Non-reflective Propagation of Kink Waves in Coronal Magnetic Loops

Propagating kink waves are ubiquitously observed in solar magnetic wave guides. We consider the possibility that these waves propagate without reflection although there is some inhomogeneity. We briefly describe the general theory of non-reflective, one-dimensional wave propagation in inhomogeneous media. This theory is then applied to kink-wave propagation in coronal loops. We consider a coronal loop of half-circle shape embedded in an isothermal atmosphere, and assume that the plasma temperature is the same inside and outside the loop. We show that non-reflective kink-wave propagation is possible for a particular dependence of the loop radius on the distance along the loop. A viable assumption that the loop radius increases from the loop footpoint to the apex imposes a lower limit on the loop expansion factor, which is the ratio of the loop radii at the apex and footpoints. This lower limit increases with the loop height; however, even for a loop that is twice as high as the atmospheric scale height, it is small enough to satisfy observational constraints. Hence, we conclude that non-reflective propagation of kink waves is possible in a fairly realistic model of coronal loops.     

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.     

Propagation and Damping of a Localized Impulsive Longitudinal Perturbation in Coronal Loops

We use linear analysis to simulate the evolution of a coronal loop in response to a localized impulsive event. The disturbance is modeled by injecting a narrow Gaussian velocity pulse near one footpoint of a loop in equilibrium. Three different damping mechanisms, namely viscosity, thermal conduction, and optically thin radiation, are included in the loop calculations. We consider homogeneous and gravitationally stratified, isothermal loops of varying length (50≤L≤400 Mm) and temperature (2≤T≤10 MK). We find that a localized pulse can effectively excite slow magnetoacoustic waves that propagate up along the loop. The amplitudes of the oscillations increase with decreasing loop temperature and increasing loop length and size of the pulse width. At T≥4 MK, the waves are dissipated by the combined effects of viscosity and thermal conduction, whereas at temperatures of 2 MK, or lower, wave dissipation is governed by radiative cooling. We predict periods in the range of 4.6?–?41.6 minutes. The wave periods remain unaltered by variations of the pulse size, decrease with the loop temperature, and increase almost linearly with the loop length. In addition, gravitational stratification results in a small reduction of the periods and amplification of the waves as they propagate up along the loop.     

慢磁声波在黑子上方冕环中的传播

太阳动力学观测站(Solar Dynamics Observatory,SDO)装载的太阳大气成像系统(Atmospheric Imaging Assembly,AIA)通过3个极紫外波段(171 (A)、193 (A)和211 (A))的观测资料展现了太阳活动区(AR11092)扇形冕环微弱的扰动传播,这种波动现象普遍存在于活动区冕环.该扰动传播起源于明亮的环足处,其传播沿冕环方向.冕环中观测到的扰动传播速度随温度升高而减小,速度范围是40～121 km/s,其值接近且小于声速.考虑投影效应以及环与视线方向的倾角大小,这正好是慢波模型所预期的.冕环的扰动周期在不同波段(3个极紫外波段)没有明显的区别,都存在3 min以及10多分钟的周期.此外,不仅仅冕环扰动表现出3 min左右的周期,色球层的黑子区域同样存在相同的振荡周期.这个结果表明黑子振荡是可以穿过色球以及过渡区到达日冕的.     

Cross-Sectional Properties of Coronal Loops

Careful examination of 43 soft X-ray loops observed by Yohkoh has revealed a number of interesting properties of the loop cross section. First, the loops tend to be only slightly ( 30%) wider at their midpoints than at their footpoints, implying less-than-expected expansion of the magnetic field. Second, the variation of width along each loop tends to be modest, implying that the cross section has an approximately circular shape. And third, cross-axis intensity profiles tend to be singly-peaked and simple, implying that the cross section is approximately uniformly filled on resolvable scales. We conclude that the energy which heats the plasma is either dissipated axially symmetrically on a scale equal to a loop diameter ( 11000 km) or else is dissipated with any spatial structure, but on a scale much smaller than a loop diameter, and then transported laterally in an axisymmetric fashion (perhaps via conduction along chaotic field lines). In their present form, none of the theoretical ideas concerning the magnetic structure and heating of loops are obviously capable of explaining all of the observed properties.     

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).     

