Time signatures of impulsively generated waves in a coronal plasma

Impulsively generated waves in solar coronal loops are numerically simulated in the frame-work of cold magnetohydrodynamics. Coronal inhomogeneities are approximated by gas density slabs embedded in a uniform magnetic field. The simulations show that an initially excited pulse results in the propagation of wave packets which correspond to both trapped and leaky waves. Whereas the leaky waves propagate outside the slab, the trapped waves occur as a result of a total reflection from the slab walls. Time signatures of these waves are made by a detection of the trapped waves at a fixed spatial location. For waves excited within the slab, time signatures exhibit periodic, quasi-periodic and decay phases. The time signatures for waves excited outside the slab, or for a multi-series of variously shaped impulses generated at different places and times, can possess extended quasi-periodic phases. The case of parallel slabs, when the presence of a second slab influences the character of wave propagation in the first slab, exhibits complex time signatures as a result of solitary waves interaction.     

The resonant excitation of transverse oscillations in coronal loops

We suggest a way of self-consistently solving the problem of the excitation and rapid damping of coronal loop oscillations observed from the TRACE (Transition Region and Coronal Explorer) satellite. Oscillations are excited on the dispersion branch of fast magnetoacoustic waves, which propagate mainly across the magnetic field. The rapid damping of the observed oscillations is governed by the dispersion spreading of the pulse of these waves that was produced, for example, by a solar flare. The fundamental oscillation period is close to the period of the fundamental mode. Dissipative processes attributable to the nonideality of the plasma and the coronal-loop footpoints play no fundamental role.     

Nonlinear Resonant Excitation of Fast Sausage Waves in Current-Carrying Coronal Loops

We consider a model of a coronal loop that is a cylindrical magnetic tube with two surface electric currents. Its principal sausage mode has no cut-off in the long-wavelength limit. For typical coronal conditions, the period of the mode is between one and a few minutes. The sausage mode of flaring loops could cause long-period pulsations observed in microwave and hard X-ray ranges. There are other examples of coronal oscillations: long-period pulsations of active-region quiet loops in the soft X-ray emission are observed. We assume that these can also be caused by sausage waves. The question arises of how the sausage waves are generated in quiet loops. We assume that they can be generated by torsional oscillations. This process can be described in the framework of the nonlinear three-wave interaction formalism. The periods of interacting torsional waves are similar to the periods of torsional oscillations observed in the solar atmosphere. The timescale of the sausage-wave excitation is not much longer than the periods of interacting waves, so that the sausage wave is excited before torsional waves are damped.     

Waves and Oscillations in the Corona – (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earth's crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.     

Oscillatory Modes of a Prominence – PCTR – Corona Slab Model

Oscillations of magnetic structures in the solar corona have often been interpreted in terms of magnetohydrodynamic waves. We study the adiabatic magnetoacoustic modes of a prominence plasma slab with a uniform longitudinal magnetic field, surrounded by a prominence – corona transition region (PCTR) and a coronal medium. Considering linear small-amplitude oscillations, we deduce the dispersion relation for the magnetoacoustic slow and fast modes by assuming evanescentlike perturbations in the coronal medium. In the system without PCTR, a classification of the oscillatory modes according to the polarisation of their eigenfunctions is made to distinguish modes with fastlike or slowlike properties. Internal and external slow modes are governed by the prominence and coronal properties, respectively, and fast modes are mostly dominated by prominence conditions for the observed wavelengths. In addition, the inclusion of an isothermal PCTR does not substantially influence the mode frequencies, but new solutions (PCTR slow modes) are present.     

Attenuation of small-amplitude oscillations in a prominence–corona model with a transverse magnetic field

