Prominence Seismology Research Articles

Negative-energy Waves in the Vertical Threads of a Solar Prominence

Solar prominences, intricate structures on the Sun’s limb, have been a subject of fascination owing to their threadlike features and dynamic behaviors. Utilizing data from the New Vacuum Solar Telescope, Chinese Hα Solar Explorer, and Solar Dynamics Observatory, this study investigates the transverse swaying motions observed in the vertical threads of a solar prominence during its eruption onset on 2023 May 11. The transverse swaying motions were observed to propagate upward, accompanied by upflowing materials at an inclination of 31° relative to the plane of the sky. These motions displayed small-amplitude oscillations with corrected velocities of around 3–4 km s−1 and periods of 13–17 minutes. Over time, the oscillations of swaying motion exhibited an increasing pattern in displacement amplitudes, oscillatory periods, and projected velocity amplitudes. Their phase velocities are estimated to be about 26–34 km s−1. An important finding is that these oscillations’ phase velocities are comparable to the upward flow velocities, measured to be around 30–34 km s−1. We propose that this phenomenon is associated with negative-energy wave instabilities, which require comparable velocities of the waves and flows, as indicated by our findings. This phenomenon may contribute to the instability and observed disruption of the prominence. By using prominence seismology, the Alfvén speed and magnetic field strength of the vertical threads have been estimated to be approximately 21.5 km s−1 and 1–3G, respectively. This study reveals the dynamics and magnetic properties of solar prominences, contributing to our understanding of their behavior in the solar atmosphere.

Comparison of Two Methods for Deriving the Magnetic Field in a Filament Channel

Understanding the magnetic structure of filament channels is difficult but essential for identifying the mechanism (s) responsible for solar eruptions. In this paper we characterize the magnetic field in a well-observed filament channel with two independent methods, prominence seismology and magnetohydrodynamics flux-rope modeling, and compare the results. In 2014 May and June, active region 12076 exhibited a complex of filaments undergoing repeated oscillations over the course of 12 days. We measure the oscillation periods in the region with both Global Oscillation Network Group Hα and Solar Dynamics Observatory (SDO) Advanced Imaging Assembly EUV images, and then utilize the pendulum model of large-amplitude longitudinal oscillations to calculate the radius of curvature of the fields supporting the oscillating plasma from the derived periods. We also employ the regularized Biot–Savart laws formalism to construct a flux-rope model of the field of the central filament in the region based on an SDO Helioseismic and Magnetic Imager magnetogram. We compare the estimated radius of curvature, location, and angle of the magnetic field in the plane of the sky derived from the observed oscillations with the corresponding magnetic-field properties extracted from the flux-rope model. We find that the two models are broadly consistent, but detailed comparisons of the model and specific oscillations often differ. Model observation comparisons such as these are important for advancing our understanding of the structure of filament channels.

Extension and validation of the pendulum model for longitudinal solar prominence oscillations

Context.Longitudinal oscillations in prominences are common phenomena on the Sun. These oscillations can be used to infer the geometry and intensity of the filament magnetic field. Previous theoretical studies of longitudinal oscillations made two simplifying assumptions: uniform gravity and semicircular dips on the supporting flux tubes. However, the gravity is not uniform and realistic dips are not semicircular.Aims.Our aim is to understand the effects of including the nonuniform solar gravity on longitudinal oscillations and explore the validity of the pendulum model with different flux-tube geometries.Methods.We first derived the equation describing the motion of the plasma along the flux tube including the effects of nonuniform gravity, yielding corrections to the original pendulum model. We also computed the full numerical solutions for the normal modes and compared them with the new pendulum approximation.Results.We find that the nonuniform gravity introduces a significant modification in the pendulum model. We also found a cut-off period; i.e., the longitudinal oscillations cannot have a period longer than 167 min. In addition, considering different tube geometries, the period depends almost exclusively on the radius of curvature at the bottom of the dip.Conclusions.We conclude that nonuniform gravity significantly modifies the pendulum model. These corrections are important for prominence seismology, because the inferred values of the radius of curvature and minimum magnetic-field strength differ substantially from those of the old model. However, we find that the corrected pendulum model is quite robust and is still valid for noncircular dips.

