No unique solution to the seismological problem of standing kink MHD waves

The aim of this paper is to point out that the classic seismological problem using observations and theoretical expressions for the periods and damping times of transverse standing magnetohydrodynamic (MHD) waves in coronal loops is better referred to as a reduced seismological problem. Reduced emphasises the fact that only a small number of characteristic quantities of the equilibrium profiles can be determined. Reduced also implies that there is no unique solution to the full seismological problem. Even the reduced seismological problem does not allow a unique solution. Bayesian inference results support our mathematical arguments and offer insight into the relationship between the algebraic and the probabilistic inversions.Comment: 10 pages, accepted in A&

The role of cooling induced by mixing in the mass and energy cycles of the solar atmosphere

In many astrophysical systems, mixing between cool and hot temperature gas/plasma through Kelvin-Helmholtz-instability-driven turbulence leads to the formation of an intermediate temperature phase with increased radiative losses that drive efficient cooling. The solar atmosphere is a potential site for this process to occur with interaction between either prominence or spicule material and the solar corona allowing the development of transition region material with enhanced radiative losses. In this paper, we derive a set of equations to model the evolution of such a mixing layer and make predictions for the mixing-driven cooling rate and the rate at which mixing can lead to the condensation of the coronal material. These theoretical predictions are benchmarked against 2.5D MHD simulations. Applying the theoretical scalings to prominence threads or fading spicules, we found that as a mixing layer grows on their boundaries this would lead to the creation of transition region material with a cooling time of ~100 s, explaining the warm emission observed as prominence threads or spicules fade in cool spectral lines without the requirement for any heating. For quiescent prominences, dynamic condensation driven by the mixing process could restore ~18 per cent of the mass lost from a prominence through downflows. Overall, this mechanism of thermal energy loss through radiative losses induced by mixing highlights the importance for considering dynamical interaction between material at different temperatures when trying to understand the thermodynamic evolution of the cool material in the solar corona.Comment: 10 pages, 9 figures, published open access versio

Mixed Properties of MHD Waves in Non-uniform Plasmas

This paper investigates the mixed properties of MHD waves in a non-uniform plasma. It starts with a short revision of MHD waves in a uniform plasma of infinite extent. In that case the MHD waves do not have mixed properties. They can be separated in Alfvén waves and magneto-sonic waves. The Alfvén waves propagate parallel vorticity and are incompressible. In addition they have no parallel displacement component. The magneto-sonic waves are compressible and in general do have a parallel component of displacement but do not propagate parallel vorticity. This clear separation has been the reason why there has been a strong inclination in the literature to use this classification in the study of MHD waves in non-uniform plasmas. The main part of this paper is concerned with MHD waves in a non-uniform plasma. It is shown that the MHD waves in that situation in general propagate both vorticity and compression and hence have mixed properties. Finally, the close connection between resonant absorption and MHD waves with mixed properties is discussed

The resonant damping of fast magnetohydrodynamic oscillations in a system of two coronal slabs

Observations of transversal coronal loop oscillations very often show the excitation and damping of oscillations in groups of coronal loops rather than in individual and isolated structures. We present results on the oscillatory properties (periods, damping rates, and spatial distribution of perturbations) for resonantly damped oscillations in a system of two inhomogeneous coronal slabs and compare them to the properties found in single slab loop models. A system of two identical coronal loops is modeled, in Cartesian geometry, as being composed by two density enhancements. The linear magnetohydrodynamic (MHD) wave equations for oblique propagation of waves are solved and the damping of the different solutions, due to the transversal inhomogeneity of the density profile, is computed. The physics of the obtained results is analyzed by an examination of the perturbed physical variables. We find that, due to the interaction between the loops, the normal modes of oscillation present in a single slab split into symmetric and antisymmetric oscillations when a system of two identical slabs is considered. The frequencies of these solutions may differ from the single slab results when the distance between the loops is of the order of a few slab widths. Oblique propagation of waves weakens this interaction, since solutions become more confined to the edges of the slabs. The damping is strong for surface-like oscillations, while sausage body-like solutions are unaffected. For some solutions, and small slab separations, the damping in a system of two loops differs substantially from the damping of a single loop.Comment: 25 pages, 9 figure

Fundamental transverse vibrations of the active region solar corona

Funding: P.A. acknowledges funding from his STFC Ernest Rutherford Fellowship (No. ST/R004285/1). M.L., R.O. and P.A. acknowledge support from the International Space Science Institute (ISSI), Bern, Switzerland to the International Team 401 ‘Observed Multi-Scale Variability of Coronal Loops as a Probe of Coro-nal Heating’ (P.I. Clara Froment and Patrick Antolin).Context. Some high-resolution observations have revealed that the active-region solar corona is filled with myriads of thin strandseven in apparently uniform regions with no resolved loops. This fine structure can host collective oscillations involving a large portionof the corona due to the coupling of the motions of the neighbouring strands. Aims. We study these vibrations and the possible observational effects. Methods. Here we theoretically investigate the collective oscillations inherent to the fine structure of the corona. We have called themfundamental vibrations because they cannot exist in a uniform medium. We use the T-matrix technique to find the normal modes ofrandom arrangements of parallel strands. We consider an increasing number of tubes to understand the vibrations of a huge numberof tubes of a large portion of the corona. We additionally generate synthetic time-distance Doppler and line broadening diagrams ofthe vibrations of a coronal region to compare with observations. Results. We have found that the fundamental vibrations are in the form of clusters of tubes where not all the tubes participate in thecollective mode. The periods are distributed over a wide band of values. The width of the band increases with the number of strands butrapidly reaches an approximately constant value. We have found an analytic approximate expression for the minimum and maximumperiods of the band. The frequency band associated with the fine structure of the corona depends on the minimum separation betweenstrands. We have found that the coupling between the strands is of large extent and the motion of one strand is influenced by themotions of distant tubes. The synthetic Dopplergrams and line-broadening maps show signatures of collective vibrations, not presentin the case of purely random individual kink vibrations. Conclusions. We conclude that the fundamental vibrations of the corona can contribute to the energy budget of the corona and theymay have an observational signature.PostprintPeer reviewe

Coronal Cooling as a Result of Mixing by the Nonlinear Kelvin-Helmholtz Instability

status: publishe

Mixed Properties of MHD Waves in Non-uniform Plasmas

status: publishe

Time dependent simulations of 2D coronal loop models

We use the time dependent code PET in order to perform time evolution simulations of damped oscillations in linetied solar coronal loops. This new numerical code has open boundary conditions implemented and is suitable to perform simulations of transversally driven plasma cylinders. In this paper, we show that a resonance is set up when driving harmonically with a frequency close to the quasimode frequency. In this resonance, all the incoming energy is dissipated. When the driver is shut down, the oscillation in and in the neighbourhood of the resonant layer decays exponentially. Using this code, we hope to show that wave heating is still a viable mechanism to heat coronal loops and to explain the observed damped loop oscillations. We will show this by proving that more energy can be dissipated per oscillation period than is observed.status: publishe

Dynamics of coronal loop oscillations recent improvements and computational aspects

We will discuss the observed, heavily damped transversal oscillations of coronal loops. These oscillations are often modeled as transversal kink oscillations in a cylinder. Several features are added to the classical cylindrical model. In our models we include loop curvature, longitudinal density stratification, and highly inhomogeneous radial density profiles.status: publishe