Using full three-dimensional magnetohydrodynamic numerical simulations, we study the effects of magnetic field sigmoidity or helicity on the properties of the fundamental kink oscillation of solar coronal loops. Our model consists of a single denser coronal loop, embedded in a plasma with dipolar force-free magnetic field with a constant alpha-parameter. For the loop with no sigmoidity, we find that the numerically determined oscillation period of the fundamental kink mode matches the theoretical period calculated using WKB theory. In contrast, with increasing sigmoidity of the loop, the actual period is increasingly smaller than the one estimated by WKB theory. Translated through coronal seismology, increasing sigmoidity results in magnetic field estimates which are increasingly shifting towards higher values, and even surpassing the average value for the highest alpha value considered. Nevertheless, the estimated range of the coronal magnetic field value lies within the mimimal/maximal limits, proving the robustness coronal seismology. We propose that the discrepancy in the estimations of the absolute value of the force-free magnetic field could be exploited seismologically to determine the free energy of coronal loops, if averages of the internal magnetic field and density can be reliably estimated by other methods.
We report and analyze the observational evidence of global kink oscillations in a solar filament as observed in H alpha by National Solar Observatory (NSO)/Global Oscillation Network Group (GONG) instrument. An M1.1-class flare in active region 11692 on 2013 March 15 induced a global kink mode in the filament lying in the south-west of AR11692.We find periods of about 61 - 67 minutes and damping times of 92 - 117 minutes at three vertical slice positions chosen in and around the filament apex. We find that the waves are damped. From the observed global kink mode period and damping time scale u…
The ubiquity of recently discovered low-amplitude decayless kink oscillations of plasma loops allows for the seismological probing of the corona on a regular basis. In particular, in contrast to traditionally applied seismology which is based on the large-amplitude decaying kink oscillations excited by flares and eruptions, decayless oscillations can potentially provide the diagnostics necessary for their forecasting. We analysed decayless kink oscillations in several distinct loops belonging to active region NOAA 12107 on 10 July 2010 during its quiet time period, when it was observed on the …
We investigate standing kink magnetohydrodynamic (MHD) oscillations in a prominence fine structure modeled as a straight and cylindrical magnetic tube only partially filled with the prominence material, and with its ends fixed at two rigid walls representing the solar photosphere. The prominence plasma is partially ionized and a transverse inhomogeneous transitional layer is included between the prominence thread and the coronal medium. Thus, ion-neutral collisions and resonant absorption are the considered damping mechanisms. Approximate analytical expressions of the period, the damping time,…
We report the observation of the first two harmonics of the horizontally polarized kink waves excited in a coronal loop system lying at south-east of AR 11719 on 2013 April 11. The detected periods of the fundamental mode ($P_1$), its first overtone ($P_2$) in the northern half, and that in the southern one are $530.2 \pm 13.3$, $300.4 \pm 27.7$, and $334.7 \pm 22.1$ s, respectively. The periods of the first overtone in the two halves are the same considering uncertainties in the measurement. We estimate the average electron density, temperature, and length of the loop system as $(5.1 \pm 0.8)…
There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds, however after flaring and coronal mass ejection events flows can become Alfvénic. In this Letter, we derive an expression for the standing kink mode frequency due to siphon flow in coronal loops, valid for both low and high speed regimes. It is found that siphon flow introduces a linear spatially dependent phase shift along coronal loops and asymmetric eigenfunctions. We demonstrate how this theory can be used to determine the kink and flow speed of oscillating coronal loops with reference to an observational c…
The ratio of the period of the fundamental mode to that of the first overtone of kink oscillations, from here on the "period ratio", is a seismology tool that can be used to infer information about the spatial variation of density along solar magnetic flux tubes. The period ratio is 2 in longitudinally homogeneous thin tubes, but it differs from 2 due to longitudinal inhomogeneity. In this paper we investigate the period ratio in longitudinally inhomogeneous prominence threads and explore its implications for prominence seismology. We numerically solve the two-dimensional eigenvalue problem of…
Coronal seismology is extensively used to estimate properties of the corona, e.g. the coronal magnetic field strength are derived from oscillations observed in coronal loops. We present a three-dimensional coronal simulation including a realistic energy balance in which we observe oscillations of a loop in synthesised coronal emission. We use these results to test the inversions based on coronal seismology. From the simulation of the corona above an active region we synthesise extreme ultraviolet (EUV) emission from the model corona. From this we derive maps of line intensity and Doppler shift…
