panels B-G represent the time sequence of Ca IIH images.
Fig. 15
Transverse motion of many spicules, from De Pontieu et al. (2007a). Panel A showsan image of the Hinode/SOT Ca II chromospheric line. Panels B and D are time-distance plotsalong the cuts labeled by 1 and 2 on panel A. Panels C and E are similar cuts but reproducedby Monte-Carlo numerical simulations of spicule motions. Table 2
Summary of observed oscillatory periods in solar limb spiculesDoppler displacement intensity speed lineNikolsky and Sazanov (1967) 1 min 1 min H α Pasachoff et al. (1968) 3-7 min >
90 km/s Ca IIWeart (1970) random random H α Nikolsky and Platova (1971) 50-70 s H α Kulidzanishvili and Nikolsky (1978) 3-7 min 3-7 min H α Gadzhiev and Nikolsky (1982) 3-6 min 3-6 min H α Kulidzanishvili and Zhugzhda (1983) 5-min 5-min H α Hasan and Keil (1984) 2-3 min >
300 km/s H α Papushev and Salakhutdinov (1994) 80-120 s 80-120 80-120 >
300 km/s H α Xia et al. (2005) 5-min 5-min EUVKukhianidze et al. (2006) 35-70 s ∼
80 km/s H α Zaqarashvili et al. (2007) 30-110 s ∼
110 km/s H α De Pontieu et al. (2007a) 100-500 s 50-200 km/s Ca II generally tilted away from the vertical. However, the transverse component seems tobe the more important and determinant component in these oscillations as the visi-ble displacement along the limb is also frequently reported. The observed periods canbe formally divided into two groups: those with shorter periods ( < ≥ − −
110 s. The two groups of oscillations arepossibly caused by different physical mechanisms, but this issue needs further studiesbefore one can conclude. Intensity oscillations are observed mostly with ∼ ∼ The propagation of disturbances along spicules can be deduced when observationsare performed at least at two different heights. Then the propagation speed can beestimated from the phase difference between oscillations at different heights (see TableII). Several authors reported the possible propagation speeds of disturbances in spicules.Pasachoff et al. (1968) found that velocity changes occur simultaneously, to within 20 s,at two distinct heights separated by 1800 km. They concluded that the propagationvelocities should be more than 90 km s − . Hasan and Keil (1984) suggested the prop-agation of signals from lower to higher heights with an estimated velocity of morethan 300 km s − . Papushev and Salakhutdinov (1994) studied the phase delays offluctuations at different heights and also concluded that the propagation speeds shouldexceed 300 km s − . However, it must be noted that a standing oscillation pattern mayalso be responsible to explain these phenomena. Indeed, Hinode/SOT observations(De Pontieu et al. (2007a)) show some evidence of upward and downward propagatingwaves, with some partially standing waves being observed. De Pontieu et al. (2007a)estimated wave phase speed in the range of 50-200 km/s.Detailed reports about wave propagation were presented by e.g. Kukhianidze et al.(2006) and Zaqarashvili et al. (2007) through analyzing the consecutive height series.Kukhianidze et al. (2006) presented three consecutive height series of Doppler velocitiesin a spicule, which show that the maximum of the Doppler velocity moves up in time(see Fig. 16). The authors suggested that this may indicate a wave phase propagation. velocity (km/s) h e i gh t ( k m ) velocity (km/s)
10 15 2040005000600070008000 velocity (km/s)
Fig. 16
Three consecutive height series of Doppler velocities in one of the spicules, adaptedfrom Kukhianidze et al. (2006). The time difference between the consecutive plots is ∼ The phase is displaced at ∼ ∼
80 km s − ,very comparable to the expected kink or Alfv´en speed at these heights.Zaqarashvili et al. (2007) presented a Fourier power as a function of frequency andheights for two different spicules shown on Fig. 17 (left panel). There is clear evidence ofpersisting oscillations along the full length of both spicules. The plot of the first spiculeshows the long white feature (feature A) located just above the frequency 0.01 s − . Thisis the oscillation with the period of ∼
