Observation of standing kink waves in solar spicules

We analyze the time series of Ca ii H-line obtained from Hinode/SOT on the solar limb. The time-distance analysis shows that the axis of spicule undergos quasi-periodic transverse displacement at different heights from the photosphere. The mean period of transverse displacement is ∼180 s and the mean amplitude is 1 arc sec. Then, we solve the dispersion relation of magnetic tube waves and plot the dispersion curves with upward steady flows. The theoretical analysis shows that the observed oscillation may correspond to the fundamental harmonic of standing kink waves.     

A statistical analysis of the SOT-Hinode observations of solar spicules and their wave-like behavior

Spicules are an important very dynamical and rather cool structure extending between the solar surface and the corona. They are partly filling the space inside the chromosphere and they are surrounded by a transition thin layer. New space observations taken with the SOT of the Hinode mission shed some light on their still mysterious formation and dynamics. Here we restrict the analysis to the most radial and the most interesting polar spicules situated at the base of the fast solar wind of coronal holes.We consider a first important parameter of spicules as observed above the solar visible limb: their apparent diameter as a function of the height above the limb which determines their aspect ratio and leads to the discussion of their magnetic origin using the flux tube approximation. We found that indeed spicules show a whole range of diameters, including unresolved “interacting spicules” (I-S), depending of the definition chosen to characterize this ubiquitous dynamical phenomenon occurring into a low coronal surrounding. Superposition effects along the line of sight have to be taken into account in order to correctly measure individual spicules and look at I-S. We take advantage of the so-called mad-max operator to reduce these effects and improve the visibility of these hair-like features. An excellent time sequence of images obtained above a polar region with the Hinode SOT through the HCaII filter with a cadence of 8 s was selected for analysis. 1-D Fourier amplitude spectra (AS) made at different heights above the limb are shown for the first time. A definite signature in the 0.18–0.25 Mm range exists, corresponding to the occurrence of the newly discovered type II spicules and, even more impressively, large Fourier amplitudes are observed in the 0.3–1.2 Mm range of diameters and spacing, in rough agreement with what historical works were reporting. Additionally, some statistically significant behavior, based on AS computed for different heights above the limb, is discussed.“Time slice or x–t diagrams” revealing the dynamical behavior of spicules are also analyzed. They show that most of spicules have multiple structures (similarly to the doublet spicules) and they show impressive transverse periodic fluctuations which were interpreted as upward kink or Alfven waves. Evidence of the helical motion in spicules is now well evidenced, the typical periods of the apparent oscillation being around 120 s. A fine analysis of the time-slice diagram as a function of the effective heights shows an interesting new feature near the 2 Mm height. We speculate on the interpretation of this feature as being a result of the dynamical specificities of the spicule helical motion as seen in these unprecedented high resolution HCaII line emission time series.     

Transverse oscillations in solar spicules induced by propagating Alfvénic pulses

The excitation of Alfvénic waves in solar spicules by localized Alfvénic pulses is investigated. A set of incompressible MHD equations in the two-dimensional x–z plane with steady flows and sheared magnetic fields is solved. Stratification due to gravity and transition region between chromosphere and corona is taken into account. An initially localized Alfvénic pulse launched below the transition region can penetrate from transition region into the corona. We show that the period of the transversal oscillations is in agreement with those observed in spicules. Moreover, it is found that the excited Alfvénic waves spread during propagation along the spicule length, and suffer efficient damping of the oscillations amplitude. The damping time of the transverse oscillations increased with decreasing k _b values.     

Phase mixing of standing Alfvén waves with shear flows in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of such waves due to phase mixing at the presence of shear flow and field in the stratified atmosphere of solar spicules. The initial flow is assumed to be directed along spicule axis and to vary linearly in the x direction and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that the shear flow and field can fasten the damping of standing Alfvén waves. In spite of propagating Alfvén waves, standing Alfvén waves in Solar spicules dissipate in a few periods. As height increases, the perturbed velocity amplitude does increase in contrast to the behavior of perturbed magnetic field. Moreover, it should be emphasized that the stratification due to gravity, shear flow and field are the facts that should be considered in MHD models in spicules.     

