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.     

Nonaxisymmetric Oscillations of Thin Twisted Magnetic Tubes

In this paper we study nonaxisymmetric oscillations of thin twisted magnetic tubes taking the density variation along the tube into account. We use the approximation of the zero-beta plasma. The magnetic field outside the tube is straight and homogeneous; however, it is twisted inside the tube. We assume that the azimuthal component of the magnetic field is proportional to the distance from the tube axis and that the tube is only weakly twisted (i.e., the ratio of the azimuthal and axial components of the magnetic field is small). Using the asymptotic analysis we show that the eigenmodes and eigenfrequencies of the kink and fluting oscillations are described by a classical Sturm – Liouville problem for a second-order ordinary differential equation. The main result is that the twist does not affect the kink mode.     

External and internal solutions for the twisted,flux-tube,prominence model

In this paper the twisted flux-tube model for the support of a prominence sheet with constant axial current density, given by Ridgway, Priest, and Amari (1991), is considered.The model is extended in Section 2 to incorporate a current sheet of finite height. The sheet is supported in a constant current density force-free field in the configuration of a twisted flux tube. The mass of the prominence sheet, using a typical height and field strength, is computed. Outside the flux tube the background magnetic field is assumed to be potential but the matching of the flux tube onto this background field is not considered here.Instead our attention is focussed, in Section 3, on the interior of the prominence. An expanded scale is used to stretch the prominence sheet to a finite width. We analytically select solutions for the internal magnetic field in this region which match smoothly onto the external force-free solutions at the prominence edge.The force balance equation applied inside the prominence then yields expressions for the pressure and density and a corresponding temperature may be computed.     

The Effect of a Twisted Magnetic Field on the Nature of Kink MHD Waves

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvénic wave in the entire loop.     

Conditions for Propagation of Torsional Waves in Solar Magnetic Flux Tubes

Propagation of torsional waves along isothermal and initially-untwisted magnetic-flux tubes embedded in the solar atmosphere is studied analytically. Conditions for wave propagation along thin and wide magnetic-flux tubes are determined, and it is shown that the propagation along thin tubes is cutoff free; however, for wide tubes the propagation is affected by a cutoff frequency. A method to determine the cutoff frequency is presented and applied to a specific model of solar magnetic flux tubes. An interesting result is that the cutoff frequency is a local quantity in the model and that its value at a given height determines the frequency that torsional tube waves must have to propagate at this height.     

Radial oscillations of coronal loops and microwave radiation from solar flares

We consider the damping mechanisms for the radial oscillations of solar coronal loops in the approximation of a thin magnetic flux tube. We show that the free tube oscillations can have a high Q if the plasma density inside the magnetic flux tube is much higher than the density outside. We analyze the effect of radial coronal-loop magnetic-field oscillations on the modulation of the microwave radiation from solar flares. In the case of a nonthermal gyrosynchrotron mechanism, the fluxes from optically thin and optically thick sources are modulated in antiphase. Based on our model, we diagnose the flare plasma. For the event of May 23, 1990, we estimate the spectral index for accelerated electrons, α≈4.4, and the magnetic-field strength in the region of energy release, B≈190 G.     

