Thin Magnetic Flux Tubes Research Articles

A Dynamical Model for the Penumbral Fine Structure and the Evershed Effect in Sunspots

Relying on the assumption that the interchange convection of magnetic flux tubes is the physical cause for the existence of sunspot penumbrae, we propose a model in which the dynamical evolution of a thin magnetic flux tube reproduces the Evershed effect and the penumbral fine structure such as bright and dark filaments and penumbral grains. According to our model, penumbral grains are the manifestation of the footpoints of magnetic flux tubes, along which hot subphotospheric plasma flows upwards with a few km/s. Above the photosphere the hot plasma inside the tube is cooled by radiative losses as it flows horizontally outwards. As long as the flowing plasma is hotter than the surroundings, it constitutes a bright radial filament. The flow confined to a thin elevated channel reaches the temperature equilibrium with the surrounding atmosphere and becomes optically thin near the outer edge of the penumbra. Here, the tube has a height of approximately 100 km above the continuum and the flow velocity reaches up to 14 km/s. Such a flow channel can reproduce the observed signatures of the Evershed effect.

The Evershed Effect in Sunspots: A Theoretical Explanation

The siphon flow model, consisting in the simulation of a flow of gas moving along a thin magnetic flux tube and driven by the pressure drop between its footpoints, is proposed to explain the observational features of the Evershed effect, one of the longstanding problems in solar physics.

Linear Waves in Force-Free Fibrils

AbstractThe advanced thin flux tube approximation for force-free thin magnetic flux tubes is used to derive a dispersion relation for linear waves. All wave modes appear to be coupled in a twisted flux tube. In the case of a weakly twisted flux tube, it has been found that torsional Alfvén waves have dispersion and produce pressure and temperature fluctuations. The effect of tube rotation is pointed out. These properties of linear waves have an impact on prominence oscillations.

A Fibril Structure Model for Stellar Prominences

AbstractExtensive observational background exists about the presence of cool material clouds embedded in the stellar coronae of rapidly rotating, late-type stars. Observations of such clouds in HKAqr (Gliese 890) and HD 197890 suggest that the clouds are at heights smaller than the star’s corotation radius and could be looked at as a phenomenon similar to that of solar prominences. Recent observations of solar prominences have reinforced the evidence about their fibril structure made of many long, thin magnetic flux tubes making angles about 25 degrees with the direction of the filament channel, with only the central 10–20% of the magnetic flux tubes filled with cool matter, which can produce a depression at the summits of the flux tubes. Then, assuming a similar structure for the stellar cool clouds, we have looked for the physical characteristics of such stellar prominences, i.e. the size of the flux tube depression, the density, temperature, half-width and supported mass of the cool region, taking into account gravity variation with height and centrifugal acceleration, since such clouds have been detected at great heights within stellar coronae belonging to rapid rotators.

Non-linear body sausage waves in thin magnetic flux tubes

The thin-flux-tube approximation developed by Zhugzhda [Phys. Plasmas 3 (1996) 10] allows one to describe analytically the weakly non-linear dynamics of long-wavelength sausage body magnetosonic waves in magnetic flux tubes. A Kortewegde Vries equation is derived for slow body waves. The weakly non-linear sausage body waves appear as narrowings of the flux tube, with rarefaction, cooling, and acceleration of a plasma flow due to the squeezing of the tube. The “breaking” of the non-linear slow body waves is discussed.

Effects of Non‐LTE Radiative Loss and Partial Ionization on the Structure of the Transition Region

In this paper we address the question of how non-LTE radiative losses with partial ionization of hydrogen and helium affects the energetics and structure of the solar transition region. To accomplish this we have constructed theoretical models of a thin rigid magnetic flux tube with a steady material flow, which is embedded vertically in the solar atmosphere. These models include the effects of material flow, conduction, non-LTE radiative transfer in H and He, and partial ionization. We find from this study that the effect of non-LTE radiative transfer with partial ionization is significant near the base of the transition region at temperatures less than 2.5 × 104 K. This leads to a 1 order of magnitude increase in the differential emission measure in comparison with the optically thin approximation with complete ionization in the low (less than 2.5 × 104 K) temperature regime. Above this region the non-LTE and opacity effects are small. In the upflow case the conductive and convective energy processes dominate to such a large extent that non-LTE radiative process and partial ionization are not important. In this work we also confirm the previous work of other authors who provided the explanation for why downflowing transition region material is much more visible than upflowing material. We present the results in a manner that gives a good physical understanding as to why this occurs.

