Dynamics Of Magnetic Flux Tubes Research Articles

Dynamics of magnetic flux tubes in accretion disks of Herbig Ae/Be stars

Abstract The dynamics of magnetic flux tubes (MFTs) in the accretion disk of typical Herbig Ae/Be star (HAeBeS) with fossil large-scale magnetic field is modeled taking into account the buoyant and drag forces, radiative heat exchange with the surrounding gas, and the magnetic field of the disk. The structure of the disk is simulated using our magnetohydrodynamic model, taking into account the heating of the surface layers of the disk with the stellar radiation. The simulations show that MFTs periodically rise from the innermost region of the disk with speeds up to 10–12 km s − 1 {{\rm{s}}}^{-1} . MFTs experience decaying magnetic oscillations under the action of the external magnetic field near the disk’s surface. The oscillation period increases with distance from the star and initial plasma beta of the MFT, ranging from several hours at r = 0.012 au r=0.012\hspace{0.33em}{\rm{au}} up to several months at r = 1 au r=1\hspace{0.33em}{\rm{au}} . The oscillations are characterized by pulsations of the MFT’s characteristics including its temperature. We argue that the oscillations can produce observed IR-variability of HAeBeSs, which would be more intense than in the case of T Tauri stars, since the disks of HAeBeSs are hotter, denser, and have stronger magnetic field.

Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

We report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants,viz.the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

Dynamics of magnetic flux tubes in accretion discs of T Tauri stars

Abstract Dynamics of slender magnetic flux tubes (MFTs) in the accretion discs of T Tauri stars is investigated. We perform simulations taking into account buoyant, aerodynamic, and turbulent drag forces, radiative heat exchange between MFT and ambient gas, and magnetic field of the disc. The equations of MFT dynamics are solved using Runge–Kutta method of the fourth order. The simulations show that there are two regimes of MFT motion in absence of external magnetic field. In the region r < 0.2 au, the MFTs of radii $0.05 \le a_0 \le 0.16\, H$ (H is the scale height of the disc) with initial plasma beta of 1 experience thermal oscillations above the disc. The oscillations decay over some time, and MFTs continue upward motion afterwards. Thinner or thicker MFTs do not oscillate. MFT velocity increases with initial radius and magnetic field strength. MFTs rise periodically with velocities up to 5–15 km s−1 and periods of 0.5–10 yr determined by the toroidal magnetic field generation time. Approximately 20 per cent of disc mass and magnetic flux can escape to disc atmosphere via the magnetic buoyancy over characteristic time of disc evolution. MFTs dispersal forms expanding magnetized corona of the disc. External magnetic field causes MFT oscillations near the disc surface. These magnetic oscillations have periods from several days to 1–3 months at r < 0.6 au. The magnetic oscillations decay over few periods. We simulate MFT dynamics in accretion discs in the Chameleon I cluster. The simulations demonstrate that MFT oscillations can produce observed IR-variability of T Tauri stars.

Dynamics of magnetic flux tubes and IR-variability of young stellar objects

We simulate the dynamics of slender magnetic flux tubes (MFTs) in the accretion disks of T Tauri stars. The dynamical equations of our model take into account aerodynamic and turbulent drag forces, and the radiative heat exchange between the MFT and ambient gas. The structure of the disk is calculated with the help of our MHD model of the accretion disks. We consider the MFTs formed at distances of 0.027−0.8 au from the star with various initial radii and plasma betas β0. The simulations show that MFTs with a weak magnetic field (β0 = 10) rise slowly with speeds less than the speed of sound. MFTs with β0 = 1 form an outflowing magnetized corona above the disk. Strongly magnetized MFTs (β0 = 0.1) can cause outflows with velocities 20 – 50 km s−1. The tubes rise periodically over times from several days to several months according to our simulations. We propose that periodically rising MFTs can absorb stellar radiation and contribute to the IR-variability of young stellar objects.

