The effect of magnetic shear on the MHD stability of a prominence model

The Hood-Anzer prominence model (Hood and Anzer, 1990) is modified to include magnetic shear. The stability properties of the model are then assessed to see if significant magnetic shear can stabilize ideal MHD disturbances. It is shown that a strong shear gradient in the magnetic field near the base of the prominence provides a stabilizing effect and realistic prominence heights are indeed possible.     

The MHD stability of a twisted flux tube prominence model

The ideal MHD stability of the 2D twisted magnetic flux tube prominence model of Cartledge and Hood (1993) is investigated. The model includes a temperature profile that varies from realistic prominence values up to typical coronal values. The prominence is considered to be of finite-width and finite height. The stability properties of the prominence models are studied by using a method that generates a separate necessary condition and a sufficient condition. These conditions give bounds on the parameters that define marginal stability. In many cases these bounds are quite close so that further, more detailed, stability calculations are not necessary. A number of parameter regimes are examined, corresponding to different profiles of the prominence temperatures, densities, and magnetic field shear. It is found that the model admits realistic stable and unstable loop lengths for observed prominence parameters when the axial magnetic field component does not vanish.     

The eruption of a prominence and coronal mass ejection which drive reconnection

Two possible limiting scenarios are proposed for the production of a coronal mass ejection. In the first the magnetic field around a prominence evolves until it loses equilibrium and erupts, which drives reconnection below the prominence and an eruption of the overlying magnetic arcade. In the second a large-scale magnetic arcade evolves until it loses equilibrium and erupts, thereby causing a prominence to erupt. In general it is likely to be the non-equilibrium of the coupled system which creates the eruption. Furthermore, large quiescent prominences are expected to be centred within the magnetic bubble of a coronal mass ejection whereas when active-region prominences erupt they are likely to be located initially to one side of the bubble.A model is set up for the eruption of a magnetically coupled prominence and coronal mass ejection. This represents a development of the Anzer and Pneuman (1982) model by overcoming two limitations of it, namely that: it is not globally stable initially and so one wonders how it can be set up in a stable way before the eruption; it has reconnection driving the CME whereas recent observations suggest that the reverse may be happening. In our model we assume that magnetic reconnection below the prominence is driven by the eruption and the driver is magnetic non-equilibrium in the coupled prominence-mass ejection system. The prominence is modelled as a twisted flux tube and the mass ejection as an overlying void and magnetic bubble. Two different models of the prominence are considered. In one a globally stable equilibrium becomes unstable when a threshold magnetic flux below the prominence is exceeded and, in the other, equilibrium ceases to exist. In both cases, the prominence and mass-ejection accelerate upwards before reaching constant velocities in a manner that is consistent with observations. It is found that the greater the reconnection that is driven by the eruption, the higher is the final speed.     

Current sheet models for inverse polarity prominences in twisted flux tubes

This paper treats the prominence model of Low (1993) to examine more complicated sheet currents than those used in the original model. Nonlinear force-free field solutions, in Cartesian coordinates, invariant in a given direction, are presented to show the possibility of an inverse-polarity prominence embedded in a large twisted flux tube. The force-free solution is matched to an external, unsheared, potential coronal magnetic field. These new solutions are mathematically interesting and allow an investigation of different profiles of the current intensity, magnetic field vector and mass density in the sheet. These prominence models show a general increase in magnetic field strength with height in agreement with observations. Other prominence properties are shown to match the observed values.     

The effect of shear on numerical models of quiescent normal-polarity prominences

The equilibrium structure of normal-polarity, quiescent prominences is investigated and the influence of magnetic shear in response to a slow, shearing, photospheric velocity discussed. The results show that the overall field structure predicted by Fiedler and Hood (1992) is largely unaffected but that magnetic shear reduces the plasma beta and lengthens and flattens the magnetic field when viewed from the side. The flatness of the field suggests that the initial condensation can form and, when the mass is sufficient, deform the field slightly into the equilibrium structure calculated here. Thus, it is postulated that the field must be highly sheared for the radiation (or condensation) time to be less than the free-fall time along the field. A simple estimate predicts that the field must lie close to the polarity inversion line with an angle in agreement with observations. Hence, it is apparent that normal polarity prominences will always be observed with a highly sheared field.It is shown that the line-of-sight field component depends on the imposed shear profile and the viewing angle and in certain cases it is possible for this field component to appear to increase with height. Any observed increase of the line-of-sight magnetic field with height may then be due to the angle of the prominence to the line of sight.     

