The shape of buoyant coronal loops in a magnetic field and the eruption of coronal transients and prominences

The equilibrium and non-equilibrium properties of a coronal loop embedded in a stratified isothermal atmosphere are investigated. The shape of the loop is determined by a balance between magnetic tension, buoyancy, and external pressure gradients. The footpoints of the loop are anchored in the photosphere; if they are moved too far apart, no equilibrium is possible and the loop erupts upwards. This critical separation is independent of the pressure differential between the loop and the external medium if the loop has enhanced magnetic field, but varies if instead the loop pressure is increased. The maximum width is proportional to the larger of the gravitational scale-height and the length-scale of the ambient field. In some circumstances, it is shown that multiple solutions exist for the tube path. These results may be relevant to the eruption of prominences during the preflare phase of two-ribbon flares and to the onset of coronal loop transients. Such eruptions may occur if the footpoint separation, internal pressure or internal magnetic field are too great.     

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.     

Impulsive brightenings and velocity transients in prominences

Observations of quiescent prominences with the Zeiss Universal Birefringent Filter at Sacramento Peak show short-lived brightenings and velocity transients in H and D₃. The larger events range in area from 25 to 170 square arc sec, have lifetimes of approximately 30 min, velocities of 30 km s^–1, and total energy excesses up to 7 × 10²⁷ ergs. These events do not disrupt the stable structure of the prominence, and are interpreted as either condensation events or low energy flares.Visiting astronomer, Sacramento Peak Observatory, operated by the Association of Universities for Research in Astronomy Inc. under contrast AST-78-17292 with the National Science Foundation.Visiting student, Sacramento Peak Observatory, operated by the Association of Universities for Research in Astronomy Inc. under contract AST-78-17292 with the National Science Foundation.     

Magnetic reconnection and coronal transients

Every two-ribbon flare observed during the Skylab period produced an observable coronal transient, provided the flare occurred close enough to the limb. The model presented here treats these two events as a combined process. Transients that occur without flares are believed to involve magnetic fields that are too weak to produce significant chromospheric emission. Adopting the hypothesis that the rising flare loop systems observed during two-ribbon flares are exhibiting magnetic reconnection, a model of a coronal transient is proposed which incorporates this reconnection process as the driving force. When two oppositely directed field lines reconnect a lower loop is created rooted to the solar surface (the flare loop) and an upper disconnected loop is produced which is free to rise. The magnetic flux of these upper loops is proposed as the driver for the transient. The force is produced by the increase in magnetic pressure under the filament and transient.A quantitative model is developed which treats the transient configuration in terms of four distinct parts- the transient itself with its magnetic field and material, the region just below the transient but above the filament, the filament with its magnetic field, and the reconnected flux beneath the filament. Two cases are considered - one in which all the prominence material rises with the transient and one in which the material is allowed to fall out of the transient. The rate of rise of the neutral line during the reconnection process is taken from the observations of the rising X-ray flare loop system during the 29 July, 1973 flare. The MHD equations for the system are reduced to four non-linear ordinary coupled differential equations which are solved using parameters believed to be realistic for solar conditions. The calculated velocity profiles, widths, etc., agree quite well with the observed properties of coronal transients as seen in white light. Since major flares are usually associated with a filament eruption about 10–15 min before the flare and since this model associates the transient with the filament eruption, we suspect that the transient is actually initiated some time before the actual flare itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Double current sheet and coronal transients

A double current sheet forms when an opposite magnetic flux emerges into a background magnetic field which has a zero field-line in the corona. It consists of an upper sheet, resulting from the squeezing of field lines near the original zero field region and a lower sheet formed in the region between the new and old fields. We use a pair of linear dipoles to model the background and a pair of line charges to model the emerging field and discuss the formation and evolution of the double current sheet. Matter will condense onto the sheets during their formation. The matter in the lower sheet comes mainly from the transition region and the photosphere; it is further cooled by radiation, giving rise to a low-temperature prominence loop. The matter in the upper sheet comes from the corona and forms a high-temperature coronal loop.This scenario seems to be realized in the coronal transient of 1984 April 14.     

