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On the support of neutrals against gravity in solar prominences  

Jaume Terradas   Submitted: 2015-03-20 05:21

Cool and dense prominences found in the solar atmosphere are known to be partially ionized because of their relative low temperature. In this Letter, we address the long-standing problem of how the neutral component of the plasma in prominences is supported against gravity. Using the multiple fluid approach we solve the time-dependent equations in two dimensions considering the frictional coupling between the neutral and ionized components of the magnetized plasma representative of a solar prominence embedded in a hot coronal environment. We demonstrate that given an initial density enhancement in the two fluids, representing the body of the prominence, the system is able to relax in the vicinity of magnetic dips to a stationary state in which both neutrals and ionized species are dynamically suspended above the photosphere. Two different coupling processes are considered in this study, collisions between ions and neutrals and charge exchange interactions. We find that for realistic conditions ions are essentially static while neutrals have a very small downflow velocity. The coupling between ions and neutrals is so strong at the prominence body that the behavior is similar to that of a single fluid with an effective density equal to the sum of the ion and neutral species. We also find that the charge exchange mechanism is about three times more efficient sustaining neutrals than elastic scattering of ions with neutrals.

Authors: J. Terradas, R. Soler, R. Oliver, \& J. L., Ballester
Projects: None

Publication Status: Accepted for publication in ApJL
Last Modified: 2015-03-20 05:51
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Rayleigh-Taylor instabilities with sheared magnetic fields  

Jaume Terradas   Submitted: 2014-02-27 05:16

Magnetic Rayleigh-Taylor (MRT) instabilities may play a relevant role in many astrophysical problems. In this work the effect of magnetic shear on the growth rate of the MRT instability is investigated. The eigenmodes of an interface and a slab model under the presence of gravity are analytically calculated assuming that the orientation of the magnetic field changes in the equilibrium, i.e., there is magnetic shear. We solve the linearised magnetohydrodynamic (MHD) equations in the incompressible regime.We find that the growth rate is bounded under the presence of magnetic shear. We have derived simple analytical expressions for the maximum growth rate, corresponding to the most unstable mode of the system. These expressions provide the explicit dependence of the growth rate on the various equilibrium parameters. For small angles the growth time is linearly proportional to the shear angle, and in this regime the single interface problem and the slab problem tend to the same result. On the contrary, in the limit of large angles and for the interface problem the growth time is essentially independent of the shear angle. In this regime we have also been able to calculate an approximate expression for the growth time for the slab configuration. Magnetic shear can have a strong effect on the growth rates of the instability. As an application of the results found in this paper we have indirectly determined the shear angle in solar prominence threads using their lifetimes and the estimation of the Alfvén speed of the structure.

Authors: Ruderman, M. S., Terradas, J., Ballester, J. L.
Projects: None

Publication Status: accpeted for publication in ApJ
Last Modified: 2014-02-27 13:37
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Damping of coronal loop kink oscillations due to mode conversion  

Jaume Terradas   Submitted: 2013-06-25 04:27

The damping of kink oscillations of a thin magnetic tube due to mode conversion, also called resonant absorption, is studied. The tube consists of a homogeneous core region and an inhomogeneous annulus, where the density monotonically decreases from its value in the core region to the value in the surrounding plasma. The annulus is assumed to be thin, so the study is carried out in the thin tube thin boundary approximation. The equation governing the amplitude variation of kink oscillations is derived. The initial value problem for this equation is solved to study the resonant damping. This means that, in particular, we study the transient state before the loop oscillates with the stationary or nearly stationary state. The results are compared with those of the direct numerical modelling, and the agreement is found to be fairly good. On the basis of the solution to the initial value problem for the governing equation, the damping time is calculated and compared with that given by the classical theory of resonant absorption. It is found that the classical theory underestimates the damping time, with the error increasing with the increase of the annulus thickness. However, the error is not large, so the damping time given by the classical theory of resonant absorption can be taken as a sufficiently good approximation.

