Twisted Flux Tube Research Articles

Solar prominences

AbstractSolar filaments (or prominences) are magnetic structures in the corona. They can be represented by twisted flux ropes in a bipolar magnetic environment. In such models, the dipped field lines of the flux rope carry the filament material and parasitic polarities in the filament channel are responsible for the existence of the lateral feet of prominences.Very simple laws do exist for the chirality of filaments, the so-called “filament chirality rules”: commonly dextral/sinistral filaments corresponding to left- (resp. right) hand magnetic twists are in the North/South hemisphere. Combining these rules with 3D weakly twisted flux tube models, the sign of the magnetic helicity in several filaments were identified. These rules were also applied to the 180° disambiguation of the direction of the photospheric transverse magnetic field around filaments using THEMIS vector magnetograph data (López Aristeet al. 2006). Consequently, an unprecedented evidence of horizontal magnetic support in filament feet has been observed, as predicted by former magnetostatic and recent MHD models.The second part of this review concerns the role of emerging flux in the vicinity of filament channels. It has been suggested that magnetic reconnection between the emerging flux and the pre-existing coronal field can trigger filament eruptions and CMEs. For a particular event, observed with Hinode/XRT, we observe signatures of such a reconnection, but no eruption of the filament. We present a 3D numerical simulation of emerging flux in the vicinity of a flux rope which was performed to reproduce this event and we briefly discuss, based on the simulation results, why the filament did not erupt.

Twisted Flux Tube Emergence From the Convection Zone to the Corona

Three-dimensional numerical simulations of a horizontal magnetic flux tube emergence with different twist are carried out in a computational domain spanning the upper layers of the convection zone to the lower corona. We use the Oslo Stagger Code to solve the full MHD equations with non-gray, non-LTE radiative transfer and thermal conduction along the magnetic lines. A magnetic flux tube is input at the bottom boundary into a weakly magnetized atmosphere. The photospheric and chromospheric response is described with magnetograms and synthetic continuum as well as Ca II H line images and velocity field distributions. In the photosphere the granular size increases when the flux tube approaches from below, as has been reported previously in the literature. In the convective overshoot region, some 200 km above the photosphere, adiabatic expansion produces cooling, darker regions with the structure of granulation cells. We also find evidence of collapsed granulation at the boundaries of the rising flux tube. Once the flux tube has crossed the photosphere, bright points related to concentrated magnetic field, vorticity, high vertical velocities, and heating by compressed material are found at heights up to 500 km above the photosphere. At greater heights, in the magnetized chromosphere, the rising flux tube produces a large, cool, magnetized bubble that tends to expel the usual chromospheric oscillations. In addition, the rising flux tube dramatically increases the chromospheric scale height, pushing the transition region and corona aside, such that the chromosphere extends up to 6 Mm above the photosphere. We find flux tube emergence through the photosphere to the lower corona to be a relatively slow process, taking of order 1 hr.

The Three‐dimensional Evolution of Buoyant Magnetic Flux Tubes in a Model Solar Convective Envelope

We present a set of three-dimensional spherical shell anelastic MHD simulations of the buoyant rise of magnetic flux tubes from the base of the convection zone to a depth of 16 Mm below the photosphere. It is found that when a twisted flux tube arches upward due to buoyancy, it rotates out of the plane and thus produces a tilt at the apex. Our simulations show that for tubes with the twist rate that is necessary for a cohesive rise, the twist-induced tilt dominates that caused by the Coriolis force, and furthermore, the twist-induced tilt is of the wrong direction (opposite to the observational Joy's law) if the twist is left-handed (right-handed) in the northern (southern) hemisphere, following the observed hemispheric preference of the sign of the active region twist. It is found that in order for the emerging tube to show the correct tilt direction (consistent with observations), the initial twist rate of the flux tube needs to be less than half of that needed for a cohesive rise. Under such conditions, severe flux loss is found during the rise. We also found that due to the asymmetric stretching of the rising tube by the Coriolis force, a field strength asymmetry develops, with the field in the leading leg (leading in the direction of rotation) of the Ω-shaped emerging tube being stronger than the field in the following leg, which results in a more compact morphology in the leading polarity of the emerging active region.