Transverse kink oscillations of inhomogeneous prominence threads: Numerical analysis and Hα forward modelling

Context. Prominence threads are very long and thin flux tubes that 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. Aims. The properties of oscillations in threads are greatly affected by the density distribution along the flux tube. Here, we aim to study how the density inhomogeneities in the longitudinal and radial directions modify the periods and damping times of kink oscillations and how this effect would be reflected in the observations. Methods. We solved the ideal magnetohydrodynamics equations using two different methods: (a) performing 3D numerical simulations and (b) solving a 2D generalised eigenvalue problem. We studied the dependence of the periods, damping times, and amplitudes of transverse kink oscillations on the ratio between the densities at the centre and at the ends of the tube, and also on the average density. We applied forward modelling to our 3D simulations to compute synthetic Hα profiles. Results. We confirm that the ratio of the period of the fundamental oscillation mode to the period of the first harmonic increases as the ratio of the central density to the footpoint density is increased, or as the averaged density of the tube is decreased. We find that the damping times due to resonant absorption decrease as the central-to-footpoint density ratio increases. Contrary to the case of longitudinally homogeneous tubes, we find that the damping-time-to-period ratio also increases as the density ratio is increased or the average density is reduced. We present snapshots and time-distance diagrams of the emission in the Hα line. Conclusions. The results presented here have implications for the field of prominence seismology. While the Hα emission can be used to detect the fundamental mode, the first harmonic is barely detectable in Hα. This may explain the lack of detections of the first harmonic. A combination of different spectral lines is required to obtain information about the period ratio and to use it to infer physical properties of the threads.

Effect of siphon flow on resonant damping of kink oscillations in magnetic flux tubes

The effect of siphon flow on kink oscillations of magnetic flux tubes is studied in the thin tube and thin boundary layer (TTTB) approximation. The presence of a transitional layer results in oscillation damping due to resonance absorption. To calculate the damping rate we use the regular perturbation method with the ratio of transitional layer thickness to tube radius as a small parameter. We found a dependence of the ratio of decrement to the oscillation frequency, γ/ω1, on the ratio, χ, of flow velocity magnitude to the Alfvén speed in the tube core. The general theoretical results are applied to a particular case where the density radial dependence in the transitional layer is linear. We consider two models. In the first model, the radial dependence of the velocity amplitude is such that the resonance in the transitional layer occurs where the flow velocity is zero. In the second model, the flow velocity is non-zero in the whole transitional layer. In both cases, γ/ω1 is an increasing function of χ. In the first case, the presence of flow can lead to an increase in γ/ω1 by more than a factor of two. In the second model, we only carry out the calculation in the case where the plasma density inside the tube is much larger than the density of the surrounding plasma. In this model, the effect of flow is less pronounced than in the first model, and the presence of flow can increase γ/ω1 by a factor of 0.25 at most. We discuss the application of the obtained results to coronal and prominence seismology. We conclude that while for typical values of velocity in coronal loops the effect of flow is weak, it can be quite substantial in prominence seismology.

Inferring physical parameters in solar prominence threads

Context. High resolution observations have permitted the resolution of solar prominences/filaments into sets of threads/fibrils. However, the values of the physical parameters of these threads and their structuring remain poorly constrained. Aims. We use prominence seismology techniques to analyse transverse oscillations in threads by comparing magnetohydrodynamic (MHD) models and observations. Methods. We applied Bayesian methods to obtain two different types of information. We first inferred the marginal posterior distribution of physical parameters such as the magnetic field strength or length of the thread, when a totally filled tube, partially filled tube, and three damping models are considered as certain; the three damping models are resonant absorption in the Alfvén continuum, resonant absorption in the slow continuum, and Cowling’s diffusion. Then, we compared the relative plausibility between alternative MHD models by computing the Bayes factors. Results. Well-constrained probability density distributions can be obtained for the magnetic field strength, length of the thread, density contrast, and parameters associated with the damping models. In a comparison of the damping models of resonant absorption in the Alfvén continuum, resonant absorption in the slow continuum, and Cowling’s diffusion due to partial ionisation of prominence plasma, the resonant absorption in the Alfvén continuum is the most plausible mechanism to explain the existing observations. Relations between periods of fundamental and first overtone kink modes with values around 1 are better explained by expressions of the period ratio in the long thread approximation, while the rest of the values are more probable in the short thread limit for the period ratio. Conclusions. Our results show that Bayesian analysis offers valuable methods to perform parameter inference and a model comparison in the context of prominence seismology.