80 s and it persists along the spicule. The mostpronounced feature (feature B) in the plot of the second spicule is colour-code indicatedby a long brighter trend located just above the frequency of 0.02 s − and persistingalong almost the whole spicule. This is the oscillation with a period of 44 s. Then,Zaqarashvili et al. calculated the relative Fourier phase between heights for the most P ha s e d i ff e r en c e ( deg r ee s ) a P ha s e d i ff e r en c e ( deg r ee s ) b Fig. 17
Left: Fourier power expressed in confidence levels as function of frequency and heightsfor two different spicules, adapted from Zaqarashvili et al. (2007). Brighter points correspondto higher power, and darker points correspond to lower one. The label 1 on the power scale(right plots) corresponds to the level of 100% confidence. Right: Relative Fourier phase as afunction of height for oscillations (a) with ∼
80 s period in the first spicule (feature A) and (b)44 s period in the second spicule (feature B). The distance between consecutive heights is ∼ pronounced features (features A and B). Right panel of Figure 17 shows the relativeFourier phase as a function of heights for (a) feature A and (b) feature B. In spite ofthe apparent linear behaviour of the phase difference, there is practically almost nophase difference between oscillations at different heights for feature A, which probablyindicates a standing-wave like pattern with period of ∼ ∼ ∼
110 km s − .Hence, based on these few observations we conclude that the propagation speedof disturbances in solar limb spicules is quiet high and may exceed 100 km s − . Thisindicates that the disturbances are of magnetic origin and they propagate with chro-mospheric Alfv´en or kink speeds that exceeds the local sound speed in spicules at theseheights (but, note that the sound speed outside spicules has almost coronal values). It is clear that the observed transverse oscillations of spicule axis can be explained andinterpreted by the waves propagating along the spicule. The two type of waves respon-sible for periodic transverse displacement of spicule axis are: kink or Alfv´en waves.If spicules are modelled as plasma jets being shot along magnetic flux tube, then thetransverse oscillations could be caused by MHD kink waves (Kukhianidze et al. (2006);Zaqarashvili et al. (2007); Erd´elyi and Fedun (2007); Ajabshirizadeh et al. (2009)). If a spicule is not stable wave guide for the tube waves, then the oscillations can becaused by Alfv´en waves (De Pontieu et al. (2007a)). Before we embark on the inter-pretation of spicule oscillations, let us briefly summarise the possible MHD modesand their main properties in an inhomogeneous magnetised plasma under lower solaratmospheric conditions.5.1 MHD waves in a uniform magnetic cylinder in the lower solar atmosphere Fig. 18
Left:
Magnetic flux tube showing a snapshot of Alfv´en wave perturbation propagat-ing in the longitudinal z -direction along field lines at the tube boundary. At a given heightthe Alf´enic perturbations are torsional oscillations, i.e. oscillations are in the ϕ -direction, per-pendicular to the background field. Note that on the other hand MHD kink waves would forcethe tube axis to oscillate. Right:
Snapshot showing Alfv´en waves propagating along a mag-netic discontinuity. Again, the key feature to note is that Alfv´enic perturbations are within the magnetic surface ( yz -plane) at the discontinuity, perpendicular to the background field ( y -direction), while the waves themselves propagate along the field lines ( z -direction). The MHDkink waves oscillate in xz -plane in this geometry. Image adapted from Erd´elyi and Fedun(2007). To simplify the bewildering complexity of the dynamic solar atmosphere, the con-cept of magnetic flux tubes is often used. In a pioneering work by Edwin and Roberts(1983), using cylindrical coordinates, it was derived the dispersion relations of MHDwaves propagating in cylindrical magnetic flux tubes. The main obstacle to be over-come when introducing the concept of flux tubes is the conversion from Cartesian tocylindrical