The formation of prominences by thermal instability: A numerical study

A two-dimensional model of prominence formation in a region containing a magnetic neutral sheet is constructed for a variety of initial conditions, assuming the coronal plasma to be described by the usual hydromagnetic approximation, with infinite electric conductivity. In each case the magnetic field is initially vertical, varying antisymmetrically with respect to the neutral sheet, to a maximum value at a distance of 70 000 km from the neutral sheet. In the first case, the plasma is initially in hydrostatic equilibrium, whereas in successive cases, the pressure is assumed to be of such a value that the plasma is in lateral equilibrium of total pressure (gas plus magnetic). In a variation of this case, the value of the solar gravitational field was artificially reduced, and the effects considered. Large lateral motions are produced in each case, thus apparently inhibiting the condensation of prominences, with the exception of the unrealistic case of artificially reduced gravity. The results suggest that consideration either of a third component of the magnetic field (horizontal and parallel to the neutral sheet), or a finite conductivity, allowing magnetic recombination across the neutral sheet, or both, would more realistically represent the problem and might thus show the development of prominences.     

The formation of solar quiescent prominences by condensation

We model the formation of solar quiescent prominences by solving numerically the non-linear, time-dependent, magnetohydrodynamic equations governing the condensation of the corona. A two-dimensional geometry is used. Gravitational and magnetic fields are included, but thermal conduction is neglected. The coronal fluid is assumed to cool by radiation and to be heated by the dissipation of mechanical energy carried by shock waves. A small, isobaric perturbation of the initial thermal and mechanical equilibrium is introduced and the fluid is allowed to relax. Because the corona with the given energy sources is thermally unstable, cooling and condensation result.When magnetic and gravitational fields are absent, condensation occurs isotropically with a strongly time-dependent growth rate, and achieves a density 18 times the initial density in 3.5 × 10⁴ s. The rapidity of condensation is limited by hydrodynamical considerations, in contrast to the treatment of Raju (1968). When both magnetic and gravitational fields are included, the rate of condensation is inhibited and denser material falls.We conclude that: (1) condensation of coronal material due to thermal instability is possible if thermal conduction is inhibited; (2) hydrodynamical processes determine, in large part, the rate of condensation; (3) condensation can occur on a time scale compatible with the observed times of formation of quiescent prominences.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Linear current instability in loop prominences

By use of the dispersion equation given by Song, Wu, and Dryer (1987) for a cylinder plasma with mass motion and gravity included, we investigate the linear current instabilities developed in loop prominences. The results indicate that the mode of linear instability depends mainly on whetherv _s ² > or not, wherev _s is the sonic velocity at heightz, =GM/(R +z) is the gravity potential,G the gravitational constant,M andR the mass and the radius of the Sun respectively. Ifv _s ² > , then the sausage instability will be dominant. Otherwise, the kink instability will be more important. A possible explanation of knot structure, which appears sometimes in solar loop prominences has been given.     

The formation of solar prominences by magnetic reconnection and condensation

A model for solar quiescent prominences nested in a Figure 8 magnetic field topology is developed. This topology is argued to be the natural consequence of the distention of bipolar regions upward into the corona. If this distention is slow enough so that hydrostatic equilibrium holds approximately along the field lines, the transverse gas pressure forces fall exponentially with height whereas the inward Lorentz forces fall as a power law. At a low height in the corona, the pressure forces cannot balance the Lorentz forces provided the field lines remain tied to the photosphere and an inward collapse with subsequent reconnection at the point of closest approach should occur. Because of initial shear in the magnetic field, the reconnection would produce isolated helices above the point of reconnection since field lines would not interact with themselves but with their neighbors. This resulting topology produces a field above the elevated neutral line which is opposite in polarity to that of the photospheric field as in the current sheet models of Kuperus and Tandberg-Hanssen (1967). Raadu and Kuperus (1973), Kuperus and Raadu (1974), and Raadu (1979) and in agreement with recent observations of Leroy (1982), and Leroy et al. (1983).Assuming the isolated helices formed by reconnection are insulated from coronal thermal conduction and heating, the radiative cooling process and condensation is considered for the temperature range of 10⁴-6000 K. This condensation results in a steady downflow to the bottom of the helices as the temperature scale-height falls, thus forming a dense, cool, prominence at the bottom of the helical configuration resting on the elevated neutral line with the remainder of the helix being essentially evacuated of material. We identify this neutral line at the bottom of the prominence with the sharp lower edge often seen when viewing quiescent prominences side-on and the evacuated helix with the coronal cavity observed around prominences when seen during total eclipses.Downflow speeds associated with the condensation process are calculated for prominence temperatures and yield velocities in the range of the observed downflows of about 1 km s^–1.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The stability of 2D current sheet models of prominences