Vertical Oscillation of a Coronal Cavity Triggered by an EUV Wave

Abstract In this paper, we report our multiwavelength observations of the vertical oscillation of a coronal cavity on 2011 March 16. The elliptical cavity with an underlying horn-like quiescent prominence was observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The width and height of the cavity are 150″ and 240″, and the centroid of cavity is 128″ above the solar surface. At ∼17:50 UT, a C3.8 two-ribbon flare took place in active region 11169 close to the solar western limb. Meanwhile, a partial halo coronal mass ejection erupted and propagated at a linear speed of ∼682 km s−1. Associated with the eruption, a coronal extreme-ultraviolet (EUV) wave was generated and propagated in the northeast direction at a speed of ∼120 km s−1. Once the EUV wave arrived at the cavity from the top, it pushed the large-scale overlying magnetic field lines downward before bouncing back. At the same time, the cavity started to oscillate coherently in the vertical direction and lasted for ∼2 cycles before disappearing. The amplitude, period, and damping time are 2.4–3.5 Mm, 29–37 minutes, and 26–78 minutes, respectively. The vertical oscillation of the cavity is explained by a global standing MHD wave of fast kink mode. To estimate the magnetic field strength of the cavity, we use two independent methods of prominence seismology. It is found that the magnetic field strength is only a few Gauss and less than 10 G.

The temporal behaviour of MHD waves in a partially ionized prominence-like plasma: Effect of heating and cooling

Context.During heating or cooling processes in prominences, the plasma microscopic parameters are modified due to the change of temperature and ionization degree. Furthermore, if waves are excited on this non-stationary plasma, the changing physical conditions of the plasma also affect wave dynamics.Aims.Our aim is to study how temporal variation of temperature and microscopic plasma parameters modify the behaviour of magnetohydrodynamic (MHD) waves excited in a prominence-like hydrogen plasma.Methods.Assuming optically thin radiation, a constant external heating, the full expression of specific internal energy, and a suitable energy equation, we have derived the profiles for the temporal variation of the background temperature. We have computed the variation of the ionization degree using a Saha equation, and have linearized the single-fluid MHD equations to study the temporal behaviour of MHD waves.Results.For all the MHD waves considered, the period and damping time become time dependent. In the case of Alfvén waves, the cut-off wavenumbers also become time dependent and the attenuation rate is completely different in a cooling or heating process. In the case of slow waves, while it is difficult to distinguish the slow wave properties in a cooling partially ionized plasma from those in an almost fully ionized plasma, the period and damping time of these waves in both plasmas are completely different when the plasma is heated. The temporal behaviour of the Alfvén and fast wave is very similar in the cooling case, but in the heating case, an important difference appears that is related with the time damping.Conclusions.Our results point out important differences in the behaviour of MHD waves when the plasma is heated or cooled, and show that a correct interpretation of the observed prominence oscillations is very important in order to put accurate constraints on the physical situation of the prominence plasma under study, that is, to perform prominence seismology.

A reexamination of a filament oscillation event on 2013 March 15

The key element in the research of solar activities is the coronal magnetic field, which is however difficult to measure directly. Filament (or prominence) oscillations offer a new approach to derive important information of the coronal magnetic field, which is called prominence seismology. However, it is vital to determine the oscillation mode before applying the prominence seismology since for a given magnetic structure of a filament, the two different modes of oscillation, namely, the longitudinal and transverse, have different eigen frequencies. In low-resolution observations, it is hard to distinguish the oscillation mode since both modes of oscillations are associated with lateral displacements, and the subtle difference between the two modes becomes unresolvable. On 2013 March 15, there is a filament oscillation event with a period of ∼63 minutes and a decay timescale of ∼105 minutes, which was explained in the literature to be a transverse oscillation or a mixture of both transversal and longitudinal components with the same period. With the analysis of the high-resolution SDO/AIA data, we reexamine the filament oscillation event, and argue that this event is a longitudinal oscillation. We tentatively propose a new method on how to identify the oscillation mode when the observational resolution is not so high. A numerical simulation is also provided in order to match the observations, which leads to the ratio between the depth and the width of the magnetic dip being 0.1.

