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.     

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.     

Model calculations of the rising motion of a prominence loop

Model calculations are presented for the rising motion of the top section of a prominence loop, which is represented by a straight flux rope immersed in a coronal medium permeated with a bipolar magnetic field. Initially the prominence is at rest, in equilibrium with the surrounding coronal medium. When the magnetic monopoles that account for the source current for the bipolar field strengthen, the upward hydromagnetic buoyancy force overcomes the downward gravitational force so that the prominence is initiated into rising motion. The illustrative examples show that prominences can move away from the solar surface by the action of the hydromagnetic buoyancy force, which is preponderant with the diamagnetic force due to the current carried by the prominence interacting with the coronal magnetic field produced by the photospheric currents, if the changes in the photospheric magnetic field are sufficiently large.     

The formation of solar prominences by magnetic reconnection and condensation

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

Magnetic energy buildup in a quadrupole field by photospheric shear motion

Using a two-dimensional, dissipative magnetohydrodynamic model, this paper presents a numerical simulation of the magnetic energy buildup in a quadrupolar field by photospheric shear motion. When electric current density is larger than a certain critical value, an anomalous resistivity is introduced in order to account for the dissipation caused by instabilities in high current regions. It is shown that like a bipolar field, a quadrupolar field can efficiently store magnetic free energy through photospheric shear motion. Electric current formed by shear concentrates on the separatrix and magnetic loops rooted in areas where the shear velocity gradient is large. The atmosphere is heated by anomalous resistive dissipation during the shear. Both magnetic and thermal energy increases nonlinearly with shearing displacement. When the anomalous resistivity increases or the critical current density decreases, the growth rate reduces for magnetic energy but goes up for thermal energy.     

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.     

CAN WE EXTRAPOLATE A MAGNETIC FIELD WHEN ITS TOPOLOGY IS COMPLEX?

In order to understand various solar phenomena controlled by the magnetic field, such as X-ray bright points, flares and prominence eruptions, the structure of the coronal magnetic field must be known. This requires a precise extrapolation of the photospheric magnetic field. Presently, only potential or linear force-free field approximations can be used easily. A more realistic modelling of the field is still an active research area because of well-known difficulties related to the nonlinear mixed elliptic-hyperbolic nature of the equations. An additional difficulty arises due to the complexity of the magnetic field structure which is caused by a discrete partition of the photospheric magnetic field. This complexity is not limited to magnetic regions having magnetic nulls (and so separatrices) but also occurs in those containing thin elongated volumes (called Quasi-Separatrix Layers) where the photospheric field-line linkage changes rapidly. There is a wide range for the thickness of such layers, which is determined by the character (bipolar or quadrupolar) of the magnetic region, by the sizes of the photospheric field concentrations and by the intensity of the electric currents. The aim of this paper is to analyse the recent nonlinear force-free field extrapolation techniques for complex coronal magnetic fields.     

The relationship between the interplanetary magnetic field inhomogeneous structure and the distribution of large-scale magnetic fields in the photosphere (1969–1975)

For the period 1969–1975, a study has been made of the dependence of the interplanetary magnetic field structure on the distribution and evolutionary properties of solar magnetic fields. By direct comparison of a sequence of synoptic charts of the photospheric magnetic field with the interplanetary magnetic field, and by applying the method of correlation analysis, it is shown that to areas with an unstable polarity of the interplanetary magnetic field there correspond regions with a complicated inverse polarity line that forms either narrow gulfs and islands against a background of the dominant polarity, or bipolar magnetic regions and their clusters. At the time of reconstruction of the photospheric magnetic field the correlation between the photospheric and interplanetary magnetic field element distributions worsens. An asymmetry of the correlation between the interplanetary and photospheric magnetic field structures of different hemispheres is found. During the period of study, the interplanetary field structure shows a better correlation with the distribution of the photospheric magnetic field at middle and lower latitudes (0°–40°) of the southern hemisphere.     

