Solar Coronal Arcade Research Articles

Dispersion and spatial structure of the coupled Alfvén and slow magnetosonic oscillations in the Solar corona

Abstract Numerical and analytical analysis of the magnetohydrodynamic (MHD) waves in Solar coronal arcades is performed. A semi-cylinder slab model of arcade is used where the field lines are represented by half-circles intersecting the photosphere, the magnetic shells are represented by nested coaxial semi-cylinders. The finite plasma pressure is taken into account. The “corrugational”perturbations are considered, that is, the perturbations with short wavelength in the direction along the arcade. In this limit, there are two oscillation modes, the Alfvén and slow magnetosonic modes, coupled due to the field line curvature. The transverse dispersion of the modes, that is, the dependence of the radial wave vector’s component kr on the wave frequency ω, is considered. It was found that the wave is concentrated in two regions of mode’s existence, where $k_r^2>0$: the Alfvén and magnetosonic transparent regions. On one side, each of them is bounded by the resonance surface, where $k_r^2 \rightarrow \infty$. On the resonance surface, the wave’s frequency is determined by the Alfvén and slow magnetosonic modes dispersion relations, respectively. On the other side, the transparent regions are bounded by cut-off frequencies where $k_{r}^2 =0$. In both transparent regions, the perturbations have both transverse electric field (characteristic for the Alfvén mode) and field aligned velocity (characteristic for the slow mode). The wave structure along the field line for several models of plasma parameters is calculated.

The nature of the frequency spectrum of shear Alfvén waves in a solar coronal arcade

Frequency power spectra are computed theoretically for shear Alfvén waves excited in a solar coronal arcade by two separate perturbations, a cosine-modulated Gaussian perturbation and an impulsive driver. The arcade is assumed to consist of potential magnetic field lines embedded in a stratified plasma. It is shown that although the power spectra have discrete frequencies for each field line, a cumulative effect of many field lines of different widths/lengths in an arcade will be that of a continuous spectrum, if seen together as one entity. The nature of the frequency power spectra can constrain the size and the type of driver.

A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades

Abstract We study intensity variations, as measured by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, in a solar coronal arcade using a newly developed analysis procedure that employs spatio-temporal autocorrelations. We test our new procedure by studying large-amplitude oscillations excited by nearby flaring activity within a complex arcade and detect a dominant periodicity of 12.31 minutes. We compute this period in two ways: from the traditional time–distance fitting method and using our new autocorrelation procedure. The two analyses yield consistent results. The autocorrelation procedure is then implemented on time series for which the traditional method would fail due to the complexity of overlapping loops and a poor contrast between the loops and the background. Using this new procedure, we discover the presence of small-amplitude oscillations within the same arcade with 9.13 and 9.81 minute periods prior and subsequent to the large-amplitude oscillations, respectively. Consequently, we identify these as “decayless” oscillations that have only been previously observed in nonflaring loop systems.

FAST MAGNETIC TWISTER AND PLASMA PERTURBATIONS IN A THREE-DIMENSIONAL CORONAL ARCADE

We present results of 3-D numerical simulations of a fast magnetic twister excited above a foot-point of the potential solar coronal arcade that is embedded in the solar atmosphere with the initial VAL-IIIC temperature profile, which is smoothly extended into the solar corona. With the use of the FLASH code, we solve 3-D ideal magnetohydrodynamic equations by specifying a twist in the azimuthal component of magnetic field in the solar chromosphere. The imposed perturbation generates torsional Alfv\'en waves as well as plasma swirls that reach the other foot-point of the arcade and partially reflect back from the transition region. The two vortex channels are evident in the generated twisted flux-tube with a fragmentation near its apex that results from the initial twist as well as from the morphology of the tube. The numerical results are compared to observational data of plasma motions in a solar prominence. The comparison shows that the numerical results and the data qualitatively agree even though the observed plasma motions occur over comparatively large spatio-temporal scales in the prominence.

Numerical simulations of the attenuation of the fundamental slow magnetoacoustic standing mode in a gravitationally stratified solar coronal arcade

Aims. We aim to explore the influence of thermal conduction on the attenuation of the fundamental standing slow magnetoacoustic mode in a two-dimensional (2D) potential arcade that is embedded in a gravitationally stratified solar corona. Methods. We numerically solve the time-dependent magnetohydrodynamic equations to find the spatial and temporal signatures of the mode. Results. We find that this mode is strongly attenuated on a time-scale of about 6 waveperiods. Conclusions. The effect of non-ideal plasma such as thermal conduction is to enhance the attenuation of slow standing waves. The numerical results are similar to previous observational data and theoretical findings for the one-dimensional plasma.