The onset of coronal transients

A model for the motion of transients in the high corona, recently given by Anzer (1978), is extended to include also the onset of a transient, associated with prominence destabilization. A comparison is made with flare instabilities, and some relevant observations are considered.     

Frequency of coronal transients and solar activity

The High Altitude Observatory's white light coronagraph aboard Skylab observed some 110 coronal transients - rapid changes in appearance of the corona - during its 227 days of operation. The longitudes of the origins of these transients were not distributed uniformly around the solar surface (51 of the 100 events observed in seven solar rotations arose from a single quadrant of longitude). Further, the frequency of transient production from each segment of the solar surface was well correlated with the sunspot number and Ca ii plage (area × brightness) index in the segment, rotation by rotation. This correlation implies that transients occur more often above strong photospheric and chromospheric magnetic fields, that is, in regions where the coronal magnetic field is stronger and, perhaps, more variable. This pattern of occurrence is consistent with our belief that the forces propelling transient material outward are, primarily, magnetic. A quantitative relation between transient production from an area and the Zürich sunspot number appropriate to that area is derived, and we speculate that the relation is independent of phase in the solar activity cycle. If true, the Sun may give rise to as many as 100 white light coronal transients per month at solar cycle maximum.Currently at Los Alamos Scientific Laboratory, Los Alamos, N.M., U.S.A.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Evidence linking coronal transients to the evolution of coronal holes

The positions of X-ray coronal transients outside of active regions observed during Skylab were superposed on H synoptic charts and coronal hole boundaries for seven solar rotations. We confirmed a detailed spatial association between the transients and neutral lines. We found that most of the transients were related to large-scale changes in coronal hole area and tended to occur on the borders of evolving equatorial holes.Skylab Solar Workshop Post-Doctoral Appointee, 1975–1977.     

Impulsive brightenings/velocity transients in quiescent solar prominences

In some quiescent prominences, areas are found where the H emission profiles are centrally reversed. By combining good spatial, spectral, and temporal resolution, the detailed behavior of these reversal regions has been investigated. Many of the regions show a growth and subsequent decay in the affected area, peak intensity, line width, and depth of the central reversal. Lifetimes of the time-varying reversal features range from 10 to more than 60 min, and they are found near the edges of the prominence fine structure. These events are similar to the impulsive events that the authors discussed in an earlier paper, and may share a common cause. The detailed behavior of the H line profiles is consistent with these reversal features being true self-reversal of the line, indicating unusually high column masses in these areas. Some models of condensation of coronal material to the prominence state predict temporary regions of high density, perhaps high enough to produce the observed reversal. This implies that reversal features are the result of on-going condensation of coronal material into already formed prominences, a result which impacts models of prominence formation and stability.Visiting Astronomer, National Solar Observatory (Sacramento Peak) of National Optical Astronomy Observatories, operated by Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

The piston model of coronal transients

In the present paper, the piston model of the coronal transient (see Hu. 1983a, b is discssed in detail, and the quantitative results of unsteady gasdynamics are applied to the coronal transient processes. The piston model explains the major features of the transient observations, such as the density profile, the geometric configuration, the kinetic process and the classifications of the coronal transient. Based on the idea of piston model, the bright feature and the dark feature of the transient are the gasdynamical response of the dense plasma ejecting into the corona, and associate with the compressed and rarefied flows, respectively. The quantitative results show that the density increment in the compressed region and the density decrement in the rarefied region are one order of magnitude larger and smaller, respectively, to the density in the quiet corona, it agrees quantitatively with the observations, and both the bright feature and dark feature are explained at the same time.     