coordinates. This change results involving Bessel functions in the dispersionrelation which are not yet possible to be solved analytically without simplification, e.g.through incompressibility or long and short wavelength approximations. Let us sum-marise here the key steps of Edwin and Roberts (1983). Consider a uniform magneticcylinder of magnetic field B ˆz confined to a region of radius a , surrounded by a uni-form magnetic field B e ˆz (see Figure 18a). To simplify the MHD equations we assumezero gravity, there are no dissipative effects and all the disturbances are linear andisentropic. Pressure (plasma and magnetic) balance at the boundary implies that p + B µ = p e + B e µ , (1) where p and p e are the pressures inside and outside the tube.Linear perturbations about this equilibrium give the following pair of equations validinside the tube, ∂ ∂t ∂ ∂t − ( c + v A ) ∇ ! ∆ + c v A ∂ ∂z ∇ ∆ = 0 , (2) ∂ ∂t − v A ∂ ∂z ! Γ = 0 , (3)where ∇ is the Laplacian operator in cylindrical coordinates ( r, φ, z ) and ∆ ≡ div v , Γ = ˆz · curl v (4)for velocity v = ( v r , v φ , v z ). A similar pair of equations to (2) and (3) are valid outsidethe tube. Fourier analysing we let ∆ = R ( r ) exp [ i ( ωt + nφ + kz ) . (5)Then equations (2) and (3) give Bessel’s equation satisfied by R ( r ) as followsd R d r + 1 r d R d r − m + n r ! R = 0 , (6)where m = ( k c − ω )( k v A − ω )( c + v A )( k c T − ω ) . (7)We have used the notation v A for the Alfv´en speed, c for the sound speed and c T for the characteristic tube speed (sub-Alfv´enic), where c T = c v A / ( c + v A ) − / . Toobtain a solution to (6) bounded at the axis ( r = 0) we must take R ( r ) = A (cid:26) I n ( m r ) , m > J n ( n r ) , n = − m > (cid:27) ( r < a ) , (8)where A is an arbitrary constant and I n , J n are Bessel functions, see e.g. Abramowitz and Stegun(1967), of order n . For a mode locked to the waveguide it is required that no energypropagates to or from the cylinder in the external region, i.e. the waves are evanescentoutside the flux tube. Therefore we take R ( r ) = A K n ( m e r ) , r > a, (9)where A is a constant and m e = ( k c e − ω )( k v Ae − ω )( c e + v Ae )( k c T e − ω ) , (10)which is taken to be positive (no leaky waves). Here, c e stands for the sound speedoutside the tube. Since we must have continuity of velocity component v r and totalpressure at the cylinder boundary r = a , this yields the dispersion relations ρ ( k v A − ω ) m e K ′ n ( m e a ) K n ( m e a ) = ρ e ( k v Ae − ω ) m I ′ n ( m a ) I n ( m a ) , (11)for surface waves ( m >
0) and ρ ( k v A − ω ) m e K ′ n ( m e a ) K n ( m e a ) = ρ e ( k v Ae − ω ) n J ′ n ( n a ) J n ( n a ) , (12)for body waves ( m = − n < n = 0,while the well-observed kink mode (non-axisymmetric) is given by n = 1. Modes with n > c e > v A > c , possiblyrepresentative for spicules, sunspots or pores both the slow and fast bands have surfaceand body modes, respectively. The slow MHD waves are in a narrow band since c ≈ c T .The slow body waves are almost non-dispersive, whereas the almost identical slowsurface sausage and kink modes are weakly dispersive (bottom zoomed out panel inFig. 19). On the other hand, if the characteristic speeds of a lower solar atmospheric Fig. 19
The solution of the dispersion relations (11)-(12) in terms of phase speed ( ω/k ) ofmodes under photospheric conditions c e > v A > c (all speeds are in km/s). The slow band iszoomed (lower panel). Image adapted from Erd´elyi (2008). flux tube render as v A > c e > c , the fast body modes do not exist since they wouldbecome leaky mode solutions of the dispersion relations (11)-(12). The MHD modespropagating along the flux tube in this case are shown in Fig. 20. Note, there is littleevidence, whether flux tubes modelling spicules, are characterised by c e > v A > c or v A > c e > c . Fig. 20
