Resonant Absorption of Alfvén Waves in Steady Coronal Loops

The effect of equilibrium flow on linear Alfvén resonances in coronal loops is studied in the compressible viscous MHD model. By means of a finite element code, the full set of linearised driven MHD equations are solved for a one-dimensional equilibrium model in which the equilibrium quantities depend only on the radial coordinate. Computations of resonant absorption of Alfvén waves for two classes of coronal loop models show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We find that a steady equilibrium shear flow can also significantly influence the resonant absorption of Alfvén waves in coronal magnetic flux tubes. The presence of an equilibrium flow may therefore be important for resonant Alfvén waves and coronal heating. A parametric analysis also shows that the resonant absorption can be strongly enhanced by the equilibrium flow, even up to total dissipation of the incoming wave.     

Resonant Absorption of Nonlinear Slow MHD Waves in Isotropic Steady Plasmas – II. Application: Resonant Acoustic Waves

Nonlinear theory of driven magnetohydrodynamic (MHD) waves in the slow dissipative layer in isotropic steady plasmas developed by Ballai and Erdélyi (Solar Phys. 180 (1998)) is used to study the nonlinear interaction of sound waves with one-dimensional isotropic steady plasmas. An inhomogeneous magnetic slab with field-aligned plasma flow is sandwiched by a homogeneous static magnetic-free plasma and by a homogeneous steady magnetic plasma. Sound waves launched from the magnetic-free plasma propagate into the inhomogeneous region interacting with the localised slow dissipative layer and are partially reflected, dissipated or transmitted by this region. The nonlinearity parameter, introduced by Ballai and Erdélyi, is assumed to be small and a regular perturbation method is used to obtain analytical wave solutions. Analytical studies of resonant absorption of sound waves show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We also find that a steady equilibrium shear flow can significantly influence the nonlinear resonant absorption in the limits of thin inhomogeneous layer and weak nonlinearity. The presence of an equilibrium flow may therefore be important for the nonlinear resonant MHD wave phenomena. A parametric analysis also shows that the nonlinear part of resonant absorption can be strongly enhanced by the equilibrium flow.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

A prominence model in a simple magnetic arcade

This paper offers an evolution scenario for a simple magnetic arcade where the frozen-in magnetic field decreases with the ascent of its arches together with the plasma. Uplift is produced by the movement of photospheric plasma with a frozen-in magnetic field, which is divergent with respect to a neutral line. A decrease in magnetic field leads to the appearance in the arcade of a height range of arches, with no high-temperature thermal equilibrium present, and to a variation of the nonequilibrium range with time. Uplift of the arcade is accompanied by the consecutive entry of new arches into this range. All arches entering the nonequilibrium range experience a transient process. Some of the earlier inquiries into the physics of this process were instrumental, in the first place, in identifying those arches which – through the production of an ascending plasma flow from the base of the arcade – are involved in the formation of a prominence (with magnetic dips appearing and evolving at the tops of these arches) and, secondly, in synthesizing a computational algorithm for the final state of the transient process, the quasi-steady-state dynamic structure of the prominence. The arcade evolution scenario, combined with the computational algorithm, constitutes a unified prominence model, a model for the transition from a simple static magnetic arcade to a quasi-steady dynamic prominence structure. The model has been used in numerical calculations of parameters of two classes of prominences: in and outside active regions. Results of the calculations are in good agreement with observations.     

Coronal MHD perturbation field generated by localized perturbers in a photospheric active region

We investigate the two-dimensional boundary value problem of the linear wave excitation in the solar corona by a pair of periodic perturbers localized at the photosphere. The physical properties of the corona allow us to consider a magnetic configuration such as a potential arcade which is in a magneto-hydrostatic equilibrium with the surrounding plasma. The model excludes the A1fvén mode and since the slow mode is absent in a potential arcade, the excited waves are then the fast magneto-acoustic modes. The characteristic magnetic field scale length is twice the scale height of the coronal plasma, assumed isothermal and the induced fluid motions are in the direction perpendicular to the magnetic field, in the cross-sectional plane of the arcade.A particular example of two localized perturbers in a photospheric active region is given, pointing out the effects produced in the perturbed fields by the variation of the different parameters involved. Such example shows that, while a modification of the linear size or the horizontal wave number of the perturbers does not affect significantly the propagating disturbances, the variation of the perturbers' frequency produces important effects. Such effects can be summarized by saying that low-frequency perturbers are able to disturb the whole coronal magnetic configuration above the active region while high-frequency perturbers only disturb the coronal region just above them, producing a channeling feature. Moreover, for high frequencies the perturbations grow withz all the way from the photosphere while for very low frequencies evanescent waves are dominant, although thanks to the influence of the medium their amplitude starts to grow from somez on.     