On non-axisymmetric magnetic equilibria in stars

In previous work, stable approximately axisymmetric equilibrium configurations for magnetic stars were found by numerical simulation. Here, I investigate the conditions under which more complex, non-axisymmetric configurations can form. I present numerical simulations of the formation of stable equilibria from turbulent initial conditions and demonstrate the existence of non-axisymmetric equilibria consisting of twisted flux tubes lying horizontally below the surface of the star, meandering around the star in random patterns. Whether such a non-axisymmetric equilibrium or a simple axisymmetric equilibrium forms depends on the radial profile of the strength of the initial magnetic field. The results could explain observations of non-dipolar fields on stars such as the B0.2 main-sequence star τ Sco or the pulsar 1E 1207.4-5209. The secular evolution of these equilibria due to Ohmic and buoyancy processes is also examined.

A Flux Emergence Model for Solar Eruptions

We have simulated the 3D emergence and interaction of two twisted flux tubes, which rise from the interior into the outer atmosphere of the Sun. We present evidence for the multiple formation and eruption of flux ropes inside the emerging flux systems and hot arcade-like structures in between them. Their formation is due to internal reconnection, occurring between oppositely directed, highly stretched and sheared fieldlines at photospheric heights. Most of the eruptions escape into the corona, but some are confined and fade away without leaving the low atmosphere. As these flux ropes erupt, new reconnected fieldlines accumulate around the main axis of the initial magnetic flux systems. We also show the complex 3D fieldline geometry and the structure of the multiple current sheets, which form as a result of the reconnection between the emerging flux systems.

A Possible Structure of the Magnetic Field in Solar Filaments Obtained by Flux Emergence

Abstract We report a result, that the emergence of a subsurface magnetic field naturally reproduces the feature of the global magnetic configuration observed in solar filaments. This was obtained by performing a three-dimensional simulation of a twisted flux tube that emerges in the shape of a multi-$\Omega$-loop in a highly stratified solar atmosphere, extending from the subsurface layer to the corona. One of the key findings is that a kinking of the twisted flux tube occurs at the site of a linkage between adjacent $\Omega$-loops. This develops a magnetic structure that has remarkable similarities to the structure of a filament, in that the inner part of the twisted flux tube can be applied to the main body of a filament, while the outer part is reminiscent of observations of filament feet and a coronal arcade overlying the main body of a filament. Based on the result, we concluded that the orientation of filaments observed on the Sun may have its origin in the handedness of a twisted magnetic field below the solar surface.

Emerging flux tubes from the solar interior into the atmosphere: effects of non-constant twist

Context. Observations of large-scale solar emergence events indicate that the magnetic field is already twisted prior to its emergence. However, the nature of twist of the pre-emergence field is largely unknown. Aims. By testing two different twist profiles for subsurface magnetic flux tubes, we aim to identify any differences in the emergence process of the field and its atmospheric signatures that occur as a result of the twist. Given that differences do occur, future comparisons of these emergence results with observations should reveal specific properties of the twist of the subsurface magnetic field. Methods. Using a 3D numerical MHD code, we consider a simple stratified model, comprising of one solar interior layer and three overlying atmospheric layers. We set a horizontal, twisted flux tube in the lowest layer and prescribe the central protion along the tube’s length to be buoyant so that it will rise towards the surface. We test two different non-constant twist profiles for the tube and perform a parameter study for each profile, looking for differences and similarities during the rise, emergence and expansion stages of the tube’s evolution. Results. We find that, irrespective of the tube’s twist profile, if the tube initially has a low tension force then it will experience greater expansion and consequential weakening of its field strength during the rise through the solar interior. Thus, upon reaching the solar surface it will fail to undergo a magnetic buoyancy instability and will not emerge into the atmosphere. For those tubes that do emerge into the atmosphere, there is little distinction between the atmospheric field and few indicators as to the initial twist profile of the tube. In general, tubes with stronger tension forces have a faster growth rate of the magnetic buoyancy instability, while tubes with weaker tension forces expand to a greater degree in the horizontal direction post-emergence. Synthesised magnetograms at the solar surface do vary between the two tested twist profiles but only in cases with initially low tension forces. Conclusions. Upon emergence, it appears that most of the specific details of the tube’s initial twist are lost. The field must initially be sufficiently twisted such that it is able to undergo a magnetic buoyancy instability but such a level of twist subsequently results in the emerging flux having generic atmospheric characteristics. Only in cases with an initially low tension force is it possible to make some distiction post-emergence by considering magnetograms at the solar surface.