Similar to Fig. 19 but for v A > c e > c . Image adapted from Erd´elyi (2008). In the incompressible limit, suitable for the description of kink waves and oscil-lations in their linear limit, ( c → ∞ , c e → ∞ ) , m and m e become | k | . The kinkand sausage modes are then given explicitly after some algebra. It is noted that thephase speed for the kink mode is not monotonic as a function of k but has a max-imum/minimum and the sausage mode is monotonically increasing/decreasing. Thismax/min feature of the kink mode is absent in the slab case, so it can be deducedto be a reflection of the geometry of the magnetic field. On the other hand, the in-compressible Alfv´en waves in magnetic tubes are polarized in the φ direction and donot lead to the displacement of the tube axes (see Figure 18a). The propagation oftorsional Alfv´en waves in vertical magnetic tubes have been studied by Hollweg (1981)and Hollweg et al. (1982).Particularly interesting processes may take place near the heights, where the Alfv´enand sound waves have similar values of phase speed. This area with β = 1 ( β =8 πp /B ), may locate somewhere between the photosphere and chromosphere. Bogdan et al.(2002, 2003) have performed 2D numerical simulations in isothermal atmosphere andhave shown the coupling between different MHD wave modes near this area. Zaqarashvili and Roberts(2006) also show that the nonlinear coupling between Alfv´en and sound waves may takeplace there.Last but not least, for completeness and for the benefit of interested readers, wenote that kink MHD wave propagation under solar coronal conditions is discussed indetails by Ruderman and Erd´elyi (2009) in this Volume.5.2 MHD kink wavesEquipped with a clear understanding of the differences between kink and Alfv´enicperturbations, as described above, let us now return to plausible interpretations of pe- riodic spicular motions. Spicules are much denser than the surrounding medium abovethe height of 2000 km (see section 2.2), therefore they may be considered as magnetictubes and the MHD wave theory can be applied in some format as outlined in theSec. 5.1. Then, the observed periodic transverse displacement of the axis probably isdue to the propagation of kink waves (see Figs. 18 and 21). Transverse kink waves canbe generated in photospheric magnetic tubes by buffeting of granular motions (Roberts(1979); Spruit (1981); Osin et al. (1999)). The waves may then propagate through thestratified chromosphere (see, e.g. Hargreaves (2008); Hargreaves and Erd´elyi (2009))and lead to the observed oscillations (Kukhianidze et al. (2006); Zaqarashvili et al.(2007)). The recent theoretical paper by Ajabshirizadeh et al. (2009) also shows thatthe kink waves with periods of ∼ coronagranulationobserverchromosphere spiculephotosphere Fig. 21
Schematic picture of propagating kink waves in spicules, adapted fromKukhianidze et al. (2006). the stratified field-free atmosphere is governed by the Klein-Gordon equation (Rae and Roberts(1982); Spruit and Roberts (1983); Hasan and Kalkofen (1999); Zaqarashvili and Skhirtladze(2008); Hargreaves (2008); Hargreaves and Erd´elyi (2009); the latter authors have evenconsidered a dissipative medium resulting in a governing equation of the type of Klein- Gordon-Burgers equation) ∂ Q∂z − c k ∂ Q∂t − Ω k c k Q = 0 , (13)where Q = ξ ( z, t ) exp ( − z/ Λ ), c k = B / p π ( ρ + ρ e ) is the kink speed, Λ is the den-sity scale height and Ω k = c k / Λ is the gravitational cut-off frequency for isothermalatmosphere (temperature inside and outside the tube is assumed to be the same andhomogeneous). Here ξ ( z, t ) is the transversal displacement of the tube, B ( z ) is thetube magnetic field, ρ ( z ) and ρ e ( z ) are the plasma densities inside and outside thetube respectively (the magnetic field and densities are functions of z , while the kinkspeed c k is constant in the isothermal atmosphere).Eq. (13) yields simple harmonic solutions exp[ i ( ωt ± k z z )] with the dispersion re-lation ω − Ω k = c k k z , (14)where ω is the wave frequency and k z is the wave number. The dispersion relationshows that waves with higher frequency than Ω k may propagate in the tube, while thelower frequency waves are evanescent. Fig. 22
Helical kink wave in a thin magnetic flux tube, adapted fromZaqarashvili and Skhirtladze (2008).