冕环电流的成因分析

将冕环电流按成因分成三种类型：对流电流、感应电流和自举电流，并分别进行了讨论。将tokamak等离子体中的自举电流的概念引入到冕环中，初步分析表明在部分冕环中也可能产生可观的自举电流。这种电流的存在将对冕环的稳定性将产生重要的影响。     

Latent Heating of Coronal Loops

This paper is aimed at establishing the relationship between the large-scale magnetic fields (LSMF), coronal holes (CH), and active regions (AR) in the Sun. The LSMF structure was analyzed by calculating the vector photospheric magnetic field under a potential approximation. Synoptic maps were drawn to study the distribution of the B field component and to isolate regions where the open field lines of the unipolar magnetic field are most radial. These are the sites of occurrence of X-ray and Hei 10830 Å coronal holes detected from the SXT/Yohkoh images. It is shown that coronal holes are usually located in LSMF regions with a typical pattern of divergentB vectors and a so-called saddle configuration.B vectors from the conjugate (spaced by 90°) coronal holes converge towards the active regions between CH. Variations in AR distort coronal holes and change their boundaries. This implies that the energy regime in CH depends on the energy supply from the active region. The LSMF structure is more stable than coronal holes, remaining practically unchanged during tens of rotations of the Sun. Thus, a peculiar magnetically coupled system of LSMF/CH/AR has been revealed. A model has been suggested to describe the interaction of the emerging toroids in the convection zone and in the photosphere. The cellular convection, that develops at the center of the toroids, is responsible for the occurrence of active regions. The model qualitatively describes the observed particularities of the LSMF/CH/AR system.     

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.     

Statistical Analysis of Periodic Oscillations in LASCO Coronal Mass Ejection Speeds

A large set of coronal mass ejections (CMEs, 3463) has been selected to study their periodic oscillations in speed in the Solar and Heliospheric Observatory (SOHO) mission’s Large Angle and Spectrometric Coronagraph (LASCO) field of view. These events, reported in the SOHO/LASCO catalog in the period of time 1996?–?2004, were selected based on having at least 11 height–time measurements. This selection criterion allows us to construct at least ten-point speed–distance profiles and evaluate kinematic properties of CMEs with a reasonable accuracy. To identify quasi-periodic oscillations in the speed of the CMEs a sinusoidal function was fitted to speed–distance profiles and the speed–time profiles. Of the considered events 22 % revealed periodic velocity fluctuations. These speed oscillations have on average amplitude equal to \(87~\mbox{km}\,\mbox{s}^{-1}\) and period \(7.8 R _{\odot}/241~\mbox{min}\) (in distance/time). The study shows that speed oscillations are a common phenomenon associated with CME propagation implying that all the CMEs have a similar magnetic flux-rope structure. The nature of oscillations can be explained in terms of magnetohydrodynamic (MHD) waves excited during the eruption process. More accurate detection of these modes could, in the future, enable us to characterize magnetic structures in space (space seismology).     

Coronal Seismology Using Transverse Oscillations of Non-planar Coronal Loops

We continue studying the robustness of coronal seismology. We concentrate on two seismological applications: the estimate of coronal scale height using the ratio of periods of the fundamental harmonic and first overtone of kink oscillations, and the estimate of magnetic-field magnitude using the fundamental harmonic. Our analysis is based on the model of non-planar coronal loops suggested by Ruderman and Scott (Astron. Astrophys. 529, A33, 2011), which was formulated using the linearized MHD equations. We show that the loop non-planarity does not affect the ratio of periods of the fundamental harmonic and first overtone, and thus it is unimportant for the estimates of the coronal scale height. We also show that the density variation along the loop and the loop non-planarity only weakly affect the estimates of the magnetic-field magnitude. Hence, using the simplest model of coronal loops, which is a straight homogeneous magnetic cylinder, provides sufficiently accurate estimates for the magnetic-field magnitude.     

Magnetic Stereoscopy of Coronal Loops in NOAA 8891

The Solar TErrestrial RElations Observatory (STEREO) requires powerful tools for the three-dimensional (3D) reconstruction of the solar corona. Here we test such a program with data from SOHO and TRACE. By taking advantage of solar rotation, a newly developed stereoscopy tool for the reconstruction of coronal loops is applied to the solar active region NOAA 8891 observed from 1 March to 2 March 2000. The stereoscopic reconstruction is composed of three steps. First, we identify loop structures in two TRACE images observed from two vantage viewpoints approximately 17 degrees apart, which corresponds to observations made about 30 hours apart. In the second step, we extrapolate the magnetic field in the corona with the linear force-free field model from the photospheric line-of-sight SOHO/MDI data. Finally, combining the extrapolated field lines and one-dimensional loop curves from two different viewpoints, we obtain the 3D loop structures with the magnetic stereoscopy tool. We demonstrate that by including the magnetic modeling this tool is more powerful than pure geometrical stereoscopy, especially in resolving the ambiguities generated by classical stereoscopy. This work will be applied to the STEREO mission in the near future.     