Observations show that small-amplitude prominence oscillations are usually damped after a few periods. This phenomenon has been theoretically investigated in terms of non-ideal magnetoacoustic waves, non-adiabatic effects being the best candidates to explain the damping in the case of slow modes. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse magnetic field to the slab axis and investigate wave damping by thermal conduction and radiative losses. The magnetohydrodynamic equations are considered in their linearised form and terms representing thermal conduction, radiation and heating are included in the energy equation. The differential equations that govern linear slow and fast modes are numerically solved to obtain the complex oscillatory frequency and the corresponding eigenfunctions. We find that coronal thermal conduction and radiative losses from the prominence plasma reveal as the most relevant damping mechanisms. Both mechanisms govern together the attenuation of hybrid modes, whereas prominence radiation is responsible for the damping of internal modes and coronal conduction essentially dominates the attenuation of external modes. In addition, the energy transfer between the prominence and the corona caused by thermal conduction has a noticeable effect on the wave stability, radiative losses from the prominence plasma being of paramount importance for the thermal stability of fast modes. We conclude that slow modes are efficiently damped, with damping times compatible with observations. On the contrary, fast modes are less attenuated by non-adiabatic effects and their damping times are several orders of magnitude larger than those observed. The presence of the corona causes a decrease of the damping times with respect to those of an isolated prominence slab, but its effect is still insufficient to obtain damping times of the order of the period in the case of fast modes.     

Loop heating by D.C. electric current and electromagnetic wave emissions simulated by 3-D EM particle code

We have shown that a current-carrying plasma loop can be heated by magnetic pinch driven by the pressure imbalance between inside and outside the loop, using a 3-dimensional electromagnetic (EM) particle code. Both electrons and ions in the loop can be heated in the direction perpendicular to the ambient magnetic field, therefore the perpendicular temperature can be increased about 10 times compared with the parallel temperature. This temperature anisotropy produced by the magnetic pinch heating can induce a plasma instability, by which high-frequency electromagnetic waves can be excited. The plasma current which is enhanced by the magnetic pinch can also excite a kinetic kink instability, which can heat ions perpendicular to the magnetic field. The heating mechanism of ions as well as the electromagnetic emission could be important for an understanding of the coronal loop heating and the electromagnetic wave emissions from active coronal regions.     

Solar Flare and CME Observations with STEREO/EUVI

STEREO/EUVI observed 185 flare events (detected above the GOES class C1 level or at >?25 keV with RHESSI) during the first two years of the mission (December 2006?–?November 2008), while coronal mass ejections (CMEs) were reported in about a third of these events. We compile a comprehensive catalog of these EUVI-observed events, containing the peak fluxes in soft X rays, hard X rays, and EUV, as well as a classification and statistics of prominent EUV features: 79% show impulsive EUV emission (coincident with hard X rays), 73% show delayed EUV emission from postflare loops and arcades, 24% represent occulted flares, 17% exhibit EUV dimming, 5% show loop oscillations or propagating waves, and at least 3% show erupting filaments. We analyze an example of each EUV feature by stereoscopic modeling of its 3D geometry. We find that EUV emission can be dominated by impulsive emission from a heated, highly sheared, noneruptive filament, in addition to the more common impulsive EUV emission from flare ribbons or the delayed postflare EUV emission that results from cooling of the soft-X-ray-emitting flare loops. Occulted flares allow us to determine CME-related coronal dimming uncontaminated from flare-related EUV emission. From modeling the time evolution of EUV dimming we can accurately quantify the initial expansion of CMEs and determine their masses. Further, we find evidence that coronal loop oscillations are excited by the rapid initial expansion of CMEs. These examples demonstrate that stereoscopic EUV data provide powerful new methods to model the 3D aspects in the hydrodynamics of flares and kinematics of CMEs.     

磁场中p模/s模的转换及黑子对声波的吸收

在柱坐标下将黑子周围的环形区域（黑子除外）内的振荡分解为朝向黑子传播的（入射的）波和离开黑子传播的（出射的）波。对无黑子的环形区域内的振荡也进行了同样的分解。将黑子周围的入射波看成是被黑子磁流管磁化了的介质（介质内的磁场基本是水平的）中的波。而无黑子区的入射波看成是非磁化介质中的波。比较这两种波在固定波数下功率随频率的分布发现，在磁化介质中不同径向除ｎ的声波（ｐ模）频率系统降低，同时功率也降低，降低的功率最高达非磁化介质中波的功率的３０％。而比较在固定频率下功率随波数的分布发现，磁场中ｆ模及ｎ＝１，２，３的ｐ模的脊向高波数方向位移，功率的降低受频率调制，即声波在某些有限的频带中被吸收。这些观测表明，在磁场中ｐ模与磁声重力波（ＭＡＧ）产生了模式混合或耦合。模式混合的存在支持了模式转换作为ｐ模式被黑子吸收的机制的解释。此外，本文还分析了转换的ＭＡＧ波进入黑子磁流管（其中的磁场基本上是垂直的）后进一步被吸收，吸收的功率最高达ＭＡＧ波的２０％。在磁流管内没有进一步观测到模式的转换     