ON THE ROBUSTNESS OF THE PENDULUM MODEL FOR LARGE-AMPLITUDE LONGITUDINAL OSCILLATIONS IN PROMINENCES

ABSTRACT Large-amplitude longitudinal oscillations (LALOs) in prominences are spectacular manifestations of solar activity. In such events nearby energetic disturbances induce periodic motions on filaments with displacements comparable to the size of the filaments themselves and with velocities larger than 20 km s − 1 ?> . The pendulum model, in which the gravity projected along a rigid magnetic field is the restoring force, was proposed to explain these events. However, it can be objected that in a realistic situation where the magnetic field reacts to the mass motion of the heavy prominence, the simplified pendulum model could be no longer valid. We have performed nonlinear time-dependent numerical simulations of LALOs considering a dipped magnetic field line structure. In this work we demonstrate that for even relatively weak magnetic fields the pendulum model works very well. We therefore validate the pendulum model and show its robustness, with important implications for prominence seismology purposes. With this model it is possible to infer the geometry of the dipped field lines that support the prominence.

MHD Seismology of a loop-like filament tube by observed kink waves

We report and analyze observational evidence of global kink oscillations in a solar filament as observed in Hα by instruments administered by National Solar Observatory (NSO)/Global Oscillation Network Group (GONG). An M1.1-class flare in active region (AR) 11692 occurred on 2013 March 15 and induced a global kink mode in the filament lying towards the southwest of AR 11692. We find periods of about 61–67 minutes and damping times of 92–117 minutes at positions of three vertical slices chosen in and around the filament apex. We find that the waves are damped. From the observed period of the global kink mode and damping timescale using the theory of resonant absorption, we perform prominence seismology. We estimate a lower cut-off value for the inhomogeneity length scale to be around 0.34–0.44 times the radius of the filament cross-section.

Prominence seismology using the period ratio of transverse thread oscillations

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 kink oscillations in a model of a prominence thread. We take into account three nonuniform density profiles along the thread. In agreement with previous works that used simple piecewise constant density profiles, we find that the period ratio is larger than 2 in prominence threads. When the ratio of the central density to that at the footpoints is fixed, the period ratio depends strongly on the form of the density profile along the thread. The more concentrated the dense prominence plasma near the center of the tube, the larger the period ratio. However, the period ratio is found to be independent of the specific density profile when the spatially averaged density in the thread is the same for all the profiles. An empirical fit of the dependence of the period ratio on the average density is given and its use for prominence seismology is discussed.

TIME EVOLUTION OF PLASMA PARAMETERS DURING THE RISE OF A SOLAR PROMINENCE INSTABILITY

We present high spatial resolution spectropolarimetric observations of a quiescent hedgerow prominence taken in the He I 1083.0 nm triplet. The observation consisted of a time series in sit-and-stare mode of 36 minutes of duration. The spectrograph's slit crossed the prominence body and we recorded the time evolution of individual vertical threads. Eventually, we observed the development of a dark Rayleigh-Taylor plume that propagated upward with a velocity, projected onto the plane of the sky, of 17 km/s. Interestingly, the plume apex collided with the prominence threads pushing them aside. We inferred Doppler shifts, Doppler widths, and magnetic field strength variations by interpreting the He I Stokes profiles with the HAZEL code. The Doppler shifts show that clusters of threads move coherently while individual threads have oscillatory patterns. Regarding the plume we found strong redshifts (9-12 km/s) and large Doppler widths (10 km/s) at the plume apex when it passed through the prominence body and before it disintegrated. We associate the redshifts with perspective effects while the Doppler widths are more likely due to an increase in the local temperature. No local variations of the magnetic field strength associated with the passage of the plume were found; this leads us to conclude that the plumes are no more magnetized than the surroundings. Finally, we found that some of the threads oscillations are locally damped, what allowed us to apply prominence seismology techniques to infer additional prominence physical parameters.