A necessary and sufficient condition for the ideal magnetohydrodynamic stability of 2D current sheet models of prominences suspended in a potential coronal field with line-tying is developed using the energy method. This condition takes the form of two simple coupled second-order differential equations which may be integrated along a field line to find marginal stability. The two conditions (85) and (86) of Anzer (1969) are now only sufficient for stability. Two current sheet models are investigated and it is shown that for a potential coronal field allowing perturbed electric currents to flow, line-tying can completely stabilize the equilibria for realistic heights.     

Rayleigh-taylor instability in solar prominences as a mechanism for dXouble-ribbon flares

In this paper, the energy storage for a spotless two-ribbon flare is discussed with reference to the morphology of the chromospheric fibrils surrounding a filament prior to the flare. Also, on the basis of the Kippenhahn-Schluter model of filaments, we discuss the instability of magnetic structure in these filaments. We found that once the gradient of the magnetic field or the curvature of the magnetic “trough” exceeds certain critical value, the Rayleigh-Taylor instability will be triggered off, leading to the sudden disappearance (Disparition Brusque) of the filament. At the same time, a neutral current sheet will be formed in the field with magnetic flux concentrated on both sides of the filament. Rapid reconnection of the field lines then lead to the onset of a two-ribbon flare.     

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.     

The nature of quiescent solar prominences

Quiescent prominences occur as long-lasting cool sheets of matter in the surrounding hot corona at the base of coronal streamers. Seen on the disk they appear as dark filaments dividing regions of opposite magnetic polarity.In this paper a theoretical model is presented, which describes the general appearance of quiescent prominences.It is shown that the neutral sheet between two regions of oppositely directed magnetic fields is thermally unstable. This gives rise to compression and cooling of coronal material to prominence material in a characteristic time of the order of one day for a field strength of 0.5 gauss in the lower corona.It is assumed that due to the finite electrical resistivity of the plasma, filamentary structures are formed by the tearing-mode resistive plasma instability. These structures are thermally insulated from the hot surroundings by the newly formed closed azimuthal magnetic field configuration.It has been shown that for fine structures with a diameter of 300 km the growth rate of the tearing-mode instability is of the same order as the cooling time. The occurrence of fine structures within the prominence is of vital importance for their origin.On leave from the Observatory Sonnenborgh at Utrecht, The Netherlands.     

The lyman alpha line in solar prominences

Solar Physics - We present simplified models for the region where Lα is formed, in the boundary between prominences and corona. The models were calculated by solving the radiation transfer in...     

Kinematics of solar prominences

Two sequences of OSO-4 spectroheliograms in Mg x and Si xii obtained during October–November 1967 and covering the intervals of 83 and 22 hr, respectively, have been analyzed to reveal quasi-periodic oscillations of EUV flux from solar sources with a periodicity of 5–14 hr. The oscillation periods of the emission flux from local sources over sunspots and magnetic field enhancements in plages without spots have been investigated in correlation with characteristics of the respective AR and plages. The greatest periods (> 8 hr) are shown to be peculiar of small sunspots or sunspot groups at the initial or final stage of their development, whereas the smallest periods ( 5–6 hr) are observed in the case of large well-developed groups at the maximum stage of development. In quiet regions on the Sun and plages without spots, the oscillation periods are 6–8 hr. The surface areas in which the oscillations are synchronous and coincide in phase have typical dimensions of 1 in quiet and 1 to 5 in active regions. These areas form a spatial structure similar to the chromospheric network and supergranules. The characteristic lifetime of the structure elements is 1.5–2 days.     