Oscillations of coronal loops and second pulsations of solar radio emission

The dispersion properties of the sausage eigenmodes of oscillations in a thin magnetic flux tube are numerically analyzed in terms of ideal magnetohydrodynamics (MHD). The period of the modes accompanied by the emission of MHD waves into the surrounding medium, which leads to acoustic damping of oscillations, is determined by the radius of the tube, not by its length. The dissipation of the sausage oscillations in comparatively high (?0.7R _⊙) and tenuous (?6 × 10⁸ cm^?3) coronal loops is considered. Their Q factor has bound found to be determined by the acoustic damping mechanism. The ratio of the plasma densities outside and inside the loop and the characteristic height of the emission source have been estimated by assuming the quasi-periodic pulsations of meter-wavelength radio emission to be related to the sausage oscillations.     

Oscillations in the Umbral Atmosphere

The results of simultaneous observations of oscillations in the chromosphere, transition region, and corona above nine sunspots are presented. The data are obtained through coordinated observing with the Solar and Heliospheric Observatory — SOHO and the Transition Region And Coronal Explorer — TRACE. Oscillations are detected above each umbra. The power spectra show one dominant frequency corresponding to a period close to 3 min. We show that the oscillations in the sunspot transition region can be modeled by upwardly propagating acoustic waves. In the corona the oscillations are limited to small regions that often coincide with the endpoints of sunspot coronal loops. Spectral observations show that oscillations in the corona contribute to the observed oscillations in the TRACE 171 Å channel observations. We show that a recent suggestion regarding a connection between sunspot plumes and 3-min oscillations conflicts with the observations.     

Radiation of magnetoacoustic waves in the interstellar medium by physical variable stars

Radially pulsating stars are shown to radiate fast and slow magnetoacoustic waves into the interstellar gas. No Alfvén waves are excited, because the oscillations are radially symmetric. Calculations were performed for the following two limiting cases: hot, weakly magnetized interstellar plasma and cold plasma with a strong magnetic field. In these limiting cases, pulsating stars excite mostly fast magnetoacoustic waves, while the excitation of slow magnetoacoustic waves is weak. Magnetogasdynamic fields of density, velocity, and magnetic-field perturbations in the interstellar medium were found. Relations were derived to calculate the radiated power and its estimates are given for various conditions in the medium. It is shown that radially stratified wave structures with wavelengths from 1 AU to several tenths of a parsec must exist in the vicinity of pulsating stars.     

The Oscillations of Coronal Loops Including the Shell

We investigate the MHD waves in a double magnetic flux tube embedded in a uniform external magnetic field. The tube consists of a dense hot cylindrical cord surrounded by a co-axial shell. The plasma and the magnetic field are taken to be uniform inside the cord and also inside the shell. Two slow and two fast magnetosonic modes can exist in the thin double tube. The first slow mode is trapped by the cord, the other is trapped by the shell. The oscillations of the second mode have opposite phases inside the cord and shell. The speeds of the slow modes propagating along the tube are close to the tube speeds inside the cord and the shell. The behavior of the fast modes depends on the magnitude of Alfvén speed inside the shell. If it is less than the Alfvén speed inside the cord and in the environment, then the fast mode is trapped by the shell and the other may be trapped under the certain conditions. In the opposite case when the Alfvén speed in the shell is greater than those inside the cord and in the environment, then the fast mode is radiated by the tube and the other may also be radiated under certain conditions. The oscillation of the cord and the shell with opposite phases is the distinctive feature of the process. The proposed model allows to explain the basic phenomena connected to the coronal oscillations: i) the damping of oscillations stipulated in the double tube model by the radiative loss, ii) the presence of two different modes of perturbations propagating along the loop with close speeds, iii) the opposite phases of oscillations of modulated radio emission, coming from the near coronal sources having sharply different densities.     