Excitation of vertical kink waves in a solar coronal arcade loop by a periodic driver

Aims. We study an oscillatory driver as a possible excitation mechanism of vertical kink loop oscillations in the ideal MHD regime.Methods. We consider a solar coronal magnetic arcade with a dense photospheric layer. The two-dimensional numerical model that we implement includes the effects of nonlinearity and line curvature on the excitation and attenuation of fast magnetosonic kink waves. We investigate the effects of a driven sinusoidal pressure pulse and compare it with the impulsive excitation by a pressure pulse that impacts the overlying loop.Results. Our numerical simulations reveal wave signatures that are reminiscent of vertical loop oscillations seen in TRACE observational data.Conclusions. We conclude that attenuation of vertical kink oscillations can be reduced to the value observed by adopting an oscillatory instead of an impulsive excitation. An oscillatory driver also naturally explains why only a small subset of all loops is excited to oscillate transversally in an active region.

Slow magnetoacoustic standing waves in a curved solar coronal slab

<i>Aims. <i/>We consider a model of a two-dimensional solar coronal arcade to explore the effects of a curved magnetic field topology on excitation and attenuation of slow magnetoacoustic standing waves.<i>Methods. <i/>The time-dependent ideal magnetohydrodynamic equations are solved numerically to find the spatial and temporal signatures of these waves.<i>Results. <i/>A pulse in gas pressure initially launched at a loop footpoint excites the fundamental mode of slow magnetoacoustic standing waves. The typical excitation time of such a wave mode is 2.5 wave periods, with a similar attenuation timescale. These values are remarkably similar to those recovered from observations by SOHO/SUMER in an Fe XIX line.<i>Conclusions. <i/>Slow magnetoacoustic standing waves are excited and attenuated more efficiently in curved magnetic field lines than in a straight magnetic slab topology. The waves supported by the magnetic arcade are in far closer agreement with observations.

A quantitative MHD study of the relation among arcade shearing, flux rope formation, and eruption due to the tearing instability

The quantitative relationship between the magnetohydrodynamic (MHD) activity of solar coronal arcade and the magnetic helicity injection, which is caused by shearing motion, has been investigated, using azimuthally symmetric model of MHD simulation. We have calculated several cases in which the width of the shearing region is varied and examined the relationship between the magnetic arcade dynamics and magnetic helicity evolution. As a result, it is found that as the shearing motion is imposed on narrower regions along each side of the magnetic inversion line, the magnetic arcade can be easily destabilized by the resistive tearing mode. However, in this case, even though reconnection driven by the tearing mode produces plasmoids, the plasmoid elevation is almost in proportion to the total amount of magnetic helicity contained in the arcade, and it is too slow to explain the trigger process of coronal mass ejections (CMEs). On the other hand, in the case where the shearing motion is imposed on the entire region, much larger magnetic helicity injection is required to injected arcade in order to destabilize the system, compared to practical helicity injection measured in the solar corona. The results suggest that it may be difficult to trigger a CME just by the axisymmetric shearing motion and that some other mechanisms should be involved in the triggering process of a CME. The results also imply that the relation between the magnetic helicity and the overlying magnetic flux can be a key parameter for the CME occurrence.

Numerical simulations of vertical oscillations of a multi-stranded coronal loop

Aims. We consider impulsively generated oscillations in a 2D model of a curved solar coronal arcade loop that consists of up to 5 strands of dense plasma. Methods. First we do a simulation for a loop which consists of two curved strands. We evaluate by means of numerical simulations the influence of the distance between the strands and their number on wave period, attenuation time, and amplitudes of standing kink waves. Results. The results of the numerical simulations reveal that only strands which are very close to each other (distance comparable to the strand width) considerably change the collective behavior of kink oscillations. More distant strands also exhibit weak coupling of the oscillations. However, their behavior can essentially be explained in terms of separate oscillating loops. We compare the numerical results with recent TRACE observational findings, and find qualitative agreement.

MHD waves in coronal magnetic arcades

We analyze the eigenmodes of the solar coronal magnetic arcade that describes the magnetic field of a bipolar active region using the eikonal method for ideal magnetohydrodynamic equations. We write out the eikonal equations for Alfven and magnetoacoustic waves and derive the equations for the amplitudes of the zeroth approximation. We construct the wave fields for Alfven and fast magnetoacoustic modes and derive the expressions for the eigenfrequencies. We show that Alfven modes of a given frequency are near a number of magnetic surfaces, while fast magnetoacoustic eigenmodes are near nonmagnetic surfaces. A discrete set of eigenfrequencies that continuously change from one surface to another corresponds to each such surface.

