A two-dimensional model for a solar prominence

A two-dimensional magnetohydrostatic model of a vertical prominence sheet is set up by allowing slow variations of the magnetic field and plasma properties with height. The width of the prominence is found to decrease with height and in many cases the field lines become less curved, while the strength of the horizontal magnetic field increases with height, in agreement with observations. Since we are only considering a local analysis, the model applies to a general prominence sheet, whether of Kippenhahn-Schlüter or Kuperus-Raadu type. The challenge in the future is to understand the detailed fine-scale microstructure which takes place in the mould formed by the present global macro-models.On leave from: Departament de Fisica, Universitat de les Illes Balears, E-07071, Palma de Mallorca, Spain.     

Two-dimensional distributions of physical parameters in the prominence of 1984 March 23

The spectral lines Hα Hβ and CaII K of a quiescent prominence are studied using the completely linearized model. The physical parameters (T_e, v_t, N_H) at several locations are obtained. Itis shown: (1) Near the axis of the prominence, kinetic temperature and hydrogen density decrease, while microturbulent velocity increases, with increasing height. (2) Near the edge, the kinetic temperature does not vary with height; but it increases from the center to the edge. (3) Hydrostatic equilibrium does not hold in prominences, and magnetic field plays an important role in supporting them.     

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.     

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.     

Vector magnetic fields in prominences

Observations of linear polarization in two resolved components of HeI D₃ are interpreted using the Hanle effect to determine vector magnetic fields in thirteen prominences. As in all vector magnetic field measurements, there is a two-fold ambiguity in field direction that is symmetric to a 180° rotation about the line-of-sight. The polar angles of the fields show a pronounced preference to be close to 90° from the local solar radius, i.e., the field direction is close to horizontal. Azimuth angles show internal consistency from point to point in a given prominences, but because of the rotational symmetry, the fields may be interpreted, in most cases, as crossing the prominence either in the same sense as the underlying photospheric fields or in the opposite sense. An exceptionally well observed large prominence of approximately planar geometry exhibits no measurable change in the vector magnetic field either with height or with location along the prominence axis. A second well observed large prominence overlying a sharply curved magnetic neutral line, when interpreted assuming that the prominence field has the same sense as the photospheric field, shows a rotation in the azimuth angle of the field relative to the observer by about 150° and relative to the local plane of the prominence by about 65°. In the alternative interpretation in which the prominence field has the opposite sense of the photospheric field, the field still rotates by 150° relative to the observer but remains essentially constant with respect to the plane of the prominence. This prominence erupted shortly after the extended observations. One good quality observation during the course of the eruption gives a vector field fully consistent with the pre-eruption field in the same segment of the prominence.     

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 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.     

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.     

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.     

External and internal solutions for the twisted,flux-tube,prominence model

In this paper the twisted flux-tube model for the support of a prominence sheet with constant axial current density, given by Ridgway, Priest, and Amari (1991), is considered.The model is extended in Section 2 to incorporate a current sheet of finite height. The sheet is supported in a constant current density force-free field in the configuration of a twisted flux tube. The mass of the prominence sheet, using a typical height and field strength, is computed. Outside the flux tube the background magnetic field is assumed to be potential but the matching of the flux tube onto this background field is not considered here.Instead our attention is focussed, in Section 3, on the interior of the prominence. An expanded scale is used to stretch the prominence sheet to a finite width. We analytically select solutions for the internal magnetic field in this region which match smoothly onto the external force-free solutions at the prominence edge.The force balance equation applied inside the prominence then yields expressions for the pressure and density and a corresponding temperature may be computed.     

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.     

On the Structure and Evolution of a Polar Crown Prominence/Filament System

Polar crown prominences, that partially circle the Sun’s poles between 60° and 70° latitude, are made of chromospheric plasma. We aim to diagnose the 3D dynamics of a polar crown prominence using high-cadence EUV images from the Solar Dynamics Observatory (SDO)/AIA at 304, 171, and 193 Å and the Ahead spacecraft of the Solar Terrestrial Relations Observatory (STEREO-A)/EUVI at 195 Å. Using time series across specific structures, we compare flows across the disk in 195 Å with the prominence dynamics seen on the limb. The densest prominence material forms vertical columns that are separated by many tens of Mm and connected by dynamic bridges of plasma that are clearly visible in 304/171 Å two-colour images. We also observe intermittent but repetitious flows with velocity 15 km?s^?1 in the prominence that appear to be associated with EUV bright points on the solar disk. The boundary between the prominence and the overlying cavity appears as a sharp edge. We discuss the structure of the coronal cavity seen both above and around the prominence. SDO/HMI and GONG magnetograms are used to infer the underlying magnetic topology. The evolution and structure of the prominence with respect to the magnetic field seems to agree with the filament-linkage model.     