Kink waves cause the transverse displacement of the entire tube. The displace-ment of tube in a simple harmonic kink wave is polarized arbitrarily and the po-larization plane depends on the excitation source. The superposition of two or morekink waves polarized in different planes may give rise to the complex motion of thetube. The process is similar to the superposition of two plane electromagnetic waves,where the waves with the same amplitudes lead to the circular polarization, whilethe waves with different amplitudes lead to the elliptical polarization. Consider, forexample, two harmonic kink waves with the same frequency but polarized in the xz and yz planes: A x = A x cos( ωt + k z z ) and A y = A y sin( ωt + k z z ). The superpo-sition of these waves sets up helical waves with a circular polarization if A x = A y (Zaqarashvili and Skhirtladze (2008)). As a result, the tube axis rotates around thevertical, while the displacement remains constant (Fig. 22). If A x = A y then the re-sulting wave is elliptically polarized. The superposition of few harmonics with differentfrequencies and polarizations may lead to an even more complex motion of the tubeaxis.5.3 Alfv´en wavesDe Pontieu et al. (2007a) suggested that the transverse displacement of spicule axis canbe explained by the propagation of Alfv´en waves excited in the photosphere by granularmotions or global oscillation patterns. They performed self-consistent 3D radiativeMHD simulations ranging in the vertical direction from the convection zone up tothe corona. A snapshot from the simulations is presented on the Fig. 23 (panel A).Their analysis shows that the field lines (red lines) in the corona, transition region,and chromosphere are continuously shaken and carry Alfv´en waves. Panels B andC are time-distance plots from the simulations and observations, respectively. Fromthe comparison between simulations and observations the authors concluded that theperiod of Alfv´en waves should lay between 100 and 500 s. However, they suggested thatvery long-lived macro spicules show some evidence of Alfv´en waves with longer periodsbetween 300 and 600 s. De Pontieu et al. (2007a) also claim that their observations andsimulations do not show the spicules as stable wave guide for kink waves. Therefore theyargue that volume-filling Alfv´en waves cause the swaying of magnetic field lines backand forth leading to the visible displacement of spicule axis. These claims are debatedby Erd´elyi and Fedun (2007): ”However, these observations also raise concerns aboutthe applicability of the classical concept of a magnetic flux tube in the apparentlyvery dynamic solar atmosphere, where these sliding jets were captured. In a classicalmagnetic flux tube, propagating Alfv´en waves along the tube would cause torsionaloscillations (see Fig. 18a in this paper earlier). In this scenario, the only observationalsignature of Alfv´en waves would be spectral line broadening. Hinode/SOT does nothave the appropriate instrumentation to carry out line width measurements . On theother hand, if these classical flux tubes did indeed exist, then the observations ofDe Pontieu et al. (2007a) would be interpreted as kink waves (i.e., waves that displacethe axis of symmetry of the flux tube like an S-shape). More detailed observations areneeded, perhaps jointly with STEREO , so that a full three-dimensional picture ofwave propagation would emerge.”5.4 Kink vs Alfv´en wavesIt is important to determine accurately which type of waves are responsible for thetransverse displacement of the tube axis (Erd´elyi and Fedun (2007); Jess et al. (2009)). We need to clarify here that, of course, Hinode/SOT can measure line width, however, notwith the desired resolution and in the desired wavelength in the context of spicule oscillations,as opposed to e.g. the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument mountedon the Dunn Solar Telescope, NSO, Sacramento Peak. Although STEREO has a limited spatial capacity for spicule observations, it can give aglobal view of the related MHD waveguide.7
Fig. 23
Comparison between observations and simulations of Alfv´en waves fromDe Pontieu et al. (2007a). A: a snapshot from 3D radiative MHD simulation. B: space-timeplot from simulations. C: space-time cut from observations.
The existence and main features of wave modes depend on the properties of the mediumwhere the waves propagate in (see Sec. 5.1). If spicules represents a magnetic fluxtube, then MHD wave theory may permit the propagation of kink and torsional Alfv´enwaves. The kink waves are global tube waves and cause the displacement of the tubeas a whole. However, most importantly let us emphasise once more that torsionalAlfv´en waves do not lead to the displacement of tube axis (Erd´elyi and Fedun (2007);Van Doorsselaere et al. (2008a); Jess et al. (2009)). Therefore, torsional Alfv´en wavesare unlikely to be the reason for the observed oscillations. However, global