Numerical simulations of impulsively generated vertical oscillations in a solar coronal arcade loop

Aims. The main aims of the paper are to carry out numerical simulations of the vertical oscillations in a coronal loop in order to determine their dependence on various parameters and to compare them with recent TRACE observations. Methods. We consider impulsively generated oscillations in a solar coronal arcade loop. The two-dimensional numerical model we implement in the ideal MHD regime includes the effects of nonlinearity and line curvature. We perform parametric studies by varying both the position and the width/strength of the pulse. Results. A pulse launched below a loop is in general found to excite multiple wave modes, in particular a vertical oscillation with many properties of a kink mode, fast mode oscillations and a slow mode pulse (or two slow mode pulses, depending on the location of the original pulse). From our parametric studies we deduce that wave periods and attenuation times of the excited waves depend on the position below the loop summit, as well as on the width of the pulse. Wider pulses launched closer to a foot-point and to the loop's apex trigger wave packets of longer period waves which are more strongly attenuated. A perturbed loop does not return to its initial state but is instead stretched, with its apex shifted upwards. As a result the perturbations propagate along the stretched loop and consequently stronger and wider pulses which stretch a loop more lead to longer period oscillations. A pulse located near one of the foot-points is found to excite a distortion mode leading to asymmetric oscillations which are distinct from the vertical or horizontal kink modes that have been identified in TRACE data.

Transverse oscillations in solar coronal loops induced by propagating Alfvénic pulses

The propagation and the evolution of Alfvenic pulses in the solar coronal arcades is investigated by means of MHD numerical simulations. Significant transverse oscillations in coronal loops, triggered by nearby flare events, are often measured in EUV lines and are generally interpreted as standing kink modes. However, the damping times of these oscillations are typically very short (from one to a few periods) and the physical mechanism responsible for the decay is still a matter of debate. Moreover, the majority of the observed cases actually appears to be better modeled by propagating, rather than standing, modes. Here we perform 2.5D compressible MHD simulations of impulsively generated Alfven waves propagating in a potential magnetic arcade (assumed as a simplified 2D loop model), taking into account the stratification of the solar atmosphere with height from the photosphere to the corona. The results show a strong spreading of the initially localized pulses along the loop, due to the variations in the Alfven velocity with height, and correspondingly an efficient damping of the amplitude of the oscillations. We believe that simple explanations based on the effects of wave propagation in highly inhomogeneous media may apply to the majority of the reported cases, and that variations of the background density and Alfven speed along the loop should be considered as key ingredients in future models.

Erratum: "Analysis of the Temperature and Emission Measure of Solar Coronal Arcades and Test of a Scaling Law of Flare/Arcade Loop Length" ([URL ADDRESS="/cgi-bin/resolve?2002ApJ...579L..45Y" STATUS="OKAY"]ApJ, 579, L45 [2002][/URL

1992 Apr 27 . . . . . . 10:15 27:08 N40W25 1.91 4.17 4.39 14.76 4.34 1.58 1.43 1.04 1992 Jul 16 . . . . . . . 03:00 34:01 N40E25 2.16 1.60 2.65 2.72 1.35 1.95 1.71 0.86 1992 Jul 20 . . . . . . . 12:40 20:08 N40E10 1.78 1.94 2.81 0.91 2.25 0.96 0.74 1.16 1992 Nov 04 . . . . . . 20:47 40:17 N30E17 1.75 3.13 2.43 6.29 1.76 2.17 2.48 0.57 1993 Jan 16 . . . . . . . 13:23 15:17 S30W20 2.21 1.77 3.86 11.03 4.01 1.51 2.07 2.26 1993 Jan 26 . . . . . . . 04:00 24:15 S35W14 1.84 3.27 4.01 9.64 2.76 1.85 1.41 0.85 1994 Mar 02 . . . . . . 16:28 25:17 S25W40 2.03 2.06 2.48 2.23 1.95 1.43 1.53 0.96 1994 Apr 14 . . . . . . 04:37 17:49 S45E57 2.14 0.76 1.96 10.91 0.76 4.58 8.56 1.0

Analysis of the Temperature and Emission Measure of Solar Coronal Arcades and Test of a Scaling Law of Flare/Arcade Loop Length

We analyze 17 arcades to study the relations between solar flares and arcades. Soft X-ray images taken with Yohkoh's soft X-ray telescope are used to derive T0, EM0, and temporal variation of Tarc and EMarc, where Tarc and T0 are the temperatures of an arcade and prearcade region and EMarc and EM0 are the volume emission measures of an arcade and prearcade region. It is found that T0 ~ 2 MK and Tarc ~ 4 MK. We also estimate prearcade coronal electron density n0 and arcade electron density narc to find that narc is comparable to n0 (narc ~ n0 ~ 108 cm-3). Using these observed EM, T, and n0, we calculate the theoretical loop length Ltheor based on the scaling law for solar and stellar flares derived by Shibata & Yokoyama and compare it with observed flare/arcade loop length Lobs. The result shows a good correlation between them (Ltheor ~ Lobs) and indicates the need of plasma β for the scaling law (Ltheor ∝ EM3/5T-8/5nβ-6/5). This supports the theory of the scaling law and is indirect evidence that flares and arcades are heated by the same magnetic reconnection mechanism.

