Three-Dimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades (original) (raw)
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Magnetohydrodynamic waves in a sheared potential coronal arcade
Astronomy and Astrophysics, 2004
We study the effects of magnetic field shear (B y 0) and longitudinal propagation of perturbations (k y 0) on the linear and adiabatic magnetohydrodynamic (MHD) normal modes of oscillation of a potential coronal arcade. In a cold plasma, the inclusion of these two effects produces the linear coupling of discrete fast modes, characterised by a discrete spectrum of frequencies and a global velocity structure, and Alfvén continuum modes, characterised by a continuous spectrum of frequencies and with a velocity perturbation confined to given magnetic surfaces in such a way that modes with mixed properties arise (Arregui et al. 2004). The wave equations governing the velocity perturbations have been solved numerically and our results show that the couplings between fast and Alfvén modes are governed by some parity rules for the symmetry of the eigenfunctions of fast and Alfvén modes in the direction along the equilibrium magnetic field. The nature of the coupling between fast and Alfvén modes can be resonant or non-resonant depending on the location of the fast mode frequency within the different Alfvén continua. Also, an important result is that in this kind of configurations coupled modes could be difficult to observe since when both magnetic field shear and longitudinal propagation are present the spatial distribution of the velocity may not be confined to low heights in the solar corona.
The Temporal Evolution of Linear Fast and Alfven MHD Waves in Solar Coronal Arcades
Highlights of Spanish Astrophysics V, 2010
The excitation and temporal evolution of fast and Alfvén magnetohydrodynamic oscillations in a two-dimensional coronal arcade are investigated. The approach is to consider an equilibrium magnetic and plasma structure and then to introduce a perturbation trying to mimic a nearby disturbance, such as a flare or filament eruption. By numerically solving the time-dependent linearised MHD wave equations the properties of the solutions have been studied. First, the properties of uncoupled fast and Alfvén waves are described. Then, longitudinal propagation of perturbations is included, and the properties of coupled waves are determined.
Magnetohydrodynamic Waves in Two-Dimensional Prominences Embedded in Coronal Arcades
The Astrophysical Journal, 2013
Solar prominence models used so far in the analysis of MHD waves in such structures are quite elementary. In this work, we calculate numerically magnetohydrostatic models in two-dimensional configurations under the presence of gravity. Our interest is in models that connect the magnetic field to the photosphere and include an overlying arcade. The method used here is based on a relaxation process and requires solving the time-dependent nonlinear ideal MHD equations. Once a prominence model is obtained, we investigate the properties of MHD waves superimposed on the structure. We concentrate on motions purely two-dimensional neglecting propagation in the ignorable direction. We demonstrate how by using different numerical tools we can determine the period of oscillation of stable waves. We find that vertical oscillations, linked to fast MHD waves, are always stable and have periods in the 4-10 min range. Longitudinal oscillations, related to slow magnetoacoustic-gravity waves, have longer periods in the range of 28-40 min. These longitudinal oscillations are strongly influenced by the gravity force and become unstable for short magnetic arcades.
Fast magnetohydrodynamic waves in a two-slab coronal structure: collective behaviour
Astronomy & Astrophysics, 2006
Aims. We study fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma slabs in a uniform magnetic field. This allows us to analyse in a simple configuration the collective behaviour of the structure due to the interaction between the slabs. Methods. We first calculate the normal modes of the system and find analytical expressions for the dispersion relation of the two-slab configuration. Next, we study the time-dependent problem of the excitation of slab oscillations by numerically solving the initial value problem. We investigate the behaviour of the system for several shapes of the initial disturbances.
On the Properties of Low‐β Magnetohydrodynamic Waves in Curved Coronal Fields
The Astrophysical Journal, 2008
The solar corona is a complex magnetic environment where several kinds of waves can propagate. In this work, the properties of fast, Alfvén, and slow magnetohydrodynamic waves in a simple curved structure are investigated. We consider the linear regime, i.e., small-amplitude waves. We study the time evolution of impulsively generated waves in a coronal arcade by solving the ideal magnetohydrodynamic equations. We use a numerical code specially designed to solve these equations in the low-regime. The results of the simulations are compared with the eigenmodes of the arcade model. Fast modes propagate nearly isotropically through the whole arcade and are reflected at the photosphere, where line-tying conditions are imposed. On the other hand, Alfvén and slow perturbations are very anisotropic and propagate along the magnetic field lines. Because of the different physical properties in different field lines, there is a continuous spectrum of Alfvén and slow modes. Curvature can have a significant effect on the properties of the waves. Among other effects, it considerably changes the frequency of oscillation of the slow modes and enhances the possible dissipation of the Alfvén modes due to phase mixing.