Alfv´en waves,which may indeed fill a significant volume in and around spicules, may cause the globaltransverse oscillations of magnetic field lines. In this latter scenario spicules may justsimply follow the oscillations of field lines and this is what De Pontieu et al. (2007a)suggest. However, it must be mentioned here, that spicules may respond to the oscil-lation of magnetic field lines slower than the surrounding plasma due to their higherdensity i.e. larger inertia. This point is not taken into account by De Pontieu et al.(2007a) and it needs to be addressed in future models.However, there are two possible difficulties associated with the Alfv´en wave scenario.Firstly, if the oscillations of spicules are due to global Alfv´en perturbations, then theneighbouring spicules should show a coherent oscillation. However, Hinode movies in-dicate the opposite, i.e. spicule movements are random and there is no sign of coherentoscillations. This incoherence partly can be caused due to the fact that spicules seenat the limb are located in different parts along the line of sight. However, detailedanalysis still can uncover the coherent oscillations and this point needs to be addressedin future. Secondly, it is not yet clear how the volume-filling Alfv´en waves would begenerated in the photosphere, where the magnetic field is rooted and concentrated influx tubes. In this regards, it seems to be more plausible that the transverse pertur-bations propagate upwards in the form of kink waves, which may be transformed intoAlfv´en-like waves in the chromosphere, where the magnetic field rapidly expands. TheAlfv´en waves also can be generated near β = 1 region due to various wave couplingprocesses (Bogdan et al. (2002, 2003); Zaqarashvili and Roberts (2006)).The kink wave scenario also has its own difficulties as the photospheric flux tubesmay be expanded in the chromosphere as we already noted above. This expansion may cause certain difficulties for the kink wave to propagate. However, plasma β becomesless than unity in higher heights, which means that the concept of magnetic tube ischanging compared to the photospheric conditions. Now, the magnetic tube means thehigher concentration of density. This is exactly the case for spicules, as their density canbe up to two order magnitude higher, than in the surrounding coronal plasma. There-fore, the spicules can be wave guide of the kink waves (at least, in classical spicules)although De Pontieu et al. (2007a) claim opposite. Propagation of transverse pulse inthe wave guide of enhanced density was recently studied by Van Doorsselaere et al.(2008b). They show that the slab with enhanced density essentially trap the initialtransverse pulse. It must be mentioned that the rapid disappearance of type II spiculesin Ca II of Hinode/SOT does not immediately mean that spicules are not stable waveguides. The disappearance can be caused due to the increase of temperature insidespicule. But the tube (i.e. higher concentration of density) still may remain. In thisregards, Erd´elyi and Fedun (2007), in the context of prominence oscillations, showedthat kink waves can be easily guided. For the recently developed theory of transversalwaves and oscillations in gravitationally and magnetically stratified flux tubes see, e.g.Verth and Erd´elyi (2008); Ruderman et al. (2008); Andries et al. (2009). The problemwhether the spicule displacements are Alfv´enic or kink waves is currently under de-bate and more sophisticated observations complemented by numerical investigationsare needed for a satisfactory solution (Erd´elyi and Fedun (2007)).5.5 Transverse pulseIt must be recognised that simple harmonic waves can hardly be excited in the dynamicsolar photosphere. A more realistic process of wave excitation is the impulsive buffetingof granules on an anchored magnetic flux tube, which may easily generate transversepulses. Such pulses may propagate upwards in the stratified atmosphere and leave the”wake” oscillating at cut -off frequency of kink waves (Zaqarashvili and Skhirtladze(2008)). The wake may be also responsible for the observed transverse oscillations ofspicule axes.For the sake of simplicity, let us consider the simplest impulsive forcing in bothtime and coordinate. Then Eq. (13) looks as (Zaqarashvili and Skhirtladze (2008)) ∂ Q∂z − c k ∂ Q∂t − Ω k c k Q = − A δ ( t ) δ ( z ) , (15)where z > −∞ , t > A is a constant and the pulse is set off at t = 0, z = 0.The solution of this equation can be written, after e.g. (Morse and Feshbach (1953)), Q = A c k δ (cid:18) t − zc k (cid:19) − c k A J " Ω k s t − z c k H (cid:20) Ω k (cid:18) t − zc k (cid:19)(cid:21) , (16)where J and H are Bessel and Heaviside functions, respectively. Eq. (16) shows thatthe wave front propagates with the kink speed c k (the first term), while the wakeoscillating at the cut-off frequency Ω k is formed behind the wave front (the secondterm) and it decays as time progresses (Rae and Roberts 1982; Spruit and Roberts1983; Hasan and Kalkofen 1999; Hargreaves 2008; Hargreaves and Erd´elyi 2009). Note,the actual mathematical form of the governing equation and its solution for kink Fig. 24
