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 stability of two classes of solar quiescent prominences

The stability properties of two prominence models are investigated by considering bounds on the marginal stability conditions. It is shown that Low's (1981) model is unstable to localized disturbances and the Hood and Anzer (1990) model is only stable for sufficiently low prominences. The latter result may be modified by including magnetic shear. It is shown that magnetic shear stabilizes coronal loops against Rayleigh-Taylor instabilities and may help to stabilize prominence models as well.     

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.     

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.     

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.     

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.     

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.     

A 2-D model for the support of a polar-crown solar prominence

We present a 2-D potential-field model for the magnetic structure in the environment of a typical quiescent polar-crown prominence. The field is computed using the general method of Titov (1992) in which a curved current sheet, representing the prominence, is supported in equilibrium by upwardly directed Lorentz forces to balance the prominence weight. The mass density of the prominence sheet is computed in this solution using a simple force balance and observed values of the photospheric and prominence magnetic field. This calculation gives a mass density of the correct order of magnitude. The prominence sheet is surrounded by an inverse-polarity field configuration adjacent to a region of vertical, open polar field in agreement with observations.A perturbation analysis provides a method for studying the evolution of the current sheet as the parameters of the system are varied together with an examination of the splitting of an X-type neutral point into a current sheet.Program Systems Institute of the Russian Academy of Sciences, Pereslavl-Zalessky 152140, Russia.     

Prominence height and vertical gradient in magnetic field

The existence of a critical height for quiescent prominences and its relationship to parameters of the magnetic field of photospheric sources are discussed. In the inverse-polarity model, stable equilibrium of a filament with a current is possible only in the region where the external field decreases with height no faster than ～1/h. Calculations of the potential magnetic field above the polarity-inversion line are compared with the observed prominence height. The prominence height is shown to actually depend on the vertical field gradient and does not exceed the level at which the exponent of field decrease is equal to unity.     

Irrotational motion in quiescent prominences

On the basis of Kippenhahn and Schlüter's magnetohydrostatic model of a quiescent prominence, an attempt has been made to study the effect of irrotational motion existing in the prominences on the magnetic field pattern in it, introducing an irrotational velocity field. It is found that, under such a condition, the magnetic field geometry in the model does not change.     

Coronal disturbances

We have studied chromospheric mass injection into an overlying coronal dipole magnetic field using a 2-D ideal magnetohydrodynamic (MHD) numerical model. The results indicate that such injection can produce magnetic field deformation conducive to active region prominences - namely, Kippenhahn-Schlüter (K-S) type configurations for stable support of injected plasma. We show the optimum conditions for such dynamical formation of K-S-type field configurations.Observations show that an active region prominence formation is preceded by the accumulation of absorptive strands above a neutral line. We hypothesize that an absorptive strand is formed by a chromospheric asymmetric mass injection into the overlying coronal magnetic field and that a necessary condition for the accumulation of the strands is that the mass injection forms a K-S-type field configuration. The results of our numerical simulation of the injection dynamics support our hypothesis. To form a K-S-type magnetic field configuration, we find that a narrow range of injection density, velocity, and magnetic field strength must be used; spicule-like, asymmetric mass injection seems favorable.The limited parameter range that exists for the formation of K-S-type magnetic field configurations in asymmetric injections may explain why active region prominences do not form everywhere on every neutral line.     

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 oscillating loop prominence of July 17, 1981

Oscillatory motions of a loop prominence observed on July 17, 1981 are analysed. The oscillations were mainly horizontal, with a period of 8 min. Restoring force was a result of magnetic tension, and assuming a simplified magnetic field configuration the expression for frequencies of oscillations is derived and compared with the observations. Taking the observed period, the strength of the magnetic field permeating the prominence is estimated as 45 G. Finally, the stability of the prominence is discussed.     

Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×10¹⁶ – 10¹⁹ Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×10¹⁶ Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.     

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.     

The structure of a prominence sheet

A one-dimensional analysis of Kippenhahn-Schlüter type is applied to a sheet of prominence material inclined at an angle, to the horizontal. It is found that the magnetic pressure across the prominence no longer has a symmetric profile, but is stronger on the lower side of the sheet. This excess in magnetic pressure is necessary to balance the component of prominence weight in that direction. A matching function is derived and allows for variations along the length of the sheet, enabling the internal prominence solution to be linked onto a given background potential field. In this way a curved prominence sheet in a potential field may be resolved. A smooth profile for the magnetic field and a continuous variation of plasma pressure across the prominence region is then possible. An example is given in which the analysis is applied to a polar-crown prominence configuration of inverse polarity and the basic properties of the prominence are determined.     

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.     

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.     

A prominence model in a simple magnetic arcade

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

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.