A New Model for Propagating Parts of EIT Waves: A Current Shell in a CME

EIT waves are observed in EUV as bright fronts. Some of these bright fronts propagate across the solar disk. EIT waves are all associated with a flare and a CME and are commonly interpreted as fast-mode magnetosonic waves. Propagating EIT waves could also be the direct signature of the gradual opening of magnetic field lines during a CME. We quantitatively addressed this alternative interpretation. Using two independent 3D MHD codes, we performed nondimensional numerical simulations of a slowly rotating magnetic bipole, which progressively result in the formation of a twisted magnetic flux tube and its fast expansion, as during a CME. We analyse the origins, the development, and the observability in EUV of the narrow electric currents sheets that appear in the simulations. Both codes give similar results, which we confront with two well-known SOHO/EIT observations of propagating EIT waves (7 April and 12 May 1997), by scaling the vertical magnetic field components of the simulated bipole to the line of sight magnetic field observed by SOHO/MDI and the sign of helicity to the orientation of the soft X-ray sigmoids observed by Yohkoh/SXT. A large-scale and narrow current shell appears around the twisted flux tube in the dynamic phase of its expansion. This current shell is formed by the return currents of the system, which separate the twisted flux tube from the surrounding fields. It intensifies as the flux tube accelerates and it is co-spatial with weak plasma compression. The current density integrated over the altitude has the shape of an ellipse, which expands and rotates when viewed from above, reproducing the generic properties of propagating EIT waves. The timing, orientation, and location of bright and faint patches observed in the two EIT waves are remarkably well reproduced. We conjecture that propagating EIT waves are the observational signature of Joule heating in electric current shells, which separate expanding flux tubes from their surrounding fields during CMEs or plasma compression inside this current shell. We also conjecture that the bright edges of halo CMEs show the plasma compression in these current shells.

Linear MHD Sausage Waves in Compressible Magnetically Twisted Flux Tubes

Oscillations of magnetic flux tubes are of great importance as they contain infor- mation about the geometry and fine structure of the flux tubes. Here we derive and analyt- ically solve in terms of Kummer's functions the linear governing equations of wave propa- gation for sausage surface and body modes (m = 0) of a magnetically twisted compressible flux tube embedded in a compressible uniformly magnetized plasma environment in cylin- drical geometry. A general dispersion relation is obtained for such flux tubes. Numerical solutions for the phase velocity are obtained for a wide range of wavenumbers and for vary- ing magnetic twist. The effect of magnetic twist on the period of oscillations of sausage surface modes for different values of the wavenumber and vertical magnetic field strength is calculated for representative photospheric and coronal conditions. These results generalize and extend previous studies of MHD waves obtained for incompressible or for compressible but nontwisted flux tubes. It is found that magnetic twist may change the period of sausage surface waves of the order of a few percent when compared to counterparts in straight non- twisted flux tubes. This information will be most relevant when high-resolution observations are used for diagnostic exploration of MHD wave guides in analogy to solar-interior studies by means of global eigenoscillations in helioseismology.

Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds

Two new analytical solutions of the self-induction equation in Riemannian manifolds are presented. The first represents a twisted magnetic flux tube or flux rope in plasma astrophysics, where the rotation of the flow implies that the poloidal field is amplified from toroidal field, in the spirit of dynamo theory. The value of the amplification depends on the Frenet torsion of the magnetic axis of the tube. Actually this result illustrates the Zeldovich stretch, twist, and fold method to generate dynamos from straight and untwisted ropes. Based on the fact that this problem was previously handled, using a Riemannian geometry of twisted magnetic flux ropes [Phys Plasmas 13, 022309 (2006)], investigation of a second dynamo solution, conformally related to the Arnold kinematic fast dynamo, is obtained. In this solution, it is shown that the conformal effect on the fast dynamo metric enhances the Zeldovich stretch, and therefore a new dynamo solution is obtained. When a conformal mapping is performed in an Arnold fast dynamo line element, a uniform stretch is obtained in the original line element.

The Effect of the Relative Orientation between the Coronal Field and New Emerging Flux. I. Global Properties

The emergence of magnetic flux from the convection zone into the corona is an important process for the dynamical evolution of the coronal magnetic field. In this paper we extend our previous numerical investigations, by looking at the process of flux interaction as an initially twisted flux tube emerges into a plane parallel, coronal magnetic field. Significant differences are found in the dynamical appearance and evolution of the emergence process depending on the relative orientation between the rising flux system and any preexisting coronal field. When the flux systems are nearly anti-parallel, the experiments show substantial reconnection and demonstrate clear signatures of a high temperature plasma located in the high velocity outflow regions extending from the reconnection region. However, the cases that have a more parallel orientation of the flux systems show very limited reconnection and none of the associated features. Despite the very different amount of reconnection between the two flux systems, it is found that the emerging flux that is still connected to the original tube, reaches the same height as a function of time. As a compensation for the loss of tube flux, a clear difference is found in the extent of the emerging loop in the direction perpendicular to the main axis of the initial flux tube. Increasing amounts of magnetic reconnection decrease the volume, which confines the remaining tube flux.

Twist transport in strongly torsioned astrophysical flux tubes

Riemannian geometrical effects on the expansion of the electron magnetohydrodynamical (EMH) superconductivity modeled twisted nonplanar thin magnetic flux tubes are considered. A solution is found which represents almost incompressible plasma flows, where the twist of flux tube is computed in terms of the continuous variation of its cross-section. It is shown that the twist increases in regions where twisted flux tube expands as in Parker’s conjecture. From computation of compression along the tube we show that when the torsion is weak a centrifugal or vorticity effect on the longitudinal direction of the tube enhances the screening effect on the “superconductor”. Throughout the paper we consider helical flux tubes where torsion and curvature of the tube are constants. Thus we show that the Parker’s conjecture is valid in a continuos manner for these type II superconducting twisted flux tubes. Throughout the paper we adopt the approximation that the radial component of the magnetic field varies so slowly along the tube axis that it can be approximated to zero along the tube. It is suggested that the models discussed here may also be applied to DNA and nanotubes.

Emergence and interaction of twisted flux tubes in the Sun

Aims. We present results from numerical simulations that study the interaction of a pair of twisted, buoyant magnetic flux tubes, which rise from the solar interior into the outer atmosphere of the Sun. The aim of our new model is to reproduce some of the dynamic solar phenomena in a self-consistent manner. Methods. We perform non-linear simulations in 2.5D numerical experiments by solving the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Lare2D). For some aspects of the problem, we consider the evolution of the system using both uniform and locally enhanced resistivity. Results. The two flux tubes start to rise at the same time but from a different height below the photosphere. The leading (first) tube, which is originally located nearer to the surface, rises and eventually expands above the photosphere forming a magnetized atmosphere for the upcoming system (second tube). Current sheets, high-velocity reconnection jets, plasmoids, loop brightnenings and arcade flare-like structures are formed, for the first time in such numerical experiments, self-consistently by the emergence, expansion and the dynamical interaction between the two emerging flux systems.