Authors: Ruderman, M. S., Terradas, J.
Projects: None

Publication Status: Published
Last Modified: 2013-06-26 11:13
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The role of Rayleigh-Taylor instabilities in filament threads  

Jaume Terradas   Submitted: 2012-03-21 02:44

Many solar filaments and prominences show short-lived horizontal threads lying parallel to the photosphere. In this work the possible link between Rayleigh-Taylor instabilities and thread lifetimes is investigated. This is done by calculating the eigenmodes of a thread modelled as a Cartesian slab under the presence of gravity. An analytical dispersion relation is derived using the incompressible assumption for the magnetohydrodynamic (MHD) perturbations. The system allows a mode that is always stable, independently of the value of the Alfvén speed in the thread. The character of this mode varies from being localised at the upper interface of the slab when the magnetic field is weak, to having a global nature and resembling the transverse kink mode when the magnetic field is strong. On the contrary, the slab model permits another mode that is unstable and localised at the lower interface when the magnetic field is weak. The growth rates of this mode can be very short, of the order of minutes for typical thread conditions. This Rayleigh-Taylor unstable mode becomes stable when the magnetic field is increased, and in the limit of strong magnetic field it is essentially a sausage magnetic mode. The gravity force might have a strong effect on the modes of oscillation of threads, depending on the value of the Alfvén speed. In the case of threads in quiescent filaments, where the Alfvén speed is presumably low, very short lifetimes are expected according to the slab model. In active region prominences, the stabilising effect of the magnetic tension might be enough to suppress the Rayleigh-Taylor instability for a wide range of wavelengths.

Authors: J. Terradas, R. Oliver, J. L. Ballester
Projects: None

Publication Status: submitted
Last Modified: 2012-03-21 13:00
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Seismology of transversely oscillating coronal loops with siphon flows  

Jaume Terradas   Submitted: 2011-01-28 02:39

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 case study. It is shown that the presence of siphon flow can cause the underestimation of magnetic field strength in coronal loops using the traditional seismological methods.

Authors: J. Terradas, I. Arregui, G. Verth, M. Goossens
Projects: None

Publication Status: submitted to ApJ Letters
Last Modified: 2011-01-28 09:15
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On the linear coupling between fast and slow MHD waves due to line-tying effects  

Jaume Terradas   Submitted: 2010-11-04 02:46

Oscillations in coronal loops are usually interpreted in terms of uncoupled magnetohydrodynamic (MHD) waves. Examples of these waves are standing transverse motions, interpreted as the kink MHD modes, and propagating slow modes, commonly reported at the loop footpoints. Here we study a simple system in which fast and slow MHD waves are coupled. The goal is to understand the fingerprints of the coupling when boundary conditions are imposed in the model. The reflection problem of a fast and slow MHD wave interacting with a rigid boundary, representing the line-tying effect of the photosphere, is analytically investigated. Both propagating and standing waves are analysed and the time-dependent problem of the excitation of these waves is considered. An obliquely incident fast MHD wave on the photosphere inevitably generates a slow mode. The frequency of the generated slow mode at the photosphere is exactly the same as the frequency of the incident fast MHD mode, but its wavelength is much smaller, assuming that the sound speed is smaller than the Alfvén speed. The main signatures of the generated slow wave are density fluctuations at the loop footpoints. We have derived a simple formula that relates the velocity amplitude of the transverse standing mode with the density enhancements at the footpoints due to the driven slow modes. Using these results it is shown that there are possible evidences in the observations of the coupling between these two modes.

Authors: Terradas, J., Andries, J., Verwichte, E.
Projects: None

Publication Status: A&A(submitted)
Last Modified: 2010-11-04 07:35
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Observational evidence of resonantly damped propagating kink waves in the solar corona  

Jaume Terradas   Submitted: 2010-07-08 01:12

In this Letter we establish clear evidence for the resonant absorption damping mechanism by analyzing observational data from the novel Coronal Multi-Channel Polarimeter (CoMP). This instrument has established that in the solar corona there are ubiquitous propagating low amplitude (approx1 km s-1) Alfvénic waves with a wide range of frequencies. Realistically interpreting these waves as the kink mode from magnetohydrodynamic (MHD) wave theory, they should exhibit a frequency dependent damping length due to resonant absorption, governed by the TGV relation showing that transversal plasma inhomogeneity in coronal magnetic flux tubes causes them to act as natural low-pass filters. It is found that observed frequency dependence on damping length (up to about 8 mHz) can be explained by the kink wave interpretation and furthermore, the spatially averaged equilibrium parameter describing the length scale of transverse plasma density inhomogeneity over a system of coronal loops is consistent with the range of values estimated from TRACE observations of standing kink modes.

Authors: G. Verth, M. Goossens, J. Terradas
Projects: None

Publication Status: ApJL (accepted)
Last Modified: 2010-07-09 19:22
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Selective spatial damping of propagating kink waves due to resonant absorption  

Jaume Terradas   Submitted: 2010-05-06 08:29

There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. In this paper we show that resonant absorption provides a simple explanation to the spatial damping of these waves. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated. The damping length of propagating kink waves due resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies the damping length is exactly inversely proportional to frequency and we denote this as the TGV relation. When moving to high frequencies the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low frequency waves and can efficiently remove high frequency waves from a broad band spectrum of kink waves. It is selective as the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Hence kink wave trains travelling along, e.g., coronal loops, will have a greater proportion of the high frequency components dissipated lower down in the atmosphere. This could have important consequences with respect to the spatial distribution of wave heating in the solar atmosphere.