Numerical Study of Three‐dimensional Magnetohydrodynamic Instability in the Solar Coronal Magnetic Arcades

Three-dimensional magnetohydrodynamic (MHD) instability in the solar coronal magnetic arcades, which are subject to the constant shearing motion at the feet, was investigated based on the numerical simulations. It was found that the magnetic arcade instability for three-dimensional modes undulating the magnetic arcade can grow if the aspect ratio (defined as the ratio of the arcade length to the width) is larger than unity. In particular, when the aspect ratio is much larger than unity, the nonlinear coupling among several modes dominates the dynamics. As a result, in a very long magnetic arcade, three-dimensional reconnection, which takes place in a limited region in the magnetic arcade, may proceed continuously.

Magnetohydrodynamic Waves in Solar Coronal Arcades

view Abstract Citations (26) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Magnetohydrodynamic Waves in Solar Coronal Arcades Oliver, R. ; Hood, A. W. ; Priest, E. R. Abstract The propagation of magnetohydrodynamic (MRD) disturbances in a solar coronal arcade is investigated. The equations of magnetoacoustic fast and slow waves are presented in a very general form: a pair of second-order, two-dimensional partial differential equations in which the two dependent variables are the components of the velocity perturbation parallel and normal to the magnetic field. In deriving these equations, a general two-dimensional equilibrium structure with no longitudinal magnetic field component has been assumed. Thus, the equations are valid for rather general configurations. Alfvén waves are decoupled from the magnetoacoustic modes and give rise to an Alfvén continuous spectrum. The solutions to the wave equations have been obtained numerically, and the perturbed restoring forces (plasma pressure gradient, magnetic pressure gradient, and magnetic tension), responsible for the oscillatory modes, have also been computed. These forces give rise to the propagation of MRD waves, and their interaction determines the physical properties of the various modes. Therefore, the spatial structure of the forces and their interplay are basic in characterizing fast and slow modes. Pure fast and pure slow waves do not exist in the present configuration, although for the considered parameter values, all modes possess either fast-mode or slow-mode properties. "Slow" modes in these two-dimensional equilibria can propagate across the magnetic field only with difficulty and so display a structure of bands, centred about certain field lines, of alternate positive and negative parallel velocity component. On the other hand, "fast" modes are isotropic in nature, and their spatial structure is not so intimately linked to the shape of field lines. In addition, as a consequence of the distinct characteristic propagation speeds of fast and slow modes, their frequencies typically differ by an order of magnitude. Publication: The Astrophysical Journal Pub Date: April 1996 DOI: 10.1086/177071 Bibcode: 1996ApJ...461..424O Keywords: MAGNETOHYDRODYNAMICS: MHD; SUN: CORONA; WAVES full text sources ADS |

Numerical bifurcation study of a nonlinear current sheet model

Results are presented of a numerical investigation of the strongly nonlinear bifurcation properties of an isothermal current sheet model which has previously been investigated in the weakly nonlinear regime by analytical methods. With the method used, the linear stability of the bifurcating branch is also checked. The results have applications in the stability of plasma systems with current sheets, e.g., the Earth’s magnetotail or solar coronal arcades.

The magnetohydrodynamic stability of coronal arcades. III - Sheared equilibrium fields

The ideal magnetohydrodynamic stability of solar coronal arcades where all the field lines are tied to the photosphere is examined. Two sets of photospheric boundary conditions are examined, and the first detailed quantitative comparison is presented. It is found that conditions where all components of the perturbation vanish at the photosphere are significantly more stable to interchange modes than those for which a displacement along the field lines is allowed there. Much stronger radial pressure gradients are needed to destabilize the former case. It is also found that three sample force-free fields are stable to all perturbations which were imposed. These results outline a pressing need for a more precise treatment of the transition region/corona boundary in stability problems. 25 references.

Hydromagnetic stability of coronal arcade structures: The effects of photospheric line tying

A model is given of the magnetic-field equilibrium and possible dynamic excitations of a solar coronal arcade. Such structures are well observed in the spectral range from Hα to X-rays and often give rise to two-ribbon flares. However, the preflare state must be stable to ideal magnetohydrodynamic disturbances, and we treat this problem with particular attention to the necessary foot-point boundary conditions. Having devised a reasonably general perturbation set, we use an energy-principle analysis to show the strong stabilizing influence of inertial field-line tying at the photosphere.