Twisted Flux Tube Research Articles

The emergence of braided magnetic fields

ABSTRACTWe study the emergence of braided magnetic fields from the top of the solar interior through to the corona. It is widely believed that emerging regions smaller than active regions are formed in the upper convection zone near the photosphere. Here, bundles of braided, rather than twisted, magnetic field can be formed, which then rise upward to emerge into the atmosphere. To test this theory, we investigate the behaviour of braided magnetic fields as they emerge into the solar atmosphere. We compare and contrast our models to previous studies of twisted flux tube emergence and discuss results that can be tested observationally. Although this is just an initial study, our results suggest that the underlying magnetic field structure of small emerging regions need not be twisted and that braided field, formed in the convection zone, could suffice.

RESONANT ABSORPTION OF AXISYMMETRIC MODES IN TWISTED MAGNETIC FLUX TUBES

ABSTRACT It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves.

THE NONLINEAR EVOLUTION OF A TWIST IN A MAGNETIC SHOCKTUBE

ABSTRACT The interaction between a small twist and a horizontal chromospheric shocktube is investigated. The magnetic flux tube is modeled using 1.5-D magnetohydrodynamics. The presence of a supersonic yet sub-Alfvénic flow along the flux tube allows the Alfvénic pulse driven at the photospheric boundary to become trapped and amplified between the stationary shock front and photosphere. The amplification of the twist leads to the formation of slow and fast shocks. The pre-existing stationary shock is destabilized and pushed forward as it merges with the slow shock. The propagating fast shock extracts the kinetic energy of the flow and launches rapid twists of 10–15 km s−1 upon each reflection. A cavity is formed between the slow and fast shocks where the flux tube becomes globally twisted within less than an hour. The resultant highly twisted magnetic flux tube is similar to those prone to kink instabilities, which may be responsible for solar eruptions. The generated torsional flux is calculated.

3D magnetic field configuration of small-scale reconnection events in the solar plasma atmosphere

The outer solar atmosphere, i.e., the corona and the chromosphere, is replete with small energy-release events, which are accompanied by transient brightening and jet-like ejections. These events are considered to be magnetic reconnection events in the solar plasma, and their dynamics have been studied using recent advanced observations from the Hinode spacecraft and other observatories in space and on the ground. These events occur at different locations in the solar atmosphere and vary in their morphology and amount of the released energy. The magnetic field configurations of these reconnection events are inferred based on observations of magnetic fields at the photospheric level. Observations suggest that these magnetic configurations can be classified into two groups. In the first group, two anti-parallel magnetic fields reconnect to each other, yielding a 2D emerging flux configuration. In the second group, helical or twisted magnetic flux tubes are parallel or at a relative angle to each other. Reconnection can occur only between anti-parallel components of the magnetic flux tubes and may be referred to as component reconnection. The latter configuration type may be more important for the larger class of small-scale reconnection events. The two types of magnetic configurations can be compared to counter-helicity and co-helicity configurations, respectively, in laboratory plasma collision experiments.

AXISYMMETRIC MODES IN MAGNETIC FLUX TUBES WITH INTERNAL AND EXTERNAL MAGNETIC TWIST

Observations suggest that twisted magnetic flux tubes are ubiquitous in the Sun's atmosphere. The main aim of this work is to advance the study of axisymmetric modes of magnetic flux tubes by modeling both twisted internal and external magnetic field, when the magnetic twist is weak. In this work, we solve the derived wave equations numerically assuming twist outside the tube is inversely proportional to the distance from its boundary. We also study the case of constant magnetic twist outside the tube and solve these equations analytically. We show that the solution for a constant twist outside the tube is a good approximation to the case where the magnetic twist is proportional to $1/r$, namely the error is in all cases less than $5.4\%$.The solution is in excellent agreement with solutions to simpler models of twisted magnetic flux tubes, i.e. without external magnetic twist. It is shown that axisymmetric Alfv\'{e}n waves are naturally coupled with magnetic twist as the azimuthal component of the velocity perturbation is nonzero. We compared our theoretical results with observations and comment on what the Doppler signature of these modes is expected to be. Lastly, we argue that the character of axisymmetric waves in twisted magnetic flux tubes can lead to false positives in identifying observations with axisymmetric Alfv\'{e}n waves.