A Multiple Flare Scenario where the Classic Long-Duration Flare Was Not the Source of a CME

A series of flares (GOES class M, M and C) and a CME were observed in close succession on 20 January 2004 in NOAA 10540. Radio observations, which took the form of types II, III and N bursts, were associated with these events. We use the combined observations from TRACE, EIT, Hα images from Kwasan, MDI magnetograms and GOES to understand the complex development of this event. Contrary to a standard interpretation, we conclude that the first two impulsive flares are part of the CME launch process while the following long-duration event flare represents simply the recovery phase. Observations show that the flare ribbons not only separate but also shift along the magnetic inversion line so that magnetic reconnection progresses stepwise to neighboring flux tubes. We conclude that “tether cutting” reconnection in the sheared arcade progressively transforms it to a twisted flux tube, which becomes unstable, leading to a CME. We interpret the third flare, a long-duration event, as a combination of the classical two-ribbon flare with the relaxation process following forced reconnection between the expanding CME structure and neighboring magnetic fields.

Resolution of the 180o Ambiguity for Inverse Horizontal Magnetic Field Configurations

A well-known problem in solar physics is that solutions for the transverse magnetic direction are ambiguous with respect to a 180° reversal in the direction. In this paper we focus on three methods for the removal of the 180° ambiguity applied to three MHD models. These methods are (1) the reference method, (2) the method of magnetic pressure gradient, and (3) the magnetic divergence-free method. All three methods are noniterative, and methods 2 and 3 are analytical and fast. We apply these methods to three MHD equilibrium model fields: (1) an analytical solution of a nonlinear force-free magnetic equilibrium from Low, (2) a simulation of an emerging twisted flux tube from Fan & Gibson, and (3) a pre-eruptive twisted magnetic flux rope equilibrium reached by relaxation from Amari et al. We measure the success of methods within horizontal field regions in the boundary, which are mathematically defined by B⊥ ∇⊥Bz > 0. When such regions overlap with the magnetic neutral lines, they are known as bald patches (BPs) or inverse topology. Our most important conclusion is that the magnetic divergence-free method is far more successful than the other two methods within BPs. This method requires a second level of measurements of the vertical magnetic field. As high-quality multilevel magnetograms will come online in the near future, our work shows that multilayer magnetic measurements will be highly desirable to objectively and successfully tackle the 180° ambiguity problem.

Dynamic and Topological Features of Photospheric and Coronal Activities Produced by Flux Emergence in the Sun

We study the emergence of magnetic fields in the solar atmosphere with a focus on photospheric and coronal activities produced by flux emergence. These activities are examined using a three-dimensional MHD simulation of an emerging flux tube. The simulation has been performed for a highly twisted flux tube (highly twisted case) and a weakly twisted one (weakly twisted case). The emerging flux tube globally forms a bipolar region associated with a flow in the photosphere. We decompose the flow into several fundamental flow components, such as rotation, expansion/contraction, and distortion. The analysis shows that as the emerging field becomes vertical, a torsional flow appears in a polarity region with intense flux, and the polarity region apparently rotates opposite to the torsional flow. We also find that the evolution of the photospheric neutral line in the highly twisted case is different from that in the weakly twisted case. We then study the coronal structure of an emerging field by focusing on the distribution of current density at the chromospheric footpoint of emerging field lines. Field lines with high current density at their footpoints display a distinct shape in both highly twisted and weakly twisted cases: the highly twisted flux tube produces the confined, sigmoidal structure of coronal loops, while the expanded loop structure appears in the weakly twisted case. Based on these results we discuss the mechanism for producing several solar phenomena, such as filament channels, flux ropes, and sigmoids.

Coronal prominence structure and dynamics: A magnetic flux rope interpretation

The solar prominence is an example of a space physics phenomenon that can be modeled as a twisted magnetic flux tube or magnetic flux “rope.” In such models the prominence is one observable part of a larger magnetic structure capable of storing magnetic energy to drive eruptions. We show how a flux rope model explains a range of observations of prominences and associated structures such as cavities and soft X‐ray sigmoids and discuss in particular the observational and dynamic consequences of three‐dimensional reconnections in and around the evolving magnetic flux rope. We demonstrate that the flux rope model can describe the prominence's preeruption structure and dynamics, loss of equilibrium, and behavior during and after an eruption in which part of the flux rope is expelled from the corona.