Fast magnetohydrodynamic oscillations in a force-free line-tied coronal arcade
Astronomy & Astrophysics, 2006
Aims. We discuss a simple model of a line-tied coronal arcade with piecewise constant density to explore the effects of curvature on radially polarised fast modes. Methods. A partial differential equation is derived for the velocity perturbation of the fast modes and it is solved analytically in terms of Bessel functions of half integer order, obtaining a dispersion relation. Results. The properties of the modes are studied in terms of the parameters. All the modes are leaky under these conditions. Besides the usual kink and sausage modes, new families are described: the vertical, swaying (longitudinal), and rocking modes arise. Conclusions. The damping rates are similar to observed rates. For thin arcades the modes are markedly different from those of a straight slab and resemble more the modes of a circular membrane.
Resonant Alfven waves in coronal arcades driven by footpoint motions
X-ray spectroscopy performed from different astronomical spacecrafts has shown that the solar corona is structured by magnetic fields having the shape of loops and arcades. These structures are formed by stretching and reconnection of magnetic fields, and remain stable from days to weeks. Also, sporadic or periodic brightenings of such structures have been detected in UV and soft X-ray observations, suggesting the existence of propagating waves and plasma heating within them. In this paper, a mechanism for the deposition of Alfvén wave energy and heating of coronal arcades via resonant absorption is investigated. An analytical solution to the linear viscous, resistive MHD equations that describes the steady state of resonant shear Alfvén oscillations in coronal arcades driven by toroidal footpoint motions is obtained. General expressions for the total amount of dissipated wave energy and for its spatial distribution within the resonant magnetic surface is derived.
1998
We study the heating of 2-D coronal arcades by linear resonant Alfvén waves that are excited by photospheric footpoint motions of the magnetic field lines. The analysis is restricted to toroidally polarised footpoint motions so that Alfvén waves are excited directly. At the magnetic surfaces where Alfvén waves, travelling back and forth along the loop-like magnetic field lines, are in phase with the footpoint motions, the oscillations grow unbounded in ideal linear MHD. Inclusion of dissipation prevents singular growth and we can look at the steady state in which the energy input at the photospheric base of the arcade is balanced by the energy dissipated at the resonance layer.
Numerical simulations of impulsively generated vertical oscillations in a solar coronal arcade loop
Astronomy and Astrophysics, 2006
Impulsively generated waves in coronal arcades are simulated numerically by an application of nonlinear ideal magnetohydrodynamic (MHD) equations. The simulations are performed in the (x, z)-plane on a non-uniform Cartesian mesh. In this geometry the magnetic field can be expressed in terms of the vector potential. The governing equations, which are applied in the limit of low plasma-β, are solved by a flux corrected transport method. The model excludes the Alfvén waves and, since the slow mode is absent in the cold plasma limit, the excited disturbances are fast magnetosonic waves. Numerical results show that for short times after the impulse is launched (i. e., in the linear regime), only motions normal to the equilibrium magnetic field get propagated away from the position of the initial displacement and that any velocity parallel to the unperturbed magnetic field lines remains essentially unchanged in time. In the nonlinear regime there is conversion between normal and parallel flow and the two velocity components propagate from the site of the initial impulse. In addition, nonlinearities that are built in the MHD equations modify the shape and speed of the propagating wavefront, an effect that becomes most noticeable where the wave amplitude is larger. The effect of nonlinearity on down-going perturbations is to speed up positive wave amplitudes and to slow down negative wave amplitudes (positive and negative refers to the sign of the normal velocity component). On the contrary, up-going positive and negative waves are slowed down and speeded up, respectively. Impulsively generated waves exhibit temporal signatures with characteristic time scales of the order of 10 s. Similar scales have been recently reported in radio observations, microwaves, and hard X-rays.
Numerical simulations of impulsively excited magnetosonic waves in two parallel solar coronal slabs
Astronomy and Astrophysics, 2007
We aim to consider impulsively-generated non-linear acoustic-gravity waves in a gravitationally-stratified stellar atmosphere. Two-dimensional hydrodynamic equations are solved numerically for an ideal plasma with a realistic temperature profile. The numerical results show that an initial pulse in vertical velocity excites a leading wave front which is followed by a dispersive wake, oscillating with a period close to the acoustic cut-off period P ac of the chromosphere. Impulses launched deeper within a low region of the stellar atmosphere result in a wake of smaller P ac . They form quasiperiodic shocks traveling from the chromosphere to the corona. The interaction of the secondary ("rebound") shocks with the chromosphere-corona transition region generates vortex motions, which may play important role the transition region dynamics.