Effect of Variable Background on an Oscillating Hot Coronal Loop

We investigate the effect of a variable, i.e. time-dependent, background on the standing acoustic (i.e. longitudinal) modes generated in a hot coronal loop. A theoretical model of 1D geometry describing the coronal loop is applied. The background temperature is allowed to change as a function of time and undergoes an exponential decay with characteristic cooling times typical for coronal loops. The magnetic field is assumed to be uniform. Thermal conduction is assumed to be the dominant mechanism for damping hot coronal oscillations in the presence of a physically unspecified thermodynamic source that maintains the initial equilibrium. The influence of the rapidly cooling background plasma on the behaviour of standing acoustic (longitudinal) waves is investigated analytically. The temporally evolving dispersion relation and wave amplitude are derived by using the Wenzel–Kramers–Brillouin theory. An analytic solution for the time-dependent amplitude that describes the influence of thermal conduction on the standing longitudinal (acoustic) wave is obtained by exploiting the properties of Sturm–Liouville problems. Next, numerical evaluations further illustrate the behaviour of the standing acoustic waves in a system with a variable, time-dependent background. The results are applied to a number of detected loop oscillations. We find a remarkable agreement between the theoretical predictions and the observations. Despite the emergence of the cooling background plasma in the medium, thermal conduction is found to cause a strong damping for the slow standing magneto–acoustic waves in hot coronal loops in general. In addition to this, the increase in the value of thermal conductivity leads to a strong decay in the amplitude of the longitudinal standing slow MHD waves.     

Magnetosonic waves in structured atmospheres with steady flows

The magnetosonic modes of magnetic plasma structures in the solar atmosphere are considered taking into account steady flows of plasma in the internal and external media and using a slab geometry. The investigation brings nearer the theory of magnetosonic waveguides, in such structures as coronal loops and photospheric flux tubes, to realistic conditions of the solar atmosphere. The general dispersion relation for the magnetosonic modes of a magnetic slab in magnetic surroundings is derived, allowing for field-aligned steady flows in either region. It is shown that flows change both qualitatively and quantitatively the characteristics of magnetosonic modes. The flow may lead to the appearance of a new type of trapped mode, namelybackward waves. These waves are the usual slab modes propagating in the direction opposite to the internal flow, but advected with the flow. The disappearance of some modes due to the flow is also demonstrated.The results are applied to coronal and photospheric magnetic structures. In coronal loops, the appearance of backward slow body waves or the disappearance of slow body waves, depending upon the direction of propagation, is possible if the flow speed exceeds the internal sound speed ( 300 km s^–1). In photospheric tubes, the disappearance of fast surface and slow body waves may be caused by an external downdraught of about 3 km s^–1.     

Multilevel Analysis of Oscillation Motions in Active Regions of the Sun

The nature of the three-minute and five-minute oscillations observed in sunspots is considered to be an effect of propagation of magnetohydrodynamic (MHD) waves from the photosphere to the solar corona. However, the real modes of these waves and the nature of the filters that result in rather narrow frequency bands of these modes are still far from being generally accepted, in spite of a large amount of observational material obtained in a wide range of wave bands. The significance of this field of research is based on the hope that local seismology can be used to find the structure of the solar atmosphere in magnetic tubes of sunspots. We expect that substantial progress can be achieved by simultaneous observations of the sunspot oscillations in different layers of the solar atmosphere in order to gain information on propagating waves. In this study we used a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromosphere – corona transition region in the layer with magnetic field B=2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to the optical ones. This implies an MHD wave traveling upward inside the umbral magnetic tube of the sunspot. For the five-minute oscillations the similarity in spectral details could be found only for optical oscillations at the chromospheric level in the umbral region or very close to it. The time delays seem to be similar. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records. Their nature still requires further observational and theoretical study for even a preliminary discussion.     

Damped Oscillations of Coronal Loops

A mechanism of damped oscillations of a coronal loop is investigated. The loop is treated as a thin toroidal flux rope with two stationary photospheric footpoints, carrying both toroidal and poloidal currents. The forces and the flux-rope dynamics are described within the framework of ideal magnetohydrodynamics (MHD). The main features of the theory are the following: i) Oscillatory motions are determined by the Lorentz force that acts on curved current-carrying plasma structures and ii) damping is caused by drag that provides the momentum coupling between the flux rope and the ambient coronal plasma. The oscillation is restricted to the vertical plane of the flux rope. The initial equilibrium flux rope is set into oscillation by a pulse of upflow of the ambient plasma. The theory is applied to two events of oscillating loops observed by the Transition Region and Coronal Explorer (TRACE). It is shown that the Lorentz force and drag with a reasonable value of the coupling coefficient (c _d ) and without anomalous dissipation are able to accurately account for the observed damped oscillations. The analysis shows that the variations in the observed intensity can be explained by the minor radial expansion and contraction. For the two events, the values of the drag coefficient consistent with the observed damping times are in the range c _d ≈2 – 5, with specific values being dependent on parameters such as the loop density, ambient magnetic field, and the loop geometry. This range is consistent with a previous MHD simulation study and with values used to reproduce the observed trajectories of coronal mass ejections (CMEs).     

