Rope Model Research Articles

Constraints on the Magnetic Field Geometry in Prominences

This paper discusses constraints on the magnetic field geometry of solar prominences derived from one-dimensional modeling and analytic theory of the formation and support of cool coronal condensations. In earlier numerical studies we identified a mechanism—thermal nonequilibrium—by which cool condensations can form on field lines heated at their footpoints. We also identified a broad range of field line shapes that can support condensations with the observed sizes and lifetimes: shallowly dipped to moderately arched field lines longer than several times the heating scale. Here we demonstrate that condensations formed on deeply dipped field lines, as would occur in all but the near-axial regions of twisted flux ropes, behave significantly differently than those on shallowly dipped field lines. Our modeling results yield a crucial observational test capable of discriminating between two competing scenarios for prominence magnetic field structure: the flux rope and sheared-arcade models.

Observational Evidence of a Magnetic Flux Rope Eruption Associated with the X3 Flare on 2002 July 15

We present the study of an eruption from the low solar atmosphere (photosphere/chromosphere) as seen in Transition Region and Coronal Explorer 1600 Angstrom images and with the Solar and Heliospheric Observatory Michelson Doppler Imager. The eruption reached its maximum at 20: 08 UT on 2002 July 15 in the NOAA Active Region 10030 ( N19degrees, W01degrees), accompanied by an X3 flare and followed by a fast-halo coronal mass ejection. The main observational results from the data are as follows: ( 1) the erupting plasma was in a rapidly rising, twisted ropelike structure; ( 2) the eruption occurred just preceding the onset of its driven flare; and (3) the morphology and magnetic flux of one slender footpoint (similar to9000 km in length) of the rope developed rapidly on the photosphere. This structure disappeared in white light and in the magnetograms within 60 minutes. This evidence supports the erupting flux rope model. Our data favor the idea that a catastrophic loss of MHD equilibrium can be the primary driving mechanism for the rapid ejection of a flux rope. This conclusion is based on the judgment that the ambient fields of the flux rope were partly opened as a result of the magnetic reconnection.

Theory of twisted trunks

Using the 2.6 m Nordic Optical Telescope we have observed a large number of elephant trunks in several Hii regions. Here, we present a small selection of this material consisting of a few large, well-developed trunks, and some smaller ones. We find that: (i) the well-developed trunks are made up of dark filaments and knots which show evidence of twisted structures, (ii) the trunks are connected with essentially two filamentary legs running in V-shape, and (iii) all trunks have the maximum extinction in their heads. We advance a theory of twisted elephant trunks which is based on the presence of magnetic flux ropes in molecular clouds where hot OB stars are formed. If the rope contains a local condensation it may adopt a V-shape as the Hii region around the hot stars expands. If, in addition, the magnetic field in the rope is suciently twisted, the rope may form a double helix at the apex of the V. The double helix is identified with the twisted elephant trunks. In order to illustrate the mechanisms behind the double helix we have constructed a mechanical analogy model of the magnetic flux rope in which the rope has been replaced by a bundle of elastic strings loaded by a weight. Experiments with the model clearly show that part of the bundle will transform into a double helix when the twist of the bundle is suciently large. We have also worked out a simple theoretical model of a mass-loaded magnetic flux rope. Numerical calculations show that a double helix will indeed form when the twist of the rope exceeds a certain critical limit. Numerical model calculations are applied to both the analogy model experiments and one of the well-developed elephant trunks. On the basis of our model we also suggest a new interpretation of the so called EGGs. The double helix mechanism is quite general, and should be active also in other suitable environments. One such environment may be the shell of supernova remnants. Another example is the expanding bubble outlined by the North Celestial Pole Loop.