Dynamics of magnetic flux tubes in an advective flow around a black hole

Entangled magnetic fields entering into an accretion flow would very soon be stretched into a dominant toroidal component due to strong differentially rotating motion inside the accretion disc. This is particularly true for weakly viscous, low angular momentum transonic or advective discs. We study the trajectories of toroidal flux tubes inside a geometrically thick flow which undergoes a centrifugal force supported shock. We also study effects of these flux tubes on the dynamics of the inflow and the outflow. We use a finite difference method (Total Variation Diminishing) for this purpose and specifically focussed on whether these flux tubes significantly affect the properties of the outflows such as its collimation and the rate. It is seen that depending upon the cross-sectional radius of the flux tubes which control the drag force, these field lines may move towards the central object or oscillate vertically before eventually escaping out of the funnel wall (pressure zero surfaces) along the vertical direction. A comparison of results obtained with and without flux tubes show these flux tubes could play pivotal role in collimation and acceleration of jets and outflows.

Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes

We theoretically explore the possibility of sausage instabilities developing on top of a kink instability in lengthening current-carrying magnetic flux tubes. Observations indicate that the dynamics of magnetic flux tubes in our cosmos and terrestrial experiments can involve topological changes faster than time scales predicted by resistive magnetohydrodynamics. Recent laboratory experiments suggest that hierarchies of instabilities, such as kink and Rayleigh-Taylor, could be responsible for initiating fast topological changes by locally accessing two-fluid and kinetic regimes. Sausage instabilities can also provide this coupling mechanism between disparate scales. Flux tube experiments can be classified by the flux tube's evolution in a configuration space described by a normalized inverse aspect-ratio k¯ and current-to-magnetic flux ratio λ¯. A lengthening current-carrying magnetic flux tube traverses this k¯–λ¯ space and crosses stability boundaries. We derive a single general criterion for the onset of the sausage and kink instabilities in idealized magnetic flux tubes with core and skin currents. The criterion indicates a dependence of the stability boundaries on current profiles and shows overlapping kink and sausage unstable regions in the k¯–λ¯ space with two free parameters. Numerical investigation of the stability criterion reduces the number of free parameters to a single one that describes the current profile and confirms the overlapping sausage and kink unstable regions in k¯–λ¯ space. A lengthening, ideal current-carrying magnetic flux tube can therefore become sausage unstable after it becomes kink unstable.

Braided magnetic fields: equilibria, relaxation and heating

We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for solar coronal heating. We investigate the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity—as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We finish by discussing the properties of the turbulent relaxation and the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor’s hypothesis.

Magnetic helicity and flux tube dynamics in the solar convection zone: Comparisons between observation and theory

Magnetic helicity, a conserved topological parameter in ideal MHD systems, conditions close to which are realized in the solar plasma, is intimately connected to the creation and subsequent dynamics of magnetic flux tubes in the solar interior. It can therefore be used as a tool to probe such dynamics. In this paper we show how photospheric observations of magnetic helicity of isolated magnetic flux tubes, manifested as the twist and writhe of solar active regions, can constrain the creation and dynamics of flux tubes in the solar convection zone and the nature of convective turbulence itself. We analyze the observed latitudinal distribution of twists in photospheric active regions, derived from solar vector magnetograms, in the largest such sample studied till‐date. We confirm and put additional constraints on the hemispheric twist helicity trend and find that the dispersion in the active region twist distribution is latitude‐independent, implying that the amplitude of turbulent fluctuations does not vary with latitude in the convection zone. Our data set also shows that the amplitude and dispersion of twist decreases with increasing magnetic size of active regions, supporting the conclusion that larger flux tubes are less affected by turbulence. Among the various theoretical models that have been proposed till‐date to explain the origin of twist, our observations best match the Σ effect model, which invokes helical turbulent buffeting of rising flux tubes as the mechanism for twist creation. Finally, we complement our analysis of twists with past observations of tilts in solar active regions and tie them in with theoretical modeling studies, to build up a comprehensive picture of the dynamics of twisted magnetic flux tubes throughout the solar convection zone. This general framework, binding together theory and observations, suggests that flux tubes have a wide range of twists in the solar convection zone, with some as high as to make them susceptible to the kink instability mechanism that results in the formation of δ spot or non‐Hale active regions.

Dynamics of magnetic flux tubes in space and laboratory plasmas

This paper gives a brief summary of topics discussed at a mini-conference on the dynamics of magnetic flux tubes in space and laboratory plasmas. This mini-conference was held as part of the Fall 2005 meeting of the American Physical Society Division of Plasma Physics.