Oscillatory Behavior in the Corona

We detect and analyze the oscillatory behavior of waves using a coronal seismology tool on sequences of coronal images. We study extreme-ultraviolet image sequences of active and quiet Sun regions and of coronal holes we identify 3- and 5-minute periodicities. In each studied region the 3- and 5-minute periodicities are similarly frequent. The number of pixels exhibiting a 3-minute periodicity is between 6 %?–?8 % and those pixels exhibiting a 5-minute periodicity is between 5 %?–?9 % of the total number of observed pixels. Our results show 3-minute oscillations along coronal loop structures but do not show 5-minute oscillations along these same loop structures. The number of pixels exhibiting 3- and 5-minute periodicities in one type of region (active Sun, quiet Sun, and coronal holes) is roughly the same for all observed regions, leading us to infer that the 3- and 5-minute oscillations are the result of a global mechanism.     

Transverse oscillations in coronal loops observed with TRACE – I. An Overview of Events,Movies, and a Discussion of Common Properties and Required Conditions

We study transverse loop oscillations triggered by 17flares and filament destabilizations; only 2 such cases have been reported in the literature until now. Oscillation periods are estimated to range over a factor of ∼15, with most values between 2 and 7 min. The oscillations are excited by filament destabilizations or flares (in 6% of the 255 flares inspected, ranging from about C3 to X2). There is no clear dependence of oscillation amplitude on flare magnitude. Oscillations occur in loops that close within an active region, or in loops that connect an active region to a neighboring region or to a patch of strong flux in the quiet Sun. Some magnetic configurations are particularly prone to exhibit oscillations: two active regions showed two, and one region even three, distinct intervals with loop oscillations. The loop oscillations are not a resonance that builds up: oscillations in loops that are excited along their entire length are likely to be near the fundamental resonance mode because of that excitation profile, but asymmetrically excited oscillations clearly show propagating waves that are damped too quickly to build up a resonance, and some cases show multiple frequencies. We discuss evidence that all oscillating loops lie near magnetic separatrices that outline the large-scale topology of the field. All magnetic configurations are more complicated than a simple bipolar region, involving mixed-polarities in the interior or vicinity of the region; this may reflect that the exciting eruptions occur only in such environments, but this polarity mixing likely also introduces the large-scale separatrices that are involved. Often the oscillations occur in conjunction with gradual adjustments in loop positions in response to the triggering event. We discuss the observations in the context of two models: (a) transverse waves in coronal loops that act as wave guides and (b) strong sensitivity to changes in the field sources for field lines near separatrices. Properties that favor model b are (1) the involvement of loops at or near separatrices that outline the large-scale topology of the field, (2) the combined occurrence of oscillations and loop translations, (3) the small period spread and similar decay time scale in a set of oscillating loops in one well-observed event, and (4) the existence of loops oscillating in antiphase with footpoints close together in two cases. All other properties are compatible with either model, except the fact that almost all of the oscillations start away from the triggering event, suggestive of an outward-pushing exciting wave more in line with model a. The spread in periods from event to event suggests that the oscillations may reflect the properties of some driver mechanism that is related to the flare or mass ejection. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014957715396     

Acoustic damping of fast kink oscillations of coronal loops

The damping of fast kink oscillations of solar coronal loops attributable to the radiation of MHD waves into the surroundings is considered in the thin-tube approximation. The oscillation damping decrement is calculated both by using a new energy method and by solving the dispersion equation for magnetic-tube eigenmodes. The two approaches are in good agreement under appropriate assumptions. The damping is negligible if MHD waves are radiated perpendicular to the magnetic field. The low Q factor of the loop oscillations in active regions found with the TRACE space telescope is associated with the generation of running waves that propagate along magnetic field lines.