Waves In Flux Tubes Research Articles

On Boundary Conditions for Magnetohydrodynamic Waves in Flux Tubes with a Pressure Jump

Abstract It is proved that the recent paper by Yelagandula on “a new insight” on the boundary conditions to be applied to magnetohydrodynamic waves in magnetic flux tubes with a finite thermal pressure jump at the boundary is fundamentally wrong. It exploits the wrong variables and assumes a fixed instead of a moving boundary.

Evolution of solar-type activity: acoustic and magnetic energy generation and propagation in $\beta $ Hydri (G2 IV)

We examine the acoustic and magnetic energy generation and propagation in beta Hydri (G2 IV). The underlying motivation for this work is based on the solar, stellar, and galactic relevance of beta Hydri (a star in the Southern hemisphere), which is readily understood as a prime example and proxy of the future Sun - thus allowing assessments and analyses of the secular decay of solar activity. Regarding the magnetic energy generation, we consider longitudinal flux tube waves. We also assess acoustic waves. For the acoustic wave energy flux, the difference between the results obtained for beta Hydri and the Sun is significantly smaller than typically attained for main-sequence stars, which is largely due to the gravity-dependence of the acoustic energy generation. Furthermore, we study the height-dependent behavior of the magnetic energy flux for different magnetic filling factors corresponding to different flux tube spreadings. Finally, we comment on possible directions of future research.

Transverse oscillations and damping of magnetic flux tubes with a thick transitional layer

ABSTRACT In this paper, the magnetohydrodynamic kink waves and their damping are investigated in a thin coronal flux tube model. The thickness of the inhomogeneous transitional layer is of the order of the tube’s radius. The governing equations are solved analytically in all regions of the tube except for the thin dissipative layer. The dispersion relation is derived and solved numerically. The oscillation frequency does not vary much when varying the thickness of the transitional layer. When the transitional layer is thin, the damping rate of the kink wave increases significantly with the increase in the thickness of the transitional layer; however, when the transitional layer is thick, the damping rate does not vary much with the increase in the thickness of the transitional layer. For small values of the thickness of the transitional layer, our results are in agreement with results obtained in the thin tube, thin boundary approximation. In flowing tubes, the effect of flow on the damping rate of the waves depends on the direction of the wave propagation and plasma flow. The resonant instability of the kink waves in flux tubes with flowing transitional layer has been investigated.

Chromospheric activity in 55 Cancri: II. Theoretical wave studies versus observations

ABSTRACT In this study, we consider chromospheric heating models for 55 Cancri in conjunction with observations. The theoretical models, previously discussed in Paper I, are self-consistent, non-linear, and time-dependent ab-initio computations encompassing the generation, propagation, and dissipation of waves. Our focus is the consideration of both acoustic waves and longitudinal flux tube waves amounting to two-component chromosphere models. 55 Cancri, a K-type orange dwarf, is a star of low activity, as expected by its age, which also implies a relatively small magnetic filling factor. The Ca ii K fluxes are computed (multi-ray treatment) assuming partial redistribution and time-dependent ionization. The theoretical Ca ii H+K fluxes are subsequently compared with observations. It is found that for stages of lowest chromospheric activity the observed Ca ii fluxes are akin, though not identical, to those obtained by acoustic heating, but agreement can be obtained if low levels of magnetic heating – consistent with the expected photospheric magnetic filling factor – are considered as an additional component; this idea is in alignment with previous proposals conveyed in the literature.

On Kelvin–Helmholtz and parametric instabilities driven by coronal waves

The Kelvin-Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the oscillatory shear flow associated with an MHD wave. We investigate the linear stability of a discontinuous oscillatory shear flow in the presence of a horizontal magnetic field within a Cartesian framework that captures the essential features of MHD oscillations in flux tubes. We derive a Mathieu equation for the Lagrangian displacement of the interface and analyse its properties, identifying two different instabilities: a Kelvin-Helmholtz instability and a parametric instability involving resonance between the oscillatory shear flow and two surface Alfv\'{e}n waves. The latter occurs when the system is Kelvin-Helmholtz stable, thus favouring modes that vary along the flux tube, and as a consequence provides an important and additional mechanism to extract energy. When applied to flows with the characteristic properties of kink waves in the solar corona, both instabilities can grow, with the parametric instability capable of generating smaller scale disturbances along the magnetic field than possible via the Kelvin-Helmholtz instability. The characteristic time-scale for these instabilities is $\sim 100$ s, for wavelengths of $200$ km. The parametric instability is more likely to occur for smaller density contrasts and larger velocity shears, making its development more likely on coronal loops than on prominence threads.