RENDERING THREE-DIMENSIONAL SOLAR CORONAL STRUCTURES

An X-ray or EUV image of the corona or chromosphere is a 2D representation of an extended 3D complex for which a general inversion process is impossible. A specific model must be incorporated in order to understand the full 3D structure. We approach this problem by modeling a set of optically-thin 3D plasma flux tubes which we render these as synthetic images. The resulting images allow the interpretation of the X-ray/EUV observations to obtain information on (1) the 3D structure of X-ray images, i.e., the geometric structure of the flux tubes, and on (2) the internal structure using specific plasma characteristics, i.e., the physical structure of the flux tubes. The data-analysis technique uses magnetograms to characterize photospheric magnetic fields and extrapolation techniques to form the field lines. Using a new set of software tools, we have generated 3D flux tube structures around these field lines and integrated the plasma emission along the line of sight to obtain a rendered image. A set of individual flux-tube images is selected by a non-negative least-squares technique to provide a match with an observed X-ray image. The scheme minimizes the squares of the differences between the synthesized image and the observed image with a non-negative constraint on the coefficients of the brightness of the individual flux-tube loops. The derived images are used to determine the specific photospheric foot points and physical data, i.e., scaling laws for densities and loop lengths. The development has led to computer efficient integration and display software that is compatible for comparison with observations (e.g., Yohkoh SXT data, NIXT, or EIT). This analysis is important in determining directly the magnetic field configuration, which provides the structure of coronal loops, and indirectly the electric currents or waves, which provide the energy for the heating of the plasma. We have used very simple assumptions (i.e., potential magnetic fields and isothermal corona) to provide an initial test of the techniques before complex models are introduced. We have separated the physical and geometric contributions of the emission for a set of flux tubes and concentrated, in this initial study, on the geometric contributions by making approximations to the physical contributions. The initial results are consistent with the scaling laws derived from the Yohkoh SXT data.     

Empirical Modeling of Radiative <Emphasis Type="Italic">versus</Emphasis> Magnetic Flux for the Sun-as-a-Star

We study the relationship between full-disk solar radiative flux at different wavelengths and average solar photospheric magnetic-flux density, using daily measurements from the Kitt Peak magnetograph and other instruments extending over one or more solar cycles. We use two different statistical methods to determine the underlying nature of these flux – flux relationships. First, we use statistical correlation and regression analysis and show that the relationships are not monotonic for total solar irradiance and for continuum radiation from the photosphere, but are approximately linear for chromospheric and coronal radiation. Second, we use signal theory to examine the flux – flux relationships for a temporal component. We find that a well-defined temporal component exists and accounts for some of the variance in the data. This temporal component arises because active regions with high magnetic-field strength evolve, breaking up into small-scale magnetic elements with low field strength, and radiative and magnetic fluxes are sensitive to different active-region components. We generate empirical models that relate radiative flux to magnetic flux, allowing us to predict spectral-irradiance variations from observations of disk-averaged magnetic-flux density. In most cases, the model reconstructions can account for 85 – 90% of the variability of the radiative flux from the chromosphere and corona. Our results are important for understanding the relationship between magnetic and radiative measures of solar and stellar variability.     

Kink Wave Propagation in Thin Isothermal Magnetic Flux Tubes

We investigated the propagation of kink waves in thin and isothermal expanding flux tubes in cylindrical geometry. By using the method of radial expansion for fluctuating variables we obtained a new kink wave equation. We show that including the radial component of the tube magnetic field leads to cutoff-free propagation of kink waves along thin flux tubes.     

Probing Twisted Magnetic Field Using Microwave Observations in an M Class Solar Flare on 11 February, 2014

This work demonstrates the possibility of magnetic-field topology investigations using microwave polarimetric observations. We study a solar flare of GOES M1.7 class that occurred on 11 February, 2014. This flare revealed a clear signature of spatial inversion of the radio-emission polarization sign. We show that the observed polarization pattern can be explained by nonthermal gyrosynchrotron emission from the twisted magnetic structure. Using observations of the Reuven Ramaty High Energy Solar Spectroscopic Imager, Nobeyama Radio Observatory, Radio Solar Telescope Network, and Solar Dynamics Observatory, we have determined the parameters of nonthermal electrons and thermal plasma and identified the magnetic structure where the flare energy release occurred. To reconstruct the coronal magnetic field, we use nonlinear force-free field (NLFFF) and potential magnetic-field approaches. Radio emission of nonthermal electrons is simulated by the GX Simulator code using the extrapolated magnetic field and the parameters of nonthermal electrons and thermal plasma inferred from the observations; the model radio maps and spectra are compared with observations. We have found that the potential-magnetic-field approach fails to explain the observed circular polarization pattern; on the other hand, the Stokes-\(V\) map is successfully explained by assuming nonthermal electrons to be distributed along the twisted magnetic structure determined by the NLFFF extrapolation approach. Thus, we show that the radio-polarization maps can be used for diagnosing the topology of the flare magnetic structures where nonthermal electrons are injected.     