Cluster electric current density measurements within a magnetic flux rope in the plasma sheet

On August 22, 2001 all 4 Cluster spacecraft nearly simultaneously penetrated a magnetic flux rope in the tail. The flux rope encounter took place in the central plasma sheet, βi ∼ 1–2, near the leading edge of a bursty bulk flow. The “time‐of‐flight” of the flux rope across the 4 spacecraft yielded Vx ∼ 700 km/s and a diameter of ∼1 Re. The speed at which the flux rope moved over the spacecraft is in close agreement with the Cluster plasma measurements. The magnetic field profiles measured at each spacecraft were first modeled separately using the Lepping‐Burlaga force‐free flux rope model. The results indicated that the center of the flux rope passed northward (above) s/c 3, but southward (below) of s/c 1, 2 and 4. The peak electric currents along the central axis of the flux rope predicted by these single‐s/c models were ∼15–19 nA/m2. The 4‐spacecraft Cluster magnetic field measurements provide a second means to determine the electric current density without any assumption regarding flux rope structure. The current profile determined using the curlometer technique was qualitatively similar to those determined by modeling the individual spacecraft magnetic field observations and yielded a peak current density of 17 nA/m2 near the central axis of the rope. However, the curlometer results also showed that the flux rope was not force‐free with the component of the current density perpendicular to the magnetic field exceeding the parallel component over the forward half of the rope, perhaps due to the pressure gradients generated by the collision of the BBF with the inner magnetosphere. Hence, while the single‐spacecraft models are very successful in fitting flux rope magnetic field and current variations, they do not provide a stringent test of the force‐free condition.

A Three-dimensional Flux Rope Model for Coronal Mass Ejections Based on a Loss of Equilibrium

A series of simulation runs are carried out to investigate the loss of equilibrium of the three-dimensional flux rope configuration of Titov & Demoulin as a suitable mechanism for the initiation of coronal mass ejections. By means of these simulations, we are able to determine the conditions for which stable equilibria no longer exist. Our results imply that it is possible to achieve a loss of equilibrium even though the ends of the flux rope are anchored to the solar surface. However, in order to have the flux rope escape, it is necessary to modify the configuration by eliminating the arcade field.

Geotail observations of magnetic flux ropes in the plasma sheet

Examination of Geotail measurements in the near‐tail (X > −30 RE) has revealed the presence of small flux ropes in the plasma sheet. A total of 73 flux rope events were identified in the Geotail magnetic field measurements between November 1998 and April 1999. This corresponds to an estimated occurrence frequency of ∼1 flux rope per 5 hours of central plasma sheet observing time. All of the flux ropes were embedded within high‐speed plasma sheet flows with 35 directed Earthward, 〈Vx〉 = 431 km/s, and 38 moving tailward, 〈Vx〉 = −451 km/s. We refer to these two populations as “BBF‐type” and “plasmoid‐type” flux ropes. The flux ropes were usually several tens of seconds in duration, and the two types were readily distinguished by the sense of their quasisinusoidal ΔBz perturbations, i.e., ∓ for the “BBF” events and ± for the “plasmoid” events. Most typically, a flux rope was observed to closely follow the onset of a high‐speed flow within ∼1–2 min. Application of the Lepping‐Burlaga constant‐α flux rope model (i.e., J = αB) to these events showed that approximately 60% of each class could be acceptably described as cylindrical, force‐free flux ropes. The modeling results yielded mean flux rope diameters and core field intensities of 1.4 RE and 20 nT and 4.4 RE and 14 nT for the BBF and plasmoid‐type events, respectively. The inclinations of the flux ropes were small relative to the GSM X–Y plane, but a wide range of azimuthal orientations were determined within that plane. The frequent presence of these flux ropes in the plasma sheet is interpreted as strong evidence for multiple reconnection X‐lines (MRX) in the near‐tail. Hence, our results suggest that reconnection in the near‐tail may closely resemble that at the dayside magnetopause where MRX reconnection has been hypothesized to be responsible for the generation of flux transfer events.

Effects of raw garlic on physical performance and learning behaviour in rats.

