One dimensional prominence threads: I. Equilibrium models 

Jaume Terradas Submitted: 20210615 10:49
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 chromosphericlike 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.
Authors: J. Terradas, M. Luna, R. Soler, R. Oliver, M. Carbonell, J. L Ballester
Projects: None

Publication Status: Accepted for publication in A&A
Last Modified: 20210616 08:40



RayleighTaylor instabilities with sheared magnetic fields 

Jaume Terradas Submitted: 20140227 05:16
Magnetic RayleighTaylor (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: 20140227 13:37



Damping of coronal loop kink oscillations due to mode conversion 

Jaume Terradas Submitted: 20130625 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: 20130626 11:13



The role of RayleighTaylor instabilities in filament threads 

Jaume Terradas Submitted: 20120321 02:44
Many solar filaments and prominences show shortlived horizontal threads lying parallel to the photosphere. In this work the possible link between RayleighTaylor 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 RayleighTaylor 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 RayleighTaylor instability for a wide range of wavelengths.
Authors: J. Terradas, R. Oliver, J. L. Ballester
Projects: None

Publication Status: submitted
Last Modified: 20120321 13:00



On the linear coupling between fast and slow MHD waves due to linetying effects 

Jaume Terradas Submitted: 20101104 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 linetying effect of the photosphere, is analytically investigated. Both propagating and standing waves are analysed and the timedependent 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: 20101104 07:35



On the nature of kink MHD waves in magnetic flux tubes 

Jaume Terradas Submitted: 20090505 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 pressureless plasma, an incompressible plasma and a compressible plasma with nonzero 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: 20090505 08:08



Subject will be restored when possible 

Jaume Terradas Submitted: 20080207 07:26
We study the excitation and damping of transverse oscillations in a multistranded model of a straight linetied 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 timedependent 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 quasimode, 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: 20080207 09:36



Subject will be restored when possible 

Jaume Terradas Submitted: 20071106 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 timedependent 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 socalled 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 normalmode 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: 20071107 08:30



Subject will be restored when possible 

Jaume Terradas Submitted: 20071106 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, 11351143, 2007
Last Modified: 20071107 08:30



Subject will be restored when possible 

Jaume Terradas Submitted: 20071106 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, 11351143, 2007
Last Modified: 20071109 02:13



Subject will be restored when possible 

Jaume Terradas Submitted: 20071106 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, 11351143, 2007
Last Modified: 20071109 02:16




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