Dynamics of Hα spicules according to spectral observations at various heights of the solar chromosphere

Almost simultaneous height sequences of 69 spicules in the Hα line have been studied. The spectra are obtained at six heights during 6 s on the east side of the solar disk with the 53-cm Lyot coronagraph of Abastumani Astrophysical Observatory. Radial velocities V _r, total intensities or equivalent widths W, full widths at half maximum of intensity (FWHM) at all heights are determined (about 300 profiles of the Hα line). It is found that:

1. Absolute values of radial velocities increase linearly with the height (see Equation (1));
2. variation of the sign of the radial velocity along single spicules was never observed.

These results combined with the findings on the spicules radial velocities and shifts obtained earlier (Kulidzanishvili and Nikolsky, 1978; Nikolsky and Platova, 1970) led us to the conclusion that the 5-min tangential oscillations of spicules involve the entire spicule at once. The intensity height scales for single spicules and for the chromosphere ‘in toto’ are determined; they turned out to be 2.5 × 10³ km and 1.9 × 10³ km respectively (see Equations (2) and (3)). The dependence curve of the Hα line half-widths Δλ on the height h is drawn. The Hα line half-width for those spicule groups which are traced at all heights (10 spicules) decreases with the height (Figure 4); for the majority (～60 spicules) it remains essentially constant. Non-thermal ‘turbulent’ velocities V _t, in Hα spicules are defined. A mean value of the ‘turbulent’ velocity V _t at T = 6000° appeared to be 20–30km s^?1. The hydrogen concentration in the spicules at 5000 km is 6 × 10¹¹ cm^?3.     

On vortex motion in chromospheric network boundaries

A large percent of spicules shows a surge-like behavior on the solar limb, supporting a multi-component model with twisted threads. The counterpart of limb spicules foot-points is investigated on the disk, and this re-examination indicates that the interpretation of transverse motion of off-limb spicules could directly be related to rotational motion at the feet of disk spicules. Related bright elements move and vary in brightness on the timescales of chromospheric oscillations. The motions are similar to random displacements of the bright elements along the network boundaries with amplitudes of about 200 to 400 km, with evidence of “spinning” or vortex motion. We find a clear evidence and in several cases for splitting process and suggesting a formation mechanism for doublet (or multi-component) spicules. A general inter chromospheric network velocity pattern with twists existing before the emergence and eruption of spicules seems to be required. In this paper a helical- kink mode propagation consistent with the new evidence of spicule multiple structure is presented and provides an explanation for the origin of the Alfvenic wave propagation along the spicules. The evidence of spinning spicules remains unclear from disk Dopplergram observations, we use a 3D time slice “column” diagrams (2D in x and y and time in z being the 3d dimension) by consecutive partly transparent slices put in perspective to show the rotational behavior at the chromospheric rosettes, and provide a wealth of information on spinning motion, helical wave propagation and splitting.     

Torsional Alfvén waves and the period ratio P 1/P 2 in spicules

The effects of both density stratification and magnetic field expansion on torsional Alfvén waves in solar spicules are studied. Also, their eigenfrequencies, eigenfunctions, and the period ratio P ₁/P ₂ are obtained with a novel mathematical method. We showed that under some circumstances this ratio can approach its observational value even though it departs from its canonical value of 2. Moreover, Eigenfunction height variations show that the oscillations amplitude are increasing towards higher heights which is in agreement with the observations. This means that with a little increase in height, amplitude of oscillations expands due to the significant decrease in the density.     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

On the role of transition region on the Alfvén wave phase mixing in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of standing Alfvén waves due to phase mixing at the presence of steady flow and sheared magnetic field in the stratified atmosphere of solar spicules. The transition region between chromosphere and corona has also been considered. The initial flow is assumed to be directed along spicule axis, and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that in contrast to propagating Alfvén waves, standing Alfvén waves dissipate in time rather than in space. Density gradients and sheared magnetic fields can enhance damping due to phase mixing. Damping times deduced from our numerical calculations are in good agreement with spicule lifetimes. Since spicules are short living and transient structures, such a fast dissipation mechanism is needed to transport their energy to the corona.     

