On the formation of coronal cavities

We present a theoretical study of the formation of a coronal cavity and its relation to a quiescent prominence. We argue that the formation of a coronal cavity is initiated by the condensation of plasma which is trapped by the coronal magnetic field in a closed streamer and which then flows down to the chromosphere along the field lines due to lack of stable magnetic support against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength; with low strength, the plasma density is not high enough for condensation to occur. Furthermore, we suggest that prominence and cavity material is supplied from the chromospheric level. Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration; a prominence requires stable magnetic support.We initiate the study by considering the stability of condensation modes of a plasma in the coronal streamer model obtained by Steinolfson et al. (1982) using a 2-D, time dependent, ideal MHD computer simulation; they calculated the dynamic interaction between outward flowing solar wind plasma and a global coronal magnetic field. In the final steady state, they found a density enhancement in the closed field region with the enhancement increasing with increasing strength of the magnetic field. Our stability calculation shows that if the density enhancement is higher than a critical value, the plasma is unstable to condensation modes. We describe how, depending on the magnetic field configuration, the condensation may produce a coronal cavity and/or initiate the formation of a prominence.NRC Research Associate.     

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.     

Magnetic modeling and tomography: First steps towards a consistent reconstruction of the solar corona

We undertake a first attempt towards a consistent reconstruction of the coronal magnetic field and the coronal density structure. We consider a stationary solar corona which has to obey the equations of magnetohydrostatics. We solve these equations with help of a newly developed optimization scheme. As a first step we illustrate how tomographic information can be included into the reconstruction of coronal magnetic fields. In a second step we use coronal magnetic field information to improve the tomographic inversion process. As input the scheme requires magnetic field measurements on the photosphere from vector-magnetographs and the line-of-sight integrated density distribution from coronagraphs. We test our codes with well-known analytic magnetohydrostatic equilibria and models. The program is planned for use within the STEREO mission.     

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.     

How To Use Magnetic Field Information For Coronal Loop Identification

The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible, e.g., in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g., potential fields (current-free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field.     

Model calculations of the rising motion of a prominence loop

Model calculations are presented for the rising motion of the top section of a prominence loop, which is represented by a straight flux rope immersed in a coronal medium permeated with a bipolar magnetic field. Initially the prominence is at rest, in equilibrium with the surrounding coronal medium. When the magnetic monopoles that account for the source current for the bipolar field strengthen, the upward hydromagnetic buoyancy force overcomes the downward gravitational force so that the prominence is initiated into rising motion. The illustrative examples show that prominences can move away from the solar surface by the action of the hydromagnetic buoyancy force, which is preponderant with the diamagnetic force due to the current carried by the prominence interacting with the coronal magnetic field produced by the photospheric currents, if the changes in the photospheric magnetic field are sufficiently large.     

Simple tests for the ideal MHD stability of line-tied coronal magnetic fields

Methods for investigating the stability of line-tied, cylindrically-symmetric magnetic fields are presented. The energy method is used and the perturbed potential energy integral is manipulated to produce simple tests that predict either stability to general coronal disturbances or instability to localized modes, both satisfying photospheric line-tying. Using these tests the maximum amount of magnetic energy, that can be stored in the coronal magnetic field prior to an instability, can be estimated. The tests are applied to four different classes of equilibria and results are obtained for both arcade and loop geometries.     

Modulational instability of self-generated magnetic fields

It is shown analytically that self-generated magnetic fields are modulationally unstable with respect to the uniform state of a plasma; such an instability would localize the magnetic field. This localized magnetic flux may well produce small-scale intermittent magnetic fields in coronal active regions or solar flares.     

Model for flare loops,fast motions,and opening of magnetic field in the corona

A model is presented for the penetration into the corona of a new magnetic field of a developing bipolar region and for its interaction with an old large-scale coronal field. An important feature of the model is a reconnection of the old and new fields inside the current sheet arising along the zero line of the total magnetic field calculated in the potential approximation. The magnetic reconnection and accumulation of plasma inside the current sheet can explain the appearance of dense coronal loops and the energy source at their tops. The plasma together with the magnetic lines is flowed into the sheet from both its sides. This fact explains the appearance of coronal cavities above the loops. If the large-scale field gradually decreases with the height, the loop motion is slowed down. The account of the dipolar structure of the magnetic field at large heights explains the possibility of a rapid break of the new field through the corona and the appearance of transients and open field regions - the coronal holes. In this case a fast rising current sheet can be a source of accelerated particles and of type II radio burst, instead of the shock wave considered usually.     