Observations on 2011 August 9 of an X6.9-class flare in active region (AR) 11263 by the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SDO), were followed by a rare detection of vertical kink oscillations in a large-scale coronal active region plasma curtain in EUV coronal lines. The damped oscillations with periods in the range 8.8-14.9 min were detected and analyzed recently. Our aim is to study the generation and propagation of the MHD oscillations in the plasma curtain taking into account realistic 3D magnetic and density structure of the curtain. We also aim a…
The Effect of Gravitational Stratification on Kink Oscillations in Curved Coronal Loops
Institute of Frontier and Interdisciplinary Science, Shandong University（山东大学前沿交叉科学研究中心）；Shandong Key Laboratory of Space Environment and Exploration Technology, Institute of Space Sciences, Shandong University（山东大学空间科学学院）
We report on three-dimensional (3D) MHD simulations of recurrent mini CME-like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions are developed as a result of repeated formation and expulsion of new flux ropes due to continous emergence and reconnection of sheared fieldlines along the polarity inversion line (PIL) of the AR. The acceleration of the eruptions is triggered by tether-cutting reconnection at the current sheet underneath the erupting field. We find that each explosive …
In this work, we report our multi-wavelength observations of the transverse oscillation of a large scale coronal loop with a length of 350 Mm. The oscillation was induced by a blowout coronal jet, which was related to a circular ribbon flare (CRF) in AR 12434 on 2015 October 16. We aim to determine the physical parameters in the coronal loop, including the Alfven speed and magnetic field strength. The jet induced kink oscillation was observed in extreme-ultraviolet (EUV) wavelengths by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Line of sight magnetogr…
Seismology of coronal loops using observations of damped transverse oscillations in combination with results from theoretical models is a tool to indirectly infer physical parameters in the solar atmospheric plasma. Existing seismology schemes based on approximations to the period and damping time of kink oscillations are often used beyond their theoretical range of applicability. These approximations assume that the variation of density across the loop is confined to a nonuniform layer much thinner than the radius of the loop, but the results of the inversion problem often do not satisfy this…
We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features, observed with imaging instruments. The method is based on the two-dimensional dual tree complex wavelet transform (DT$\mathbb{C}$WT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes imitating exponentially decaying, mult…
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 undergoes quasi-periodic transverse displacement. We determined the period of transverse displacement as ~40-150 s and the mean amplitude as ~ 0.1-0.5 arcsec. For the oscillation wavelength of $λ$ ~ 1/0.06 arcsec ~ 11500 km, the estimated kink speed is ~ 13-83 km/s. We obtained the magnetic field strength in spicules as B_0 = 2 - 12.5 G and the energy flux as 7 - 227 J/m^-2s.
We analyse the oscillatory properties of resonantly damped transverse kink oscillations in two-dimensional prominence threads. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary non-uniformly in both the transverse and the longitudinal directions.We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving…
We present the formation and eruption of a sigmoidal filament driven by rotating network magnetic fields (RNFs) near the center of the solar disk, which was observed by the one-meter aperture New Vacuum Solar Telescope (NVST) at Fuxian Solar Observatory (FSO) on 2018 July 12. Counterclockwise RNFs twist two small-scale filaments at their northeastern foot-point region, giving a rotation of nearly 200 degree within about 140 minutes. The motion of the RNF has a tendency to accelerate at first and then decelerate obviously, as the average rotation speed increased from 10 to 150 ,and then slowed …
We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube and thin boundary approximations. For the inverse problem, we adopt a Bayesian approach to infer the most probable values of the relevant parameters, for given observed periods and damping times, and to extract their confidence levels. The posterior probability distribution functions are obtained by means of Markov Chain Monte Carlo simulations, incorporating…
Magnetohydrodynamic (MHD) kink waves have been observed frequently in solar coronal flux tubes, which makes them a great tool for seismology of the solar corona. Here, the effect of viscosity is studied on the evolution of kink waves. To this aim, we solve the initial value problem for the incompressible linearized viscous MHD equations in a radially inhomogeneous flux tube in the limit of long wavelengths. Using a modal expansion technique the spatio-temporal behavior of the perturbations is obtained. We confirm that for large Reynolds numbers representative of the coronal plasma the decremen…