A Numerical Model of MHD Waves in a 3D Twisted Solar Flux Tube

We generalize our analytical and numerical models of the solar flux tube on twisted magnetic-field lines. The basic equations and numerical methods have much in common with those of Murawski et al. (Astron. Astrophys. 577, A126, 2015); the new and important issue is the twisted magnetic-field component that couples explored torsional Alfven and magnetoacoustic waves. In these models we specify a magnetic-flux function and derive general analytical formulas for the equilibrium mass density and a gas pressure. We use the developed models, which can be adopted for any axisymmetric structure with twisted and untwisted magnetic lines, to simulate the MHD waves. These waves are excited by a localized pulse in the azimuthal velocity component that is launched at the top of the solar photosphere. Their propagation through the solar chromosphere and transition region to the solar corona reveals a complex scenario of twisted magnetic-field lines and flows associated with torsional Alfven and magnetoacoustic waves.

Physical role of topological constraints in localized magnetic relaxation

Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical plasmas such as the Sun's corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here, we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, whereas for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region.

Kelvin–Helmholtz instability in solar cool surges

We study the conditions for onset of Kelvin–Helmholtz (KH) instability in a cool solar surge observed in NOAA AR 8227 on 1998 May 30. The jet with speeds in the range of 45–50kms−1, width of 7Mm, and electron number density of 3.83×1010cm−3 is assumed to be confined in a twisted magnetic flux tube embedded in a magnetic field of 7G. The temperature of the plasma flow is of the order of 105K while that of its environment is taken to be 2×106K. The electron number density of surrounding magnetized plasma has a typical value for the TR/lower corona region of 2×109cm−3. Under these conditions, the Alfvén speed inside the jet is equal to 78.3kms−1. We model the surge as a moving magnetic flux tube for two magnetic field configurations: (i) a twisted tube surrounded by plasma with homogeneous background magnetic field, and (ii) a twisted tube which environment is plasma with also twisted magnetic field. The magnetic field twist in given region is characterized by the ratio of azimuthal to the axial magnetic field components evaluated at the flux tube radius. The numerical studies of appropriate dispersion relations of MHD modes supported by the plasma flow in both magnetic field configurations show that the Kelvin–Helmholtz instability can only occur for MHD waves propagating in axial direction, but with high negative azimuthal mode numbers, and the instability occurs at sub-Alfvénic critical flow velocities in the range of 24–60kms−1.

Magnetohydrostatics of a vertical flux tube in the solar atmosphere: Coronal loops, a model of a ring flare filament

The magnetohydrostatic theory of a twisted magnetic flux tube (rope) immersed in a realistic solar atmosphere is presented in a closed analytical form for the first time. General formulas that allow the equilibrium plasma density, pressure, and temperature distributions inside an axisymmetric vertical flux tube to be calculated from its magnetic structure, which is assumed to be known (fixed), have been derived. An analytical model of the external hydrostatic medium free of a magnetic field, the solar atmosphere, where the temperature profile of the semi-empirical tabulated Avrett-Loeser model is used, has been constructed. The distribution of plasma parameters in a twisted magnetic flux tube at small deviations of its internal magnetic structure from the force-free one has been calculated as an example of applying the general theoretical formulas. Since the tube cross section does not change with height, the constructed model can be applied to describe the vertical parts of coronal loops. It has been found that the plasma density in the magnetic flux tube rises when the field twisting exceeds the force-free level and falls with decreasing field twisting compared to the force-free level. This property of a twisted magnetic flux tube is of fundamental importance for justifying the mechanism of flare energy release in magnetic flux ropes. A model of a flare in a ring chromospheric configuration is considered.