Limb Spicules from the Ground and from Space

We amassed statistics for quiet-sun chromosphere spicules at the limb using ground-based observations from the Swedish 1-m Solar Telescope on La Palma and simultaneously from NASA’s Transition Region and Coronal Explorer (TRACE) spacecraft. The observations were obtained in July 2006. With the 0.2 arcsecond resolution obtained after maximizing the ground-based resolution with the Multi-Object Multi-Frame Blind Deconvolution (MOMFBD) program, we obtained specific statistics for sizes and motions of over two dozen individual spicules, based on movies compiled at 50-second cadence for the series of five wavelengths observed in a very narrow band at Hα, on-band and at ± 0.035 nm and ± 0.070 nm (10 s at each wavelength) using the SOUP filter, and had simultaneous observations in the 160 nm EUV continuum from TRACE. The MOMFBD restoration also automatically aligned the images, facilitating the making of Dopplergrams at each off-band pair. We studied 40 Hα spicules, and 14 EUV spicules that overlapped Hα spicules; we found that their dynamical and morphological properties fit into the framework of several previous studies. From a preliminary comparison with spicule theories, our observations are consistent with a reconnection mechanism for spicule generation, and with UV spicules being a sheath region surrounding the Hα spicules.     

Solar spicules observed through a K-filter

Some properties of the solar spicules as observed outside the limb through a Halle K-filter at the centre of the line are investigated. The observations have been made at the Pic-du-Midi Observatory. The results are as follows: (a) The chromosphere at the limb appears more diffuse in the K line than in the H line, the spicules being not well resolved. (b) The ratio of spicule intensity to the background intensity increases with height, as in the case of H spicules, but it is, in every height, smaller than that in H. (c) The spicule mean width is measured photometrically and found equal to 1900 km. (d) The lifetime is found to be 4.5 min. (e) The mean chromospheric height is estimated to be 6.000 km.     

Spectral observations of spicules at two heights in the solar chromosphere

An observational program at the Sacramento Peak Observatory in 1965 provided high-dispersion spectra of the solar chromosphere in several spectral regions simultaneously. These regions included various combinations of the spectral lines Hα, Hβ and H?, the D₃-line of Hei, the infrared triplet of Oi, and the H- and K-lines and the infrared triplet of Caii. With the use of an image slicer the observations were made simultaneously at two heights in the solar chromosphere separated by several thousand kilometers. From these data we draw the following conclusions:

1. Emission of different lines arises in the same chromospheric features. The intensity ratio of lines of different elements varies significantly from spicule to spicule. For the H- and K-lines of ionized calcium, this ratio remains constant, independent of wavelength throughout the line, overall intensity, and height in the chromosphere. Two rare-earth lines in the wing of the H-line show no spicular structure at all.
2. The line-of-sight velocities of many features reverse as a function of time, although most spicules show velocities in only one direction. The simultaneous spectra at two heights show most spicules to have the same line-of-sight velocity at both. There may be an additional class of features, mostly rapidly moving, whose members have line-of-sight velocities that increase with height. These features comprise perhaps 10% of the total. Velocity changes occur simultaneously, to within 20 sec, at two heights separated by 1800 km, indicating velocities of propagation of hundreds of km/sec. The velocity field of individual features is often quite complicated; many spectral features are inclined to the direction of dispersion, implying that differential mass motions are present.
3. The existence of anomalously broad H and K profiles is real. Even with high dispersion and the best seeing, such profiles are not resolved into smaller features. The central reversal in K, H and Hα appears to remain unshifted when the wings are displaced in wavelength, indicating that the reversal is non-spicular.

     

Magneto-acoustic wave oscillations in solar spicules

Some observations suggest that solar spicules show small amplitude and high frequency oscillations of magneto-acoustic waves, which arise from photospheric granular forcing. We apply the method of MHD seismology to determine the period of kink waves. For this purposes, the oscillations of a magnetic cylinder embedded in a field-free environment is investigated. Finally, diagnostic diagrams displaying the oscillatory period in terms of some equilibrium parameters are provided to allow a comparison between theoretical results and those coming from observations.      

