Twisted Magnetic Flux Tube Research Articles

Coronal energy release by MHD avalanches

Context. Magnetohydrodynamic (MHD) instabilities, such as the kink instability, can trigger the chaotic fragmentation of a twisted magnetic flux tube into small-scale current sheets that dissipate as aperiodic impulsive heating events. In turn, the instability could propagate as an avalanche to nearby flux tubes and lead to a nanoflare storm. Our previous work was devoted to related 3D MHD numerical modeling, which included a stratified atmosphere from the solar chromosphere to the corona, tapering magnetic field, and solar gravity for curved loops with the thermal structure modelled by plasma thermal conduction, along with optically thin radiation and anomalous resistivity for 50 Mm flux tubes. Aims. Using 3D MHD modeling, this work addresses predictions for the extreme-ultraviolet (EUV) imaging spectroscopy of such structure and evolution of a loop, with an average temperature of 2–2.5 MK in the solar corona. We set a particular focus on the forthcoming MUSE mission, as derived from the 3D MHD modeling. Methods. From the output of the numerical simulations, we synthesized the intensities, Doppler shifts, and non-thermal line broadening in 3 EUV spectral lines in the MUSE passbands: Fe IX 171 Å, Fe XV 284 Å, and Fe XIX 108 Å, emitted by ∼1 MK, ∼2 MK, and ∼10 MK plasma, respectively. These data were detectable by MUSE, according to the MUSE expected pixel size, temporal resolution, and temperature response functions. We provide maps showing different view angles (front and top) and realistic spectra. Finally, we discuss the relevant evolutionary processes from the perspective of possible observations. Reults. We find that the MUSE observations might be able to detect the fine structure determined by tube fragmentation. In particular, the Fe IX line is mostly emitted at the loop footpoints, where we might be able to track the motions that drive the magnetic stressing and detect the upward motion of evaporating plasma from the chromosphere. In Fe XV, we might see the bulk of the loop with increasing intensity, with alternating filamentary Doppler and non-thermal components in the front view, along with more defined spots in the topward view. The Fe XIX line is very faint within the chosen simulation parameters; thus, any transient brightening around the loop apex may possibly be emphasized by the folding of sheet-like structures, mainly at the boundary of unstable tubes. Conclusions. In conclusion, we show that coronal loop observations with MUSE can pinpoint some crucial features of MHD-modeled ignition processes, such as the related dynamics, helping to identify the heating processes.

Coronal energy release by MHD avalanches

Context. A possible key element for large-scale energy release in the solar corona is a magnetohydrodynamic (MHD) kink instability in a single twisted magnetic flux tube. An initial helical current sheet progressively fragments in a turbulent way into smaller-scale sheets. Dissipation of these sheets is similar to a nanoflare storm. Since the loop expands in the radial direction during the relaxation process, an unstable loop can disrupt nearby stable loops and trigger an MHD avalanche. Aims. Exploratory investigations have been conducted in previous works with relatively simplified loop configurations. In this work, we address a more realistic environment that comprehensively accounts for most of the physical effects involved in a stratified atmosphere typical of an active region. The questions we investigate are whether the avalanche process will be triggered, with what timescales, and how will it develop as compared with the original, simpler approach. Methods. We used three-dimensional MHD simulations to describe the interaction of magnetic flux tubes, which have a stratified atmosphere with chromospheric layers, a thin transition region to the corona, and a related transition from high-β to dlow-β regions. The model also includes the effects of thermal conduction and of optically thin radiation. Results. Our simulations address the case where one flux tube amongst a few is twisted at the footpoints faster than its neighbours. We show that this flux tube becomes kink unstable first in conditions in agreement with those predicted by analytical models. It then rapidly affects nearby stable tubes, instigating significant magnetic reconnection and dissipation of energy as heat. In turn, the heating brings about chromospheric evaporation as the temperature rises up to about 107 K, close to microflare observations. Conclusions. This work confirms, in more realistic conditions, that avalanches are a viable mechanism for the storing and release of magnetic energy in plasma confined in closed coronal loops as a result of photospheric motions.