Non-adiabatic discrete Alfvén waves in coronal loops and prominences

Discrete Alfvén waves in coronal loops and prominences are investigated in non-ideal magnetohydrodynamics. The non-ideal effects included are anisotropic, thermal conduction, and optically thin radiation. The classic ideal Alfvén continuum is not altered by these non-ideal effects, but the discrete Alfvén modes, which exist under certain conditions above or below the Alfvén continuum in ideal MHD, are shown to be influenced by non-adiabatic effects.The existence of discrete, non-adiabatic Alfvén waves, and their damping and overstability are examined for 1D cylindrical equilibrium states with twisted magnetic fields. First, analytic results are obtained for modes of high radial order by means of a WKB-analysis. The subspectrum of discrete Alfvén modes is computed with a numerical code, with particular emphasis on the modes of low radial order. The results show that discrete Alfvén waves are of potential importance for solar applications and also that the information obtained with the WKB-analysis is of limited use in this context.Research Assistant of the Belgian National for Scientific Research.     

Homologous type II radio bursts and coronal transients

The homology of seven successive type II solar radio bursts, which occurred at the times of flares from an active region near the solar west limb on 1980, July 27–29, is described, together with evidence for coronal mass outflows accompanying these bursts. It is argued that homologous type II bursts imply that the corona is restructured in a similar manner by successive coronal transients.     

The ‘melon-seed’ mechanism and coronal transients

Adopting the point of view that a coronal transient is a defined magnetic structure, it must be diamagnetic with respect to the external ambient magnetic field, i.e., the external field lines cannot penetrate the structure. If this is so, an integral approach involving only external forces can be very useful for studying the conditions for acceleration and large-scale dynamical behavior of the transient.After a discussion of a suggested transient configuration based upon observations of prominences, flare loops, and transient - filament relative orientations observed by Trottet and MacQueen (1980), we demonstrate the diamagnetic approach to this problem through a particularly simplified model. Necessary conditions for upward acceleration of the transient are discussed in some detail. One such plausible initiation mechanism is shown to be a constriction of the structure near its base by the external forces. This mechanism not only can provide the upward acceleration for the transient but is also compatible with the observation of hot rising flare loops during two-ribbon flare which show evidence for magnetic reconnection.We have studied the equilibrium conditions and dynamical behavior of the transient using this mechanism for two limiting cases - that in which the gas pressure in the structure dominates over the magnetic pressure and that in which the magnetic pressure dominates. For both cases, the required equilibrium conditions are compatible with observed coronal parameters. The dynamical behavior upon inward constriction, however, resembles the observed characteristics for transients best for the magnetically dominated case. For example, in the pressure-dominated case, the required temperatures for acceleration appear somewhat high being in excess of about 1.9 × 10⁶ K. If, in addition, the internal temperature declines adiabatically during the outward motion, the structure does not reach inifinity unless its initial temperature exceeds about 3 × 10⁶ K but stops a some radial distance, returns to the Sun only to be accelerated outward again in the same fashion. The rather stringent requirements on internal temperature for the pressure-dominated case in addition to the expectation that pressure-dominated transients should evolve into a thin pencil shape instead of maintaining an approximately self-similar profile as observed are strong arguments in favor of the magnetically dominated case.Based upon the above results, we suggest that the reconnection process evidenced in two-ribbon flares may not necessarily be the result of the relaxation of a locally open field configuration produced by the transient as described by Kopp and Pneuman (1976) but, instead, that the acceleration of the transient and the two-ribbon flare both may be produced by a common force, namely that provided by the constricting effect of the external magnetic field displaced by the presence of the structure.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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 kinematics of solar inner coronal transients

Solar Physics - The kinematic properties of a dozen ‘loop-like’ coronal transients have been examined over the range 1.2–2.4 R⊙ from Sun center. Values and trends of...     