Physics of solar prominences

Summary Conclusion This colloquium on solar prominences - the first ever held - has shown that a major part of activity in prominence research in recent years concentrated on both observation and computation of the magnetic conditions which were found to play a crucial role for the development and the maintainance of prominences. Remarkable progress was made in fine-scale measurements of photospheric magnetic fields around filaments and in internal field measurements in prominences. In addition, important information on the structure of the magnetic fields in the chromosphere adjacent to the filaments may be derived from high resolution photographs of the H fine structure around filaments which have become available recently; unfortunately, an unambiguous determination of the vector field in the chromosphere is not yet possible.It is quite clear, now, that stable filaments extend along neutral lines which divide regions of opposite longitudinal magnetic fields. Different types of neutral lines are possible, depending on the history and relationship of the opposite field regions. There is convincing evidence that the magnetic field in the neighbouring chromosphere may run nearly parallel to the filament axis and that there are two field components in stable prominences: an axial field dominant in the lower parts and a transverse field dominant in the higher parts.Methods for the computation of possible prominence field configurations from measured longitudinal photospheric fields were developed in recent years. In a number of cases (e.g. for loop prominences) the observed configuration could be perfectly represented by a force-free or even a potential field; poor agreement was found between computed and measured field strengths in quiescent prominences. In order to reconcile both of them it is necessary to assume electric currents. Unambiguous solutions will not be found until measurements of the vector field in the photosphere and in the prominences are available.The two-dimensional Kippenhahn-Schlüter model is still considered a useful tool for the study of prominence support and stability. However, a more refined model taking into account both field components and considering also thermal stability conditions is available now. It was proposed that quiescent prominences may form in magnetically neutral sheets in the corona where fields of opposite directions meet.As for the problem of the origin of the dense prominence material there are still two opposite processes under discussion. The injection of material from below, which was mainly applied to loop prominences, has recently been considered also a possible mechanism for the formation of quiescent prominences. On the other hand, the main objections against the condensation mechanism could be removed: it was shown that (1) sufficient material is available in the surrounding corona, and that (2) coronal matter can be condensed to prominence densities and cooled to prominence temperatures in a sufficiently short time.The energy balance in prominences is largely dependent on their fine structure. It seems that a much better radiative loss function for optically thin matter is now available. The problem of the heat conduction can only be treated properly if the field configuration is known. Very little is known on the heating of the corona and the prominence in a complicated field configuration. For the optically thick prominences the energy balance becomes a complicated radiative transfer problem.Still little is known on the first days of prominence development and on the mechanism of first formation which, both, are crucial for the unterstanding of the prominence phenomenon. As a first important step, it was shown in high resolution H photographs that the chromospheric fine structure becomes aligned along the direction of the neutral line already before first filament appearance. More H studies and magnetic field measurements are badly needed.Recent studies have shown that even in stable prominences strong small-scale internal rotational or helical motions exist; they are not yet understood. On the other hand, no generally agreed interpretation of large-scale motions of prominences seems to exist. A first attempt to explain the ascendance of prominences, the Disparitions Brusques, as the result of a kink instability was made recently.New opportunities in prominence research are offered by the study of invisible radiations: X-rays and meterwaves provide important information, not available otherwise, on physical conditions in the coronal surroundings of prominences; EUV observations will provide data on the thin transition layer between the cool prominence and the hot coronal plasma.Mitt. aus dem Fraunhofer Institut No. 111.     

Eruptive instability of cylindrical prominences

The stability of prominences and the dynamics of an eruption are studied. The prominence is represented by an uniformly twisted, curved, magnetic tube, anchored at both ends in the photosphere. Several stages of the eruption are analyzed, from the pre-eruptive phase and the onset of the instability, up to the late phases of the process. Before the eruption, the prominence evolves through a series of equilibrium states, slowly ascending either due to an increase of the electric current or to mass loss. The eruption starts when the ratio of the current to the total mass attains a critical value after which no neighbouring equilibrium exists. The linearized equation of motion was used to obtain the instability threshold, which is presented in a form enabling comparison with the observations. The height at which the prominence erupts depends on the twist, and is typically comparable with the footpoint half-separation. Low-lying prominences are stable even for large twists. The importance of the external field reconnection below the filament, and the mass loss through the legs in the early phases of the eruption is stressed. The oscillations of stable prominences with periods on the Alfvén time-scale are discussed. The results are compared with the observations.     

Gravitational ballooning instability of prominences

Prominences can be unstable to a gravitational ballooning instability of the Rayleigh-Taylor type. A two-dimensional generalized Kippenhahn-Schlüter prominence equilibrium is constructed. Its stability to ideal, three-dimensional, short-wavelength line-tied perturbations is analyzed. The instability requires a critical vertical density gradient. For a given magnetic field strength, the instability is sensitive to the angle at which the magnetic field lines cross the prominence. An approximate, sufficient, threshold condition is consistent with typical prominence parameters.     