The effects of garlic (Allium sativum Linn.) on physical performance and learning behaviour were evaluated in male rats (7-8 months old, weighing 250-400 g) by comparison with the effects of pentoxifylline, a haemorheological agent with antiplatelet activity. The tests were designated as experiment A and experiment B, both conducted in two consecutive 4-week sessions. In experiment A, the rats performed in a learning maze model during the first 4 weeks then followed by moving along the rope model for another 4 weeks. In experiment B, the rats were first tested in a rotarod treadmill for 4 weeks and then a step down test model for another 4 weeks. Each experiment consisted of four groups with 6-8 rats per group. Aqueous garlic homogenate at doses of 1 and 2 g (of raw garlic)/kg/day were given orally to group 1 and group 2, respectively, while pentoxifylline dispersion at a dose of 200 mg/kg/day was given to group 3. Group 4 served as the control group and was given water. All tests (maze model, rope model, rotarod model and step down model) were performed three times a week. The number of successful tasks and the acquisition time in 1 week intervals were used for the statistical analysis. The present results demonstrated that neither aqueous garlic homogenate at both doses nor pentoxifylline exhibited any benefit in the maze model or the rotarod model. Garlic only at the lower dose and pentoxifylline however, showed benefit in the rope model and step down model. These findings may provide some evidence to support the beneficial effect of long-term garlic consumption on physical performance and learning behaviour in normal subjects.

3D Coronal magnetic field from vector magnetograms: non-constant-αforce-free configuration of the active region NOAA 8151

The Active Region 8151 (AR 8151) observed in February 1998 is the site of an eruptive event associated with a fila- ment and a S-shaped structure, and producing a slow Coronal Mass Ejection (CME). In order to determine how the CME occurs, we compute the 3D coronal magnetic field and we derive some relevant parameters such as the free magnetic energy and the relative magnetic helicity. The 3D magnetic configuration is reconstructed from photospheric magnetic magnetograms (IVM, Mees Solar Observatory) in the case of a non-constant- force-free (nl) field model. The reconstruction method is divided into three main steps: the analysis of vector magnetograms (transverse fields, vertical density of electric current, ambiguity of 180), the numerical scheme for the nl magnetic field, the interpretation of the computed magnetic field with respect to the observations. For AR 8151, the nl field matches the coronal observations from EIT/SOHO and from SXT/Yohkoh. In particu- lar, three characteristic flux tubes are shown: a highly twisted flux tube, a long twisted flux tube and a quasi-potential flux tube. The maximum energy budget is estimated to 2:6 10 31 erg and the relative magnetic helicity to 4:7 10 34 G 2 cm 4 .F rom the simple photospheric magnetic distribution and the evidence of highly twisted flux tubes, we argue that the flux rope model is the most likely to describe the initiation mechanism of the eruptive event associated with AR 8151.

Elemental Abundances and Post–Coronal Mass Ejection Current Sheet in a Very Hot Active Region

A peculiar young active region was observed in 1998 March with the Ultraviolet Coronagraph Spectrometer (UVCS) over the southwest limb. The spectra showed strong emission in the λ974 line of fluorine-like iron, [Fe XVIII], which is brightest at an electron temperature of 106.8 K, and lines of Ne IX, [Ca XIV], [Ca XV], Fe XVII, [Ni XIV], and [Ni XV]. It is the only active region so far observed to show such high temperatures 0.5 R☉ above the solar limb. We derive the emission measure and estimate elemental abundances. The active region produced a number of coronal mass ejections (CMEs). After one CME on March 23, a bright post-CME arcade was seen in EIT and Yohkoh/SXT images. Between the arcade and the CME core, UVCS detected a very narrow, very hot feature, most prominently in the [Fe XVIII] line. This feature seems to be the reconnection current sheet predicted by flux rope models of CMEs. Its thickness, luminosity, and duration seem to be consistent with the expectations of the flux rope models for CME. The elemental abundances in the bright feature are enhanced by a factor of 2 compared to those in the surrounding active region, i.e., a first ionization potential enhancement of 7-8 compared to the usual factor of 3-4.

