The Effect of Flows on Transverse Oscillations of Coronal Loops

In this paper we study kink oscillations of coronal loops in the presence of flows. Using the thin-tube approximation we derive the general governing equation for kink oscillations of a loop with the density varying along the loop in the presence of flows. This equation remains valid even when the density and flow are time dependent. The derived equation is then used to study the effect of flows on eigenfrequencies of kink oscillations of coronal loops. The implication of the obtained results on coronal seismology is discussed.     

日冕中无衰减振荡的研究进展

日冕中冕环的无衰减横向振荡(简称无衰减振荡)自2012年被发现以来,受到了广泛的关注.无衰减振荡具有在日冕中广泛存在以及振幅无明显变小的特性,使之在解释日冕加热和冕震学诊断上都具有相当的潜力.总结了日冕中无衰减振荡的研究进展,包括观测研究得到的一系列结果、提出的理论和数值模型以及基于无衰减振荡进行冕震学诊断的一些尝试,并且展望了未来可以进一步开展的研究.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

Seismology of Oscillating Flux Tube with Twisted Magnetic Field and Plasma Flow

Transverse oscillations of a thin coronal loop in a zero-beta plasma in the presence of a twisted magnetic field and flow are investigated. The dispersion relation is obtained in the limit of weak twist. The twisted magnetic field modifies the phase difference and asymmetry of standing kink oscillations caused by the flow. Using data from observations the kink speed and flow speed have been determined. The presence of the twisted magnetic field can cause underestimation or overestimation of the flow speed in coronal loops depending on the direction of the flow and twisted magnetic field, but a twisted magnetic field has little effect on the estimated value of the kink speed.     

The Effect of a Twisted Magnetic Field on the Nature of Kink MHD Waves

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvénic wave in the entire loop.     

Kink oscillations of asymmetric coronal loops

The free oscillations of coronal loops with a constant density and a variable magnetic field changing according to parabolic laws are investigated. Using our developed method, we derive the wave equations with constant coefficients that describe the kink oscillations of symmetric and asymmetric magnetic flux tubes. For such models, we obtain analytical expressions for the oscillation spectra and amplitudes as well as the magnitudes and directions of the displacements of the extrema of the fundamental and first modes relative to their values for homogeneous tubes. For the first mode of an asymmetric loop, we have determined the dependence of the coordinate displacement for the internal node on the ratios of the magnetic field strengths in its asymmetric parts and the ratio of the amplitudes at the extremum points.     

Radiation effects on the MHD wave behavior in the solar corona

The effect of radiation losses on the dispersion and damping of magnetohydrodynamic waves in the solar corona is studied. The conditions are determined under which radiation losses are most appreciable. A damping of kink modes of coronal loops with plasma temperatures within 10⁶–10^6.3 K and 10^6.3–10⁷ K are compared. It is concluded that the radiation damping dominates in the temperature range 10⁶–10^6.3 K, which can cause the observed fast damping of kink oscillations of coronal loops. Radiation losses should be taken into account in full magnetohydrodynamic equations with radiative transfer.     

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.     

Observation of kink waves and their reconnection-like origin in solar spicules

We analyze the time series of Ca?ii H-line obtained from Hinode/SOT on the solar limb. We follow three cases of upwardly propagating kink waves along a spicule and inverted Y-shaped structures at the cusp of it. 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 ～175 s and the mean amplitude is 1 arc?sec. The oscillation periods are increasing linearly with height which may be counted as the signature that the spicule is working as a low pass filter and allows only the low frequencies to propagate towards higher heights. The oscillations amplitude is increasing with height due to decrease in density. The phase speeds are increasing until some heights and then decreasing which may be related to the small scale reconnection at the spicule basis. We conclude that transversal displacement of spicules axis can be related to the propagation of kink waves along them. Moreover, we observe signatures of small-scale magnetic reconnection at the cusp of spicules which may excite kink waves.     

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.     

Magneto‐seismology of the solar atmosphere

Magnetohydrodynamic (MHD) waves in solar coronal loops, which were previously only predicted by theory have actually been detected with space‐borne instruments. These observations have given an important and novel tool to measure fundamental parameters in the magnetically embedded solar corona. This paper will illustrate how information about the magnetic and density structure along coronal loops can be determined by measuring the frequency or amplitude profiles of standing fast kink mode oscillations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonaxisymmetric Oscillations of Thin Twisted Magnetic Tubes

In this paper we study nonaxisymmetric oscillations of thin twisted magnetic tubes taking the density variation along the tube into account. We use the approximation of the zero-beta plasma. The magnetic field outside the tube is straight and homogeneous; however, it is twisted inside the tube. We assume that the azimuthal component of the magnetic field is proportional to the distance from the tube axis and that the tube is only weakly twisted (i.e., the ratio of the azimuthal and axial components of the magnetic field is small). Using the asymptotic analysis we show that the eigenmodes and eigenfrequencies of the kink and fluting oscillations are described by a classical Sturm – Liouville problem for a second-order ordinary differential equation. The main result is that the twist does not affect the kink mode.     