Kelvin-Helmholtz instability in coronal mass ejecta in the lower corona

We model an imaged Kelvin-Helmholtz (KH) instability on a coronal mass ejecta (CME) in the lower corona by investigating conditions under which kink ($m = 1$) and $m = -3$ magnetohydrodynamic (MHD) modes in an uniformly twisted flux tube moving along its axis become unstable. We employ the dispersion relations of MHD modes derived from the linearised magnetohydrodynamic equations. We assume real wave numbers and complex angular wave frequencies, namely complex wave phase velocities. The dispersion relations are solved numerically at fixed input parameters (taken from observational data) and various mass flow velocities. It is shown that the stability of the modes depends upon four parameters, the density contrast between the flux tube and its environment, the ratio of the background magnetic fields in the two media, the twist of the magnetic field lines inside the tube, and the value of the Alfv\'en Mach number (the ratio of the tube velocity to Alfv\'en speed inside the flux tube). For a twisted magnetic flux tube at a density contrast of $0.88$, background magnetic field ratio of $1.58$, and a normalised magnetic field twist of $0.2$, the critical speed for the kink ($m = -3$) mode (where $m$ is the azimuthal mode number) is $678$ km\,s$^{-1}$ just as it is observed. The growth rate for this harmonic at KH wavelength of $18.5$ Mm and ejecta width of $4.1$ Mm is equal to $0.037$ s$^{-1}$, in agreement with observations. KH instability of the $m = -3$ mode may also explain why the KH vortices are seen only at the one side of arising CME. The good agreement between observational and computational data shows that the imaged KH instability on CME can be explained in terms of emerging KH instability of the $m = -3$ MHD mode in twisted magnetic flux tube moving along its axis.

Evidence of Twisted Flux-Tube Emergence in Active Regions

Elongated magnetic polarities are observed during the emergence phase of bipolar active regions (ARs). These extended features, called magnetic tongues, are interpreted as a consequence of the azimuthal component of the magnetic flux in the toroidal flux-tubes that form ARs. We develop a new systematic and user-independent method to identify AR tongues. Our method is based on determining and analyzing the evolution of the AR main polarity inversion line (PIL). The effect of the tongues is quantified by measuring the acute angle [τ] between the orientation of the PIL and the direction orthogonal to the AR main bipolar axis. We apply a simple model to simulate the emergence of a bipolar AR. This model lets us interpret the effect of magnetic tongues on parameters that characterize ARs (e.g. the PIL inclination and the tilt angles, and their evolution). In this idealized kinematic emergence model, τ is a monotonically increasing function of the twist and has the same sign as the magnetic helicity. We systematically apply our procedure to a set of bipolar ARs (41 ARs) that were observed emerging in line-of-sight magnetograms over eight years. For most of the cases studied, the tongues only have a small influence on the AR tilt angle since tongues have a much lower magnetic flux than the more concentrated main polarities. From the observed evolution of τ, corrected for the temporal evolution of the tilt angle and its final value when the AR is fully emerged, we estimate the average number of turns in the subphotospherically emerging flux-rope. These values for the 41 observed ARs are below unity, except for one. This indicates that subphotospheric flux-ropes typically have a low amount of twist, i.e. highly twisted flux-tubes are rare. Our results demonstrate that the evolution of the PIL is a robust indicator of the presence of tongues and constrains the amount of twist in emerging flux-tubes.

The evolution of writhe in kink-unstable flux ropes and erupting filaments

The helical kink instability of a twisted magnetic flux tube has been suggested as a trigger mechanism for solar filament eruptions and coronal mass ejections (CMEs). In order to investigate if estimations of the pre-emptive twist can be obtained from observations of writhe in such events, we quantitatively analyze the conversion of twist into writhe in the course of the instability, using numerical simulations. We consider the line tied, cylindrically symmetric Gold–Hoyle flux rope model and measure the writhe using the formulae by Berger and Prior which express the quantity as a single integral in space. We find that the amount of twist converted into writhe does not simply scale with the initial flux rope twist, but depends mainly on the growth rates of the instability eigenmodes of higher longitudinal order than the basic mode. The saturation levels of the writhe, as well as the shapes of the kinked flux ropes, are very similar for considerable ranges of initial flux rope twists, which essentially precludes estimations of pre-eruptive twist from measurements of writhe. However, our simulations suggest an upper twist limit of ∼6π for the majority of filaments prior to their eruption.