Type II radio emission in coronal transients

Recent observations demonstrate that some type II radio bursts (a) occur below the top of coronal white light loops in the early stages and (b) travel faster than white light transients when both data sources are recorded concurrently. These characteristics are examined with numerical simulations of a coronal transient in combination with the suggestion by Holman and Pesses (1983) that shock drift acceleration may be the originating mechanism for type II emission. The simulated angular relation between the transient shock normal and the upstream magnetic field, along with requirements on this orientation in order that shock drift be effective, lead naturally to the observed spatial relationship (in the lower corona) and relative velocities of white-light transients and type II bursts. The large type II velocities do not directly correspond to either material or shock motion, but are due to the production of emission at different locations along the shock surface. In addition, the model coincides with the hypothesis that the shocks generating the coronal type II emission also produce interplanetary SA (shock-accelerated) events.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A magnetohydrodynamic theory of coronal loop transients

A magnetohydrodynamic theory is presented for coronal loop transients. It is shown that the heliocentrifugal motion of a transient loop, as exhibited by the translational displacement of the axis of the loop, is driven by the magnetohydrodynamic buoyancy force exerted by the ambient medium. Self-induced hydromagnetic force, which includes the magnetic force produced by the internally driven current and the thermal force produced by the pressure imbalance between the internal and external gas pressures, causes the peripheral expansion of the loop, as exhibited by the lateral broadening and longitudinal stretching. This contention is substantiated by an analysis based on a model structure for a coronal loop.Besides accounting for the acceleration and expansion of a transient loop, this magnetohydrodynamic theory also provides an explanation for the initial ejection of a coronal loop from stationary equilibrium. Magnetic unwinding in consequence of abrupt magnetic activities at the solar surface will cause the periphery of a stationary coronal loop to expand. The increase in volume will enhance the magnetohydrodynamic buyoyancy force to exceed the gravitational force. Once a coronal loop is ejected from the solar surface, it will be continually accelerated and undergo expansion. Eventually a transient loop will blend with the ambient solar wind. This is also indicated by the theory presented in this paper.     

Mass flow in loop type coronal transients

The white light coronagraph on Skylab observed many loop type coronal transients. These loops travel through the coronagraph's field of view (2–6R ) over a period of a few hours, after which the legs of the loops usually remain visible for a few days. In this paper we investigate the temporal changes in density and mass per unit length measured along the legs of such loops during the several days after the initial eruption. Examination of 8 transients shows that the mass and density in the legs decrease during the few hours after the top of the loop has travelled beyond the coronagraph's field of view. The mass and density then increase slowly, during the next one half to one day, then decrease again over approximately the same period. These changes are generally shown to be too rapid to be explained by solar rotation, indicating that the transient legs have a lifetime of only a few days.The results of a detailed study of the transient of 10 August 1973 are compared with the results from theoretical calculations. For the top of the loop a one-dimensional flow problem is solved, assuming a balance between gravity, inertia, and pressure gradients. The legs are modeled by a flow in a tube of constant cross section. Models for the flow in the legs were calculated under the assumption that the mass distribution is close to hydrostatic equilibrium. Using these models we can estimate that approximately 5 × 10¹⁴ g of material flow outward through the legs of this transient. We also find that the best fit to the observed average density gradient is obtained with a temperature of 1.7 × 10⁶ K.On leave from Max-Planck Institut für Physik und Astrophysik, Munich, Germany.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Eruptive prominences of 1980 april 27 observed during STIP interval — X

Observations and analyses of two similar eruptive prominences on the north-east limb observed on 1980 April 27 at 0231 and 0517 UT, which are associated with the Boulder active region No. 2416 are presented. Both the eruptive prominences gave rise to white-light coronal transients as observed by C/P experiment of High Altitude Observatory on the Solar Maximum Mission. Type II and moving type IV radio bursts are reported in association with the first Hα eruptive prominence at 0231 UT. Both the Hα eruptive prominences showed pulse activity with a quasi-periodicity of about 2–4 min. We estimate a magnetic field in the eruptive prominence of about 100 G and a build-up rate ∼ 10²⁶ ergs^-1. The high build-up rate indicates that the shearing of the photospheric magnetic field, which fed the energy into the filament, was rapid. It is proposed that fast-moving Hα features must have initiated the observed coronal transients. From Hα, type II and coronal-transient observations, we estimate a magnetic field of 2.8 G at 1.9R⊙ from the disc centre, which agrees well with the earlier results.