On the Properties of Low‐β Magnetohydrodynamic Waves in Curved Coronal Fields (original) (raw)
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Three-Dimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades
Astrophysical Journal, 2010
We numerically investigate the excitation and temporal evolution of oscillations in a two-dimensional coronal arcade by including the three-dimensional propagation of perturbations. The time evolution of impulsively generated perturbations is studied by solving the linear, ideal magnetohydrodynamic (MHD) equations in the zero-β approximation. As we neglect gas pressure the slow mode is absent and therefore only coupled MHD fast and Alfvén modes remain. Two types of numerical experiments are performed. First, the resonant wave energy transfer between a fast normal mode of the system and local Alfvén waves is analyzed. It is seen how, because of resonant coupling, the fast wave with global character transfers its energy to Alfvénic oscillations localized around a particular magnetic surface within the arcade, thus producing the damping of the initial fast MHD mode. Second, the time evolution of a localized impulsive excitation, trying to mimic a nearby coronal disturbance, is considered. In this case, the generated fast wavefront leaves its energy on several magnetic surfaces within the arcade. The system is therefore able to trap energy in the form of Alfvénic oscillations, even in the absence of a density enhancement such as that of a coronal loop. These local oscillations are subsequently phase-mixed to smaller spatial scales. The amount of wave energy trapped by the system via wave energy conversion strongly depends on the wavelength of perturbations in the perpendicular direction, but is almost independent from the ratio of the magnetic to density scale heights.
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 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.
Apparent Cross-Field Superslow Propagation of Magnetohydrodynamic Waves in Solar Plasmas
The Astrophysical Journal, 2015
In this paper we show that the phase mixing of continuum Alfvén waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic field. This phenomenon could be erroneously interpreted as fast magnetosonic waves. The cross-field propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.
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.
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.
Monthly Notices of the Royal Astronomical Society, 2013
We present a two-dimensional (2D) magnetohydrodynamic (MHD) model of magnetoacoustic-gravity waves in the gravitationally stratified solar corona that is shaped by a realistic (VAL-C, Vernazza Avrett Loeser model C) temperature profile and curved magnetic field lines. These waves are triggered by an initial Gaussian pulse in the horizontal component of velocity, that is, launched either just below or above the transition region. The time-dependent ideal MHD equations are solved numerically with the use of the FLASH code. The numerical results reveal conversion of a horizontal flow into its vertical counterpart, oscillations of the transition region and vertical jets of cold plasma penetrating the solar corona. The wavelet analysis of the mass-density variations at a fixed detection point leads to the oscillation period of about 180 s, which corresponds to 3-min oscillations observed in solar active regions.
EVOLUTION OF MAGNETOHYDRODYNAMIC WAVES IN LOW LAYERS OF A CORONAL HOLE
The Astrophysical Journal, 2014
Although a coronal hole is permeated by a magnetic field with a dominant polarity, magnetograms reveal a more complex magnetic structure in the lowest layers, where several regions of opposite polarity of typical size of the order of 10 4 km are present. This can give rise to magnetic separatrices and neutral lines. MHD fluctuations generated at the base of the coronal hole by motions of the inner layer of the solar atmosphere may interact with such inhomogeneities, leading to the formation of small scales. This phenomenon is studied on a 2D model of a magnetic structure with an X-point, using 2D MHD numerical simulations. This model implements a method of characteristics for boundary conditions in the direction outer-pointing to Sun surface to simulate both wave injection and exit without reflection. Both Alfvénic and magnetosonic perturbations are considered, and they show very different phenomenology. In the former case, an anisotropic power-law spectrum forms with a dominance of perpendicular wavevectors at altitudes ∼10 4 km. Density fluctuations are generated near the X-point by Alfvén wave magnetic pressure and propagate along open fieldlines at a speed comparable to the local Alfvén velocity. An analysis of energy dissipation and heating caused by the formation of small scales for the Alfvénic case is presented. In the magnetosonic case, small scales form only around the X-point, where a phenomenon of oscillating magnetic reconnection is observed to be induced by the periodic deformation of the magnetic structure due to incoming waves.
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.