Impulsively excited wave trains are of considerable interest in solar coronal seismology. To our knowledge, however, it remains to examine the three-dimensional (3D) dispersive propagation of impulsive kink waves in straight, field-aligned, symmetric, low-beta, slab equilibria that are structured only in one transverse direction. We offer a study here, starting with an analysis of linear oblique kink modes from an eigenvalue problem perspective. Two features are numerically found for continuous and step structuring alike, one being that the group and phase velocities may lie on opposite sides …
We present a Bayesian seismology inversion technique for propagating magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The technique uses theoretical predictions for the spatial damping of propagating kink waves in transversely inhomogeneous coronal waveguides. It combines wave amplitude damping length scales along the waveguide with theoretical results for resonantly damped propagating kink waves to infer the plasma density variation across the oscillating structures. Provided the spatial dependence of the velocity amplitude along the propagation direction is measured…
We study recent observations of propagating fluctuations in a prominence foot with Hinode Solar Optical Telescope (SOT) high-resolution observations in Ca~II and H alpha emission which we identify as nonlinear fast magnetosnic waves. Here we analyze further the observations of propagating waves and flows with Interface Region Imaging Spectrograph (IRIS) Mg~II slit jaw images, in addition to Hinode/SOT Ca~II images. We find that the waves have typical periods in the range of 5 - 11 minutes and wavelengths in the plane of the sky (POS) of about 2000 km, while the flows in narrow threads have typ…
Recent observations have revealed the ubiquitous presence of magnetohydrodynamic (MHD) waves and oscillations in the solar corona. The aim of this review is to present recent progress in the observational study of four types of wave (or oscillation) phenomena mainly occurring in active region coronal loops, including (i) flare-induced slow mode oscillations, (ii) fast kink mode oscillations, (iii) propagating slow magnetoacoustic waves, and (iv) ubiquitous propagating kink (Alfvenic) waves. This review not only comprehensively outlines various aspects of these waves and coronal seismology, but…
Standing oscillations with multiple periods were found in a number of atmospheric structures on the Sun. The ratio of the period of the fundamental to twice the one of its first overtone, $P_1/2P_2$, is important in applications of solar magneto-seismology. We examine how field-aligned flows impact $P_1/2P_2$ of standing modes in solar magnetic cylinders. For coronal loops, the flow effects are significant for both fast kink and sausage modes. For kink ones, they reduce $P_1/2P_2$ by up to 17\% relative to the static case even when the density contrast between the loop and its surroundings app…
Kink oscillations of coronal loops, i.e., standing kink waves, is one of the most studied dynamic phenomena in the solar corona. The oscillations are excited by impulsive energy releases, such as low coronal eruptions. Typical periods of the oscillations are from a few to several minutes, and are found to increase linearly with the increase in the major radius of the oscillating loops. It clearly demonstrates that kink oscillations are natural modes of the loops, and can be described as standing fast magnetoacoustic waves with the wavelength determined by the length of the loop. Kink oscillati…
An eruption event launched from solar active region (AR) NOAA 11719 is investigated based on coronal EUV observations and photospheric magnetic field measurements obtained from Solar Dynamic Observatory. The AR consists of a filament channel originating from major sunspot and its south section is associated with inverse-S sigmoidal system as observed in AIA passbands. We regard the sigmoid as the main body of the flux rope (FR). There also exists a twisted flux bundle crossing over this FR. This overlying flux bundle transforms in shape similar to kink-rise evolution which has correspondence w…
This paper separately evaluates the effects of inclination and asymmetry of solar coronal loops on the resonant absorption of kink magnetohydrodynamic (MHD) oscillations. We modelled a typical coronal loop by a straight and axisymmetric cylindrical magnetic flux tube filled with cold plasma. We solved the dispersion relation numerically for different values of the longitudinal mass density stratification. We show that, in inclined and asymmetric loops, the frequencies and their corresponding damping rates of the fundamental and first-overtone modes of kink oscillations are smaller in compariso…
In the applications of solar magneto-seismology(SMS), employing the ratio of the period of the fundamental mode to twice the one of its first overtone, $P_1/2P_2$, plays an important role. We examine how field-aligned flows affect the dispersion properties, and hence the period ratios, of standing modes supported by magnetic slabs in the solar atmosphere. We numerically solve the dispersion relations and devise a graphic means to construct standing modes. For coronal slabs, we find that the flow effects are significant, for the fast kink and sausage modes alike. For the kink ones, they may red…
