Solar Flux Tubes Research Articles

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.

Solitary wave propagation in solar flux tubes

The aim of the present work is to investigate the excitation, time-dependent dynamic evolution, and interaction of nonlinear propagating (i.e., solitary) waves on vertical cylindrical magnetic flux tubes in compressible solar atmospheric plasma. The axisymmetric flux tube has a field strength of 1000G at its footpoint, which is typical for photospheric regions. Nonlinear waves that develop into solitary waves are excited by a footpoint driver. The propagation of the nonlinear signal is investigated by solving numerically a set of fully nonlinear 2.0D magnetohydrodynamic (MHD) equations in cylindrical coordinates. For the initial conditions, axisymmetric solutions of the linear dispersion relation for wave modes in a magnetic flux tube are applied. In the present case, we focus on the sausage mode only. The dispersion relation is solved numerically for a range of plasma parameters. The equilibrium state is perturbed by a Gaussian at the flux tube footpoint. Two solitary solutions are found by solving the full nonlinear MHD equations. First, the nonlinear wave propagation with external sound speed is investigated. Next, the solitary wave propagating close to the tube speed, also found in the numerical solution, is studied. In contrast to previous analytical and numerical works, here no approximations were made to find the solitary solutions. A natural application of the present study may be spicule formation in the low chromosphere. Future possible improvements in modeling and the relevance of the photospheric chromospheric transition region coupling by spicules is suggested.

MHD waves in magnetically twisted solar atmospheric flux tubes

The propagation of surface and body linear MHD modes in a twisted magnetic flux tube embedded in a magnetically twisted plasma environment is considered. The dispersion relation for surface and body modes is derived assuming constant external twisted field. Analytic approximate solutions to the dispersion equation are found for the long and short wave length cases.It was found, that in case the twisted component of the magnetic field in the environment of the flux tube is constant the index of Bessel functions in the corresponding dispersion relation is not integer. In the particular case of a homogen magnetic twist the total pressure is found to be constant across the boundary of the flux tube.

Atmospheric oscillations in solar magnetic flux tubes

The response of an exponentially diverging magnetic flux tube embedded in an isothermal solar atmosphere to the propagation of transverse tube waves and random transverse pulses generated in the solar convection zone is studied analyt- ically. General solutions are presented and applied to solar flux tubes located in the interior region and at the boundary of supergranulation cells. It is shown that the period of the free oscillations driven by transverse waves and pulses ranges from 7 to 10 min for the considered values of the tube magnetic field, and that these oscillations decay in time as t −3/2 . Since the observational signatures of these transverse oscillations are hard to detect, we also consider the generation of longitudinal tube waves by nonlinear mode coupling and the excitation of free atmospheric oscillations by longitudinal waves. Our results show that the basic properties of oscillations driven by transverse and longitudinal tube waves are different. While transverse waves excite oscillations with 7−10 min periods, oscillations by longitudinal waves have periods near 3 min. This is consistent with the observed 3-min oscillations inside the supergranule cells but inconsistent with the 7-min oscillations observed in the chro- mospheric network. We suggest that an explanation of the observed 7-min oscillations might be found by taking into account a more realistic structure of flux tubes located in the magnetic network.

Radiative Transfer Effects and the Dynamics of Small‐Scale Magnetic Structures on the Sun

The dynamical consequences of radiative energy transport on the evolution of gas confined to small-scale magnetic structures on the Sun are studied. Convective collapse, which transforms weak-field structures into intense structures of field strengths in the 1-2 kG range on the photosphere, is strongly influenced by radiative heating from the surroundings and cooling due to losses in the vertical direction. We first present analytic results in the quasi-adiabatic approximation to attempt a qualitative understanding of the influence of radiative effects on the convective stability of flux tubes. We demonstrate the destabilizing action of vertical radiative losses, that tend to enhance convective collapse and produce strong tubes at a relatively smaller horizontal scale than those expected from calculations based solely on horizontal radiative energy transport. Our calculations clearly point to an asymmetry between upflow and downflow perturbations—only the latter are amplified in the presence of vertical radiative transport. Using a realistic model of the solar atmospheric structure and treating radiative transfer in the diffusion and Eddington approximations, we next perform numerical stability analyses and produce size (flux)-strength relations for solar flux tubes. Our results provide a physical explanation for the observed flux-dependent (equivalently size-dependent) field strengths of the solar small-scale magnetic structures in the form of weak intranetwork and strong network components.