Numerical Simulation of Solar Magnetic Flux Emergence Using the AMR–CESE–MHD Code

Magnetic flux emergence from the solar interior to the atmosphere is believed to be a key process in the formation of solar active regions and driving solar eruptions. Due to the limited capabilities of observations, the flux emergence process is commonly studied using numerical simulations. In this paper, we develop a numerical model to simulate the emergence of a twisted magnetic flux tube from the convection zone to the corona, using the AMR–CESE–MHD code, which is based on the conservation-element solution-element method, with adaptive mesh refinement. The results of our simulation agree with those of many previous studies with similar initial conditions, but by using different numerical codes. In the early stage, the flux tube rises from the convection zone, being driven by magnetic buoyancy, until it reaches close to the photosphere. The emergence is decelerated there, and with the piling up of the magnetic flux, the magnetic buoyancy instability is triggered, which allows the magnetic field to partially enter into the atmosphere. Meanwhile, two gradually separated polarity concentration zones appear in the photospheric layer, transporting the magnetic field and energy into the atmosphere through their vortical and shearing motions. Correspondingly, the coronal magnetic field is also reshaped into a sigmoid configuration, containing a thin current layer, which resembles the typical pre-eruptive magnetic configuration of an active region. Such a numerical framework of magnetic flux emergence as established will be applied to future investigations of how solar eruptions are initiated in flux emergence active regions.

A robust estimation of the twist distribution in magnetic clouds

Context. Magnetic clouds (MCs) are observed in situ by spacecraft. The rotation of their magnetic field is typically interpreted as the crossing of a twisted magnetic flux tube, or flux rope, which was launched from the solar corona. Aims. The detailed magnetic measurements across MCs permit us to infer the flux rope characteristics. Still, the precise spatial distribution of the magnetic twist is challenging, and thus is debated. Methods. In order to improve the robustness of the results, we performed a superposed epoch analysis (SEA) of a set of well observed MCs at 1 au. While previous work was done using the MC central time, we here used the result of a fitted flux rope model to select the time of the closest approach to the flux rope axis. This implies a precise separation of the in- and outbound regions to coherently phase the observed signals. We also searched for and minimised the possible biases such as magnetic asymmetry and a finite impact parameter. Results. We applied the SEA to derive the median profiles both for the flux rope remaining when crossed by the spacecraft and to recover the one present before erosion. In particular, the median azimuthal B component is nearly a linear function of the radius. More generally, the results confirm our previous results realised without such a deep analysis. The twist profile is nearly uniform in the flux rope core, with a steep increase at the border of the flux rope and with similar profiles in the in- and outbound regions. The main difference with our previous study is a larger twist by ∼20%.

Direct evidence that twisted flux tube emergence creates solar active regions

The magnetic nature of the formation of solar active regions lies at the heart of understanding solar activity and, in particular, solar eruptions. A widespread model, used in many theoretical studies, simulations and the interpretation of observations, is that the basic structure of an active region is created by the emergence of a large tube of pre-twisted magnetic field. Despite plausible reasons and the availability of various proxies suggesting the accuracy of this model, there has not yet been a methodology that can clearly and directly identify the emergence of large pre-twisted magnetic flux tubes. Here, we present a clear signature of the emergence of pre-twisted magnetic flux tubes by investigating a robust topological quantity, called magnetic winding, in solar observations. This quantity detects the emerging magnetic topology despite the significant deformation experienced by the emerging magnetic field. Magnetic winding complements existing measures, such as magnetic helicity, by providing distinct information about field line topology, thus allowing for the direct identification of emerging twisted magnetic flux tubes.

On the Stabilization of a Twisted Magnetic Flux Tube

Abstract The linear magnetohydrodynamic stability of a shielding magnetic flux rope with a surface current under coronal solar conditions is analyzed in the framework of an energy principle. The equation describing the potential energy change induced by disturbances of the equilibrium was derived. It has been shown that the surface reverse current shielding the azimuthal component of the magnetic field lines outside a flux rope stabilizes the development of kink- and flute-type instabilities in the long-wavelength limit independently of the cross-sectional radial profile of current density. Kink modes are the most unstable ones as their generation requires less energy than other modes. Based on the obtained dispersion relation for kink oscillations, we proposed a new expression for the determination of magnetic field components of the twisted loop.

The Effect of Weak Magnetic Twist on Resonant Absorption of Slow Sausage Waves in Magnetic Flux Tubes

Abstract Observations show that twisted magnetic flux tubes are present throughout the Sun’s atmosphere. The main aim of this work is to obtain the damping rate of sausage modes in the presence of weak magnetic twist. Using the connection formulae obtained by Sakurai et al., we investigate resonant absorption of the sausage modes in the slow continuum under photospheric conditions. We derive the dispersion relation and solve it numerically, and consequently obtain the frequencies and damping rates of the slow surface sausage modes. We conclude that the magnetic twist can result in strong damping in comparison with the untwisted case.