The Linear Response of a Magnetic Flux Tube to Buffeting by Externalp‐Modes. I.

The linear response of a thin vertical magnetic flux tube to buffeting by p-modes in the ambient atmosphere is examined with the aim of understanding the interaction of acoustic modes with sausage tube waves. The idealized case of an isothermal atmosphere is considered, which has the mathematical advantage that the differential equation for the vertical component of the Lagrangian displacement in the tube can be solved analytically. A lower boundary condition is employed that permits the tube wave to leak out through this boundary. This has the important consequence that the p-mode interaction with flux tubes does not exhibit a resonant behavior. The detailed behavior of the vertical displacement in the tube and its dependence on various parameters are examined. An equation for the wave energy in a thin flux tube is derived along with analytic expressions for the wave energy density and vertical energy flux. The variation of the tube response Ξ (defined as the ratio of the total wave energy, integrated over the length of the tube, to the p-mode energy in the external atmosphere) is investigated for different values of the dimensionless external horizontal wavenumber Kx, mode order n, and β, where β is the ratio of the gas to magnetic pressure in the tube that, by assumption, is constant with depth. It is found that when n is small, the response of the tube increases gradually with Kx until reaching a maximum, and thereafter it drops very sharply. As n increases, the maximum shifts to lower values of Kx. For fixed values of Kx and β, Ξ increases with n and then falls off after reaching a maximum. A similar dependence of Ξ on β is found. Line widths of p-modes are also calculated, and their dependence on Kx and frequency is studied. Finally, an application of the results to the solar atmosphere is discussed, and the limitations of the model are pointed out.

The Dirac–Hamiltonian in an Aharonov–Bohm Gauge Field and its Self-Adjoint Extensions

By using the spherical coordinates in (3+1) dimensions we study the self-adjointness of the Dirac–Hamiltonian in an Aharonov–Bohm gauge field of an infinitely thin magnetic fluxtube. It is shown that the angular part of the Dirac–Hamiltonian requires self-adjoint extensions. These self-adjoint extensions are parametrized by a 2×2 unitary matrix.

Magnus force in superfluids and superconductors

The forces on the vortex, transverse to its velocity, are considered. In addition to the superfluid Magnus force from the condensate (superfluid component), there are transverse forces from thermal quasiparticles and external fields violating the translational invariance. The forces between quasiparticles and the vortex originate from interference of quasiparticles with trajectories on the left and on the right from the vortex like similar forces for electrons interacting with the thin magnetic-flux tube (the Aharonov-Bohm effect). These forces are derived in the Born approximation for phonons from the equations of superfluid hydrodynamics, and for BCS quasiparticles from the Bogolyubov-de Gennes equations. The effect of external fields violating translational invariance is analyzed for vortices in the two-dimensional Josephson junction array. The symmetry analysis of the classical equations for the array shows that the total transverse force on the vortex vanishes. Therefore the Hall effect which is linear in the transverse force is absent also. This means that the Magnus force from the superfluid component exactly cancels with the transverse force from the external fields. The results of other approaches are also brought together for discussion.

Radiative heating and the buoyant rise of magnetic flux tubes in the solar interior