Kink mode <Emphasis Type="Italic">m</Emphasis> = 1 in a thin plasma filament with discontinuous vertical magnetic field

In this paper, we study the conditions of realization and stability of kink modes with azimuthal wave numbers m = ±1 in a cylindrical plasma filament with a twisted magnetic field and a homogeneous current along its axis. We assume that there are vertical constant magnetic fields inside and outside of the filament; the filament is surrounded by current-free plasma; and outside of its boundary, the azimuthal magnetic field decreases inversely in proportion to the distance from the filament’s border. The dispersion equations for stable and unstable modes are obtained in the approximation of “thin” plasma filament. The analysis of the equations for the case of discontinuous vertical magnetic field at the filament’s boundary is provided. The conditions of propagation of the wave modes have been defined. We have obtained that the unstable modes with m = ±1 cannot be realized. The results of this work can be applied to the interpretation of the solar magnetic flux tubes’ behavior using measurements provided by the spacecrafts.     

Oscillatory Modes of a Prominence – PCTR – Corona Slab Model

Oscillations of magnetic structures in the solar corona have often been interpreted in terms of magnetohydrodynamic waves. We study the adiabatic magnetoacoustic modes of a prominence plasma slab with a uniform longitudinal magnetic field, surrounded by a prominence – corona transition region (PCTR) and a coronal medium. Considering linear small-amplitude oscillations, we deduce the dispersion relation for the magnetoacoustic slow and fast modes by assuming evanescentlike perturbations in the coronal medium. In the system without PCTR, a classification of the oscillatory modes according to the polarisation of their eigenfunctions is made to distinguish modes with fastlike or slowlike properties. Internal and external slow modes are governed by the prominence and coronal properties, respectively, and fast modes are mostly dominated by prominence conditions for the observed wavelengths. In addition, the inclusion of an isothermal PCTR does not substantially influence the mode frequencies, but new solutions (PCTR slow modes) are present.     

Microwave Mode Coupling Above Active Regions as a Coronal Density Diagnostic

It is well recognized that the phenomenon of depolarization (the conversion of polarized radio emission into unpolarized emission) of microwaves over solar active regions can be used to infer the coronal electron density once the coronal magnetic field is known. In this paper we explore this technique using an active region for which we have excellent radio data showing depolarization at two frequencies, and for which we have an excellent magnetic field model which has been tested against observations. We show that this technique for obtaining coronal densities is very sensitive to a number of factors. When Cohen's (1960) theory where depolarization is due to magnetic field rotation alone is used, the result is particularly sensitive to the location of the surface on which the magnetic field is orthogonal to the line of sight. Depending on whether we take into account the presence of electric currents in the photosphere or not, their extrapolation into the corona can result in very different heights being deduced for the location of the depolarization strip, and this changes the density which is then deduced from the depolarization condition. Such extreme sensitivity to the magnetic field model requires that field extrapolations be able to accurately predict the polarity of magnetic fields up to coronal heights as high as 10⁵ km in order to exploit depolarization as a density diagnostic.     

Current sheet creation by a super-Alfvénic jet in a bipolar field

Energy accumulation in a current sheet (CS) can occur during the injection of a fast plasma jet in a perpendicular magnetic field. A similar situation can occur in the solar corona when a flux of plasma appears under a magnetic arch. The flare can be produced at the CS disruption. The CS creation during plasma jet interaction with the magnetic field is demonstrated by numerical MHD simulation. The choice of dimensionless parameters Re, Re_m,, II, which are suitable for simulation of coronal phenomena, is discussed. When jet injection ceases, the CS evolution produces an unstable state and fast magnetic energy dissipation is observed.     