Transverse oscillations of thin threads in solar prominences are frequently reported in high-resolution observations. Two typical features of the observations are that the oscillations are damped in time and that simultaneous mass flows along the threads are detected. Flows cause the dense threads to move along the prominence magnetic structure while the threads are oscillating. The oscillations have been interpreted in terms of standing magnetohydrodynamic (MHD) kink waves of the magnetic flux tubes which support the threads. The damping is most likely due to resonant absorption caused by pla…
Coronal loops exist ubiquitously in the solar atmosphere. These loops puzzle astronomers over half a century. Solar magneto-seismology (SMS) provides a unique way to constrain the physical parameters of coronal loops. Here, we study the evolution of oscillations of a coronal loop observed by the Atmospheric Imaging Assembly (AIA). We measure geometric and physical parameters of the loop oscillations. In particular, we find that the mean period of the oscillations increased from 1048 to 1264 s during three oscillatory cycles. We employ the differential emission measure method and apply the tool…
Using MHD seismology by observed kink waves, the magnetic field profile of a coronal streamer has been investigated. STEREO-B/EUVI temporal image data on 7 March 2012 shows an evolution of two consecutive EUV waves that interact with the footpoint of a coronal streamer evident in the co-spatial and co-temporal STEREO-B/COR-I observations. The evolution of EUV waves is clearly evident in STEREO-B/EUVI, and its energy exchange with coronal streamer generates kink oscillations. We estimate the phase velocities of the kink wave perturbations by tracking it at different heights of the coronal strea…
Using the spectroscopic imaging capabilities of the Swedish Solar Telescope, we aim to provide the first investigation on the nature and dynamics of elongated absorption features (fibrils) observed in H$α$ in the internetwork. We observe and identify a number of internetwork fibrils, which form away from the kilogauss, network magnetic flux, and we provide a synoptic view on their behaviour. The internetwork fibrils are found to support wave-like behaviour, which we interpret as Magnetohydrodynamic (MHD) kink waves. The properties of these waves, that is, amplitude, period, and propagation spe…
We describe the long-term evolution of a bipolar non-Hale active region which was observed from October, 1995, to January, 1996. Along these four solar rotations the sunspots and subsequent flux concentrations, during the decay phase of the region, were observed to move in such a way that by December their orientation conformed to the Hale-Nicholson polarity law. The sigmoidal shape of the observed soft X-ray coronal loops allows us to determine the sense of the twist in the magnetic configuration. This sense is confirmed by extrapolating the observed photospheric magnetic field, using a linea…
Observed oscillations of coronal loops in EUV lines have been successfully used to estimate plasma parameters in the inner corona (< 0.2 R_0, where R_0 is the solar radius). However, coronal seismology in EUV lines fails for higher altitudes because of rapid decrease in line intensity. We aim to use radio observations to estimate the plasma parameters of the outer solar corona (> 0.2 R_0). We use the large Ukrainian radio telescope URAN-2 to observe type IV radio burst at the frequency range of 8-32 MHz during the time interval of 09:50-12:30 UT in April 14, 2011. The burst was connected to C2…
The cross sections of solar coronal loops are suggested to be rarely circular. We examine linear kink oscillations in straight, density-enhanced, magnetic cylinders with elliptical cross-sections by solving the three-dimensional magnetohydrodynamic equations from an initial-value-problem perspective. Motivated by relevant eigen-mode analyses, we distinguish between two independent polarizations, one along the major axis (the M-modes) and the other along the minor one (the m-modes). We find that, as happens for coronal loops with circular cross-sections, the apparent damping of the transverse d…
Coronal loop oscillations are common phenomena in the solar corona, which are often classified as decaying and decayless oscillations. Using the high-resolution observation measured by the Extreme Ultraviolet Imager (EUI) onboard the Solar Orbiter, we statistical investigate small-scale transverse oscillations with short periods (<200 s) of coronal loops in an active region, i.e., NOAA 12965. A total of 111 coronal loops are identified in EUI 174 A images, and they all reveal transverse oscillations without any significant decaying, regarding as decayless oscillations. Oscillatory periods are …
In this study, the properties of wavefunctions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero-βapproximation. A single three-dimensional wave equation (eigen value problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method (FEM). Wavefunctions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink and fluting modes. Concerning the amplit…
We studied a flare onset process in terms of stability of a three-dimensional (3D) magnetic field in active region 12371 producing an eruptive M6.5 flare in 2015 June 22. In order to reveal the 3D magnetic structure, we first extrapolated the 3D coronal magnetic fields based on time series of the photospheric vector magnetic fields under a nonlinear force-free field (NLFFF) approximation. The NLFFFs nicely reproduced the observed sigmoidal structure which is widely considered to be preeruptive magnetic configuration. In particular, we found that the sigmoid is composed of two branches of shear…
Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves. In particular, recent observations show that standing oscillations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. We investigate the consequences for wave-based coronal heating of higher harmonics and what coronal heating observational …
Fundamental standing modes and their overtones play an important role in coronal seismology. We examine how a significant field-aligned flow affects standing modes supported by coronal loops, modeled here as cold magnetic slabs. Of particular interest are the period ratios of the fundamental to its $(n-1)$-th overtone ($P_1/nP_n$) for both kink and sausage modes, and the threshold half-width-to-length ratio for sausage modes. For standing kink modes, the flow significantly reduces $P_1/nP_n$ in general, the effect being particularly strong for larger $n$ and when the density contrast $ρ_0/ρ_e$…
The detection of multiple mode harmonic kink oscillations in coronal loops enables to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic fl…
We report the first results of a magnetohydrodynamic (MHD) simulation of the development of a homologous sequence of three coronal mass ejections (CMEs) and demonstrate their so-called cannibalistic behavior. These CMEs originate from the repeated formations and partial eruptions of kink unstable flux ropes as a result of continued emergence of a twisted flux rope across the lower boundary into a pre-existing coronal potential arcade field. The simulation shows that a CME erupting into the open magnetic field created by a preceding CME has a higher speed. The second of the three successive CME…
Prominence threads are very long and thin flux tubes which are partially filled with cold plasma. Observations have shown that transverse oscillations are frequent in these solar structures. The observations are usually interpreted as the fundamental kink mode, while the detection of the first harmonic remains elusive. Here, we aim to study how the density inhomogeneity in the longitudinal and radial directions modify the periods and damping times of kink oscillations, and how this effect would be reflected in observations. We solve the ideal magnetohydrodynamics equations through two differen…
Since their discovery by SDO/AIA in EUV, rapid (phase speeds of 1000 km/s), quasi-periodic, fast-mode propagating wave trains (QFPs) have been observed accompanying many solar flares. They typically propagate in funnel-like structures associated with the expanding magnetic field topology of the active regions (ARs). The waves provide information on the associated flare pulsations and the magnetic structure through coronal seismology. The reported waves usually originate from a single localized source associated with the flare. Here, we report the first detection of counter-propagating QFPs ass…
Using data obtained by the high temporal and spatial resolution Rapid Oscillations in the Solar Atmosphere (ROSA) instrument on the Dunn Solar Telescope, we investigate at an unprecedented level of detail transverse oscillations in chromospheric fine structures near the solar disk center. The oscillations are interpreted in terms of propagating and standing magnetohydrodynamic kink waves. Wave characteristics including the maximum transverse velocity amplitude and the phase speed are measured as a function of distance along the structure's length. Solar magneto-seismology is applied to these m…
High resolution observations have permitted to resolve the solar prominences/filaments as sets of threads/fibrils. However, the values of the physical parameters of these threads and their structuring remain poorly constrained. We use prominence seismology techniques to analyse transverse oscillations in threads through the comparison between magnetohydrodynamic (MHD) models and observations. We apply Bayesian methods to obtain two different types of information. We first infer the marginal posterior distribution of physical parameters, such as the magnetic field strength or the length of the …
Magnetoacoustic waves in solar magnetic flux tubes may be affected by the presence of background rotational flows. Here, we investigate the behaviour of $m=0$ and $m=\pm 1$ modes of a magnetic flux tube in the presence of linear background rotational flows embedded in a photospheric environment. We show that the inclusion of a background rotational flow is found to have little effect on the obtained eigensolutions for the axisymmetric $m=0$ sausage mode. However, solutions for the kink mode are dependent on the location of the flow resonance modified by the slow frequency. A background rotatio…
Key Laboratory of Solar Activity and Space Weather, School of Aerospace, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学深圳航天学院太阳活动与空间天气重点实验室）；Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick（华威大学物理部聚变、太空与天体物理中心）；G-LAMP NEXUS Institute/School of Space Research, Kyung Hee University（庆熙大学太空研究学院 G-LAMP NEXUS 研究所）；Centro de Investigacion en Astronomía, Universidad Bernardo O’Higgins（贝尔纳多·奥希金斯大学天文学研究中心）；Institute of Solar-Terrestrial Physics SB RAS（俄罗斯科学院西伯利亚分院太阳-地球物理研究所）