We study the effect of radiative heating on the evolution of thin magnetic flux tubes in the solar interior and on the eruption of magnetic flux loops to the surface. Magnetic flux tubes experience radiative heating because (1) the mean temperature gradient in the lower convection zone and the overshoot region deviates substantially from that of radiative equilibrium, and hence there is a non-zero divergence of radiative heat flux; and (2) the magnetic pressure of the flux tube causes a small change of the thermodynamic properties within the tube relative to the surrounding field-free fluid, resulting in an additional divergence of radiative heat flux. Our calculations show that the former constitutes the dominant source of radiative heating experienced by the flux tube. In the overshoot region, the radiative heating is found to cause a quasi-static rising of the toroidal flux tubes with an upward drift velocity ∼ 10-3|δ| cm s-1, where δ ≡ ∇e − ∇ad < 0 describes the subadiabaticity in the overshoot layer. The upward drift velocity does not depend sensitively on the field strength of the flux tubes. Thus in order to store toroidal flux tubes in the overshoot region for a period comparable to the length of the solar cycle, the magnitude of the subadiabaticity δ(< 0) in the overshoot region must be as large as ∼ 3 × 10−4. We discuss the possibilities for increasing the magnitude of δ and for reducing the rate of radiative heating of the flux tubes in the overshoot region. Using numerical simulations we study the formation of ‘Ω’-shaped emerging loops from toroidal flux tubes in the overshoot region as a result of radiative heating. The initial toroidal tube is assumed to be non-uniform in its thermodynamic properties along the tube and lies at varying depths beneath the base of the convection zone. The tube is initially in a state of neutral buoyancy with the internal density of the tube plasma equal to the local external density. We find from our numerical simulations that such a toroidal tube rises quasi-statically due to radiative heating. The top portion of the nonuniform tube first enters the convection zone and may be brought to an unstable configuration which eventually leads to the eruption of an anchored flux loop to the surface. Assuming reasonable initial parameters, our numerical calculations yield fairly short rise times (2–4 months) for the development of the emerging flux loops. This suggests that radiative heating is an effective way of causing the eruption of magnetic flux loops, leading to the formation of active regions at the surface.

Bound states of an electron in the field of the magnetic string

We consider bound states of an electron in the field of a thin magnetic flux tube which are due to the anomaly of its magnetic moment. The binding energies appear to grow when decreasing the radius of the flux tube while keeping the anomaly fixed until the gap between electron and positron levels vanishes. We discuss possible implications for the ground state of QED.

Helicity conservation in the Aharonov-Bohm scattering of Dirac particles.

We show that the helicity operator \ensuremath{\Lambda} for a particle in the presence of an infinitely thin magnetic flux tube requires, as the Hamiltonian H, for its complete determination as a self-adjoint operator, the specification of boundary conditions (BC's) that have to be chosen out of a four-parameter family of admissible ones. To each value of the parameters there corresponds a self-adjoint operator with eigenfunctions and eigenvalues determined by the associated BC's. For each choice of the dynamics H we investigate under which conditions the corresponding BC is also admissible for the helicity \ensuremath{\Lambda}. When this happens, and only when this happens, it is possible for H and \ensuremath{\Lambda} to satisfy identical BC's. Although their actions formally commute before specification of boundary conditions, only identical BC's will ensure effective commutativity, in the sense that they will have a complete set of common eigenfunctions and that \ensuremath{\Lambda} will be a conserved quantity. We show this to be the case only for a special (but large) class of BC's. Our results imply that helicity conservation, although imposing some restrictions on the choice of the dynamics, does not solve the problem of the indeterminacy in the choice of BC's in the Aharonov-Bohm scattering of Dirac particles. Our results also show that it is possible to choose BC's such that both helicity is conserved and the Aharonov-Bohm symmetry (\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\varphi}+1) is preserved, where \ensuremath{\varphi} is the magnetic flux in natural units.

The Small-Scale Photospheric Magnetic Field as an Indicator of the Dynamo

AbstractThe presently widely accepted view that the solar dynamo operates near the base of the convective zone makes it difficult to relate the magnetic fields observed in the solar atmosphere to the fields in the dynamo layer. The large amount of observational data concerning photospheric magnetic fields could in principle be used to impose constraints on dynamo theory, but in order to infer these constraints the above mentioned “missing link” between the dynamo and surface fields should be found. This paper proposes such a link by modeling the passive vertical transport of thin magnetic flux tubes through the convective zone.

The configuration of the loop-like structure of the solar atmosphere

An integral, governing steady flows in an isolated thin magnetic flux tube in the hydrostatic plane-stratified atmosphere, has been obtained. The integral, that we named as the shape integral, is expressed as (1 − M A 2) B cos θ = const. Here M A 2 is the Alfven Mach number, B is the magnetic field strength and θ is the flux tube inclination to the horizontal. The shape integral should hold for most loop models because it represents just the momentum balance laws and has no relation to any energy balance mode. Its application to the isothermal and static cases is discussed and illustrated.