Effective string rope model for the initial stages of ultra-relativistic heavy ion collisions

Different approaches to describe initial stages of relativistic heavy ion collisions are discussed qualitatively and quantitatively. An effective string rope model is presented for heavy ion collisions at RHIC energies. Our model takes into account baryon recoil for both target and projectile, arising from the acceleration of partons in an effective field, F μν , produced in the collision. The typical field strength (string tension) for RHIC energies is about 5–12 GeV /fm, what allows us to talk about “string ropes”. The results show that a QGP forms a tilted disk, such that the direction of the largest pressure gradient stays in the reaction plane, but deviates from both the beam and the usual transverse flow directions. The produced initial state can be used as an initial condition for further hydrodynamical calculations. Such initial conditions lead to the creation of third flow component.

Emergence and Drastic Breakdown of a Twisted Flux Rope to Trigger Strong Solar Flares in NOAA Active Region 9026

An emerging twisted flux rope model to explain the drastic evolution of a flare-productive NOAA Active Region 9026 is presented. The drastic changes in the δ-type sunspot configuration were found to start shortly before the big flares of 2000 June 6: (1) rapid proper motions of sunspots started at the both sides of the central δ sunspot about 7 hr prior to the strong flare activity, (2) the collapse of the central δ sunspot with its disintegration and partial disappearance started about 3 hr before the strong flare activity, (3) a switchback-shaped and strongly sheared magnetic neutral line was formed with intruding motions of sunspots into the opposite magnetic polarities, and (4) the direction of the neutral line rapidly rotated clockwise at the same time when the switchback neutral line was formed. To explain these outstanding features of the sunspot evolution, we constructed a schematic model of an emerging twisted flux rope in which the central writhe helicity of the flux rope could be formed by continuous transformation of the twist helicity by means of the kink instability in the course of its emergence through the convection zone.

The draping of heliospheric magnetic fields upstream of coronal mass ejecta

The propagation of a fast coronal mass ejection through the interplanetary medium results in compression and draping of existing heliospheric magnetic fields, forming an upstream sheath. Such sheaths are a common context for planar magnetic structures, where the magnetic field is ordered into laminar sheets. A technique is presented to estimate the location of spacecraft with respect to the large‐scale structure of ejecta which they encounter. The technique employs the characteristics of sheath planar magnetic structures, assuming that they are formed by field‐line draping. The technique's results for four magnetic clouds encountered by the Ulysses spacecraft are compared to those of a flux rope model. Very good agreement is found, suggesting that this is a promising technique for estimating an ejection's location from single‐spacecraft data.

The critical role of stewardship in fund raising: the Coaches vs. Cancer campaign

This article examines the critical role of stewardship in the process of fund raising. In an analysis of the Coaches vs. Cancer campaign, the authors illustrate the limitations of the public relations ROPE model in explaining fund raising success, and support Kelly’s contention that addition of a fifth step to the model, the stewardship step, better explains campaign effectiveness.

Mechanism of Coronal Mass Ejections Triggered by Emerging Flux

The origin of coronal mass ejections (CMEs) is an interesting, while still mysterious, subject in solar physics. As well, the relationship between CMEs and solar flares is poorly understood. This paper attempts to provide answers to these questions on the base of the flux rope model, and put forward a trigger mechanism for CMEs. The work is motivated by an interesting discovery of the relation between reconnection-favored emerging flux and CMEs (Feynman and Martin 1995), i.e., such emerging flux, either within the filament channel or on the outer edge of the channel, can trigger CMEs.In the consideration of Aly’s constraint, a detached flux rope model was proposed for the pre-CME configuration. A quadrupolar magnetic field with a flux rope is introduced as the initial magnetic configuration in current research. Since our trigger mechanism is magnetic in nature, gravity is omitted. Emerging flux is simulated by changing the local magnetic flux at the bottom boundary.