Authors: J. Terradas, M. Goossens, G. Verth
Projects: None

Publication Status: submitted to A&A
Last Modified: 2010-05-07 06:51
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The effect of longitudinal flow on resonantly damped kink oscillations  

Jaume Terradas   Submitted: 2009-12-22 02:40

The most promising mechanism acting towards damping the kink oscillations of coronal loops is resonant absorption. In this context most of previous studies neglected the effect of the obvious equilibrium flow along magnetic field lines. The flows are in general sub-Alfvénic and hence comparatively slow. Here we investigate the effect of an equilibrium flow on the resonant absorption of linear kink MHD waves in a cylindrical magnetic flux tube with the aim of determining the changes in the frequency of the forward and backward propagating waves and in the modification of the damping times due to the flow. A loop model with both the density and the longitudinal flow changing in the radial direction is considered. We use the thin tube thin boundary (TTTB) approximation in order to calculate the damping rates. The full resistive eigenvalue problem is also solved without assuming the TTTB approximation. Using the small ratio of flow and Alfvén speeds we derive simple analytical expressions to the damping rate. The analytical expressions are in good agreement with the resistive eigenmode calculations. Under typical coronal conditions the effect of the flow on the damped kink oscillations is small when the characteristic scale of the density layer is similar or smaller than the characteristic width of the velocity layer. However, in the opposite situation the damping rates can be significantly altered, specially for the backward propagating wave which is undamped while the forward wave is overdamped.

Authors: J. Terradas, M. Goossens, I. Ballai
Projects: None

Publication Status: Submitted to A&A
Last Modified: 2009-12-22 11:49
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On the nature of kink MHD waves in magnetic flux tubes  

Jaume Terradas   Submitted: 2009-05-05 04:03

Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfvén. The possibility that these waves have mixed properties is often ignored. The goal of this work is to study and determine the nature of MHD kink waves. This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma with non-zero plasma pressure which allows for MHD radiation. In all three cases the frequency and the damping rate are for practical purposes the same as they differ at most by terms proportional to (k_z R)^2. In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetised flux tube is the magnetic tension force. The total pressure gradient force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfvén frequency, i.e. in the resonant layer. Kink waves are very robust and do not care about the details of the MHD wave environment. The adjective fast is not the correct adjective to characterise kink waves. If an adjective is to be used it should be Alfvénic. However, it is better to realise that kink waves have mixed properties and cannot be put in one single box.

Authors: M. Goossens, J. Terradas, J. Andries, I. Arregui, J. L. Ballester
Projects: None

Publication Status: Submitted to A&A
Last Modified: 2009-05-05 08:08
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Excitation of standing kink oscillations in coronal loops  

Jaume Terradas   Submitted: 2009-02-02 10:18

In this work we review the efforts that have been done to study the excitation of the standing fast kink body mode in coronal loops. We mainly focus on the time-dependent problem, which is appropriate to describe flare or CME induced kink oscillations. The analytical and numerical studies in slab and cylindrical loop geometries are reviewed. We discuss the results from very simple one-dimensional models to more realistic (but still simple) loop configurations. We emphasise how the results of the initial value problem complement the eigenmode calculations. The possible damping mechanisms of the kink oscillations are also discussed.

Authors: Jaume Terradas
Projects: None

Publication Status: Submitted to SSR
Last Modified: 2009-02-03 08:14
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Nonlinear Instability of kink oscillations due to shear motions  

Jaume Terradas   Submitted: 2008-09-23 02:28

First results from a high-resolution three-dimensional nonlinear numerical study of the kink oscillation are presented. We show in detail the development of a shear instability in an untwisted line-tied magnetic flux tube. The instability produces significant deformations of the tube boundary. An extended transition layer may naturally evolve as a result of the shear instability at a sharp transition between the flux tube and the external medium. We also discuss the possible effects of the instability on the process of resonant absorption when an inhomogeneous layer is included in the model. One of the implications of these results is that the azimuthal component of the magnetic field of a stable flux tube in the solar corona, needed to prevent the shear instability, is probably constrained to be in a very specific range.