The magnetic non-equilibrium of buoyant flux tubes in the solar corona

The equilibrium shape of a slender flux tube in the stratified solar atmosphere is studied. The path is determined by a balance between the downwards magnetic tension, which depends on the curvature of the loop, and the upwards buoyancy force. Previous results for untwisted slender tubes are extended to include twisted tubes embedded in an external magnetic field.The path of an untwisted tube in an atmosphere with an ambient magnetic field is calculated. For a given footpoint separation, the height of the tube is lowered by increasing the strength of the external magnetic field. If the footpoints are slowly moved apart, the tube rises, until a threshold separation is reached beyond which there is no possible equilibrium height. This threshold width does not depend on the strength of the external field.The effects of twisting up a curved loop are studied, using an extension of results obtained for slender curved tubes with a straight axis. It is shown that for a twisted tube of given width, there can be two possible values of the equilibrium height. If, however, the tube is twisted more than a certain amount or if the footpoints are too widely separated there is no equilibrium. The critical footpoint separation for non-equilibrium is smaller for a twisted tube that an untwisted one.Twisting a tube or moving its feet apart is thus likely to result in non-equilibrium, causing the tube to rise indefinitely under the influence of the unbalanced buoyant force. It is suggested that this phenomenon could be important in the preflare stage of a large two-ribbon solar flare, by causing the initial slow rise of an active region filament. As well as being involved in the onset of an erupting prominence, this non-equilibrium may also be relevant to the formation of coronal loop transients.     

3-D non-linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward-slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non-rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The adiabatic cooling of the protons in the solar wind: The case where the interplanetary magnetic-field is of spiral form

This is a sequel to the paper by Eyni and Kaufman (1971) in which the coordinate systems with respect to the magnetic direction and solar radial-direction were assumed coincident. In the present account, it is shown that the theoretical expression for the proton cooling derived in that paper is still applicable in the case of the spiral magnetic-field provided the appropriate transformation of kinetic temperature from the magnetic direction to the radial direction as derived here is used. A detailed comparison is made between the present model and other models based on the spiral form of the magnetic field; the agreement is satisfactory.     

Interchange stability of a rapidly rotating magnetosphere

A rotation-dominated magnetosphere is unstable to magnetic flux-tube interchange motions if and only if the plasma content of a unit magnetic flux tube is a decreasing function of distance from the spin axis. For a spin-aligned dipole field the marginally stable distribution is approximately ρr^9/2 = constant, where ρ is the plasma mass density at the radial distance r in the equatorial plane. Plasma filling the Jovian magnetosphere from internal sources would initially violate this stability criterion so that interchange motions would act to establish the marginally stable distribution.     

Observations of Unresolved Photospheric Magnetic Fields in Solar Flares Using Fe i and Cr i Lines

The structure of the photospheric magnetic field during solar flares is examined using echelle spectropolarimetric observations. The study is based on several Fe i and Cr i lines observed at locations corresponding to brightest Hα emission during thermal phase of flares. The analysis is performed by comparing magnetic-field values deduced from lines with different magnetic sensitivities, as well as by examining the fine structure of I±V Stokes-profiles’ splitting. It is shown that the field has at least two components, with stronger unresolved flux tubes embedded in weaker ambient field. Based on a two-component magnetic-field model, we compare observed and synthetic line profiles and show that the field strength in small-scale flux tubes is about 2?–?3 kG. Furthermore, we find that the small-scale flux tubes are associated with flare emission, which may have implications for flare phenomenology.     