Multiple magnetic clouds in interplanetary space

An interplanetary magnetic cloud (MC) is usually considered the byproduct of a coronal mass ejection (CME). Due to the frequent occurrence of CMEs, multiple magnetic clouds (multi-MCs), in which one MC catches up with another, should be a relatively common phenomenon. A simple flux rope model is used to get the primary magnetic field features of multi-MCs. Results indicate that the magnetic field configuration of multi-MCs mainly depends on the magnetic field characteristics of each member of multi-MCs. It may be entirely different in another situation. Moreover, we fit the data from the Wind spacecraft by using this model. Comparing the model with the observations, we verify the existence of multi-MCs, and propose some suggestions for further work.

Coronal mass ejections and emerging flux

This paper reviews our recent progress in the numerical study of coronal mass ejections (CMEs) based on flux rope model, which shows that when the reconnection-favored emerging flux appears either within or on the outer edge of the filament channel, the flux rope would lose its equilibrium, and be ejected, while a current sheet is formed below the flux rope. For the case with emergence within the filament channel, even small flux is enough to trigger the loss of equilibrium, however, there is a threshold for the emerging flux on the outer edge of the filament channel. Given that anomalous resistivity sets in (e.g. when the current density exceeds a critical value), fast reconnection is resulted in, leading to fast eruption of the flux rope and localized flare (either impulsive-type or LDE-type depending on the height of the reconnection point) near the solar surface. The numerical results can well explain why CMEs are not centered on flares and provide hints for CME-flare spatial and temporal relationships.

A test of real‐time prediction of magnetic cloud topology and geomagnetic storm occurrence from solar signatures

On the basis of the location, orientation, and surrounding magnetic field configuration of an erupting filament observed on September 27, 1997, an Earth‐encounter with a magnetic cloud having specific topological properties and an ensuing geomagnetic storm were predicted for September 30, assuming an average Sun‐Earth transit time. A subsequent comparison with solar wind and geomagnetic data surrounding September 30 yielded a mixed level of success. Although a geomagnetic storm occurred on October 1, ironically, the strong southward magnetic field responsible for it was not encountered at the leading edge of the cloud, as predicted, but rather in the preceding sheath. In retrospect, the most likely sources of the southward field in the sheath were either a preceding CME or magnetic flux from high in the corona, not draped or turbulent flux from the ambient solar wind as is often supposed. With the aid of a flux rope model, we show that the elevation and polarity of the cloud axis and the chirality of the cloud were predicted correctly but that the trajectory of the spacecraft (and Earth) through what was deduced to be the leg of a flux rope loop precluded encounter with its leading southward field. The storm began with a sudden commencement near 0100 UT on October 1, corresponding to passage of a shock‐like discontinuity, and the Dst storm index reached a minimum of −108 nT 14 hours later at 1500 UT. The leading edge of the cloud, however, coincident with the onset of counterstreaming electrons confirming its identification, was not encountered until 1700 UT. The disagreement between the predicted and actual arrival time reflects not only the lack of speed prediction capabilities but also the inability to predict whether encounter will be head‐on with the apex of a flux rope loop or, as deduced in this case, passage through one of its legs.

Multiple spacecraft flux rope modeling of the Bastille Day magnetic cloud

The Bastille Day magnetic cloud in July 2000 occurred with NEAR in conjunction with the Earth at a radial distance of 1.76 AU and 1.9° from the Earth‐Sun line. Propagation time from ACE at 0.99 AU to NEAR indicates the cloud did not decelerate significantly between the Earth and 1.76 AU. Using a non‐force‐free, kinematic flux rope model we find the rope contained 130 TWb of magnetic flux, was oriented with clock and cone angles of 50° and 83°, and had a radius of 0.25 AU at ACE. At NEAR its radius had expanded to 0.43 AU. Simultaneous modeling of ACE and NEAR data indicate the axial and poloidal magnetic fields vary as R−1.4 and R−1.2 where R is heliocentric distance. Magnetosheath thicknesses of 0.14 AU and 0.23 AU indicate the rope cross section is elongated normal to the cloud axis and the radial direction.