Dynamics of magnetic flux tubes in close binary stars

Surface reconstructions of active close binary stars based on photometric and spectroscopic observations reveal non-uniform starspot distributions, which indicate the existence of preferred spot longitudes (with respect to the companion star). We consider the equilibrium and linear stability of toroidal magnetic flux tubes in close binaries to examine whether tidal effects are capable to initiate the formation of rising flux loops at preferred longitudes near the bottom of the stellar convection zone. The tidal force and the deviation of the stellar structure from spherical symmetry are treated in lowest-order perturbation theory assuming synchronised close binaries with orbital periods of a few days. The frequency, growth time, and spatial structure of linear eigenmodes are determined by a stability analysis. We find that, despite their small magnitude, tidal effects can lead to a considerable longitudinal asymmetry in the formation probability of flux loops, since the breaking of the axial symmetry due to the presence of the companion star is reinforced by the sensitive dependence of the stability properties on the stellar stratification and by resonance effects. The orientation of preferred longitudes of loop formation depends on the equilibrium configuration and the wave number of the dominating eigenmode. The change of the growth times of unstable modes with respect to the case of a single star is very small.

Dynamics of magnetic flux tubes in close binary stars

Observations of magnetically active close binaries with orbital periods of a few days reveal the existence of starspots at preferred longitudes (with respect to the direction of the companion star). We numerically investigate the non-linear dynamics and evolution of magnetic flux tubes in the convection zone of a fast-rotating component of a close binary system and explore whether the tidal effects are able to generate non-uniformities in the surface distribution of erupting flux tubes. Assuming a synchronised system with a rotation period of two days and consisting of two solar-type components, both the tidal force and the deviation of the stellar structure from spherical shape are considered in lowest-order perturbation theory. The magnetic field is initially stored in the form of toroidal magnetic flux rings within the stably stratified overshoot region beneath the convection zone. Once the field has grown sufficiently strong, instabilities initiate the formation of rising flux loops, which rise through the convection zone and emerge at the stellar surface. We find that although the magnitude of tidal effects is rather small, they nevertheless lead to the formation of clusters of flux tube eruptions at preferred longitudes on opposite sides of the star, which result from the cumulative and resonant character of the action of tidal effects on rising flux tubes. The longitude distribution of the clusters depends on the initial parameters of flux tubes in the overshoot region like magnetic field strength and latitude, implying that there is no globally unique preferred longitude along a fixed direction.

Do tidal effects determine the spot distribution on active binaries?

Observations of spot distributions on active binaries indicate the existence of preferred longitudes, which are more pronounced if the system period is shorter. This suggests that this effect is caused by the proximity of the companion star. We explore whether preferred longitudes can be explained by tidal effects on the dynamics of magnetic flux tubes, which are thought to give rise to starspots upon emergence at the stellar surface. We find that in the case of fast-rotating binaries flux tubes erupting at mid latitudes show indeed a considerably non-uniform longitudinal distribution.

Magnetic flux tubes inside the sun

Bipolar magnetic active regions are the largest concentrations of magnetic flux on the Sun. In this paper, the properties of active regions are investigated in terms of the dynamics of magnetic flux tubes which emerge from the base of the solar convection zone, where the solar cycle dynamo is believed to operate, to the photosphere. Flux tube dynamics are computed with the “thin flux tube” approximation, and by using magnetohydrodynamics simulation. Simulations of active region emergence and evolution, when compared with the known observed properties of active regions, have yielded the following results: (1) The magnetic field at the base of the convection zone is confined to an approximately toroidal geometry with a field strength in the range 3–10×104 G. The latitude distribution of the toroidal field at the base of the convection zone is more or less mirrored by the observed active latitudes; there is not a large poleward drift of active regions as they emerge. The time scale for emergence of an active region from the base of the convection zone to the surface is typically 2–4 months. (2) The tilt of active regions is due primarily to the Coriolis force acting to twist the diverging flows of the rising flux loops. The dispersion in tilts is caused primarily by the buffeting of flux tubes by convective motions as they rise through the interior. (3) Coriolis forces also bend active region flux tube shapes toward the following (i.e., antirotational) direction, resulting in a steeper leg on the following side as compared to the leading side of an active region. When the active region emerges through the photosphere, this results in a more rapid separation of the leading spots away from the magnetic neutral line as compared to the following spots. This bending motion also results in the neutral line being closer to the following magnetic polarity. (4) The properties of the strongly sheared, flare productive δ-spot active regions can be accounted for by the dynamics of highly twisted Ω loops that succumb to the helical kink instability as they emerge through the solar interior.