The formation of the Ca ii K line in a spinning spicule

The emission of the Ca ii K line from a spinning cylindrical spicule model is considered. In order to reproduce the observed spicule K line profiles, the model must have both radial and axial gradients in N _e and T _e. The rotating spicule model is optically thin at all heights and is hotter and more dense than a stationary model computed in a previous paper. It is proposed that the so-called Type I and Type II spicules may be structurally the same features, with different rotational velocities.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Estimation of spicule magnetic field using observed kink waves

We apply the method of MHD seismology to estimate the magnetic field in spicules using observed kink waves. We include the effects of gravitational stratification, the neglect of which leads to an error of around 30% in the estimation of the magnetic field. With stratification included, we find the magnetic field in spicules in the range of 8–16 G. We also estimate a density of 7.4 × 10⁻¹⁰ kg m⁻³ in spicules. The estimated values of magnetic field and density are in agreement with the available observations. Improved measurement of height, oscillation period, and plasma density in spicules will further enhance the precision of this method.     

Resonant interactions of modes in coronal magnetic flux tubes

Nonlinear resonant interactions of different kinds of fast magnetosonic (FMS) waves trapped in the inhomogeneity of a low- plasma density, stretched along a magnetic field (as, for example, in coronal loops) are investigated. A set of equations describing the amplitudes of interactive modes is derived for an arbitrary density profile. The quantitative characteristics of such interactions are found. The decay instability of the wave with highest frequency is possible in the system. If amplitudes of interactive modes have close values, the long-period temporal and spatial oscillations are in the system.For a quantitative illustration, the parabolic approximation of the transverse density profile has been chosen. Dispersion relations of FMS waves trapped in a low- plasma slab with a parabolic transverse density profile are found. The transverse structure of the waves in this case can be expressed through Hermitian polynomials. The interaction of kink and sausage waves is investigated. The sausage wave, with a sufficiently large amplitude, may be unstable with respect to the decay into two kink waves, in particular. The spatial scale of a standing wave structure and the time spectrum of radiation are formed due to the nonlinear interactions of loop modes which contain information about the parameters of the plasma slab.     

Polar observations of plasma waves in and near the dayside magnetopause/magnetosheath

The plasma wave instrument (PWI) on board the Polar spacecraft made numerous passages of the dayside magnetopause and several probable encounters with the magnetosheath during the years 1996 and 1997. During periods of relatively high density, the PWI antenna-receiver system is coupled to the plasma and oscillates. The oscillations have been shown (cf. Radio Sci. 36 (2001) 203) to be indicative of periods of higher plasma density and plasma flows, possibly associated with magnetic reconnection. We have studied the plasma waves observed on three distinct magnetopause passes distinguished by the presence of these oscillations of the PWI receivers, and we report on the data obtained near, but not during, the times of the oscillations and the possible role of these waves in magnetic reconnection. Sweep-frequency receiver and high-resolution waveform data for some of these times are presented. The plasma wave measurements on each of the passes are characterized by turbulence. The most stable waves are whistler mode emissions typically of several hundred hertz that are seen intermittently in these regions. The data indicate the presence of impulsive solitary-like wave structures with strong electric fields both parallel and perpendicular to the magnetic field near, but not always within, suspected reconnection sites. The solitary waves show the highest occurrence when observed with electrostatic electron cyclotron waves. These latter waves have been observed in the past in the cusp, polar magnetosphere, and auroral regions and therefore may represent excursions into the cusp, but also indicate the presence of low-energy electron beams. Turbulence near the lower hybrid frequency, low-frequency EM waves, and impulsive monopolar electrostatic pulses are seen throughout the magnetopause and particularly near regions of large decrease in the local magnetic field and enhanced field-aligned flows, the suspected reconnection sites. The absence of significant solitary wave signatures within suspected reconnection sites may require modifications to some reconnection models.     