Solar magnetic fields and geomagnetic events

Some interplanetary studies lead one to expect that the toroidal fields of individual active regions are directly related to their heliospheric structure. Other studies conclude that the large‐scale solar dipolar field is more important. We have carried out two studies that bear on these apparently conflicting views. We first studied geomagnetic events temporally associated with the eruption of 18 individual coronal X‐ray sigmoids, which occurred while the large‐scale solar dipolar magnetic field pointed southward. We found that if a coronal flux rope model is used to interpret magnetic structure, eruptions with a southward leading magnetic field are associated with stronger geomagnetic storms, but those with a northward leading field are associated with more storms. We next studied three full magnetic cycles, solar cycles 17–22. We examined the temporal variation of the ratio of the geomagnetic Ap index to the sunspot number. We found no statistically compelling fluctuations of this quantity on solar cycle timescales that are in phase with the reversal of active region polarities. On the other hand, we found a weak tendency for fluctuations that are in phase with the reversal of the large‐scale solar dipole field. From these two studies we infer that the magnetic structure of individual active regions plays a role in geomagnetic events, but their geoeffectiveness is complicated by asymmetries in the leading and following magnetic field and density. We conclude that simple cycle‐dependent generalizations have only statistical significance, and cannot dependably be used to predict the geomagnetic effects of a given solar eruption.

Multispacecraft modeling of the flux rope structure of interplanetary coronal mass ejections: Cylindrically symmetric versus nonsymmetric topologies

Data taken shortly after the launch of the Pioneer Venus spacecraft (PVO) has allowed us to compare an interplanetary coronal mass ejection (ICME) event observed nearly simultaneously on August 27, 1978, by the PVO and ISEE 3 spacecraft. During this period the spacecraft are in close proximity, separated by 0.02 AU radially and 12° (0.21 AU) in azimuth. Both PVO and ISEE 3 observe similar magnetic flux rope signatures within the ICME. Cylindrically symmetric flux rope fits to the observations indicate the handedness of the magnetic flux rope seen at PVO is the same as at ISEE 3, but the peak fields are not. Moreover, symmetric modeling of the magnetic rope observations returns flux rope diameters that are less than the azimuthal separation distance between the spacecraft. Thus, if the cylindrically symmetric model were correct, the two observations could not occur within the same rope, meaning that at least two separate flux ropes would be associated with the same ICME event. The axial orientations of these two ropes differ slightly, with the PVO rope having a clock angle of 238° and a cone angle of 82° and the ISEE 3 rope having a clock angle of 196° and a cone angle of 56° in solar equatorial coordinates. Applying instead a noncylindrically symmetric flux rope model and simultaneously inverting both time series results in a single stretched rope having a cross‐flow diameter of 0.86 AU, ∼4 times its radial thickness, a clock angle of 220°, and a cone angle of 74°. The stretched rope contains ∼50 TWb of magnetic flux, nearly twice the amount given for the cylindrically symmetric fit at PVO and a factor of 5 greater than the symmetric fit at ISEE 3. These values are consistent with the amount of magnetic flux observed in active regions on the Sun. While the individual cylindrically symmetric models adequately fit the single spacecraft data, the stretched rope model provides the simplest explanation of the multipoint observations and is consistent with a CME expanding in azimuthal diameter as it attempts to subtend a constant angle at the Sun of 45° as it convects outward. Although the inversion technique used does not require the field to be force‐free, there are at most only slight deviations from a force‐free configuration within the symmetric ropes and significant plasma forces only at the east and west ends of the nonsymmetric flux rope.