Models of flux tubes from constrained relaxation

We study the relaxation of a compressible plasma to an equili� brium with flow. The constraints of conservation of mass, energy, angular momentum, crosshelicity and relative magnetic helicity are imposed. Equilibria corresponding to the energy extrema while conserving these invariants for parallel flows yield three classes of solutions and one of them with an increasing radial density profile, relevant to solar flux tubes is presented.

The Thermal Nonequilibrium of Prominences

We present numerical simulations and analytic theory for the thermal nonequilibrium of solar coronal flux tubes that have a stretched-out, dipped geometry, appropriate for a prominence/filament. Our simulations indicate that if the heating in such a flux tube is localized near the chromosphere, then condensations appear which undergo a continuous cycle of formation, motion, and destruction, even though the heating and all other imposed conditions on the loop are purely time independent. We show how this nonsteady evolution can be understood in terms of simple scaling-law theory. The implications of thermal nonequilibrium for observations of the solar corona are discussed. We argue that the model can explain both the formation of prominence condensations and recent observations of their dynamics.

Models of Flux Tubes from Constrained Relaxation

AbstractWe study the relaxation of a compressible plasma to an equilibrium with flow. The constraints of conservation of mass, energy, angular momentum, cross-helicity and relative magnetic helicity are imposed. Equilibria corresponding to the energy extrema while conserving these invariants for parallel flows yield three classes of solutions and one of them with an increasing radial density profile, relevant to solar flux tubes is presented.

On Analysis of Dual Spacecraft Stereoscopic Observations to Determine the Three-Dimensional Morphology and Plasma Properties of Solar Coronal Flux Tubes

By using two spacecraft equipped with multi-bandpass X-ray telescopes, it is possible to obtain direct 3-dimensional morphology of coronal structures which is essential for understanding the energetics and dynamics of the solar atmosphere. X-ray observations taken only in orbit about the Earth are inadequate to fully resolve the 3-dimensional nature of the solar corona. These Earth-orbit observations produce 2-dimensional images and an appropriate model must be included to derive the 3-dimensional structures from the line-of-sight information. Stereoscopic observations from space will remove this limitation and are needed if we are to improve our knowledge of the 3-dimensional morphology of the corona.

Signatures of Acoustic and Magnetic Waves in Solar and Stellar Coronae

Time-dependent dynamical calculations of the radiating gas in solar coronal flux tubes are used to identify features of UV spectral-line profiles that can reveal the direction in which wave energy flows through the solar transition region. The profile features survive spatial and temporal averaging through nonlinear dependencies of line emission coefficients on thermal properties of the plasma that are correlated with fluid velocities. This approach can be applied to stellar and other unresolved sources, as well as the solar atmosphere. It can be regarded as a new angle of attack on the long-standing problem of determining coronal heating mechanisms. The approach requires low noise data of high spectral resolution. Therefore, it can take advantage of some unique properties of the SUMER instrument on SOHO. We make specific predictions for SUMER data that, in principle, can test whether energy propagates upward or downward in coronal flux tubes, thus allowing one to discriminate between competing theories of coronal heating. We are acquiring SUMER data in an attempt to do this.

Dynamical effects in solar photospheric flux tubes

The interaction of an intense flux tube, extending vertically through the photosphere, with p-modes in the ambient medium is modelled by solving the time dependent MHD equations in the thin flux tube approximation. It is found that a resonant interaction can occur, which leads to the excitation of flux tube oscillations with large amplitudes. The resonance is not as sharp as in the case of an unstratified atmosphere, but is broadened by a factor proportional toH−2, whereH is the local pressure scale height. In addition, the inclusion of radiative transport leads to a decrease in the amplitude of the oscillations, but does not qualitatively change the nature of the interaction.

Surface currents on models of force-free solar magnetic flux tubes

A model of a cylindrically symmetric, force-free magnetic field consisting of a sequence of concentric layers with piecewise-constant α is used to construct models of the surface currents on isolated, force-free magnetic flux tubes. Two boundary conditions are considered: a current-neutralized flux tube (Bφ = 0, Bz φ 0, Bz ≠ O at r > r0), and an isolated current-carrying flux tube (Bφ ≠ 0, Bz = 0 at r > r0). A single-a model that is current-neutralized is a reverse-field pinch, and is unacceptable as a model for a solar flux tube. Examples of two-α models for a current-neutralized flux tube are presented. The models of the surface currents satisfying either boundary condition are shown to simplify considerably when the surface layer is thin. A model consisting of several layers, with piecewise-constant α, may be used to find an approximate solution for a force-free flux tube with an arbitrarily specified current profile.