磁对消引起的日珥扰动

采用二维三分量理想磁流体力学模型,研究光球磁对消引起的日珥扰动．日珥下方光球表面的磁对消将磁通量向日珥传输,引起日珥内部磁通量和磁螺度增加．日珥的状态与所积累的磁通量（或磁螺度）有关．数值结果显示,如果日珥磁通的相对增量δＦ（或相应的磁螺度相对增量δＨ）较小,日珥只略微上升和膨胀,并不离开光球;而对于较大的δＦ或δＨ）;日珥将脱离光球,悬浮在低层日冕中,在其下方形成垂直电流片．     

Numerical models of quiescent normal polarity prominences

We present 2-D numerical models of quiescent solar prominences with normal magnetic polarity. These models represent an extension to the classical Kippenhahn-Schlüter model in that the prominence is treated as having finite width and height and the external coronal field is matched smoothly to the internal prominence field so that there are no current sheets at the prominence sides. Using typical prominence and coronal values we find solutions to the generalised Grad-Shafranov equation which illustrate the necessary magnetic support. We also discuss some extensions to the basic model.     

The fibril structure of prominences

We suggest that the fibril structure of prominences may be caused by filamentation during its formation by radiative instability. We also discuss the effects of other types of instability and give a mechanism for the formation of vertical threads. The models indicate that highly inhomogeneous density structures can exist in the presence of smooth profiles for the plasma pressure and magnetic field. In our particular models the plasma pressure of a fibril prominence is higher and the vertical magnetical field is weaker than in a uniform prominence model, while the mass is substantially smaller.     

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.     

Alfvén waves and turbulence in quiescent prominences

In the dynamical model of quiescent prominences presented in this paper, it is assumed that the ever-changing velocity field and brightness of the fine structure is due to MHD turbulence driven by an Alfvén-wave flux from below. It is shown that these waves become highly non-linear and are dissipated over relatively short scales in prominence matter. For magnetic field strengths lower than those observed in quiescent prominences, no closed arch structure can exist with the physical parameters observed. For higher field strengths the conditions for the creation of turbulence are not fulfilled. The momentum gained by prominence matter in the dissipation process, is shown to be of the right order of magnitude to provide the supporting force against gravity. ‘Edge’ effects find a simple explanation within the framework of this hypothesis. In the upper regions of a prominence one result of the dissipation may be the formation of open magnetic configurations, in keeping with the presence of streamers connected with quiescent prominences. Observational tests are proposed and discussed.     

The nature of velocity fields in quiescent prominences

It is shown that for certain definite conditions of symmetry imposed on the permitting magnetic field geometry for an isothermal case in Kippenhahn and Schlüter's (1957) model of a quiescent prominence, any irrotational velocity field would quickly get converted to rotational.     

A self-consistent model of a thermally balanced quiescent prominence in magnetostatic equilibrium in a uniform gravitational field

We present a theoretical model of quiescent prominences in the form of an infinite vertical sheet. Self-consistent solutions are obtained by integrating simultaneously the set of nonlinear equations of magnetostatic equilibrium and thermal balance. The basic features of the models are: (1) The prominence matter is confined to a sheet and supported against gravity by a bowed magnetic field. (2) The thermal flux is channelled along magnetic field lines. (3) The thermal flux is everywhere balanced by Low's (1975b) hypothetical heat sink which is proportional to the local density. (4) A constant component of the magnetic field along the length of the prominence shields the cool plasma from the hot surrounding. We assume that the prominence plasma emits more radiation than it absorbs from the radiation fields of the photosphere, chromosphere and corona, and we interpret the above hypothetical heat sink to represent the amount of radiative loss that must be balanced by a nonradiative energy input. Using a central density and temperature of 10¹¹ particles cm^–3 and 5000 K respectively, a magnetic field strength between 2 to 10 gauss and a thermal conductivity that varies linearly with temperature, we discuss the physical properties implied by the model. The analytic treatment can also be carried out for a class of more complex thermal conductivities. These models provide a useful starting point for investigating the combined requirements of magnetostatic equilibrium and thermal balance in the quiescent prominence.     

Helical structures around quiescent solar prominences computed from observable magnetic fields

We analyse the magnetic support of solar prominences in two-dimensional linear force-free fields. A line current is added to model a helical configuration, well suited to trap dense plasma in its bottom part. The prominence is modeled as a vertical mass-loaded current sheet in equilibrium between gravity and magnetic forces.We use a finite difference numerical technique which incorporates both vertical photospheric and horizontal prominence magnetic field measurements. The solution of this mixed boundary problem generally presents singularities at both the bottom and top of the model prominence. The removal of the singularities is achieved by superposition of solutions. Together with the line current equilibrium, these three conditions determine the amplitude of the magnetic field in the prominence, the flux below the prominence and the current intensity, for a given height of the line current. A numerical check of accuracy in the removal of singularities, is done by using known analytical solutions in the potential limit.We have investigated both bipolar and quadrupolar photospheric regions. In this mixed boundary problem the polarity of the field component orthogonal to the prominence is mainly fixed by the imposed height of the line current. For bipolar regions above (respectively below) a critical height the configuration is inverse (respectively normal). For quadrupolar regions the polarity is reversed if we refer the prominence polarity to the closest photospheric polarities. We introduce the polarity of the component parallel to the prominence axis with reference to a sheared arcade. Increasing the shear with fixed boundary conditions can increase or decrease the mass supported depending on the configuration.     