Propagation of transverse kink pulse in stratified vertical magnetic flux tubes, adaptedfrom Zaqarashvili and Skhirtladze (2008). A rapid propagation of the pulse is seen, which isfollowed by the oscillating wake. The pulse propagates with the kink speed and the wakeoscillates with the cut-off period. The amplitude of the pulse (and wake) increases with heightdue to the decreasing density. and longitudinal oscillations in a gravitationally stratified and anchored magnetic fluxtube is very similar, see e.g. Sutmann et al. (1998); Musielak and Ulmschneider (2001);Ballai et al. (2006) for more details.Fig. 24 shows the plot of the transverse displacement ξ ( z, t ) = Q ( z, t ) exp ( z/ Λ ),where Q is expressed by the second term of Eq. (16). A rapid propagation of thepulse is found, which is followed by the oscillating wake (the time is normalizedby the cut-off period T k = 2 π/Ω k ). Just after the propagation of the pulse, thetube begins to oscillate with the cut-off period at each height. The amplitudes ofpulse and wake increase upwards due to the density reduction, but the oscillationsat each height decay in time. A very similar and resembling behaviour was foundby Fleck and Deubner (1989); Fleck and Schmitz (1991); Schmitz and Fleck (1998);Erd´elyi et al. (2007); Malins and Erd´elyi (2007) for longitudinal oscillations.Hence, the transverse and impulsive action on the magnetic tube at t = 0 nearthe base of the photosphere (as set at z = 0) excites the upward propagating kinkpulse, while the tube in the photosphere oscillates at the photospheric kink cut-offperiod, which can be estimated as ∼ ∼ It is most likely, that the anchored magnetic flux tube undergoes granular buffet-ing from many directions. Therefore, the superposition of consecutive pulses may setup a helical motion of tube axis with the cut-off period (Zaqarashvili and Skhirtladze(2008)). The helical motion of spicule axis first has been observed by Gadzhiev and Nikolsky(1982) from simultaneous observation of Doppler velocity and visual displacements. Therecent Hinode/SOT movies also show complex motions of spicule axis. Fig. 25 (upperpanels) show the observed trajectories of spicule axis with respect to the photosphere,adopted from Gadzhiev and Nikolsky (1982). The lower panel shows the superpositionof two wakes at the height of 250 km above the photosphere, numerically simulated byZaqarashvili and Skhirtladze (2008), by solving the Klein-Gordon governing equation.The first wake corresponds to the pulse imposed along the x -direction and the secondwake is the result of another pulse generated in the y -direction with a different ampli-tude. The observed period of helical motions is in the range of 3-6 mins, which maycorrespond well with the kink cut-off period in the chromosphere. A very similar phe-nomenon was recently observed in fibril orientation by Koza et al. (2007). Therefore, Fig. 25
Upper panels: Observed trajectories of the motion of two distinct spicules, adaptedfrom Gadzhiev and Nikolsky (1982). Lower panel: Simulated helical motion of the tube axis atthe height of 250 km measured from the solar surface, due to the propagation of two consecutivetransverse pulses polarized in perpendicular planes, adapted from Zaqarashvili and Skhirtladze(2008). the oscillation of wakes behind a transverse pulse may explain the visible transverse dis-placement of spicule axis observed by De Pontieu et al. (2007a) with Hinode/SOT. Thecut-off period is similar or slightly shorter than the mean life time of spicules, thereforethe oscillations are difficult to detect as it is noted by De Pontieu et al. (2007a). It mustbe mentioned, however, that the photosphere/chromosphere is in much more complexand dynamic state than it is described by this simple theoretical approach. Therefore, it is desirable to perform more sophisticated numerical simulations of transverse pulsepropagation from the photosphere up to the corona. Spicules are one of the most plausible tracers and trackers of the energy coupling andenergy transport from the lower solar photosphere towards the upper corona by meansof MHD waves. These waves may induce the oscillatory phenomena in the chromo-sphere, which are frequently detected in limb spicules. Periodic perturbations, e.g. informs of oscillations, are observed by both spectroscopic and imaging observations. Letus summarize the main observed oscillatory phenomena (see also Table 2): – Oscillations in limb spicules are more frequently observed in Doppler shifts and inthe visible displacement of spicule axis, which probably indicate the presence oftransversal motions of spicules as a whole. – The observed oscillation periods can be formally divided into two groups: thosewith shorter ( < ≥ – The most frequently observed oscillations are with period ranges of 50 −
110 s and3 − – The propagation of the actual oscillations is rather difficult to detect. However, therelative Fourier phase between oscillations at different heights indicates the prop-agation speed of ∼