Three-Dimensional Nonlinear Force-Free Field Reconstruction of Solar Active Region 11158 by Direct Boundary Integral Equation

A three-dimensional coronal magnetic field is reconstructed for the NOAA active region 11158 on 14 February 2011. A GPU-accelerated direct boundary integral equation (DBIE) method is implemented which is approximately 1000 times faster than the original DBIE used on solar non-linear force-free field modeling. Using the SDO/HMI vector magnetogram as the bottom boundary condition, the reconstructed magnetic field lines are compared with the projected EUV loop structures as observed in the front-view (SDO/AIA) and the side-view (STEREO-A/B) images for the first time; they show very good agreement three-dimensionally. A quantitative comparison with some stereoscopically reconstructed coronal loops shows that the average misalignment angles in our model are at the same order as the state-of-the-art results obtained from reconstructed coronal loops. It is found that the observed coronal loop structures can be grouped into a number of closed and open field structures with some central bright coronal loop features around the polarity inversion line. The reconstructed highly sheared magnetic field lines agree very well with the low-lying sigmoidal filament along the polarity inversion line. This central low-lying magnetic field loop system must have played a key role in powering the flare. It should be noted that while a strand-like coronal feature along the polarity inversion line may be related to the filament, one cannot simply interpret all the coronal bright features along the polarity inversion line as manifestation of the filament without any stereoscopic information.     

A Manifestation of Negative Energy Waves in the Solar Atmosphere

Magnetosonic modes of magnetic structures of the solar atmosphere in the presence of inhomogeneous steady flows are considered. It is shown that, when the speed of the steady flow exceeds the phase speed of one of the modes, the mode has negative energy, and can be subject to an over-stability due to the negative energy wave instabilities. It is shown that registered steady flows in the solar atmosphere, with speeds below the threshold of the Kelvin–Helmholtz instability, can provide the existence of the magnetosonic negative energy wave phenomena. In particular, in isolated photospheric magnetic flux tubes, there are kink surface modes with negative energy, produced by the external granulation downflows. Dissipative instability of these modes due to finite thermal conductivity and explosive instability due to nonlinear coupling of these modes with Alfvén waves are discussed. For coronal loops, it is found that only very high-speed flows (>300 km s^-1) can produce negative energy slow body modes. In solar wind flow structures, both slow and fast body modes have negative energy and are unstable.     

NONLINEAR MHD SIMULATIONS OF WAVE DISSIPATION IN FLUX TUBES

The phase mixing and resonant dissipation of Alfvén waves is studied in both the 'closed' magnetic loops and the 'open' coronal holes observed in the hot solar corona. The resulting energy transfer from large to small length scales contributes to the heating of these magnetic structures. The nonlinear simulations show that the periodically varying shear flows that occur in the resonant layers are unstable. In coronal holes, the phase mixing of running Alfvén waves is speeded up by the 'flaring out' of the magnetic field lines in the lower chromosphere.     

Evolving coronal holes and interplanetary erupting stream disturbances

Coronal holes and interplanetary disturbances are important aspects of the physics of the Sun and heliosphere. Interplanetary disturbances are identified as an increase in the density turbulence compared with the ambient solar wind. Erupting stream disturbances are transient large-scale structures of enhanced density turbulence in the interplanetary medium driven by the high-speed flows of low-density plasma trailing behind for several days. Here, an attempt has been made to investigate the solar cause of erupting stream disturbances, mapped by Hewish & Bravo (1986) from interplanetary scintillation (IPS) measurements made between August 1978 and August 1979 at 81.5 MHz. The position of the sources of 68 erupting stream disturbances on the solar disk has been compared with the locations of newborn coronal holes and/or the areas that have been coronal holes previously. It is found that the occurrence of erupting stream disturbances is linked to the emergence of new coronal holes at the eruption site on the solar disk. A coronal hole is indicative of a radial magnetic field of a predominant magnetic polarity. The newborn coronal hole emerges on the Sun, owing to the changes in magnetic field configuration leading to the opening of closed magnetic structure into the corona. The fundamental activity for the onset of an erupting stream seems to be a transient opening of pre-existing closed magnetic structures into a new coronal hole, which can support highspeed flow trailing behind the compression zone of the erupting stream for several days.     