EVOLUTION AND INFLEXIONAL INSTABILITY OF TWISTED MAGNETIC FLUX TUBES

This paper presents new results concerning evolution and inflexional instability of twisted magnetic flux tubes in the solar corona. Inflexional configurations, attained when the curvature of the tube axis vanishes, are generally present in coronal magnetic structures and are invariably associated with the early stages of kink formation. New equations for the Lorentz force in orthogonal curvilinear coordinates are applied to study the behaviour of twisted flux tubes in presence of inflexion points. We find that inflexional flux tubes are in disequilibrium and evolve spontaneously to inflexion-free configurations, possibly in braid form. These results have important applications for solar coronal structures. First, they prove that the evolution and relaxation of twisted magnetic fields into braid form is a generic feature, confirming the observational evidence of highly twisted and braided structures present in the solar corona. Secondly, they demonstrate that inflexions can trigger kink instabilities, providing a fundamental mechanism for modeling outbreaks of energy into heat, emitted by flares, microflares and mass ejections.     

On the Connection Between Mean Field Dynamo Theory and Flux Tubes

Mean field dynamo theory deals with various mean quantities and does not directly throw any light on the question of existence of flux tubes. We can, however, draw important conclusions about flux tubes in the interior of the Sun by combining additional arguments with the insights gained from solar dynamo solutions. The polar magnetic field of the Sun is of order 10 G, whereas the toroidal magnetic field at the bottom of the convection zone has been estimated to be 100000 G. Simple order-of-magnitude estimates show that the shear in the tachocline is not sufficient to stretch a 10 G mean radial field into a 100000 G mean toroidal field. We argue that the polar field of the Sun must get concentrated into intermittent flux tubes before it is advected to the tachocline. We estimate the strengths and filling factors of these flux tubes. Stretching by shear in the tachocline is then expected to produce a highly intermittent magnetic configuration at the bottom of the convection zone. The meridional flow at the bottom of the convection zone should be able to carry this intermittent magnetic field equatorward, as suggested recently by Nandy and Choudhuri (2002). When a flux tube from the bottom of the convection zone rises to a region of pre-existing poloidal field at the surface, we point out that it picks up a twist in accordance with the observations of current helicities at the solar surface.     

Magnetic Disconnections at the Boundary of a Small Interplanetary Magnetic Flux Rope Associated with a Reconnection Exhaust

A local current sheet and a subsequent small interplanetary magnetic-flux rope were observed on 1 April 2003 by Wind and the Advanced Composition Explorer (ACE). A Petschek reconnection-like exhaust crossing of the local current sheet was identified using the Walén test. The Wind spacecraft re-entered the reconnection exhaust after the main exhaust encounter, and the reentry may be due to a spatial fold of the current-sheet surface itself. The absence of parallel strahls and the presence of antiparallel strahls on either side of the current sheet suggest that the magnetic-field lines before the exhaust and in the subsequent small flux rope are all open. The \(180^{\circ}\) pitch-angle strahls were clearly absent, and halo-suprathermal electron pitch-angle distributions were observed in the exhaust. This finding means that the open field lines of the magnetic-flux rope were reconnecting to the adjacent open field lines to produce U-shaped field lines disconnected from the Sun. These observations provide direct evidence that the magnetic fields of the interplanetary small magnetic-flux rope were disconnecting from the Sun through magnetic reconnection. This type of disconnected event potentially has important implications for the magnetic-flux budget of the heliosphere.     

Sausage MHD Waves in Incompressible Flux Tubes with Twisted Magnetic Fields

Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general. This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts.     

Solar Flare Activity and Variability of Electric Current Helicity

1 INTRODUCTIONRecently Bao, Zhang, Ai, and Zhang (1999), using Huairou vector magnetograph data,have shown that the average current helicity (h.) or the curreflt helicity imbalance ph of activeregions change rapidly after so1ar flares. Up'an the onset of flares it tends to decrease for a fewhours and then to increase again, whereas ifQ some cases the flare promotes an increase in thecurrent helicity The observations led to tbe fol1owing conclusions: (1) raPid and substantialchanges of c…