RECURRENT EXPLOSIVE ERUPTIONS AND THE “SIGMOID-TO-ARCADE” TRANSFORMATION IN THE SUN DRIVEN BY DYNAMICAL MAGNETIC FLUX EMERGENCE

We report on three-dimensional (3D) MHD simulations of recurrent mini CME-like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions are developed as a result of repeated formation and expulsion of new flux ropes due to continous emergence and reconnection of sheared fieldlines along the polarity inversion line (PIL) of the AR. The acceleration of the eruptions is triggered by tether-cutting reconnection at the current sheet underneath the erupting field. We find that each explosive eruption is followed by reformation of a sigmoidal structure and a subsequent sigmoid-to-flare arcade transformation in the AR. These results might have implications for recurrent CMEs and eruptive sigmoids/flares observations and theoretical studies.

Kelvin-Helmholtz instability of twisted magnetic flux tubes in the solar wind

Solar wind plasma is supposed to be structured in magnetic flux tubes carried from the solar surface. Tangential velocity discontinuity near the boundaries of individual tubes may result in Kelvin-Helmholtz instability, which may contribute into the solar wind turbulence. While the axial magnetic field may stabilize the instability, a small twist in the magnetic field may allow to sub-Alfvenic motions to be unstable. We aim to study the Kelvin-Helmholtz instability of twisted magnetic flux tube in the solar wind with different configurations of external magnetic field. We use magnetohydrodynamic equations in the cylindrical geometry and derive the dispersion equations governing the dynamics of twisted magnetic flux tube moving along its axis in the cases of untwisted and twisted external fields. Then we solve the dispersion equations analytically and numerically and found thresholds for Kelvin-Helmholtz instability in both cases of external field. Both analytical and numerical solutions show that the Kelvin-Helmholtz instability is suppressed in the twisted tube by external axial magnetic field for sub-Alfvenic motions. However, even small twist in the external magnetic field allows the Kelvin-Helmholtz instability to be developed for any sub-Alfvenic motions. The unstable harmonics correspond to vortices with high azimuthal mode numbers, which are carried by the flow. Twisted magnetic flux tubes can be unstable to Kelvin-Helmholtz instability when they move with small speed relative to main solar wind stream, then the Kelvin-Helmholtz vortices may significantly contribute into the solar wind turbulence.

On magnetic reconnection and flux rope topology in solar flux emergence

We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic (MHD) solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection (CME), we discuss the implications of our findings for solar eruptions.

Sub-photosphere to Solar Atmosphere Connection

Magnetic fields extend from the solar interior through the atmosphere. The formation and evolution of active regions can be studied by measuring subsurface flows with local helioseismology. The emergence of magnetic flux from the solar convection zone is associated with acoustic perturbation signatures. In near-surface layers, the average dynamics can be determined for emerging regions. MHD simulations of the emergence of a twisted flux tube show how magnetic twist and free energy are transported from the interior into the corona and the dynamic signatures associated with such transport in the photospheric and sub-photospheric layers. The subsurface twisted flux tube does not emerge into the corona as a whole in emerging active regions. Shear flows at the polarity inversion line and coherent vortical motions in the subsurface flux tubes are the major means by which twist is transported into the corona, leading to the formation of sigmoid-shaped coronal magnetic fields capable of driving solar eruptions. The transport of twist can be followed from the interior by using the kinetic helicity of subsurface flows as a proxy of magnetic helicity; this quantity holds great promise for improving the understanding of eruptive phenomena. Waves are not only vital for studying the link between the solar interior and the surface but for linking the photosphere with the corona as well. Acoustic waves that propagate from the surface into the magnetically structured, dynamic atmosphere undergo mode conversion and refraction. These effects enable atmospheric seismology to determine the topography of magnetic canopies in the solar atmosphere. Inclined magnetic fields lower the cut-off frequency so that low frequency waves can leak into the outer atmosphere. Recent high resolution, high cadence observations of waves and oscillations in the solar atmosphere, have lead to a renewed interest in the potential role of waves as a heating mechanism. In light of their potential contribution to the heating of the solar atmosphere, some of the recent observations of waves and oscillations and ongoing modelling efforts are reviewed.