Phase mixing of propagating Alfvén waves in a stratified atmosphere: solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Recent observations by Hinode/SOT showed that the spicules mostly exhibit upward propagating high frequency waves. Here we investigate the dissipation of such waves due to phase mixing in stratified environment of solar spicules. Since they are highly dynamic structures with speeds at about significant fractions of the Alfvén phase speed, we take into account the effects of steady flows. Our numerical simulations show that in the presence of stratification due to gravity, damping takes place in space than in time. The exponential damping low, \operatornameexp(-\operatornameAt³)\operatorname{exp}(-\operatorname{At}^{3}), is valid under spicule conditions, however the calculated damping time is much longer than the reported spicule lifetimes from observations.     

The Evolution of Quasi-Separatrix Layer in Two Solar Eruptive Events

Quasi-separatrix layer, also called as QSL, is a region where magnetic connectivity changes drastically, and mostly well coincides with the location of flare ribbons in observations. The research on the relations of this topological structure with the 3-dimensional magnetic reconnection, and solar flares has attracted more and more attention. In this paper, using the theory of QSL we investigate a C5.7 classical two-ribbon solar flare (event 1) which occurred at AR11384 on 2011 December 26, and an M6.5 solar flare (event 2) which occurred at AR12371 on 2015 June 22, respectively. Combining the multi-wavelength data of AIA (Atmospheric Imaging Assembly) and vector magnetogrames of HMI (Helioseismic and Magnetic Imager) onboard SDO (Solar Dynamics Observatory), we extrapolate the coronal magnetic field using the PF (Potential Field) and NLFFF (Nonlinear Force Free Field) models, and calculate the evolution of the AR (Active Region) magnetic free energy. Then, we calculate the logarithmic distribution of Q-factors (magnetic squashing factor) at different heights above the solar photosphere with the results of the PF and NLFFF extrapolations, in order to determine the location of QSL. Afterward, we investigate the evolutionary relation between the QSLs at different heights above the solar photosphere and the flare ribbons observed at the corresponding heights. Finally, we study the multi-wavelength evolution features of the 2 flare events, and obtain by calculation the mean slip velocities of magnetic lines in the event 2 at 304 Å and 335 Å to be 4.6 km s^-1 and 6.3 km s^-1, respectively. We find that the calculated location of QSL in the chromosphere and corona is in good agreement with the location of flare ribbons at the same height, and the QSLs at different heights have almost the same evolutionary behavior in time as the flare ribbons of the corresponding heights, which highlights the role of QSL in the research of 3D magnetic reconnection and solar flare, and we suggest that the energy release in the flare of event 2 may be triggered by the magnetic reconnection at the place of QSL. We also suggest that the QSL is very important for us to study the essential relation between the 3D and 2D magnetic reconnections.     

Atmospheric waves (≈ 10 min–30 days) in the mesosphere and thermosphere at saskatoon (52°N, 107°W), October 1978–September 1979

Partial reflection radiowave wind observations have been made continuously at Saskatoon for 1 year (September 1978–August 1979). The winds have been obtained in real-time from a twin micro-processor system, that produces profiles (32 heights from 49 to 142km) at 5-min intervals: daytime/night-time profiles normally involve values from $\text{60}\text{70}$ to 120 km.These data have been analyzed to give the daily mean wind and the amplitudes and phases of planetary, tidal (24, 12 h) and internal gravity (I.G.) waves (0.20 ? τ ? 6h). There are oscillations in the mean daily wind, with periods of 2–30 days: the disturbance from 60 to 100 km caused by the stratwarm of February and March is documented. The characteristics of the semi-diurnal tide undergo significant changes in vertical wavelength and time of maxima between summer months (May–August) and winter months (November–February): during summer the S²₂ mode (λ_z ? 150km) seems to dominate, and in other months a mixture of modes (λ_z ? 50km) exist. The diurnal tide is less regular, but during winter and spring λ_z ? 30–60 km, and for other months is very large, suggesting the S_?1¹ mode. Energy densities and scale heights (h₀) are given, and the relative magnitudes of these for the various waves are discussed with respect to height and season: there is a general trend for the growth of the wave amplitude with height (shown by h₀) to increase in the order planetary, tidal and I.G. waves (h₀, ～3–15 km): largest values are in winter and spring. Wave energies are largest in winter, decrease during spring and increase throughout late summer and fall.