Synthetic hydrogen spectra of prominence oscillations

Context. Prominence oscillations have been mostly detected using Doppler velocity, although there are also claimed detections by means of periodic variations in half-width or line intensity. However, scarce observational evidence exists about simultaneous detection of oscillations in several spectral indicators. Aims. Our main aim here is to explore the relationship between spectral indicators, such as Doppler shift, line intensity, and line half-width, and the linear perturbations excited in a simple prominence model. Methods. Our equilibrium background model consists of a bounded, homogeneous slab, which is permeated by a transverse magnetic field, having prominence-like physical properties. Assuming linear perturbations, the dispersion relation for fast and slow modes has been derived, as well as the perturbations for the different physical quantities. These perturbations have been used as the input variables in a one-dimensional radiative transfer code, which calculates the full spectral profile of the hydrogen H-alpha and H-beta lines. Results. We have found that different oscillatory modes produce spectral indicator variations in different magnitudes. Detectable variations in the Doppler velocity were found for the fundamental slow mode only. Substantial variations in the H-beta line intensity were found for specific modes. Other modes lead to lower and even undetectable parameter variations. Conclusions. To perform prominence seismology, analysis of the H-alpha and H-beta spectral line parameters could be a good tool to detect and identify oscillatory modes.

Prominence Seismology

AbstractQuiescent solar prominences are cool and dense plasma clouds located inside the hot and less dense solar corona. They are highly dynamic structures displaying flows, instabilities, oscillatory motions, etc. The oscillations have been mostly interpreted in terms of magnetohydrodynamic (MHD) waves, which has allowed to perform prominence seismology as a tool to determine prominence physical parameters difficult to measure. Here, several prominence seismology applications to large and small amplitude oscillations are reviewed.

The promise of Bayesian analysis for prominence seismology

AbstractWe propose and use Bayesian techniques for the determination of physical parameters in solar prominence plasmas, combining observational and theoretical properties of waves and oscillations. The Bayesian approach also enables to perform model comparison to assess how plausible alternative physical models/mechanisms are in view of data.

DUAL TRIGGER OF TRANSVERSE OSCILLATIONS IN A PROMINENCE BY EUV FAST AND SLOW CORONAL WAVES:SDO/AIA ANDSTEREO/EUVI OBSERVATIONS

We analyze flare-associated transverse oscillations in a quiescent solar prominence on 2010 September 8–9. Both the flaring active region and the prominence were located near the west limb, with a favorable configuration and viewing angle. The full-disk extreme ultraviolet (EUV) images of the Sun obtained with high spatial and temporal resolution by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory show flare-associated lateral oscillations of the prominence sheet. The STEREO-A spacecraft, 815 ahead of the Sun–Earth line, provides an on-disk view of the flare-associated coronal disturbances. We derive the temporal profile of the lateral displacement of the prominence sheet by using the image cross-correlation technique. The displacement curve was de-trended and the residual oscillatory pattern was derived. We fit these oscillations with a damped cosine function with a variable period and find that the period is increasing. The initial oscillation period (P0) is ∼28.2 minutes and the damping time (τD) ∼ 44 minutes. We confirm the presence of fast and slow EUV wave components. Using STEREO-A observations, we derive a propagation speed of ∼250 km s−1 for the slow EUV wave by applying the time-slice technique to the running difference images. We propose that the prominence oscillations are excited by the fast EUV wave while the increase in oscillation period of the prominence is an apparent effect, related to a phase change due to the slow EUV wave acting as a secondary trigger. We discuss implications of the dual trigger effect for coronal prominence seismology and scaling law studies of damping mechanisms.

Prominence seismology using ground- and space-based observations

Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD) waves. This interpretation opens the door to perform prominence seismology, whose main aim is to determine physical parameters in magnetic and plasma structures (prominences) that are difficult to measure by direct means. Here, two prominence seismology applications are presented.

Prominence Oscillations

Prominences are intriguing, but poorly understood, magnetic structures of the solar corona. The dynamics of solar prominences has been the subject of a large number of studies, and of particular interest is the study of prominence oscillations. Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD) waves. This interpretation opens the door to perform prominence seismology, whose main aim is to determine physical parameters in magnetic and plasma structures (prominences) that are difficult to measure by direct means. Here, we review the observational information gathered about prominence oscillations as well as the theoretical models developed to interpret small amplitude oscillations and their temporal and spatial attenuation. Finally, several prominence seismology applications are presented.

Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads

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 the linear resistive magnetohydrodynamic (MHD) equations. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Implications for prominence seismology, the physics of resonantly damped kink modes in two-dimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.