Waves in solar magnetic flux tubes: the observational signature of undamped longitudinal tube waves

Linear calculations of undamped longitudinal waves in thin solar magnetic flux tubes are presented. The influence of such waves, having a variety of parameters, on the Stokes I and V profiles of eight photospheric spectral lines is studied. Diagnostics based on the Stokes parameters of the properties of flux tube waves, in particular of the amount of energy transported by them into the upper solar atmosphere, are developed. For propagating waves it is found that, with an appropriate choice of spectral lines, a lower limit on the transported energy can be set by observing the zero-crossing wavelength of Stokes V, while an upper limit can be derived from the line-widths. The importance of radiative transfer effects and of the thermodynamic changes associated with the waves are pointed out

Siphon flows in isolated magnetic flux tubes. III - The equilibrium path of the flux-tube arch

It is shown how to calculate the equilibrium path of a thin magnetic flux tube in a stratified, nonmagnetic atmosphere when the flux tube contains a steady siphon flow. The equilbrium path of a static thin flux tube in an infinite stratified atmosphere generally takes the form of a symmetric arch of finite width, with the flux tube becoming vertical at either end of the arch. A siphon flow within the flux tube increases the curvature of the arched equilibrium path in order that the net magnetic tension force can balance the inertial force of the flow, which tries to straighten the flux tube. Thus, a siphon flow reduces the width of the arched equilibrium path, with faster flows producing narrower arches. The effect of the siphon flow on the equilibrium path is generally greater for flux tubes of weaker magnetic field strength. Examples of the equilibrium are shown for both isothemal and adiabatic siphon flows in thin flux tubes in an isothermal external atmosphere.

Waves and Oscillations in Magnetic Fluxtubes

According to observational data solar magnetic fields have a pronounced filamentary structure. Theoretical investigations of plasmas containing structured magnetic fields, including the study of the properties of these structures and their interactions with associated gas flows, are of great importance for our understanding of the basic processes in the solar atmosphere, whose structure and dynamics are dominated by magnetic fields. In the present review theoretical models of thin magnetic fluxtubes and their behaviour in the ambient plasma are discussed.

On the resonance scattering of sound by slender magnetic flux tubes

The impact of excited tube modes (resonances) on the acoustic scattering properties of slender flux tubes, which is relevant to the interaction of the solar five-minute oscillations with the thin intense magnetic flux tubes that dot the solar surface, is theoretically discussed. Quantitative examples are given which take into account the influence of the finite size of the flux tube on the resonance locations and widths. The practical implications of the theory for observations are considered. 31 refs.

The equilibrium structure of a thin magnetic flux tube. III - The effects of molecular CO absorption

La structure d'une atmosphere stellaire et du tube de flux magnetique qui lui est associe est determinee en tenant compte des opacites de H − et de CO. L'effet de refroidissement cause par la presence de CO est mis en evidence

Siphon flows in isolated magnetic flux tubes

Previous studies of siphon flows in magnetic flux tubes have been limited to the case of a low-β plasma, appropriate for an embedded flux tube in the solar corona or chromosphere. Here the author studies steady siphon flows in isolated, thin magnetic flux tubes surrounded by field-free gas, with plasma β ≥ 1, appropriate for conditions in the solar photosphere. The author presents the basic equations governing steady siphon flows in a thin, isolated magnetic flux tube, and discusses the case of a purely horizontal flux tube, for which gravitational forces do not come into play. Qualitative features of isothermal flows in elevated, arched flux tubes are then studied. The author presents the results of some numerical computations of isothermal siphon flows in arched flux tubes and discusses the nature of critical flows and the need for standing "tube shocks" in these flows. Finally, he discusses applications to intense magnetic flux tubes in the solar photosphere and considers the possible interpretation of the Evershed flow in the penumbral photosphere of a sunspot as a siphon flow along isolated magnetic flux tubes.