Solar magnetic flux tube simulations with time-dependent ionization

In the present work we expand the study of time-dependent ionization previously identified to be of pivotal importance for acoustic waves in solar magnetic flux tube simulations. We focus on longitudinal tube waves (LTW) known to be an important heating agent of solar magnetic regions. Our models also consider new results of wave energy generation as well as an updated determination of the mixing length of convection now identified as 1.8 scale heights in the upper solar convective layers. We present 1-D wave simulations for the solar chromosphere by studying tubes of different spreading as function of height aimed at representing tubes in environments of different magnetic filling factors. Multi-level radiative transfer has been applied to correctly represent the total chromospheric emission function. The effects of time-dependent ionization are significant in all models studied. They are most pronounced behind strong shocks and in low density regions, i.e., the middle and high chromosphere. Concerning our models of different tube spreading, we attained pronounced differences between the various types of models, which were largely initiated by different degrees of dilution of the wave energy flux as well as the density structure partially shaped by strong shocks, if existing. Models showing a quasi-steady rise of temperature with height are obtained via monochromatic waves akin to previous acoustic simulations. However, longitudinal flux tube waves are identified as insufficient to heat the solar transition region and corona in agreement with previous studies.

Magnetic Solitons: Unified Mechanism for Moving Magnetic Features

In a highly dynamic environment with sources and sinks of energy, flux tubes do not in general obey local conservation laws, nor do the ensembles of flux tubes that exhibit collective phenomena. We use the approach of energetically open dissipative systems to study nonlinear waves in flux tubes and their role in the dynamics of the overlying atmosphere. We present results of theoretical and observational studies of the properties of moving magnetic features (MMFs) around sunspots and the response of the overlying atmosphere to various types of MMFs. We show that all types of MMFs, often having conflicting properties, can be described on a unified basis by employing the model of shocks and solitons propagating along the penumbral filaments co-aligned with Evershed flows. The model is also consistent with the response of the upper atmosphere to individual MMFs, which depends on their type. For example, soliton-type bipolar MMFs mainly participate in the formation of a moat and do not carry much energy into the upper atmosphere, whereas shock-like MMFs, with the appearance of single-polarity features, are often associated with chromospheric jets and microflares.

Properties of longitudinal flux tube waves

We discuss the analytic properties of longitudinal tube waves taking into account ambient wind flows. This is an extension of the studies of Papers I and II, which assumed a mean flow speed of zero and also dealt with a simplified horizontal pressure balance. Applications include the study of longitudinal flux tube waves in stars with significant mass loss and the heat- ing and dynamics of plumes in the solar wind. Slow magnetosonic waves, also called longitudinal waves, have been observed in solar plumes and are likely an important source of heating. We show that the inclusion of ambient wind flows considerably alters the limiting shock strength as well as the energy damping length of the waves.

Dynamical processes in flux tabes and their role in chromospheric heating

We model the dynamical interaction between magnetic flux tubes and granules in the solar photosphere which leads to the excitation of transverse (kink) and longitudinal (sausage) tube waves. The investigation is motivated by the interpretation of network oscillations in terms of flux tube waves. The calculations show that for magnetic field strengths typical of the network, the energy flux in transverse waves is higher than in longitudinal waves by an order of magnitude. But for weaker fields, such as those that might be found in internetwork regions, the energy fluxes in the two modes are comparable. Using observations of footpoint motions, the energy flux in transverse waves is calculated and the implications for chromospheric heating are pointed out.

Dynamical Processes in Flux Tribes and their Role in Chromospheric Heating

AbstractWe model the dynamical interaction between magnetic flux tubes and granules in the solar photosphere which leads to the excitation of transverse (kink) and longitudinal (sausage) tube waves. The investigation is motivated by the interpretation of network oscillations in terms of flux tube waves. The calculations show that for magnetic field strengths typical of the network, the energy flux in transverse waves is higher than in longitudinal waves by an order of magnitude. But for weaker fields, such as those that might be found in internetwork regions, the energy fluxes in the two modes are comparable. Using observations of footpoint motions, the energy flux in transverse waves is calculated and the implications for chromospheric heating are pointed out.

Excitation of Oscillations in Photospheric Flux Tubes through Buffeting by External Granules

We examine the excitation of transverse (kink) and longitudinal (sausage) waves in magnetic flux tubes by granules in the solar photosphere. The investigation is motivated by the interpretation of network oscillations in terms of flux tube waves. We model the interaction between a granule, with a specified transverse velocity, and a vertical flux tube in terms of the Klein-Gordon equation, which we solve analytically as an initial value problem for both wave modes, assuming the same external impulse. The calculations show that for magnetic field strengths typical of the network, the energy flux in transverse waves is higher than in longitudinal waves by an order of magnitude, in agreement with the chromospheric power spectrum of network oscillations observed by Lites, Rutten, & Kalkofen. But for weaker fields, such as those that might be found in internetwork regions, the energy fluxes in the two modes are comparable. This result implies that if there are internetwork oscillations in magnetic flux tubes, they must show the cutoff periods of both longitudinal and transverse modes at 3 minutes and at 7 minutes or longer. We also find that granules with speeds of about 2 km s-1 can efficiently excite transverse oscillations in frequent short-duration (typically 1 minute) bursts that can heat the corona.