The structure of coronal arcades and the formation of solar prominences

The temperature and density are obtained for coronal plasma in thermal and hydrostatic equilibrium and located in a force-free magnetic arcade. The isotherms are found to be inclined to the magnetic field lines and so care should be taken in inferring the magnetic structure from observed emission.When the coronal pressure becomes too great, the equilibrium ceases to exist and the material cools to form a quiescent prominence. The same process can be initiated at low heating rates when the width or shear of the arcade exceeds a critical value.We suggest that the prominence should be modelled as a dynamic structure with plasma always draining downwards. Material is continually sucked up along field lines of the ambient arcade and into the region lacking a hot equilibrium, where it cools to form new prominence material.     

Influence of a uniform coronal magnetic field on solar p modes: coupling to slow resonant MHD waves

The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field and a constant sound speed, on top of an adiabatic interior having a linear temperature profile. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. In order to avoid Alfvén resonances, the analysis is restricted to propagation parallel to the coronal magnetic field. Parallel propagating oscillation modes in this equilibrium model have already been studied by Evans and Roberts (1990). However, they avoided the resonant coupling to slow continuum modes by a special choice of the temperature profile. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. The resonant layer is correctly dealt with in ideal MHD by a proper treatment of the logarithmical branch cut of the hypergeometric function. The result of the resonant coupling with cusp waves is twofold. The eigenfrequencies become complex and the real part of the frequency is shifted. The shift of the real part of the frequency is not negligible and within the limit of observational accuracy. This indicates that resonant interactions should definitely be taken into account when calculating the frequencies of the global solar oscillations.     

Non-equilibrium of a cylindrical magnetic arcade

A cylindrically-symmetric magnetic arcade with its axis on the photosphere is perturbed by means of an alteration in the pressure along the base. The perturbation is examined with a view to finding equilibrium configurations close to the original equilibrium. It is found that equilibria can only be found when the integral of the excess pressure along the base is zero. In other cases no equilibria can be found and the arcade is likely either to collapse or, in the case of a coronal mass ejection, to erupt. For an initial arcade whose field increases linearly with radial distance from the axis, the neighbouring equilibria have been found.     

Corrugation Instability of a Coronal Arcade

We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed.     

Quasi-static evolution in multiple arcades

The slow dynamical evolution of solar atmospheric magnetic field structures via the equilibrium equation has been the subject of a number of investigations. In many of these studies the quasi-static evolution of the field and the associated plasma has been investigated for a single arcade structure. In this paper we present results for multiple arcade structures. For multiple arcades we do not find bifurcations and the consequent multiple solutions as the field is evolved through a sequence of equilibrium states, in contrast to the findings for single arcade. Further we show that particular polarity arrangements within a pair of arcade structures lead to quite different topologies of the field as it is evolved. When new flux emerges from the photospheric boundary under a pre-existing magnetic arcade the results suggest that such a mechanism will initiate coronal mass ejection.     

The Effect of a Twisted Magnetic Field on the Nature of Kink MHD Waves

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvénic wave in the entire loop.     

Formation of solar prominences by photospheric shearing motions

A numerical simulation is performed to investigate the prominence formation in a magnetic arcade by photospheric shearing motions. A two-and-a-half-dimensional magnetohydrodynamic (MHD) code is used, in which the gravitational force, radiative cooling, thermal conduction and a simplified form of coronal heating are included. It is found that a footpoint shear induces an expansion of the magnetic arcade and cooling of the plasma in it. Simultaneously the denser material from the lower part of the arcade is pulled up by the expanding field lines. A local enhancement of radiative cooling is thus effected, which leads to the onset of thermal instability and the condensation of coronal plasma. The condensed material grows vertically to form a sheet-like structure making dips on field lines, leading to the formation of the Kippenhahn- Schlüter type prominence. The mass of the prominence is found to be supplied not only by the condensation of the material in the vicinity but also by the siphon-type upflows. The upward growth of the vertical sheet-structure of the prominence is saturated at a certain stage and the newly condensed material is found to slide down from above the prominence along magnetic field lines. This drainage of material leads to the formation of an arc-shaped cavity of low density and low pressure around the prominence. The problem of force and heat balance is addressed and the prominence is found to be not in a static equilibrium but in a dynamic interaction with its environment.     

Thermal equilibria of coronal magnetic arcades

A coronal magnetic arcade can be thought of as consisting of an assembly of coronal loops. By solving equations of thermal equilibrium along each loop and assuming a base temperature of 2 × 10⁴ K, the thermal structure of the arcade can be found. By assuming a form for the plasma pressure in the arcade, the possible thermal structures can be shown to depend on three parameters. Arcades can contain hot loops with summits hotter than 400 000 K, cool loops at temperatures less than 80 000 K along their lengths, hot-cool loops with cool summits and cool footpoints but hotter intermediate portions, and warm loops, cooler than 80 000 K along most of their lengths but with summits as hot as 400 000 K. For certain arcades, there exist regions where more than one kind of loop is possible. If the parameters describing the arcade are varied, it is possible for non-equilibrium to occur when a type of solution ceases to exist. For example, hot or warm loops can cease to exist so that only cool solutions are possible when the arcade size or pressure is decreased, while warm or cool loops may give way to hot-cool loops when the heating is reduced or the pressure is increased.     