A numerical simulation of two-dimensional radiative equilibrium in magnetostatic flux tubes. II - Computational results

view Abstract Citations (25) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Numerical Simulation of Two-dimensional Radiative Equilibrium in Magnetostatic Flux Tubes. II. Computational Results Pizzo, V. J. ; MacGregor, K. B. ; Kunasz, P. B. Abstract We apply a recently developed numerical procedure for obtaining self-consistent radiative and mechanical equilibria of solar magnetostatic flux tubes. The tubes are modeled as localized but continuous field concentrations in a 2D slab geometry, and the radiation is treated in the LTE limit. The reduced opacities in the tube lead to the lateral intrusion of radiative flux into the tube, with subsequent modification of the internal atmosphere. Our calculations show that the effect is negligible, however, when the diameter of the tube exceeds the scale height of the atmosphere in the surface layers or if convective energy transport in the tube is itself sufficient to produce a thermal stratification close to that in the surrounding photosphere. That is, 2D radiative effects are likely to be important only in small tubes in which the upward convective energy flux is strongly suppressed. The treatment of the underlying convective layers appears to be of paramount importance in determining the computed surface properties. Publication: The Astrophysical Journal Pub Date: August 1993 DOI: 10.1086/173044 Bibcode: 1993ApJ...413..764P Keywords: Magnetic Field Configurations; Magnetic Flux; Magnetohydrodynamics; Solar Convection (Astronomy); Solar Magnetic Field; Boundary Conditions; Iteration; Radiative Transfer; Stellar Models; Solar Physics; MAGNETOHYDRODYNAMICS: MHD; RADIATIVE TRANSFER; SUN: ATMOSPHERE full text sources ADS | Related Materials (1) Part 1: 1993ApJ...404..788P

A numerical simulation of two-dimensional radiative equilibrium in magnetostatic flux tubes. I - The model

view Abstract Citations (19) References (22) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Numerical Simulation of Two-dimensional Radiative Equilibrium in Magnetostatic Flux Tubes. I. The Model Pizzo, V. J. ; MacGregor, K. B. ; Kunasz, P. B. Abstract We describe an efficient numerical procedure for obtaining self-consistent radiative and mechanical equilibria of solar magnetostatic flux tubes. The flux tube is treated as a localized but continuous concentration of magnetic flux in a two-dimensional slab geometry. Starting from some given initial atmosphere, we compute a preliminary magnetostatic equilibrium state by a nonlinear iterative technique, subject to certain boundary conditions on the magnetic field. Given the resulting spatial distribution of opacities (derived from the initial run of temperature and density along each field line), and with knowledge of a distant radiation field incident upon the magnetic region, the radiative state of the atmosphere is computed by the short-characteristics method assuming gray, LTE conditions. The new temperature derived from the angle-averaged radiation field is used to update the hydrostatic atmosphere for the magnetostatic calculation, and so on, until both mechanical and radiative balance is attained. Publication: The Astrophysical Journal Pub Date: February 1993 DOI: 10.1086/172333 Bibcode: 1993ApJ...404..788P Keywords: Magnetohydrostatics; Solar Atmosphere; Solar Magnetic Field; Stellar Models; Radiative Transfer; Sunspots; Solar Physics; MAGNETOHYDRODYNAMICS: MHD; RADIATIVE TRANSFER; SUN: ATMOSPHERE; SUN: SUNSPOTS full text sources ADS | Related Materials (1) Part 2: 1993ApJ...413..764P

Influence of heating rate on the condensational instability

We determine by analysis and numerical simulation the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. We first derive a dispersion relation for infinitesimal disturbances to a condensationally unstable fluid subject to heating rates which are functions of temperature and thermal pressure. This relation leads to an algebraic model for predicting solar flux tube stability in the longwavelength limit as a function of temperature. We find that linear stability depends strongly on the heating rate. We then present the results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube. Different heating rates lead to quite different nonlinear evolution, as evidenced by the behaviour of the global internal energy. Almost all of the heating rates that we consider produce saturation in bifurcated states, but at somewhat different temperatures and mass densities.

