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Register a new userOne dimensional prominence threads: I. Equilibrium models
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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.
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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.
Prominence threads are dense and cold structures lying on curved magnetic fields that can be suspended in the solar atmosphere against gravity. The gravitational stability of threads, in the absence of non-ideal effects, is comprehensively investigated in the present work by means of an elementary but effective model. Based on purely hydrodynamic equations in one spatial dimension and applying line-tying conditions at the footpoints of the magnetic field lines, we derive analytical expressions for the different feasible equilibria and the corresponding frequencies of oscillation. We find that the system allows for stable and unstable equilibrium solutions subject to the initial position of the thread, its density contrast and length, and the total length of the magnetic field lines. The transition between the two types of solutions is produced at specific bifurcation points that have been determined analytically in some particular cases. When the thread is initially at the top of the concave magnetic field, that is at the apex, we find a supercritical pitchfork bifurcation, while for a shifted initial thread position with respect to this point the symmetry is broken and the system is characterised by an S-shaped bifurcation. The plain results presented in this paper shed new light on the behaviour of threads in curved magnetic fields under the presence of gravity and help to interpret more complex numerical magnetohydrodynamics (MHD) simulations about similar structures.
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.
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 solved the radiative transfer and statistical equilibrium equations in a two-dimensional cross-section of a cylindrical structure oriented horizontally and lying above the solar surface. The cylinder is filled with a mixture of hydrogen and helium and is illuminated at a given altitude from the solar disc. We constructed simple models made from a single thread or from an ensemble of several threads along the line of sight. This first use of two-dimensional, multi-thread fine structure modelling combining hydrogen and helium radiative transfer allowed us to compute synthetic emergent spectra from cylindrical structures and to study the effect of line-of-sight integration of an ensemble of threads under a range of physical conditions. We analysed the effects of variations in temperature distribution and in gas pressure. We considered the effect of multi-thread structures within a given field of view and the effect of peculiar velocities between the structures in a multi-thread model. We compared these new models to the single thread model and tested them with varying parameters. These new computations show, for the first time, the effect of integrating the radiation emitted in H and He lines by several cylindrical threads that are static or moving along the line of sight. They can be used to interpret high-spatial and spectral resolutions of cylindrical structures found in the solar atmosphere, such as cool coronal loops or prominence threads.
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