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Register a new userMagnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads
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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.
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Threads are the building blocks of solar prominences and very often show longitudinal oscillatory motions that are strongly attenuated with time. The damping mechanism responsible for the reported oscillations is not fully understood yet. To understand the oscillations and damping of prominence threads it is mandatory to investigate first the nature of the equilibrium solutions that arise under static conditions and under the presence of radiative losses, thermal conduction and background heating. This provides the basis to calculate the eigenmodes of the thread models. The nonlinear ordinary differential equations for hydrostatic and thermal equilibrium under the presence of gravity are solved using standard numerical techniques and simple analytical expressions are derived under certain approximations. The solutions to the equations represent a prominence thread, i.e., a dense and cold plasma region of a certain length that connects with the corona through a prominence corona transition region (PCTR). The solutions can also match with a chromospheric-like layer if a spatially dependent heating function localised around the footpoints is considered. We have obtained static solutions representing prominence threads and have investigated in detail the dependence of these solutions on the different parameters of the model. Among other results, we have shown that multiple condensations along a magnetic field line are possible, and that the effect of partial ionisation in the model can significantly modify the thermal balance in the thread and therefore their length. This last parameter is also shown to be comparable to that reported in the observations when the radiative losses are reduced for typical thread temperatures.
Previous works indicate that the frequency ratio of second and first harmonics of kink oscillations has tendency towards 3 in the case of prominence threads. We aim to study the magnetohydrodynamic oscillations of longitudinally inhomogeneous prominence threads and to shed light on the problem of frequency ratio. Classical Sturm--Liouville problem is used for the threads with longitudinally inhomogeneous plasma density. We show that the spatial variation of total pressure perturbations along the thread is governed by the stationary Schr{o}dinger equation, where the longitudinal inhomogeneity of plasma density stands for the potential energy. Consequently, the equation has bounded solutions in terms of Hermite polynomials. Boundary conditions at the thread surface lead to transcendental dispersion equation with Bessel functions. Thin flux tube approximation of the dispersion equation shows that the frequency of kink waves is proportional to the expression alpha(2n+1), where alpha is the density inhomogeneity parameter and n is the longitudinal mode number. Consequently, the ratio of the frequencies of second and first harmonics tends to 3 in prominence threads. Numerical solution of the dispersion equation shows that the ratio only slightly decreases for thicker tubes in the case of smaller longitudinal inhomogeneity of external density, therefore the thin flux tube limit is a good approximation for prominence oscillations. However, stronger longitudinal inhomogeneity of external density may lead to the significant shift of frequency ratio for wider tubes and therefore the thin tube approximation may fail. The tendency of frequency ratio of second and first harmonics towards 3 in prominence threads is explained by the analogy of the oscillations with quantum harmonic oscillator, where the density inhomogeneity of the threads plays a role of potential energy.
We numerically investigate the excitation and temporal evolution of oscillations in a two-dimensional coronal arcade by including the three-dimensional propagation of perturbations. The time evolution of impulsively generated perturbations is studied by solving the linear, ideal magnetohydrodynamic (MHD) equations in the zero-beta approximation. As we neglect gas pressure the slow mode is absent and therefore only coupled MHD fast and Alfven modes remain. Two types of numerical experiments are performed. First, the resonant wave energy transfer between a fast normal mode of the system and local Alfven waves is analyzed. It is seen how, because of resonant coupling, the fast wave with global character transfers its energy to Alfvenic oscillations localized around a particular magnetic surface within the arcade, thus producing the damping of the initial fast MHD mode. Second, the time evolution of a localized impulsive excitation, trying to mimic a nearby coronal disturbance, is considered. In this case, the generated fast wavefront leaves its energy on several magnetic surfaces within the arcade. The system is therefore able to trap energy in the form of Alfvenic oscillations, even in the absence of a density enhancement such as that of a coronal loop. These local oscillations are subsequently phase-mixed to smaller spatial scales. The amount of wave energy trapped by the system via wave energy conversion strongly depends on the wavelength of perturbations in the perpendicular direction, but is almost independent from the ratio of the magnetic to density scale heights.
Small-scale magnetic field concentrations (magnetic elements) in the quiet Sun are believed to contribute to the energy budget of the upper layers of the Suns atmosphere, as they are observed to support a large number of MHD modes. In recent years, kink waves in magnetic elements were observed at different heights in the solar atmosphere, from the photosphere to the corona. However, the propagation of these waves has not been fully evaluated. Our aim is to investigate the propagation of kink waves in small magnetic elements in the solar atmosphere. We analysed spectropolarimetric data of high-quality and long duration of a photospheric quiet Sun region observed near the disk center with the spectropolarimeter CRISP at the Swedish Solar Telescope (SST), and complemented by simultaneous and co-spatial broad-band chromospheric observations of the same region. Our findings reveal a clear upward propagation of kink waves with frequency above $~2.6$ mHz. Moreover, the signature of a non-linear propagation process is also observed. By comparing photospheric to chromospheric power spectra, no signature of an energy dissipation is found at least at the atmospheric heights at which the data analysed originate. This implies that most of the energy carried by the kink waves (within the frequency range under study $< 17$ mHz) flows to upper layers in the Suns atmosphere.
Fine-structure dynamics in solar prominences holds critical clues to understanding their physical nature of significant space-weather implications. We report evidence of rotational motions of horizontal helical threads in two active-region prominences observed by the emph{Hinode} and/or emph{IRIS} satellites at high resolution. In the first event, we found transverse motions of brightening threads at speeds up to 55~km~s$^{-1}$ seen in the plane of the sky. Such motions appeared as sinusoidal space--time trajectories with a typical period of $sim$390~s, which is consistent with plane-of-sky projections of rotational motions. Phase delays at different locations suggest propagation of twists along the threads at phase speeds of 90--270~km~s$^{-1}$. At least 15 episodes of such motions occurred in two days, none associated with any eruption. For these episodes, the plane-of-sky speed is linearly correlated with the vertical travel distance, suggestive of a constant angular speed. In the second event, we found Doppler velocities of 30--40~km~s$^{-1}$ in opposite directions in the top and bottom portions of the prominence, comparable to the plane-of-sky speed. The moving threads have about twice broader line widths than stationary threads. These observations, when taken together, provide strong evidence for rotations of helical prominence threads, which were likely driven by unwinding twists triggered by magnetic reconnection between twisted prominence magnetic fields and ambient coronal fields.
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