A New Model for Propagating Parts of EIT Waves: A Current Shell in a CME

EIT waves are observed in EUV as bright fronts. Some of these bright fronts propagate across the solar disk. EIT waves are all associated with a flare and a CME and are commonly interpreted as fast-mode magnetosonic waves. Propagating EIT waves could also be the direct signature of the gradual opening of magnetic field lines during a CME. We quantitatively addressed this alternative interpretation. Using two independent 3D MHD codes, we performed nondimensional numerical simulations of a slowly rotating magnetic bipole, which progressively result in the formation of a twisted magnetic flux tube and its fast expansion, as during a CME. We analyse the origins, the development, and the observability in EUV of the narrow electric currents sheets that appear in the simulations. Both codes give similar results, which we confront with two well-known SOHO/EIT observations of propagating EIT waves (7 April and 12 May 1997), by scaling the vertical magnetic field components of the simulated bipole to the line of sight magnetic field observed by SOHO/MDI and the sign of helicity to the orientation of the soft X-ray sigmoids observed by Yohkoh/SXT. A large-scale and narrow current shell appears around the twisted flux tube in the dynamic phase of its expansion. This current shell is formed by the return currents of the system, which separate the twisted flux tube from the surrounding fields. It intensifies as the flux tube accelerates and it is co-spatial with weak plasma compression. The current density integrated over the altitude has the shape of an ellipse, which expands and rotates when viewed from above, reproducing the generic properties of propagating EIT waves. The timing, orientation, and location of bright and faint patches observed in the two EIT waves are remarkably well reproduced. We conjecture that propagating EIT waves are the observational signature of Joule heating in electric current shells, which separate expanding flux tubes from their surrounding fields during CMEs or plasma compression inside this current shell. We also conjecture that the bright edges of halo CMEs show the plasma compression in these current shells.     

Linear and non-linear MHD wave propagation in steady-state magnetic cylinders

The propagation of linear and non-linear magnetohydrodynamic (MHD) waves in a straight homogeneous cylindrical magnetic flux tube embedded in a homogeneous magnetic environment is investigated. Both the tube and its environment are in steady state. Steady flows break the symmetry of forward (field-aligned) and backward (anti-parallel to magnetic field) propagating MHD wave modes because of the induced Doppler shifts. It is shown that strong enough flows change the sense of propagation of MHD waves. The flow also induces shifts in cut-off values and phase-speeds of the waves. Under photospheric conditions, if the flow is strong enough, the slow surface modes may disappear and the fast body modes may become present. The crossing of modes is also observed due to the presence of flows. The effect of steady-state background has to be considered particularly carefully when evaluating observation signatures of MHD waves for diagnostics in the solar atmosphere.     

Heating of coronal loops by fast mode MHD waves

A possible mechanism for the formation and heating of coronal loops through the propagation and damping of fast mode waves is proposed and studied in detail. Loop-like field structures are represented by a dipole field with the point dipole at a given distance below the solar surface. The density of the medium is determined by hydrostatic equilibrium along the field lines in an isothermal atmosphere. The fast mode waves propagating outward from the coronal base are refracted into regions with a low Alfvén speed and suffer collisionless damping when the gas pressure becomes comparable to the magnetic pressure. The propagation and damping of these waves are studied for three different cases: a uniform density at the coronal base, a density depletion within a given flux tube, and a density enhancement within a given flux tube. The fast mode waves are found to be important in the formation and heating of the loops if the wave energy flux density is of the order 10⁵ ergs cm^-2 s^-1 at the coronal base.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

Sausage Mode Propagation in a Thick Magnetic Flux Tube

The aim of this paper is to model the propagation of slow magnetohydrodynamic (MHD) sausage waves in a thick expanding magnetic flux tube in the context of the quiescent (VAL-C) solar atmosphere. The propagation of these waves is found to be described by the Klein–Gordon equation. Using the governing MHD equations and the VAL-C atmosphere model we study the variation of the cut-off frequency along and across the magnetic tube guiding the waves. Due to the radial variation of the cut-off frequency the flux tubes act as low frequency filters for the waves.     

Linear MHD Wave Propagation in Time-Dependent Flux Tube

The propagation of magnetohydrodynamic (MHD) waves is an area that has been thoroughly studied for idealised static and steady state magnetised plasma systems applied to numerous solar structures. By applying the generalisation of a temporally varying background density to an open magnetic flux tube, mimicking the observed slow evolution of such waveguides in the solar atmosphere, further investigations into the propagation of both fast and slow MHD waves can take place. The assumption of a zero-beta plasma (no gas pressure) was applied in Williamson and Erdélyi (Solar Phys. 2013, doi: 10.1007/s11207-013-0366-9 , Paper I) is now relaxed for further analysis here. Firstly, the introduction of a finite thermal pressure to the magnetic flux tube equilibrium modifies the existence of fast MHD waves which are directly comparable to their counterparts found in Paper I. Further, as a direct consequence of the non-zero kinetic plasma pressure, a slow MHD wave now exists, and is investigated. Analysis of the slow wave shows that, similar to the fast MHD wave, wave amplitude amplification takes place in time and height. The evolution of the wave amplitude is determined here analytically. We conclude that for a temporally slowly decreasing background density both propagating magnetosonic wave modes are amplified for over-dense magnetic flux tubes. This information can be very practical and useful for future solar magneto-seismology applications in the study of the amplitude and frequency properties of MHD waveguides, e.g. for diagnostic purposes, present in the solar atmosphere.     