Magnetoacoustic oscillations in spatially periodic solar coronal structures

This paper is concerned with the propagation properties of the magnetoacoustic wave across the magnetic field embedded in plasma whose density varies periodically along the propagation direction. Such spatial structures are arcades of solar post-flare coronal loops. The model problem of wave propagation along the arcade implies analyzing the dispersion properties of the Hill equation. Oscillations in the range of seconds are the response of the arcade to an impulsive disturbance.     

Total resonant absorption of acoustic oscillations in sunspots

The question of total resonant absorption of acoustic oscillations in sunspots is studied for cylindrical 1-D flux tubes that are stratified only in the radial direction and surrounded by a uniform, non-magnetic plasma. The numerical investigation of Goossens and Poedts (1992) in linear resistive MHD is taken further by increasing the strength of the azimuthal magnetic field in the equilibrium flux tubes. For relatively strong azimuthal magnetic fields, total absorption is found over a relatively wide range of spot radii.     

Theoretical study of onset conditions for solar eruptive processes

We apply the model of quasistatic equilibrium sequences to describe the time development of magnetic field structures in the plasma of the solar corona, and to determine onset points of a dynamical evolution. The representation of the magnetic field by Euler potentials provides a realistic modeling of the photospheric boundary conditions. We present a numerical method suited for the computation of magnetohydrodynamic equilibrium states and for analysing their stability against perturbations within ideal MHD. Pressure and magnetic footpoint displacement can be prescribed separately as boundary conditions. We consider magnetic arcade structures typical for large two-ribbon flares. Our results indicate that a finite pressure gradient seems to be essential for the existence of onset points. Furthermore, it is shown that magnetic shear destabilizes for intermediate values, but can have a stabilizing effect for a large amount of shear.     

Phase mixing of standing Alfvén waves with shear flows in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of such waves due to phase mixing at the presence of shear flow and field in the stratified atmosphere of solar spicules. The initial flow is assumed to be directed along spicule axis and to vary linearly in the x direction and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that the shear flow and field can fasten the damping of standing Alfvén waves. In spite of propagating Alfvén waves, standing Alfvén waves in Solar spicules dissipate in a few periods. As height increases, the perturbed velocity amplitude does increase in contrast to the behavior of perturbed magnetic field. Moreover, it should be emphasized that the stratification due to gravity, shear flow and field are the facts that should be considered in MHD models in spicules.     

Influence of relativistic effects and vacuum polarization on the transfer of gyroresonance radiation and the stability of the atmospheres of compact stars

We consider the transfer of radiation and calculate the force of its pressure in the electron gyroresonance line in the atmospheres of magnetic degenerate stars. We specify the atmospheric parameters for which an outflow of plasma is possible under radiation pressure in the cyclotron line. We show that the permittivity tensor of a mildly relativistic plasma in a strong magnetic field found by applying relativistic corrections to the cyclotron resonance condition and by taking into account the vacuum polarization and recoil effects during photon scattering should be used to obtain proper results. We have determined the real and imaginary parts of the refractive indices and the polarization coefficients for normal electromagnetic waves when scattering dominates over absorption. Relativistic effects, which change greatly the dispersion and resonant absorption of waves propagating almost perpendicular to the magnetic field, and vacuum polarization have been found to change qualitatively the gyroresonance radiation spectrum and pressure for a wide range of parameters of stellar magnetospheres.     

SUMER Observations of the Evolution and the Disappearance of a Solar Prominence

The mechanisms that lead to the formation and the disappearance of prominences are poorly understood, at present. An arch-shaped prominence was observed with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer on board the Solar and Heliospheric Observatory (SOHO) on 31 March–1 April 1996. The observations were performed at three wave-bands in the Lyman continuum. Ten successive images were obtained at 41-minute time intervals. Based on computed models of Gouttebroze, Heinzel, and Vial (1993), we have determined the temperature distribution of the prominence using the intensity ratio of 876 Å and 907 Å. The observed time sequence shows that parts of the prominence disappear possibly by heating, while other parts exhibit heating and cooling with apparent outward motion. We model the heat input with the linearized MHD equations using a prescribed initial density and a broad-band spectrum of Alfvén waves. We find a good qualitative agreement with observations. In the model the prominence is heated by the resonant absorption of Alfvén waves with frequencies that match the resonant condition for a particular flux tube structure that is determined by the magnetic field topology and plasma density.