Evolution of rising helical prominences in a nonuniform atmosphere

Recent coronagraph observations of rising priminences such as in the 14 April and 5 May, 1980 coronal transient events, as well as other older observations, have shown evidence for helical structure in the prominences. If this is true, then a study of the dynamical evolution of rising helical structures in a nonuniform atmosphere is worthwhile. For this study, three important considerations become apparent: (1) Since the ends of the prominence remain rooted in the photosphere, significant stretching of the configuration will result as it rises, (2) due to the fall-off with height of the external quantities, such as gas and magnetic pressure, the prominence will experience time-varying boundary conditions as it rises, and (3) significant lateral expansion of the prominence is expected as the external conditions weaken with height. The interplay of all these effects togehter result in a quite complex dynamical behavior of the prominence.We have tried to obtain some insight into this general problem through a simple model - that of a helical pinch rising in a low beta atmosphere under the influence of an ambient external magnetic field which declines in strength with radial distance from the solar center. Under the general assumptions of an internal uniform, but time-varying, temperature and neglecting gravitational stratification within the prominence, expressions are derived for associated variations in the prominence structure as it rises. We discuss in some detail, particular quantities which are potentially most accessible to observation such as prominence radius, density, and pitch angle as they vary with height during the eruptive process.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Homologous prominence non-radial eruptions: A case study

The present study provides important details on homologous eruptions of a solar prominence that occurred in active region NOAA 10904 on 2006 August 22. We report on the pre-eruptive phase of the homologous feature as well as the kinematics and the morphology of a forth from a series of prominence eruptions that is critical in defining the nature of the previous consecutive eruptions. The evolution of the overlying coronal field during homologous eruptions is discussed and a new observational criterion for homologous eruptions is provided. We find a distinctive sequence of three activation periods each of them containing pre-eruptive precursors such as a brightening and enlarging of the prominence body followed by small surge-like ejections from its southern end observed in the radio 17 GHz. We analyse a fourth eruption that clearly indicates a full reformation of the prominence after the third eruption. The fourth eruption although occurring 11 h later has an identical morphology, the same angle of propagation with respect to the radial direction, as well as similar kinematic evolution as the previous three eruptions. We find an important feature of the homologous eruptive prominence sequence that is the maximum height increase of each consecutive eruption. The present analysis establishes that all four eruptions observed in Hα are of confined type with the third eruption undergoing a thermal disappearance during its eruptive phase. We suggest that the observation of the same direction of the magnetic flux rope (MFR) ejections can be consider as an additional observational criterion for MFR homology. This observational indication for homologous eruptions is important, especially in the case of events of typical or poorly distinguishable morphology of eruptive solar phenomena.     

Magnetic field evolution during prominence eruptions and two-ribbon flares

Simple models for the MHD eruption of a solar prominence are presented, in which the prominence is treated as a twisted magnetic flux tube that is being repelled from the solar surface by magnetic pressure forces. The effects of different physical assumptions to deal with this magneto-hydrodynamically complex phenomenon are evaluated, such as holding constant the prominence current, radius, flux or twist or modelling the prominence as a current sheet. Including a background magnetic field allows the prominence to be in equilibrium initially with an Inverse Polarity and then to erupt due to magnetic non-equilibrium when the background magnetic field is too small or the prominence twist is too great. The electric field at the neutral point below the prominence rapidly increases to a maximum value and then declines. Including the effect of gravity also allows an equilibrium with Normal Polarity to exist. Finally, an ideal MHD solution is found which incorporates self-consistently a current sheet below the prominence and which implies that a prominence will still erupt and form a current sheet even if no reconnection occurs. When reconnection is allowed it is, therefore, driven by the eruption.     

Periodic structures in quiescent prominences

The observed structural periodicities in quiescent prominences and filaments are examined in terms of the instability of a plasma supported by a magnetic field against gravity. It is suggested that the spacing of arch-like structures may be identified with the most unstable wavelength of the interface between the prominence and the supporting magnetic field. The results of analysis further suggest that the observed spacing of periodic structures corresponds to the supporting magnetic field which lies at an angle 90° to 60° with respect to the long axis of the prominence.     

Coronal mass ejections: Some possibilities for prediction

The onset stage of coronal mass ejections (CMEs) is difficult to observe and is poorly studied. In spite of their practical importance, methods for CME predictions with sufficient lead times are only in the nascent stages of development. The most probable CME mechanism is a catastrophic loss of equilibrium of a large-scale current system in the corona (a flux rope). A twisted magnetic rope is maintained by the tension of field lines of photospheric sources until parameters of the system reach critical values and the equilibrium is lost. Unfortunately, there is low-density plasma (coronal cavity) in most of the rope volume; thus, it is difficult to observe a rope. However, the lower parts of the helical field lines of a rope are fine traps for the dense cold plasma of prominences. Thus, prominences are the best tracers of flux ropes in the corona. The maximal height up to which the rope is in stable equilibrium can be found by analyzing the distribution of the magnetic field generated by photospheric sources in the corona. Comparing this critical height with the actually observed prominence height, one can estimate the probability of the loss of equilibrium by a magnetic rope with a following eruption of prominences and coronal mass ejections.     

Nonradial eruption of a kinking filament observed from STEREO

On 5 April 2008, a filament at the periphery of an active region was observed by the Extreme Ultraviolet Imager telescope aboard the STEREO-A spacecraft, which showed up as a prominence eruption in the field-of-view from STEREO-B. The filament at STEREO-A 304 Å was first lengthened toward a region with weak overlying magnetic field so evolved as a large-scale one consisting of bright and dark threads twisting with each other, and then the portion below the weak field underwent an eruption. Meanwhile, the corresponding STEREO-B 304 Å prominence threads exhibited a kinking structure and tilting motion, with its center deflecting from the radial direction. By using three-dimension (3D) reconstruction technology, we obtain the 3D topology for the kinked prominence when its apex arrived at 1.4 radii, from which a clockwise rotation of about 90° is found in the course of the eruption. By comparing the 3D structure with the magnetic-field configuration computed by using the Potential-Field Source-Surface (PFSS) model, it is suggested that the filament erupted against the rather weaker than stronger overlying magnetic field, which make it appear to tilt toward one side.     

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.