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.     

Cutoff frequency and the reflection of vertically propagating magnetoacoustic gravity waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere stratified in the field of gravity, we investigate the main patterns of vertical propagation of magnetoacoustic gravity waves (MAGWs) in the approximation of a horizontal potential magnetic field. We have established that the cutoff frequency for MAGWs below which they cannot propagate does not depend on the magnetic field strength and is equal to that for acoustic gravity waves, the Lamb frequency. The cutoff frequency is shown to be unaffected by the linear interaction between counterpropagating MAGWs that results from a nonuniform height distribution of the Alfvén velocity and that causes the reflection of propagating waves at relatively large heights.     

磁场中p模/s模的转换及黑子对声波的吸收

在柱坐标下将黑子周围的环形区域（黑子除外）内的振荡分解为朝向黑子传播的（入射的）波和离开黑子传播的（出射的）波。对无黑子的环形区域内的振荡也进行了同样的分解。将黑子周围的入射波看成是被黑子磁流管磁化了的介质（介质内的磁场基本是水平的）中的波。而无黑子区的入射波看成是非磁化介质中的波。比较这两种波在固定波数下功率随频率的分布发现，在磁化介质中不同径向除ｎ的声波（ｐ模）频率系统降低，同时功率也降低，降低的功率最高达非磁化介质中波的功率的３０％。而比较在固定频率下功率随波数的分布发现，磁场中ｆ模及ｎ＝１，２，３的ｐ模的脊向高波数方向位移，功率的降低受频率调制，即声波在某些有限的频带中被吸收。这些观测表明，在磁场中ｐ模与磁声重力波（ＭＡＧ）产生了模式混合或耦合。模式混合的存在支持了模式转换作为ｐ模式被黑子吸收的机制的解释。此外，本文还分析了转换的ＭＡＧ波进入黑子磁流管（其中的磁场基本上是垂直的）后进一步被吸收，吸收的功率最高达ＭＡＧ波的２０％。在磁流管内没有进一步观测到模式的转换     

Numerical Simulations of Torsional Alfvén Waves in Axisymmetric Solar Magnetic Flux Tubes

We numerically investigate Alfvén waves propagating along an axisymmetric and non-isothermal solar flux tube embedded in the solar atmosphere. The tube magnetic field is current-free and diverges with height, and the waves are excited by a periodic driver along the tube magnetic field lines. The main results are that the two wave variables, the velocity and magnetic field perturbations in the azimuthal direction, behave differently as a result of gradients of the physical parameters along the tube. To explain these differences in the wave behavior, the time evolution of the wave variables and the resulting cutoff period for each wave variable are calculated and used to determine regions in the solar chromosphere where strong wave reflection may occur.     

Surface waves on a magnetic cylinder

The problem of surface wave propagation on a magnetised cylindrical plasma is investigated allowing for different axial magnetic fields inside and outside the flux tube. Properties of surface waves for symmetric and asymmetric modes of perturbations are investigated idealising the material inside and outside the cylinder to be insulator or infinitely conducting both in compressible and incompressible approximations for the tube material.     

Acoustic wave ducting along magnetic flux tubes in the sunspot regions

The acoustic waves generated in the solar atmosphere propagate globally as well as upwards. These waves interact with the solar magnetic field structures and are ducted upwards. The velocity of these modified acoustic waves is shown to vary in a modelled solar atmosphere. The solar plasma propagating upwards with these waves are likely to alter the observed features of spicules, granules, and supergranules during changing phases of sunspot regions.     

Non-reflective Propagation of Kink Waves in Coronal Magnetic Loops

Propagating kink waves are ubiquitously observed in solar magnetic wave guides. We consider the possibility that these waves propagate without reflection although there is some inhomogeneity. We briefly describe the general theory of non-reflective, one-dimensional wave propagation in inhomogeneous media. This theory is then applied to kink-wave propagation in coronal loops. We consider a coronal loop of half-circle shape embedded in an isothermal atmosphere, and assume that the plasma temperature is the same inside and outside the loop. We show that non-reflective kink-wave propagation is possible for a particular dependence of the loop radius on the distance along the loop. A viable assumption that the loop radius increases from the loop footpoint to the apex imposes a lower limit on the loop expansion factor, which is the ratio of the loop radii at the apex and footpoints. This lower limit increases with the loop height; however, even for a loop that is twice as high as the atmospheric scale height, it is small enough to satisfy observational constraints. Hence, we conclude that non-reflective propagation of kink waves is possible in a fairly realistic model of coronal loops.     