STABILITY AND DYNAMICS OF A FLUX ROPE FORMED VIA FLUX EMERGENCE INTO THE SOLAR ATMOSPHERE

We study the stability and dynamics of a flux rope formed through the emergence of a twisted magnetic flux tube into the solar atmosphere. A three-dimensional magnetohydrodynamic simulation has been performed to investigate several key factors affecting the dynamics of the flux rope. The stability of the flux rope is examined by deriving the decay index of the coronal magnetic field surrounding the flux rope. We investigate a transition between the quasi-static and dynamic states of the flux rope through an analysis of the curvature and scale height of emerging magnetic field. A practical application of this analysis for global eruptions is also considered.

κH-Mechanism of a Solar Eruption Produced Self-Consistently by Flux Emergence

Abstract We report on a new magnetohydrodynamic simulation for the sequence evolution of a magnetic field from emergence to eruption on the Sun. The magnetic field in the shape of a twisted flux tube emerging below the solar surface forms a pre-eruptive structure in the corona, which is composed of expanding envelop flux and a quasi-static inner core called flux rope; this inner core eventually seems to erupt. The evolution proceeds self-consistently; that is, any preexisting coronal magnetic field that causes additional side effects on the evolution of the emerging magnetic field is not assumed. This highlights a possible eruption mechanism inherent in the dynamic nature of the emerging magnetic field. The mechanism is characterized by two key quantities: the curvature ($ \kappa$ ) and the scale height ($ H$ ) of the emerging magnetic field.

Space Weather: from Solar Eruptions to Magnetospheric Storms

Space weather can be defined as a topic dealing with the variable conditions in the Sun, solar wind, magnetosphere and ionosphere that may be hazardous to man-made systems in space and on ground and endanger human health and life. This definition has a strongly application-oriented flavor. Positive consequences of space weather activities during the last 10-15 years have been increasing dialogues between various fields of solar-terrestrial physics and between the science and technology communities. At the same time expectations of increased funding have contributed to opportunism and promises of useful space weather services that have not always been based on sound physical understanding. If we have sufficient in situ and remote observations, we can make useful specifications of the environmental conditions practically in real time. However, forecasting is difficult, in particular if we want to forecast the conditions at the Earth based on solar observations. As space weather involves a wide range of scientific topics from solar eruptions to current induction in conductors buried in ground, the space weather community comprises scientists with very different backgrounds. Some are specialists in interaction of solar wind shocks with the Earth's magnetopause but ignorant of how the Sun drives the shock. Others may know all details of twisted flux tubes on the Sun but think that the magnetospheric response may be characterized by one single parameter. This tutorial review aims at advancing the understanding of space weather as an integrated system, from its origins in the Sun, to the near-Earth environment.

Solar filament eruptions and their physical role in triggering coronal mass ejections

Solar filament eruptions play a crucial role in triggering coronal mass ejections (CMEs). More than 80% of eruptions lead to a CME. This correlation has been studied extensively during the past solar cycles and the last long solar minimum. The statistics made on events occurring during the rising phase of the new solar cycle 24 is in agreement with this finding. Both filaments and CMEs have been related to twisted magnetic fields. Therefore, nearly all the MHD CME models include a twisted flux tube, called a flux rope. Either the flux rope is present long before the eruption, or it is built up by reconnection of a sheared arcade from the beginning of the eruption.In order to initiate eruptions, different mechanisms have been proposed: new emergence of flux, and/or dispersion of the external magnetic field, and/or reconnection of field lines below or above the flux rope. These mechanisms reduce the downward magnetic tension and favor the rise of the flux rope. Another mechanism is the kink instability when the configuration is twisted too much. In this paper we open a forum of discussions revisiting observational and theoretical papers to understand which mechanisms trigger the eruption. We conclude that all the above quoted mechanisms could bring the flux rope to an unstable state. However, the most efficient mechanism for CMEs is the loss-of-equilibrium or torus instability, when the flux rope has reached an unstable threshold determined by a decay index of the external magnetic field.