The Solar Dynamo and Emerging Flux – (Invited Review)

The largest concentrations of magnetic flux on the Sun occur in active regions. In this paper, the properties of active regions are investigated in terms of the dynamics of magnetic flux tubes which emerge from the base of the solar convection zone, where the solar cycle dynamo is believed to operate, to the photosphere. Flux tube dynamics are computed using the ‘thin flux tube’ approximation, and by using MHD simulation. Simulations of active region emergence and evolution, when compared with the known observed properties of active regions, have yielded the following results: (1) The magnetic field at the base of the convection zone is confined to an approximately toroidal geometry with a field strength in the range (3-10) × 104 G. The latitude distribution of the toroidal field at the base of the convection zone is more or less mirrored by the observed active latitudes; there is not a large poleward drift of active regions as they emerge. The time scale for emergence of an active region from the base of the convection zone to the surface is typically 2-4 months. The equatorial gap in the distribution of active regions has two possible origins; if the toroidal field strength is close to IO5 G, it is due to the lack of equilibrium solutions at low latitude; if it is closer to 3 x IO4 G, it may be due to modest poleward drift during emergence. (2) The tilt of active regions is due primarily to the Coriolis force acting to twist the diverging flows of the rising flux loops. The dispersion in tilts is caused primarily by the buffeting of flux tubes by convective motions as they rise through the interior. (3) The Coriolis force also bends the active region flux tube shape toward the following (i.e., anti-rotational) direction, resulting in a steeper leg on the following side as compared to the leading side of an active region. When the active region emerges through the photosphere, this results in a more rapid separation of the leading spots away from the magnetic neutral line as compared to the following spots. This bending motion also results in the neutral line being closer to the following magnetic polarity. (4) Active regions behave kinematically after they emerge because of ‘dynamic disconnection’, which occurs because of the lack of a solution to the hydrostatic equilibrium equation once the flux loop has emerged. This could explain why active regions decay once they have emerged, and why the advection-diffusion description of active regions works well after emergence. Smaller flux tubes may undergo ‘flux tube explosion’, a similar process, and provide a source for the constant emergence of small-scale magnetic fields. (5) The slight trend of most active regions to have a negative magnetic twist in the northern hemisphere and positive twist in the south can be accounted for by the action of Coriolis forces on convective eddies, which ultimately writhes active region flux tubes to produce a magnetic twist of the correct sign and amplitude to explain the observations. (6) The properties of the strongly sheared, flare productive δ-spot active regions can be accounted for by the dynamics of highly twisted Ω loops that succumb to the helical kink instability as they emerge through the solar interior.

Dynamics of Local Isolated Magnetic Flux Tubes in a Rapidly Rotating Stellar Atmosphere

The dynamics of magnetic flux tubes in a rapidly rotating stellar atmosphere is considered. We focus on the effects and signatures of the instability of the flux tube emergence influenced by the Coriolis force. We present the results from a linear stability analysis and discuss its possible signatures during the course of the evolution of G-type and M-type stars. We carried out three-dimensional magnetohydrodynamical simulations of local isolated magnetic flux tubes under a magnetic buoyancy instability in co-rotating Cartesian coordinates. We have found that the combination of the buoyancy instability and the Coriolis effect gives rise to a mechanism to twist the emerging magnetic flux tube into a helical structure. The tilt angle, east-west asymmetry, and magnetic helicity of the twisted flux tubes in the simulations have been studied in detail. The linear and nonlinear analyses provide hints as to what kind of pattern of large spots in young M-type main-sequence stars might be observed. We have found that young and old G-type stars may have different distributions of spots, while M-type stars may always have low-latitude spots. The size of stellar spots may decrease when a star becomes older, due to a decrease in the magnetic field. A qualitative comparison with solar observations is also presented.