Thermal instability of coronal neutral sheets and the formation of quiescent prominences

It is argued that the quiscent prominences are a natural consequence of the formation and thermal instability of current sheets in the corona. Thus observation and theory of prominences can give vital information on the presence of currents and the topology of magnetic fields in the corona. Conversely by developing the theory of the structure and evolution of current sheets under coronal conditions we can attempt to gain a comprehensive understanding of the structure, evolution, and mass and energy balance of quiescent prominences. A stability analysis for coronal material permeated by a vertical magnetic field rooted in the photosphere, indicates that a condensation will take the form of a thin vertical wedge of cool matter. The development of a finite condensation is followed and it is shown that photospheric line tying is only important in the initial stages. A perturbation analysis of vertical motions at the neutral sheet shows that thermal instability can lead to overstable oscillations. Cooling of coronal material can lead to both upward and downward mass motions, and gravitational energy release is important to the thermal balance of prominences. Relevant optical and radio observations are discussed. Synoptic observations of the development of active regions and magnetic fields are needed to test the basic hypothesis of the formation of prominences from neutral sheets.     

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.     

Interplanetary disturbances produced by a simulated solar flare and equatorially-fluctuating heliospheric current sheet

A recently developed nonplanar, time-dependent magnetohydrodynamic (MHD) model (Wuet al., 1983) was used to study the interplanetary disturbances produced by a compound event in the heliosphere. That is, a steady-state interplanetary medium is first disturbed by a simulated equatorially-fluctuating current sheet. After a few days (100 hr), the disturbed interplanetary medium is again perturbed by a solar-flare-generated shock wave. Attention is directed toward the differences that are caused by the presence of the equatorially-fluctuating (warped) current sheet.     

Preflare activity of solar prominences

The preflare activity of a plage filament is analysed from H observations made with the Multichannel Subtractive Double Pass Spectrograph (MSDP) of the Meudon Solar Tower. The June 22, 1980 event is studied and interpreted in terms of preflare heating of a filament, connected to the rise of emerging flux, and the relative approach of pores of different magnetic polarity, prior to the onset of a two-ribbon flare.The region with enhanced magnetic field, around the filament, begins to brighten slowly 20 min before the triggering of the flare, in the center of H. Filament dark material begins to rise rapidly while the brightest point on one side drifts towards it, 6 min before the onset of the two-ribbon flare. Simultaneously the absorbing material separates from the remaining part of the filament.In the discussion, we suggest that most of the observed features may be the consequence of emergence of new magnetic flux and the related reconnection processes.     

Modern observations of solar prominences

We review observational studies of solar prominences with some reference to theoretical understandings. We lay emphasis on the following findings: (1) An important discovery was made by Leroy, Bommier, and Sahal-Bréchot concerning the direction of the magnetic field inside some high-altitude, high-latitude prominences, where the field vector points in the opposite direction from the one which would be expected from the potential field calculated from the observed photospheric magnetic field. (2) Landman suggests the possibility of a high total density of 10^–11 g cm ^–3 for the main body of quiescent prominences, 50 times higher than the value hitherto believed. (3) Flow patterns, nearly parallel to the magnetic neutral lines, were detected in the 10⁵ K plasma near and in prominences. (4) Coronal loop structures were found overlying prominences as viewed from X-ray photographs. We propose also an evolutionary scheme by taking the magnetic field topologies into account.The fundamental question why a prominence is present remains basically unanswered.     

A solar flare model including the formation and destruction of the current sheet in the corona

A numerical simulation method is used to show the possibility of forming a current sheet in the solar corona in an active region with four magnetic poles. The evolution of the quasi-stationary current sheet can lead to its transfer to an unsteady state. The MHD instability of this sheet causes its decay, accompanied by a set of events which characterizes the solar flare. The electrodynamical model of a solar flare includes a system of field-aligned currents typical of a magnetospheric substorm. Several events in substorms and solar flares are explained by the generation of field-aligned currents.     

Modulational instability of fast magnetosonic waves emitted from a pinching current sheet

We investigate how fast magnetosonic waves can be produced from a pinching current sheet, by using 3-D MHD code. We show that after magnetic pinch of the current sheet due to pressure imbalance, the current sheet begins to expand by an excess of plasma pressure at the center of the current sheet. During the expansion phase, strong fast magnetosonic waves can be created at the steep region of the density gradient and propagate away from the current sheet. It is shown that the fast magnetosonic waves become unstable against modulational instability, as found by Sakai (1983). After the emission of the fast magnetosonic waves, the current sheet will relax to a new equilibrium state, where the current sheet can be heated by adiabatic compression. The emission processes of the fast magnetosonic waves from the current sheet, as well as the modulational instability of these waves that can lead to effective plasma heating through the Landau damping of the slow waves, are important for an understanding of coronal heating and coronal transient brightening.