The Effect of Magnetic and Density Differences on the Fast Kink Oscillations of Neighboring Coronal Loops

It is reasonable that neighboring coronal loops may obtain similar momentum during a flare. The fast kink oscillations (FKOs) between them are thus mainly influenced by their physical differences. We discuss the dependencies of FKO on the physical properties of coronal loops in a low-\(\beta \) thin-tube approximation. From the analysis, we obtain the analytic relationship between the density [\(\rho _{\mathrm{i}}\)] and magnetic field [\(B\)] of loops and the corresponding period [\(\tau \)] and amplitude [\(A\)] of FKO, which may provide us with a powerful tool to diagnose the physical differences between neighboring loops.     

Radio Pulsating Structures with Coronal Loop Contraction

We present a multi-wavelength study of a solar eruption event on 20 July 2004, comprising observations in H??, EUV, soft X-rays, and in radio waves with a wide frequency range. The analyzed data show both oscillatory patterns and shock wave signatures during the impulsive phase of the flare. At the same time, large-scale EUV loops located above the active region were observed to contract. Quasi-periodic pulsations with ???10 and ???15 s oscillation periods were detected both in microwave??C?millimeter waves and in decimeter??C?meter waves. Our calculations show that MHD oscillations in the large EUV loops ?C but not likely in the largest contracting loops ?C could have produced the observed periodicity in radio emission, by triggering periodic magnetic reconnection and accelerating particles. As the plasma emission in decimeter??C?meter waves traces the accelerated particle beams and the microwave emission shows a typical gyrosynchrotron flux spectrum (emission created by trapped electrons within the flare loop), we find that the particles responsible for the two different types of emission could have been accelerated in the same process. Radio imaging of the pulsed decimetric??C?metric emission and the shock-generated radio type II burst in the same wavelength range suggest a rather complex scenario for the emission processes and locations. The observed locations cannot be explained by the standard model of flare loops with an erupting plasmoid located above them, driving a shock wave at the CME front.     

Ballooning Instability in Coronal Flare Loops

Within the framework of ideal magnetohydrodynamics the excitation of the ballooning instability in a toroidal coronal loop with a radius of cross section a and a radius of curvature R is analyzed by using the energy method. Kink oscillations are able to excite the ballooning instability when the plasma beta parameter β>2a/R. It has been suggested that this can result in the formation of cusp-shaped coronal loops. Modulation of gyrosynchrotron emission caused by kink oscillations is considered. The intensity of gyrosynchrotron emission for optically thin sources is the most sensitive to Alfvén disturbances. The obtained theoretical results are discussed in the light of Yohkoh, SOHO, TRACE, RHESSI, and Nobeyama observations.     

Dissipation of Standing Slow Magnetoacoustic Waves in Hot Coronal Loops

The damping of standing slow waves in hot (T>6 MK) coronal loops of semicircular shape is revisited in both the linear and nonlinear regimes. Dissipation by thermal conduction, compressive viscosity, radiative cooling, and heating are examined for nonstratified and stratified loops. We find that for typical conditions of hot SUMER loops, thermal conduction increases the period of damped oscillations over the sound-crossing time, whereas the decay times are mostly shaped by compressive viscosity. Damping from optically thin radiation is negligible. We also find that thermal conduction alone results in slower damping of the density and velocity waves compared to the observations. Only when compressive viscosity is added do these waves damp out at the same rate as the observed rapidly decaying modes of hot SUMER loop oscillations, in contrast to most current work, which has pointed to thermal conduction as the dominant mechanism. We compare the linear predictions with numerical hydrodynamic calculations. Under the effects of gravity, nonlinear viscous dissipation leads to a reduction of the decay time compared to the homogeneous case. In contrast, the linear results predict that the damping rates are barely affected by gravity.     

Propagation of the Slow Magnetoacoustic Waves in Coronal Loops Above Sunspots

The observations from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) have revealed the weak dis- turbances (WDs) propagating in the fan-like coronal loops of the active region (AR 11092) at 171 ?A, 193 ?A, and 211 ?A. These WDs seem to be a common phenomenon in this part of the active region. The disturbances originate from the bright loop foot, and propagate along the loops. The observed propagation speed decreases with the increasing temperature, and varies between 40 km/s and 121 km/s, close to and less than the sound speed in coronal loops. Consid- ering the projection effect and the different angles of the loops with respect to the line of sight, this is exactly what the slow-wave model expects. The wavelet analysis shows that the periods of the WDs observed in different wavebands have no signi?cant difference, the two distinct periods, 3 min and more than 10 min, are all detected in the three EUV wavebands. Not only the coronal loops but also the sunspot region in the chromosphere exhibit intensity oscillations with a period of the order of 3 min. This result suggests that the sunspot oscillations can propagate into the corona through the chromosphere and transition region.     

Wave propagation in a magnetic cylinder

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvénic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvénic-type, oscillations arise only in high density (strictly, low Alfvén velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.     

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