High mode magnetohydrodynamic waves propagation in a twisted rotating jet emerging from a filament eruption

We study the conditions under which high mode magnetohydrodynamic (MHD) waves propagating on a rotating jet emerging from the filament eruption on 2013 April 10--11 can became unstable against the Kelvin--Helmholtz instability (KHI). The evolution of jet indicates the blob like structure at its boundary which could be one of the observable features of the KHI development. We model the jet as a twisted rotating axially moving magnetic flux tube and explore the propagation characteristics of the running MHD modes on the basis of dispersion relations derived in the framework of the ideal magnetohydrodynamics. It is established that unstable MHD waves with wavelengths in the range of $12$--$15$~Mm and instability developing times from $1.5$ to $2.6$~min can be detected at the excitation of high mode MHD waves. The magnitude of the azimuthal mode number $m$ crucially depends upon the twist of the internal magnetic field. It is found that at slightly twisted magnetic flux tube the appropriate azimuthal mode number is $m = 16$ while in the case of a moderately twisted flux tube it is equal to $18$.

Kelvin–Helmholtz instability in a twisting solar polar coronal hole jet observed by SDO/AIA

We investigate the conditions under which the fluting (m=2), m=3, and m=12 magnetohydrodynamic (MHD) modes in a uniformly twisted flux tube moving along its axis become unstable in order to model the Kelvin–Helmholtz (KH) instability in a twisting solar coronal hole jet near the northern pole of the Sun. We employed the dispersion relations of MHD modes derived from the linearized MHD equations. We assumed real wavenumbers and complex angular wave frequencies, namely complex wave phse velocities. The dispersion relations were solved numerically at fixed input parameters (taken from observational data) and varying degrees of torsion of the internal magnetic field. It is shown that the stability of the modes depends upon five parameters: the density contrast between the flux tube and its environment, the ratio of the external and internal axial magnetic fields, the twist of the magnetic field lines inside the tube, the ratio of transverse and axial jet’s velocities, and the value of the Alfvén Mach number (the ratio of the tube axial velocity to Alfvén speed inside the flux tube). Using a twisting jet of 2010 August 21 by SDO/AIA and other observations of coronal jets we set the parameters of our theoretical model and have obtained that in a twisted magnetic flux tube of radius of 9.8Mm, at a density contrast of 0.474 and fixed Alfvén Mach number of ≅0.76, for the three MHD modes there exist instability windows whose width crucially depends upon the internal magnetic field twist. It is found that for the considered modes an azimuthal magnetic field of 1.3–1.4G (computed at the tube boundary) makes the width of the instability windows equal to zero, that is, it suppress the KH instability onset. On the other hand, the times for developing KH instability of the m=12 MHD mode at instability wavelengths between 15 and 12Mm turn out to be in the range of 1.9–4.7min that is in agreement with the growth rates estimated from the temporal evolution of the observed unstable jet’s blobs in their initial stage.

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.

Energy Release in Driven Twisted Coronal Loops

In the present study we investigate magnetic reconnection in twisted magnetic fluxtubes with different initial configurations. In all considered cases, energy release is triggered by the ideal kink instability, which is itself the result of applying footpoint rotation to an initially potential field. The main goal of this work is to establish the influence of the field topology and various thermodynamic effects on the energy release process. Specifically, we investigate convergence of the magnetic field at the loop footpoints, atmospheric stratification, as well as thermal conduction. In all cases, the application of vortical driving at the footpoints of an initally potential field leads to an internal kink instability. With the exception of the curved loop with high footpoint convergence, the global geometry of the loop change little during the simulation. Footpoint convergence, curvature and atmospheric structure clearly influences the rapidity with which a loop achieves instability as well as the size of the subsequent energy release. Footpoint convergence has a stabilising influence and thus the loop requires more energy for instability, which means that the subsequent relaxation has a larger heating effect. Large-scale curvature has the opposite result: less energy is needed for instability and so the amount of energy released from the field is reduced. Introducing a stratified atmosphere gives rise to decaying wave phenomena during the driving phase, and also results in a loop that is less stable.

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.

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.

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.

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.

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.