Segmentation of Loops from Coronal EUV Images

We present a procedure to extract bright loop features from solar EUV images. In terms of image intensities, these features are elongated ridge-like intensity maxima. To discriminate the maxima, we need information about the spatial derivatives of the image intensity. Commonly, the derivative estimates are strongly affected by image noise. We therefore use a regularized estimation of the derivative, which is then used to interpolate a discrete vector field of ridge points; these “ridgels” are positioned on the ridge center and have the intrinsic orientation of the local ridge direction. A scheme is proposed to connect ridgels to smooth, spline-represented curves that fit the observed loops. Finally, a half-automated user interface allows one to merge or split curves or eliminate or select loop fits obtained from this procedure. In this paper we apply our tool to one of the first EUV images observed by the SECCHI instrument onboard the recently launched STEREO spacecraft. We compare the extracted loops with projected field lines computed from near-simultaneous magnetograms measured by the SOHO/MDI Doppler imager. The field lines were calculated by using a linear force-free field model. This comparison allows one to verify faint and spurious loop connections produced by our segmentation tool and it also helps to prove the quality of the magnetic-field model where well-identified loop structures comply with field-line projections. We also discuss further potential applications of our tool such as loop oscillations and stereoscopy.     

Nonlinear Kink Oscillations of Coronal Magnetic Loops

We studied nonlinear kink oscillations of a thin magnetic tube using the cold-plasma approximation. We assumed that the plasma density varies along the tube but does not vary in the radial direction. Using the regular perturbation method, we show that the nonlinearity does not affect the oscillation amplitude. We also calculated the nonlinear correction to the oscillation frequency, which is proportional to the oscillation amplitude squared. As an example, we considered nonlinear oscillations of a coronal magnetic loop of half-circle shape in an isothermal atmosphere with equal plasma temperatures inside and outside the loop.     

Determination of the True Shape of Coronal Loops

Using line of sight velocity measurements from the SUMER and CDS instruments aboard SOHO, in conjunction with a simple geometrical model, we reconstructed the true, 3D shape and the velocity of plasma flow along coronal loops. The projection of the loop on the sky and the position of the footpoints define a family of curves. Assuming that the loop is located on a plane, the line of sight velocity can be used to select the most plausible solution. For two loops, observed in the Ne viii? 770 Å and O v? 630 Å spectral lines, we find asymmetric, subsonic uni-directional flows, with velocity maxima of ≈?80 km?s^?1 near the footpoints. The loops are highly inclined with respect to the vertical, by 55^○ and 70^○, respectively; thus the true height of the loop tops from the photospheric level is ≈?20^′′, comparable to the isothermal scale height.     

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.     

A Code for Automated Tracing of Coronal Loops Approaching Visual Perception

We develop a new numerical code with automated feature extraction, customized for tracing of coronal loops, a method we call Oriented Coronal CUrved Loop Tracing (OCCULT), which for the first time breaks even with the results of visual tracing. The method used is based on oriented-directivity tracing of curvi-linear features, but in contrast to other general feature-extraction algorithms, it is customized for solar EUV and SXR images by taking advantage of the specific property that coronal loops have large curvature radii compared with their widths. We evaluate the performance of this new code by comparing the cumulative distribution of loop lengths, the median and maximum loop lengths, the completeness of detection, and the congruency of the detected features with other numerical codes and visual tracings. We find that the new code closely approaches the results of visual perception and outperforms the other existing numerical codes. This algorithm is useful for the 3D reconstruction of the geometry, motion, and oscillations of coronal loops, with single or stereoscopic spacecraft, as well as for modeling of the loop hydrodynamics and the coronal magnetic field.     

Dissipation of Longitudinal Oscillations in Stratified Nonisothermal Hot Coronal Loops

We investigate the damping of longitudinal (i.e., slow or acoustic) waves in nonisothermal, hot (T≥ 5.0 MK), gravitationally stratified coronal loops. Motivated by SOHO/SUMER and Yohkoh/SXT observations, and by taking into account a range of dissipative mechanisms such as thermal conduction, compressive viscosity, radiative cooling, and heating, the nonlinear governing equations of one-dimensional hydrodynamics are solved numerically for standing-wave oscillations along a magnetic field line. A semicircular shape is chosen to represent the geometry of the coronal loop. It was found that the decay time of standing waves decreases with the increase of the initial temperature, and the periods of oscillations are affected by the different initial footpoint temperatures and loop lengths studied by the numerical experiments. In general, the period of oscillation of standing waves increases and the damping time decreases when the parameter that characterises the temperature at the apex of the loop increases for a fixed footpoint temperature and loop length. A relatively simple second-order scaling polynomial between the damping time and the parameter determining the apex temperature is found. This scaling relation is proposed to be tested observationally. Because of the lack of a larger, statistically relevant number of observational studies of the damping of longitudinal (slow) standing oscillations, it can only be concluded that the numerically predicted decay times are well within the range of values inferred from Doppler shifts observed by SUMER in hot coronal loops.     

Surface and Fundamental Modes of Oscillations in Thin Coronal Loops

Astronomy Letters - The oscillations in thin magnetic flux tubes in the solar corona are considered. The surface and fundamental modes of oscillations are shown to be the main modes of fast and...