110 km s − . In some oscillations, perhaps caused by standingpatterns, waves seem to be present with very high phase speeds ( >
300 km s − ).The observed oscillations in spicules are most likely due to the propagation oftransverse waves from the photosphere towards the corona. There are several possibleinterpretations of these oscillatory phenomena: – Kink waves propagating along slender magnetic flux tubes, where spicules areformed on field lines close to the axis. The kink waves lead to the transverse oscil-lations of spicules as a whole. – Volume-filling Alfv´en waves propagating in surroundings of spicules. The Alfv´enwaves result in the oscillation of the ubiquitous magnetic field lines. These oscilla-tions force the spicules to periodic displacement of their axes. – Transverse pulses excited in the photospheric magnetic flux tube by means of buffet-ing of granules. The pulses may propagate upwards in the stratified atmosphere andleave ”wakes” behind, which oscillate at the kink cut-off frequency of the stratifiedvertical magnetic flux tube. The wakes can be responsible for the observed ≥ F ∼ n e c k v g , where v g is the granularvelocity, say 1-2 km s − . Then, for the photospheric electron density of 2 · cm − and Alfv´en speed of 10 km s − , the estimated energy flux is ∼ · erg cm − s − (taking v g as 1.25 km/s).The same energy flux under spicule conditions (i.e. electron density of 2 · cm − and Alfv´en speed of 100 km s − ) requires the wave velocity in spicules to be about 385km/s. The expansion of magnetic tube with height may alter the estimation. However, spicule density is almost two magnitude higher compared to the other part of the tube.Therefore, even if spicules occupy only 1% of the tube cross section, the energy storiedin spicule oscillations is comparable to the oscillation energy of remaining part of thetube. Therefore, even if the wave transmission efficiency is less than 100 %, the observedvelocity is much lower than expected. This discrepancy can be resolved if the oscillationsare caused by the wake behind a transversal pulse: in this case almost the entire energyof the initial perturbation is carried by the pulse, while the energy of the wake is muchsmaller . Therefore, even if the filling factor of magnetic tubes is 1%, the energy fluxcarried by pulses is more than enough to heat the solar chromosphere/corona.6.1 Targets for future observationsMore observations from space satellites and ground based coronagraphs are needed fora better and conclusive understanding of oscillatory events in solar limb spicules. Thereare few highlighted targets for future observations: It is important to perform an analysis of phase relations between oscillations in neigh-bouring spicules. If spicule oscillations are caused by global Alfv´en waves or they arerelated to global photospheric oscillations, then the transverse displacement of spiculesshould show some spatial coherence i.e. a few neighbouring spicules should move inphase along the limb. Superposition of different spicule groups located along the line ofsight could complicate the task, but careful analysis still may reveal some coherence.Hinode/SOT time series in Ca II H and H α lines seem to be an excellent data for suchanalysis work. A study the phase relation of transverse displacements of a particular spicule at dif-ferent heights would allow us to infer whether the oscillations are due to standing orpropagating wave patterns. Phase delays between different heights would determinethe phase speed of perturbations, thus, the physical nature of the waves. Spectroscopicconsecutive height series from ground based coronagraphs or time series of images frome.g. Hinode/SOT would allow to infer the wave length, phase speed or frequency ofoscillations. These latter important diagnostic parameters may be then used to develop spicule seismology as suggested by Zaqarashvili et al. (2007).
Propagation of transverse pulses can be traced through a careful analysis of time seriesfrom e.g. Hinode/SOT. It is also important to search for oscillations of spicule axis atthe kink or Alfv´en cut-off frequency as estimated in the chromosphere. Polar macro-spicules are probably the best targets for such work, as their life time is long enoughwhen compared to the cut-off period. Acknowledgements
This paper review was born out of the discussions that took place atthe International Programme ”Waves in the Solar Corona” of the International Space Sci-ence Institute (ISSI), Bern. The authors thank for the financial support and great hospitalityreceived during their stay at ISSI. TZ acknowledges Austrian Fond zur F¨orderung der wis-senschaftlichen Forschung (project P21197-N16) and Georgian National Science Foundationgrant GNSF/ST06/4-098. RE acknowledges M. K´eray for patient encouragement and is alsograteful to NSF, Hungary (OTKA, Ref. No. K67746) and the Science and Technology FacilitiesCouncil (STFC), UK for the financial support received.
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