Coronal general magnetic field evolution as a new parameter of the solar cycle

The magnetic field lines of the corona associated with the solar-cycle surface general magnetic field are calculated by a potential-field approximation to study the solar-cycle evolution of the geometry of the coronal field. The surface field evolution used here is the radial field evolution, predicted by a model of the solar cycle driven by the dynamo action of the global convection, and justified observationally using Mount Wilson magnetic synoptic chart data. The evolution of the calculated coronal general field is now good for comparison with observations and shows the following. (i) The field of the polar and high-altitude corona has dipolar structure in almost all phases of the solar cycle except in a short time interval around maximum phase despite the quadrupolar structure of the general magnetic field at the surface; quadrupolar field forms loop-like structure in the lower corona. The almost-dipolar structure of the polar and high-latitude corona and the loop formation of the equatorial lower corona explain the appearance of the undisturbed minimum corona observed at eclipses. (ii) The polar field lines are directed almost radially at the minimum phase, which should be responsible for polar plumes. The field lines slowly open up to participate in the loop-like structure of the equatorial lower corona, and rapidly change their structure and polarity at the maximum phase, to resume the almost radial configuration slowly, (iii) During the rapidly changing maximum phase, the field lines do not penetrate deep into the interplanetary space resulting in the absence of polar plumes and the appearance of the circular corona- the maximum corona. In this phase, the coronal field should not be approximated by a dipole field. The surface field evolution which can explain such behaviors of the corona is characteristic of the solar-cycle process dominated by the latitudinal gradient of the differential rotation. If the radial gradient dominated in the subsurface process, the coronal evolution would look quite different and would show latitudinal propagation of enhancement of activity. Although nonaxisymmetric features should be superposed on the axisymmetric general field to express the real corona, the general field can be a basic coronal field in studying long-term interaction between the convection zone and the interstellar space especially in studying the magnetic braking of the solar rotation.     

Resonant interactions of modes in coronal magnetic flux tubes

Nonlinear resonant interactions of different kinds of fast magnetosonic (FMS) waves trapped in the inhomogeneity of a low- plasma density, stretched along a magnetic field (as, for example, in coronal loops) are investigated. A set of equations describing the amplitudes of interactive modes is derived for an arbitrary density profile. The quantitative characteristics of such interactions are found. The decay instability of the wave with highest frequency is possible in the system. If amplitudes of interactive modes have close values, the long-period temporal and spatial oscillations are in the system.For a quantitative illustration, the parabolic approximation of the transverse density profile has been chosen. Dispersion relations of FMS waves trapped in a low- plasma slab with a parabolic transverse density profile are found. The transverse structure of the waves in this case can be expressed through Hermitian polynomials. The interaction of kink and sausage waves is investigated. The sausage wave, with a sufficiently large amplitude, may be unstable with respect to the decay into two kink waves, in particular. The spatial scale of a standing wave structure and the time spectrum of radiation are formed due to the nonlinear interactions of loop modes which contain information about the parameters of the plasma slab.     

An investigation of the large-scale magnetic field variations in the corona prior to and after CME eruptions

The magnetic field changes in the corona at the site of coronal mass ejections (CMEs) have been investigated using the potential field-source surface model. It is shown that a CME is accompanied by the opening of closed field lines that formed the streamer's helmet base prior to the onset of a coronal disturbance. Two to three days after the appearance of the CME, the field configuration at the location of the coronal ejection reverts approximately to the state pre-existing before the generation of the CME. The appearance of small transient open magnetic tubes has been found after eruption of the coronal mass. These magnetic tubes seem to be the analogs for transient coronal holes.Taking into account the results of calculations of the field changes in the neighbourhood of the CME occurrence site, we have suggested a possible mechanism governing the spatio-temporal correlation between some flares and CMEs. Also, a possible mechanism has been proposed for field reconfiguration in the corona, leading to loss of the equilibrium of the magnetic configuration and to the subsequent generation of a CME in the region of coronal streamer chains separating coronal holes with same-polarity magnetic field.