Non-Riemannian geometry of twisted flux tubes

New examples of the theory recently proposed by Ricca [PRA(1991)] on the generalization of Da Rios-Betchov intrinsic equations on curvature and torsion of classical non-Riemannian vortex higher-dimensional string are given. In particular we consider applications to 3-dimesional fluid dynamics, including the case of a twisted flux tube and the fluid rotation. In this case use is made of Da Rios equation to constrain the fluid. Integrals on the Cartan connection are shown to be related to the integrals which represent the total Frenet torsion and total curvature. By analogy with the blue phases twisted tubes in liquid crystals, non-Riemannian geometrical formulation of the twisted flux tube in fluid dynamics is obtained. A theorem by Ricca and Moffatt on invariant integrals for the Frenet curvature is used to place limits on the Cartan integrals. The stationary incompressible flow case is also addressed in the non-Riemannian case where Cartan torsion scalars are shown to correspond to abnormalities of the congruence. Geodesic motion is shown to be torsionless. Vorticity is shown to be expressed in terms of abnormalities of the congruence, which is analogous to the result recenly obtained [Garcia de Andrade,PRD(2004)], where the vorticity of the superfluid plays the role of Cartan contortion vector in the context of analog gravity.

Evolving Photospheric Flux Concentrations and Filament Dynamic Changes

We analyze the role of weak photospheric flux concentrations that evolve in a filament channel, in the triggering of dynamic changes in the shape of a filament. The high polarimetric sensitivity of THEMIS allowed us to detect weak flux concentrations (few Gauss) associated with the filament development. The synoptic instruments (MDI, SOLIS) even if their sensitivity is much less than THEMIS were useful to follow any subsequent strengthening of these flux concentrations after their identification in the THEMIS magnetograms. We found that (1) the northern part of the filament develops an Hα barb at the same time that weak minority polarity elements develop near a plage; (2) a section in the southern part of the Hα filament gradually disappears and later reforms at the same time that several mixed-polarity magnetic elements appear, then subsequently cancel or spread away from each other. These changes correspond to increases in EUV emission, as observed by TRACE, EIT, and CDS. This suggests that the plasma is temporarily heated along the filament spine. An idealized sequence of force-free models of this filament channel, based on plasma-supporting magnetic dips occurring in the windings of a very weakly twisted flux tube, naturally explains the evolution of its southern part as being due to changes in the topology of the coronal magnetic field as the photospheric flux concentrations evolve.

3D simulations identifying the effects of varying the twist and field strength of an emerging flux tube

Aims. We investigate the effects of varying the magnetic field strength and the twist of a flux tube as it rises through the solar interior and emerges into the atmosphere. Methods. Using a 3D numerical MHD code, we consider a simple stratified model, comprising of one solar interior layer and three overlying atmospheric layers. We set a horizontal, twisted flux tube in the lowest layer. The specific balance of forces chosen results in the tube being fully buoyant and the temperature is decreased in the ends of the tube to encourage the formation of an Ω-shape along the tube’s length. We vary the magnetic field strength and twist independently of each other so as to give clear results of the individual effects of each parameter. Results. We find a self-similar evolution in the rise and emergence of the flux tube when the magnetic field strength of the tube is modified. During the rise through the solar interior, the height of the crest and axis, the velocity of the crest and axis, and the decrease in the magnetic field strength of the axis of the tube are directly dependent upon the initial magnetic field strength given to the tube. No such self-similarity is evident when the twist of the flux tube is changed, due to the complex interaction of the tension force on the rise of the tube. For low magnetic field strength and twist values, we find that the tube cannot fully emerge into the atmosphere once it reaches the top of the interior since the buoyancy instability criterion cannot be fulfilled. For those tubes that do advance into the atmosphere, when the magnetic field strength has been modified, we find further self-similar behaviour in the amount of tube flux transported into the atmosphere. For the tubes that do emerge, the variation in the twist results in the buoyancy instability, and subsequent emergence, occurring at different locations along the tube’s length.