Current-Vortex Filament and Soliton-Like Waves in Weakly Ionized Plasmas

We present results of magnetic flux-tube waves propagating along a current loop in a weakly ionized plasma, by means of a 3-D Neutral-MHD simulation code. After an impulsive velocity perturbation, the magnetic wave takes a tube structure and behaves as an isolated and stable string, to say a magnetic flux-tube soliton. Its velocity is associated with the electric current of the loop and a vortex induced inside the tube. There exists an interval of the electric current, where the velocity of the soliton is nearly proportional to the current. While on the stronger current region the velocity of the soliton is almost constant. The characteristics of the magnetic flux-tube soliton observed in this simulation can be explained for a simple MHD model, in which we give necessary treatments to reduce the equation of current-vortex filament to a frame of integrable system.

Effect of Newtonian Cooling on Waves in a Magnetized Isothermal Atmosphere

We examine the influence of nonadiabatic effects on the modes of an isothermal stratified magnetic atmosphere. The present investigation is a continuation of earlier work by Hasan and Christensen-Dalsgaard (1992) and Banerjee, Hasan, and Christensen-Dalsgaard (1995, 1996), where the interaction of various elementary modes in a stratified magnetized atmosphere was studied in the purely adiabatic limit. The inclusion of radiative dissipation based on Newton's law of cooling demonstrates the importance of this effect in the study of magnetoatmospheric waves. We analyze the physical nature of magnetoacoustic gravity (or MAG) oscillations in the presence of Newtonian cooling and find that the eigenfrequency curves in the diagnostic diagram, as in the previous analysis, undergo avoided crossings. However, the qualitative nature of the mode interaction is strongly influenced by radiative dissipation, which leads to strong mode damping in the avoided-crossing regions. We demonstrate this effect for the interaction between the Lamb mode and a magnetic mode. Our results could be important in the analysis of waves in flux tubes on the Sun.

Viscous computations of resonant absorption of MHD waves in flux tubes by fem

A numerical code is presented for computing the stationary state of resonant absorption of MHD waves in cylindrical flux tubes in linear, compressible, and viscous MHD. The full viscosity stress tensor is included in the code with the five viscosity coefficients as given by Braginskii (1965). Also non-zero plasma pressure effects are taken into account, and the finite elements discretization with the Galerkin method has been used. The implementation of the stress tensor and the numerical accuracy of the tensorial viscous MHD code are scrutinized in test case. The test case involves the absorption of waves in cylindrical flux tubes considered by Lou (1990) and Goossens and Poedts (1992) in the context of absorption of acoustic oscillations. The results for the absorption rates obtained with the tensorial viscous code agree completely with the results obtained by Lou in a scalar viscous MHD and by Goossens and Poedts in resistive MHD. This verifies not only the complicated tensor viscous code but again proves that the absorption rate is independent of the actual dissipation mechanism.

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

Nonlinear Waves in Flux Tubes

Some results of nonlinear studies of flux tube oscillations are summarized showing that each step made towards the real conditions of the solar atmosphere opens the existence of qualitatively new effects which form the basis of strongly nonlinear dynamics. Among these effects are, for example: explosive instability in the presence of negative energy waves which leads to an efficient and fast energy release; the generation of secondary plasma flows and current drive which strongly influence the evolution of magnetic flux tubes and their stability conditions; formation of shocks and solitary waves, temporal brightening of flux tubes and others.

The Observational Signature of Flux Tube Waves and an Upper Limit on the Energy Flux Transported by Them

The influence of undamped linear longitudinal tube waves on Stokes V profiles is considered. A rough upper limit is set on the energy flux transported by such waves through the photosphere. It is found that this upper limit is larger than the flux in the quiet sun. However, due to the small filling factor of the magnetic elements, the total luminosity of flux tube waves is unlikely to be larger than that of acoustic waves when averaged over the whole sun. Therefore, probably both kinds of waves contribute to chromospheric heating. However, the derived upper limit does not rule out that flux tube waves can significantly enhance the chromospheric brightness in active regions and the supergranular network where the magnetic filling factor is large.

On the generation of flux tube waves in stellar convection zones. I - Longitudinal tube waves driven by external turbulence

The source functions and the energy fluxes for wave generation in magnetic flux tubes embedded in an otherwise magnetic field-free, turbulent, and compressible fluid are derived. The calculations presented here assume that the tube interior is not itself turbulent, e.g., that motions within the flux tube are due simply to external excitation. Specific results for the generation of longitudinal tube waves are presented.

Leaky and non-leaky oscillations in magnetic flux tubes

An extensive analysis, both analytic and numerical, of waves in flux tubes imbedded in (possibly) magnetic surroundings is given. It is shown that any wave confined to the tube and its neighbourhood can be put into one of seven categories. Simple criteria for deciding the existence of each type in any particular case are derived. Many other (leaky) modes are found which excite waves in the external medium and thereby lose energy to the surroundings. A number of asymptotic analyses allow much information to be gained about these without the need for numerical solution of the complicated equations involved. Three particular cases, pertaining to photospheric flux tubes, Hα fibrils, and coronal loops, are considered in detail.