Dark envelope solitons of fast magnetosonic surface waves in solar flux tubes

We have studied the modulational stability of a finite-amplitude fast sausage magnetosonic surface wave traveling along a thin magnetic slab in the solar photosphere (chromosphere). The equation governing the evolution of the fast-wave envelope modulated by a slow wave driven by the ponderomotive force proves to be the cubic nonlinear Schrodinger equation which in photospheric conditions admits only dark envelope soliton solutions. The possibility of the existence of such solitary waves in the solar atmosphere is discussed.

On magnetohydrodynamic solitons in jets

Nonlinear solitary wave propagation in a compressible magnetic beam model of an extragalactic radio jet is examined and shown to lead to solitons of the Benjamin-Ono type. A number of similarities between such magnetic beam models of jets and models of solar photospheric flux tubes are pointed out and exploited. A single soliton has the appearance of a symmetric bulge on the jet which propagates faster than the jet's flow.

Particle propagation effects on wave growth in a solar flux tube

view Abstract Citations (25) References (43) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Particle Propagation Effects on Wave Growth in a Solar Flux Tube White, S. M. ; Melrose, D. B. ; Dulk, G. A. Abstract The evolution of a distribution of electrons is followed after they are injected impulsively at the top of a coronal magnetic loop, with the objective of studying the plasma instabilities which result. At early times the downgoing electrons have beamlike distributions and amplify electrostatic waves via the Cerenkov resonance; the anomalous Doppler resonance is found to be less important. Slightly later, while the electrons are still predominantly downgoing, they are unstable to cyclotron maser generation of z-mode waves with omega(p) much less than Omega, or to second harmonic x-mode waves. The energetics of these instabilities, including saturation effects and heating of the ambient plasma, are discussed. It is suggested that coalescence of two z-mode waves generated by cyclotron maser emission of the downgoing electrons may produce the observed microwave spike bursts. Publication: The Astrophysical Journal Pub Date: September 1986 DOI: 10.1086/164512 Bibcode: 1986ApJ...308..424W Keywords: Magnetohydrodynamic Stability; Particle Acceleration; Plasma Diagnostics; Solar Flares; Solar Magnetic Field; Cerenkov Radiation; Cyclotron Radiation; Electron Distribution; Solar Physics; PARTICLE ACCELERATION; SUN: FLARES; SUN: MAGNETIC FIELDS full text sources ADS |

Convective instability in a solar flux tube. I - Nonlinear calculations for an adiabatic inviscid fluid

The temporal evolution of a slender flux tube extending vertically in the convection zone of the Sun is modeled by numerical solution of the MHD equaitons. Initial states in hydrostatic equilibrium and for which ..beta.. (the ratio of the thermal to magnetic pressure at the initial epoch) is constant with depth are considered. The time-dependent response of these states to a velocity perturbation is examined. When the perturbation is a downflow, convective collapse of the flux tube occurs when ..beta..> or approx. =2. The numerical solutions are followed for long enough times for the instability to be quenched. An important finding to emerge is that the final state is not a steady one, but rather a stationary oscillating one. The surface magnetic field in the final state has an average value of about 1400 G, with an oscillating amplitude of approx.200 G. There is an oscillating flow with an amplitude of approx.600 m s/sup -1/ with an average value that is approximately zero. The observational implications of these results are discussed.

Cool luminous stars

A broad theme emerging from IUE and Einstein observations of cool stars is that magnetic fields control the structure and energy balance of the outer atmospheres of these stars. I summarize the phenomena associated with magnetic fields in the Sun and show that similar phenomena occur in cool luminous stars. High dispersion spectra are providing unique information concerning densities, atmospheric extension, and emission line widths. A recent unanticipated discovery is that the transition lines are redshifted (an antiwind) in β Dra (G2 Ib) and perhaps other stars, which I interpret as indicating downflows in closed magnetic flux tubes as are seen in the solar flux tubes above sunspots. Finally, I classify the G and K giants and supergiants into three groups — active stars, quiet stars, and hybrid stars — depending on whether their atmospheres are dominated by closed magnetic flux tubes, open field geometries, or a predominately open geometry with a few closed flux tubes embedded.