Magnetically Uplifted Clumps in Cooling Flow Clusters

view Abstract Citations (10) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Magnetically Uplifted Clumps in Cooling Flow Clusters Zoabi, Essam ; Soker, Noam ; Regev, Oded Abstract We study the dynamics of magnetic flux tubes in cooling flow clusters. The cluster magnetic fields are assumed to be confined within these long tubes. The tubes are assumed to be deformed into an initial U shape, and we show that the magnetic tension forces can uplift the lower segments of the tubes to the height of the "tube feet," or even higher. For magnetic flux tubes having magnetic pressure of ~> 10% of the thermal pressure, radii of 5 kpc, and with a distance of 25 kpc between the feet of the tubes, the magnetic tension can lift dense, and therefore cool, material up to ~10 kpc above the feet. Thus, if the feet are anchored at r = 25 kpc, the magnetic tension can uplift material from r ~ 10 kpc out to r ~ 35 kpc, where r is the distance from the cluster center. We propose that such a process may explain X-ray filaments and clumps that. have been found recently in the central regions of several cooling flow clusters. We discuss the effects which should be included in future calculations in order to make the model more realistic and test it against observations. Publication: The Astrophysical Journal Pub Date: March 1996 DOI: 10.1086/176965 Bibcode: 1996ApJ...460..244Z Keywords: GALAXIES: COOLING FLOWS; GALAXIES: MAGNETIC FIELDS; GALAXIES: INTERGALACTIC MEDIUM; MAGNETOHYDRODYNAMICS: MHD full text sources ADS | data products SIMBAD (7)

Forces on magnetic flux tubes moving in inhomogeneous flows

view Abstract Citations (5) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Forces on Magnetic Flux Tubes Moving in Inhomogeneous Flows Moreno-Insertis, F. ; Ferriz-Mas, A. ; Schussler, M. Abstract The back-reaction of an incompressible two-dimensional flow of constant strain to the accelerated motion of a straight cylinder is calculated in the general case that the flow is inhomogeneous, nonstationary, and with nonvanishing (although constant) vorticity. The resulting enhanced inertia of the cylinder is basically given by its relative acceleration with respect to the background flow. Further force terms that appear because of the nonstationary and inhomogeneity of the background flow are the following: a force identical to that experienced by the mass elements of the unperturbed flow at the position of the axis of the cylinder; the customary lift force because of the circulation around the body; finally, a force term that appears only with nonvanishing relative speed between the body and the background flow and which is related to the energy which has to be imparted by the body to the surrounding fluid in order to adapt the perturbation to the new local velocity. The results have application to the dynamics of magnetic flux tubes in the convection zone and atmosphere of the Sun as well as to other astrophysical problems. Publication: The Astrophysical Journal Pub Date: February 1994 DOI: 10.1086/173758 Bibcode: 1994ApJ...422..652M Keywords: Flow Equations; Flow Theory; Fluid Flow; Magnetic Fields; Magnetic Flux; Magnetohydrodynamics; Astronomical Models; Incompressible Flow; Mathematical Models; Solar Atmosphere; Solar Convection (Astronomy); Astrophysics; HYDRODYNAMICS; MAGNETOHYDRODYNAMICS: MHD full text sources ADS |

Flux Tubes and Dynamos

The structure of solar surface magnetic fields, the way they erupt from the the convection zone below, and processes like flux expulsion and fragmentation instabilities support the view that magnetic flux in a stellar convection zone is in an intermittent, fragmented state which can be described as an ensemble of magnetic flux tubes. Depending on size and field strength, the dynamics of magnetic flux tubes can strongly differ from the behavior of a passive, diffuse field which is often assumed in conventional mean-field dynamo theory. Observed properties of active regions like emergence in low latitudes, Hale's polarity rules, tilt angles, and the process of sunspot formation from smaller fragments, together with theoretical considerations of the dynamics of buoyant flux tubes indicate that the magnetic structures which erupt in an emerging active region are not passive to convection and originate in a source region (presumably an overshoot layer below the convection zone proper) with a field strength of at least 105 G, far beyond the equipartition field strength with respect to convective flows. We discuss the consequences of such a situation for dynamo theory of the solar cycle and consider the possibility of dynamo models on the basis of flux tubes. A simple, illustrative example of a flux tube dynamo is presented.