Interpretation of multiwavelength observations of November 5, 1980 solar flares by the magnetic topology of AR 2766

We present a detailed analysis of the magnetic topology of AR 2776 together with Hα UV, X-rays, and radio observations of the November 5, 1980 flares in order to understand the role of the active region large-scale topology on the flare process. As at present the coronal magnetic field is modeled by an ensemble of sub-photospheric sources whose positions and intensities are deduced from a least-square fit between the computed and observed longitudinal magnetic fields. Charges and dipole representations are shown to lead to similar modeling of the magnetic topology provided that the number of sources is great enough. However, for AR 2776, departure from a potential field has to be taken into account, therefore a linear force-free field extrapolation is used. The locations of the four bright off-band Hα kernels in quadrupolar active regions have been studied previously. In this new study the active region is bipolar and shows a two-ribbon structure. We show that these two ribbons are a consequence of the bipolar photospheric field (the four kernels of quadrupolar regions merge into two bipolar regions). The two ribbons are found to be located at the intersection of the separatrices with the chromosphere when the shear, deduced from the fibril direction, is taken into account. This study supports the hypothesis that magnetic energy is stored in field-aligned currents and released by magnetic reconnection at the location of the separator, before being transported along field lines to the chromospheric level. It is also possible that part of the magnetic energy could be stored and released on the separatrices. Our study shows that meeting just one of two conditions- the presence of intense coronal currents or of a separator in a magnetic field configuration - is not sufficient for flaring. In order to release the stored energy, the coronal currents need either to be formed along the separatrices or to be transported towards the separator or separatrices. The location of the observed photospheric current concentrations on the computed separatrices supports this view. Member of the Carrera del Investigador Científico, CONICET.     

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.     

On the maximum energy release in flux-rope models of Eruptive Flares

We determine the photospheric boundary conditions which maximize the magnetic energy released by a loss of ideal-MHD equilibrium in two-dimensional flux-rope models. In these models a loss of equilibrium causes a transition of the flux rope to a lower magnetic energy state at a higher altitude. During the transition a vertical current sheet forms below the flux rope, and reconnection in this current sheet releases additional energy. Here we compute how much energy is released by the loss of equilibrium relative to the total energy release. When the flux-rope radius is small compared to its height, it is possible to obtain general solutions of the Grad-Shafranov equation for a wide range of boundary conditions. Variational principles can then be used to find the particular boundary condition which maximizes the magnetic energy released for a given class of conditions. We apply this procedure to a class of models known as cusp-type catastrophes, and we find that the maximum energy released by the loss of equilibrium is 20.8% of the total energy release for any model in this class. If the additional restriction is imposed that the photospheric magnetic field forms a simple arcade in the absence of coronal currents, then the maximum energy release reduces to 8.6%.     

Catastrophe of Coronal Magnetic Flux Ropes Caused by Photospheric Motions

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, we carried out numerical simulations to investigate the equilibrium and evolution properties of a magnetic configuration that consists of a coronal magnetic flux rope and a partly open photospheric background field, which is equivalent to that produced by a two-patch magnetic source on the photospheric surface. The axial and annular magnetic fluxes of the flux rope are given and fixed. The global magnetic configuration evolves in response to three types of changes of the background field: decreasing of the distance between the two sources, shrinking of the size of each source, and increasing of the shear in the closed component of the background field. As a result, the geometrical parameters of the flux rope, i.e. the height of the rope axis, the half-width of the rope and the length of the vertical current sheet below the rope, change due to the variation of the background field. It is shown that for a given coronal magnetic flux rope in a partly open background field, the variation of the geometrical parameters of the flux rope displays a catastrophic behavior, namely, there exists a critical point for each case, at which an infinitesimal change of the background field leads to a loss of equilibrium, and thus a jump of the flux rope. The implication of such a catastrophe in solar active phenomena is briefly discussed.     

Magnetic-field structure associated with coronal streamers

An interesting coronal structure was observed during the solar eclipse of May 30, 1965. This comprised a series of bright arches centered approximately on a quiescent prominence. A bright ray originated near the top of one of the arches and pointed almost radially away from the photosphere. The ray could be followed for 1.5 solar radii and was deflected towards a direction parallel to the equatorial plane. By comparing the photographs with Fraunhofer maps and magnetograms, the following interpretation of the structure was obtained. The prominence lies above the neutral line of an extended bipolar magnetic region. The bright arches coincide with flux tubes arising from small photospheric regions of enhanced magnetic-field strength. The ray represents a projection view of a thin region of enhanced plasma density in the neighborhood of a current sheet which separates two flux tubes of opposite polarity. The ray is interpreted as a coronal streamer, and it is suggested that all streamers are related to current sheets.     

Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003

We present and interpret observations of two morphologically homologous flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both flares displayed four homologous Hα ribbons and were both accompanied by coronal mass ejections (CMEs). The central flare ribbons were located at the site of an emerging bipole in the centre of the active region. The negative polarity of this bipole fragmented in two main pieces, one rotating around the positive polarity by ≈ 110° within 32 hours. We model the coronal magnetic field and compute its topology, using as boundary condition the magnetogram closest in time to each flare. In particular, we calculate the location of quasi-separatrix layers (QSLs) in order to understand the connectivity between the flare ribbons. Though several polarities were present in AR 10501, the global magnetic field topology corresponds to a quadrupolar magnetic field distribution without magnetic null points. For both flares, the photospheric traces of QSLs are similar and match well the locations of the four Hα ribbons. This globally unchanged topology and the continuous shearing by the rotating bipole are two key factors responsible for the flare homology. However, our analyses also indicate that different magnetic connectivity domains of the quadrupolar configuration become unstable during each flare, so that magnetic reconnection proceeds differently in both events.     

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.     

An Improved Approach to Non-Force-Free Coronal Magnetic Field Extrapolation

We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys. 235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.     

Quiescent prominences - where are they formed?

A survey of two years (1973 and 1979) of quiescent prominences reveals that substantially more (20 and 96% more, respectively, in the two years surveyed) quiescent prominences were formed on neutral lines between bipolar regions than on neutral lines inside bipolar regions.Present prominence models are based on the magnetic field configuration of the neutral lines of single bipolar regions, possibly because it is assumed that most prominences evolved from there. In view our new finding, a new model is needed in which the evolution begins at the boundary of two adjacent bipolar regions.     

Formation of Solar Delta Active Regions： Twist and Writhe of Magnetic Ropes

We analyze the process of formation of delta configuration in some well-known super active regions based on photospheric vector magnetogram observations. It is found that the magnetic field in the initial developing stage of some delta active regions shows a potential-like configuration in the solar atmosphere, the magnetic shear develops mainly near the magnetic neutral line with magnetic islands of opposite polarities, and the large-scale photospheric twisted field forming gradually later. Some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, supposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and not entirely consistent with the relationship with magnetic shear in some delta active regions. (3) T     

The relationship between the slowly varying component of solar radio emission and large scale photospheric magnetic field patterns

Daily solar radio flux observations have been examined for a relationship to the large-scale photospheric magnetic field structure. Interplanetary magnetic field sector boundaries were used to indicate boundaries between photospheric field regions of opposite polarity. An enhancement in emission was found about four days before the boundary central meridian passage. Most of the effect came from emission near toward-to-away type boundaries. A higher level of emission appears to be associated with toward field regions than with away field regions.     

Quadrupolar Dimmings During a Partial Halo Coronal Mass Ejection Event

We present detailed observations of the formations of four distinct coronal dimmings during a flare of 17 September 2002, which was followed by an eruption of a huge coronal loop system, and then an over-and-out partial halo coronal mass ejection (CME), with the same direction as the loop system eruption but laterally far offset from the flare site. Among the four dimmings, two compact ones were symmetrically located in the opposite polarity regions immediately adjacent to the highly sheared magnetic polarity inversion line in the flare region, and hence were probably composed of bipolar double dimmings due to a flux-rope eruption and represented its evacuated footpoints. However, another nearby compact dimming and a remote diffuse one were formed in the opposite polarity footpoint regions of the eruptive loop system, and thus probably consisted of a pair of dimmings magnetically linked by the erupting loop system and also indicated its evacuated footpoints. The loop system might have played a role in guiding the erupting flare field and producing the over-and-out CME, but its eruption might simply have been pushed out by the erupting flare field, because there was no reconnection signature between them. From comparison with a derived potential-field source-surface (PFSS) magnetic configuration, our observations consistently suggest that the dimmings were formed in pairs and originated from the eruptions of the two different magnetic systems. We thus define them as “quadrupolar dimmings.”