Authors: J. Terradas, J. Andries, M. Goossens, I. Arregui, R. Oliver, J. L. Ballester
Projects: None

Publication Status: ApJL, in press
Last Modified: 2008-09-23 18:09
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Subject will be restored when possible  

Jaume Terradas   Submitted: 2008-02-07 07:26

We study the excitation and damping of transverse oscillations in a multi-stranded model of a straight line-tied coronal loop. The transverse geometry of our equilibrium configuration is quite irregular and more realistic than the usual cylindrical loop model. By numerically solving the time-dependent ideal magnetohydrodynamic equations in two dimensions we show how the global motion of the whole bundle of strands, excited by an external disturbance, is converted into localized Alfvénic motions due to the process of resonant absorption. This process produces the attenuation of the transverse oscillations. At any location in the structure two dominant frequencies are found, the frequency of the global mode, or quasi-mode, and the local Alfvén frequency. We find that the mechanism of mode conversion, due to the coupling between fast and Alfvén waves, is not compromised by the complicated geometry of the model. We also show that it is possible to have energy conversion not only at the external edge of the composite loop but also inside the structure. The implications of these results and their relationship with the observations are discussed.

Authors: J. Terradas, I. Arregui, R. Oliver, J. L. Ballester, J. Andries, M. Goossens
Projects:

Publication Status: ApJ (in press)
Last Modified: 2008-02-07 09:36
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Subject will be restored when possible  

Jaume Terradas   Submitted: 2007-11-06 11:54

The role of leaky waves in the coronal loop oscillations observed by TRACE is not yet clearly understood. In this work, the excitation of fast waves in solar coronal loops modelled as dense plasma cylindrical tubes in a uniform straight magnetic field is investigated. We study the trapped and especially leaky modes (whose energy escapes from the tube) that result from an initial disturbance by solving the time-dependent problem numerically. We find that the stationary state of the tube motion is given by the trapped normal modes. By contrast, the transient behaviour between the initial and the stationary phase is dominated by wave leakage. The so-called trig leaky modes are clearly identified since the transient behaviour shows periods and damping times that are in agreement with the values calculated from the normal-mode analysis. Consequently, these radiating modes have physical significance. However, we have not found any evidence for the excitation of other types of modes, such as the principal leaky kink mode.

Authors: Terradas, J., Andries, J., & Goossens, M.
Projects: None

Publication Status: Solar Physics, Accepted
Last Modified: 2007-11-07 08:30
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Subject will be restored when possible  

Jaume Terradas   Submitted: 2007-11-06 11:48

Flares and eruptions in the solar corona generate oscillations of loops which have been interpreted as eigenmodes (mainly the fundamental kink mode, although other modes can also be excited). From the theoretical point of view the excitation of the tube eigenmodes due to an initial disturbance has not been studied in much detail. The main aim of this work is to calculate for a given initial disturbance the amount of energy that is deposited in the trapped fast mode oscillation, how it depends on the initial perturbation and how it is distributed among the different eigenmodes (kink and fluting and also the longitudinal harmonics). We calculate, using analytical expressions, the amplitude and the energy of the oscillation of the magnetic tube for different kinds of initial excitations. We find that external excitations deposit a small amount of energy in the tube. We show that fluting modes have quite small energies in comparison with the energy of the kink mode (around three orders of magnitude for the first fluting mode). On the contrary, the longitudinal fundamental mode and the longitudinal harmonics have energies of the same order of magnitude. In addition, we find that the loop length and density contrast can be important factors that determine the amount of energy that is trapped by the loop. The energy deposited in loops is typically six orders of magnitude smaller than the energy of the initial disturbance (for external excitations). However, it strongly depends on the distance of the initial perturbation and also on the loop properties (length and density). Fluting modes in coronal loops are very difficult to excite. Longitudinal harmonics are in principle more easily excited.

Authors: Terradas, J., Andries, J., & Goossens, M.
Projects: None

Publication Status: A&A 469, 1135-1143, 2007
Last Modified: 2007-11-07 08:30
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Subject will be restored when possible  

Jaume Terradas   Submitted: 2007-11-06 11:48

Flares and eruptions in the solar corona generate oscillations of loops which have been interpreted as eigenmodes (mainly the fundamental kink mode, although other modes can also be excited). From the theoretical point of view the excitation of the tube eigenmodes due to an initial disturbance has not been studied in much detail. The main aim of this work is to calculate for a given initial disturbance the amount of energy that is deposited in the trapped fast mode oscillation, how it depends on the initial perturbation and how it is distributed among the different eigenmodes (kink and fluting and also the longitudinal harmonics). We calculate, using analytical expressions, the amplitude and the energy of the oscillation of the magnetic tube for different kinds of initial excitations. We find that external excitations deposit a small amount of energy in the tube. We show that fluting modes have quite small energies in comparison with the energy of the kink mode (around three orders of magnitude for the first fluting mode). On the contrary, the longitudinal fundamental mode and the longitudinal harmonics have energies of the same order of magnitude. In addition, we find that the loop length and density contrast can be important factors that determine the amount of energy that is trapped by the loop. The energy deposited in loops is typically six orders of magnitude smaller than the energy of the initial disturbance (for external excitations). However, it strongly depends on the distance of the initial perturbation and also on the loop properties (length and density). Fluting modes in coronal loops are very difficult to excite. Longitudinal harmonics are in principle more easily excited.