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.     

A model for quiescent solar prominences with normal polarity

A class of 2-D models of solar quiescent prominences, with normal polarity, is presented. These represent an extension to the Kippenhahn-Schlüter model for which the prominence configuration matches smoothly onto an external non-potential coronal solution of a constant field. Using typical prominence values a model is constructed which also matches the coronal conditions. It is found that the magnetic field component along the prominence influences the internal structure of the prominence. A simple extension to the basic models is indicated as a means of taking a lower boundary of the prominence and eliminating parasitic polarities in the photosphere.     

The stability of a velocity shear in the presence of an inhomogeneous magnetic field

The stability of a velocity shear in the presence of a parallel but non-uniform magnetic field is considered in general terms. Two special cases are then investigated; (i) the well known case of a plane interface at which a discontinuity in the magnetic field coincides with the velocity shear; (ii) an axially symmetric flow in which discontinuities in the magnetic and velocity fields occur at a cylindrical surface whose axis is parallel to the flow. In the first case the flow is stabilized if the rms Alfvén velocity of the magnetic field exceeds the shear velocity; a result consistent with that obtained by other writers. In the second case it is shown that the discontinuity in the magnetic field increases the stability of the system. The significance of this result for the stability of the flux ropes associated with sunspots in the solar convection zone is considered.     

A two-dimensional model for a solar prominence: Effect of an external magnetic field

Using analytical approximations we study the effects of different external magnetic configurations on the half-width, mass, and internal magnetic structure of a quiescent solar prominence, modelled as a thin vertical sheet of cool plasma. Firstly, we build up a zeroth-order model and analyse the effects produced by a potential coronal field or a constant- force-free field. This model allows us to obtain the half-width and mass of the prominence for different values of the external field, pressure and shear angle. Secondly, the effects of these external magnetic configurations on a two-dimensional model proposed by Ballester and Priest (1987) are studied. The main effects are a change of the half-width with height, an increase of the mass, a decrease of the magnetic field strength with height and a change in the shape of the magnetic field lines.     

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.     

A model for an inverse-polarity prominence supported in a dip of a quadrupolar region

We investigate the formation and support of solar prominences in a quadrupolar magnetic configuration. The prominence is modeled as a current sheet with mass in equilibrium in a two-dimensional field. The model possesses an important property which is now thought to be necessary, namely that the prominence forms within the dip, rather than the dip being created by the prominence.The approach of two bipolar regions of the same sign gives a natural way to form a dip in the magnetic field in a horizontal band above the photospheric polarity inversion line. As the approach proceeds, the height of the dip region decreases but, in agreement with observations, a corridor, free of significant magnetic field, is needed in order to obtain a dip at low heights.Support is achieved locally just as for normal-polarity configurations, so the model avoids the strong self-pinching effect of several inverse-polarity configurations (such as the Kuperus and Raadu model). The role of the strong field component along the prominence axis, which is here modelled by a uniform field in that direction, may well be to provide the necessary thermal properties for prominence formation.The model thus has several attractive features which make it credible for inverse polarity prominences: (i) both the dip and the inverse orientation are naturally present; (ii) prominence formation is by converging rather than shearing motions, in agreement with observations; converging photospheric motions induce a horizontal upward motion in the filament; (iii) the orientation of the axial field, opposite to what is expected from differential rotation, is naturally accounted for; (iv) the observed relation between chromospheric and prominence magnetic field strengths is naturally reproduced; (v) the field configuration is more complex than a simple bipole, in agreement with observations.     

Modeling of prominence threads in magnetic fields: Levitation by incompressible MHD waves

The nature of thin, highly inclined threads observed in quiescent prominences has puzzled solar physicists for a long time. When assuming that the threads represent truly inclined magnetic fields, the supporting mechanism of prominence plasma against gravity has remained an open issue. This paper examines the levitation of prominence plasma exerted by weakly damped MHD waves in nearly vertical magnetic flux tubes. It is shown that the wave damping, and resulting `radiation pressure', caused predominantly by ion-neutral collisions in the `cold' prominence plasma, may balance the acceleration of gravity provided the oscillation frequency is 2 rad s^–1 (f0.5 Hz). Such short wave periods may be the result of small-scale magnetic reconnections in the highly fragmentary magnetic field of quiescent prominences. In the proposed model, the wave induced levitation acts predominantly on plasma – neutral gas mixtures.