Authors: Terradas, J., Andries, J., & Goossens, M.
Projects:

Publication Status: A&A 469, 1135-1143, 2007
Last Modified: 2007-11-09 02:13
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Subject will be restored when possible  

Jaume Terradas   Submitted: 2007-11-06 11:48

Flares and eruptions in the solar corona generate oscillations of loops which have been interpreted as eigenmodes (mainly the fundamental kink mode, although other modes can also be excited). From the theoretical point of view the excitation of the tube eigenmodes due to an initial disturbance has not been studied in much detail. The main aim of this work is to calculate for a given initial disturbance the amount of energy that is deposited in the trapped fast mode oscillation, how it depends on the initial perturbation and how it is distributed among the different eigenmodes (kink and fluting and also the longitudinal harmonics). We calculate, using analytical expressions, the amplitude and the energy of the oscillation of the magnetic tube for different kinds of initial excitations. We find that external excitations deposit a small amount of energy in the tube. We show that fluting modes have quite small energies in comparison with the energy of the kink mode (around three orders of magnitude for the first fluting mode). On the contrary, the longitudinal fundamental mode and the longitudinal harmonics have energies of the same order of magnitude. In addition, we find that the loop length and density contrast can be important factors that determine the amount of energy that is trapped by the loop. The energy deposited in loops is typically six orders of magnitude smaller than the energy of the initial disturbance (for external excitations). However, it strongly depends on the distance of the initial perturbation and also on the loop properties (length and density). Fluting modes in coronal loops are very difficult to excite. Longitudinal harmonics are in principle more easily excited.

Authors: Terradas, J., Andries, J., & Goossens, M.
Projects:

Publication Status: A&A 469, 1135-1143, 2007
Last Modified: 2007-11-09 02:16
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Damped coronal loop oscillations: time-dependent results  

Jaume Terradas   Submitted: 2006-03-03 09:21

The excitation and damping of transversal coronal loop oscillations is studied using a one-dimensional model of a line-tied cylindrical loop. By solving the time-dependent magnetohydrodynamic (MHD) equations we show how an initial disturbance produced in the solar corona induces kink mode oscillations. We analyze the effect of the disturbance on a loop with a non-uniform boundary layer and investigate the damping of such disturbance due to resonant absorption. We find that the period and attenuation time of the time-dependent results agree with the calculations of the corresponding quasi-mode (i.e. the kink mode resonantly coupled to Alfvén modes) and that the resonant absorption mechanism is capable of damping the oscillations almost immediately after the excitation. We study in detail the behavior of solutions in the inhomogeneous layer and show how the energy of the global oscillation is converted into torsional oscillations in the inhomogeneous layer. In addition, we estimate that the amplitude of the torsional oscillations is, for large magnetic Reynolds numbers and for thick layers, between four and six times the amplitude of the initial transversal motions. The implications of these results and their relationship with the observations are discussed.

Authors: Terradas, J., Oliver, R., Ballester, J. L.
Projects: None

Publication Status: ApJ(accepted)
Last Modified: 2006-03-08 09:44
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Abstracts by Author
On the support of neutrals against gravity in solar prominences
Rayleigh-Taylor instabilities with sheared magnetic fields
Damping of coronal loop kink oscillations due to mode conversion
The role of Rayleigh-Taylor instabilities in filament threads
Seismology of transversely oscillating coronal loops with siphon flows
On the linear coupling between fast and slow MHD waves due to line-tying effects
Observational evidence of resonantly damped propagating kink waves in the solar corona
Selective spatial damping of propagating kink waves due to resonant absorption
The effect of longitudinal flow on resonantly damped kink oscillations
On the nature of kink MHD waves in magnetic flux tubes
Excitation of standing kink oscillations in coronal loops
Nonlinear Instability of kink oscillations due to shear motions
Subject will be restored when possible
Subject will be restored when possible
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Damped coronal loop oscillations: time-dependent results

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