Influence of magnetic field on propagation of five-minute oscillations in the sun’s atmosphere: Phase shifts

From results of spectral (in Ba II λ 455.4-nm line) and spectropolarimetric (in Fe I λλ 1564.3–1565.8-nm lines) observations of the active region (an isolated faculae at the solar disk center) with the German vacuum tower telescope (VTT) at the Institute of Astrophysics on the Canary Islands, the peculiarities of propagation of five-minute oscillations from the photosphere base (h = 0 km) to the lower chromosphere (h = 650 km) were investigated. At the height of the continuum formation (h = 0 km), the nature of wave propagation in the active region does not differ much from that in the quiet region: 80–90% of the investigated areas are occupied by waves moving up and down. In the lower chromosphere (h = 650 km), differences in the behavior of the waves are fundamental. In a quiet area, the waves become standing for 90% of the cases. In contrast to this, in the presence of moderate and strong magnetic fields (B = 30–180 mT), in 47% of the cases, the waves are running upward, which gives the principal possibility to heat the active region. The investigations revealed the presence of the waves in the active region, for which the phase shift Φ _T,V of the temperature and velocity oscillations is between ?90° and 0°. These waves cannot propagate in a quiet atmosphere.     

Wave propagation in a magnetically structured atmosphere

The propagation of waves in a magnetic slab embedded in a magnetic environment is investigated. The possible modes of propagation are examined from the general dispersion relation, both analytically and numerically, for disturbances which are evanescent in the environment. Approximate dispersion relations governing propagation in a slender slab of field are derived both from the general dispersion relation and from an application of the slender flux tube approximation.Several different situations, representative of both photospheric and coronal conditions, are considered. In general, the structures are found to support both fast and slow, body and surface, waves. Under coronal conditions, for two dimensional propagation, disturbances propagate as fast and slow body waves. The fast body waves are analogous to the ducted shear waves of seismology (Love waves).     

Present and Future Observing Trends in Atmospheric Magnetoseismology

With modern imaging and spectral instruments observing in the visible, EUV, X-ray, and radio wavelengths, the detection of oscillations in the solar outer atmosphere has become a routine event. These oscillations are considered to be the signatures of a wave phenomenon and are generally interpreted in terms of magnetohydrodynamic (MHD) waves. With multiwavelength observations from ground- and space-based instruments, it has been possible to detect waves in a number of different wavelengths simultaneously and, consequently, to study their propagation properties. Observed MHD waves propagating from the lower solar atmosphere into the higher regions of the magnetized corona have the potential to provide excellent insight into the physical processes at work at the coupling point between these different regions of the Sun. High-resolution wave observations combined with forward MHD modeling can give an unprecedented insight into the connectivity of the magnetized solar atmosphere, which further provides us with a realistic chance to reconstruct the structure of the magnetic field in the solar atmosphere. This type of solar exploration has been termed atmospheric magnetoseismology. In this review we will summarize some new trends in the observational study of waves and oscillations, discussing their origin and their propagation through the atmosphere. In particular, we will focus on waves and oscillations in open magnetic structures (e.g., solar plumes) and closed magnetic structures (e.g., loops and prominences), where there have been a number of observational highlights in the past few years. Furthermore, we will address observations of waves in filament fibrils allied with a better characterization of their propagating and damping properties, the detection of prominence oscillations in UV lines, and the renewed interest in large-amplitude, quickly attenuated, prominence oscillations, caused by flare or explosive phenomena.     

Long-Period Oscillations in Polar Plumes as Observed by cds on Soho

We examine spectral time series of the transition region line Ov 629Å, observed with the Coronal Diagnostic Spectrometer (CDS) on the SOHO spacecraft in July 1997. Both Fourier and wavelet transforms have been applied independently to the analysis of plume oscillations in order to find the most reliable periods. The wavelet analysis allows us to derive the duration as well as the periods of the oscillations. Our observations indicate the presence of compressional waves with periods of 10–25 min. We have also detected a 11±1 min periodicity in the network regions of the north polar coronal hole. The waves are produced in short bursts with coherence times of about 30 min. We interpret these oscillations as outward propagating slow magneto-acoustic waves, which may contribute significantly to the heating of the lower corona by compressive dissipation and which may also provide enough energy flux for the acceleration of the fast solar wind. The data support the idea that the same driver is responsible for the network and plume oscillations with the network providing the magnetic channel through which the waves propagate upwards from the lower atmosphere to the plumes.     

Explanation of dominant oblique radio emission at Jupiter and comparison to the terrestrial case

The Io-Jupiter S-bursts are series of quasi-periodic impulsive decameter radio emissions from the magnetic flux tube connecting Jupiter to its closest galilean satellite Io. This paper discusses the possibility, suggested by previous works by Hess et al., that the S-bursts are triggered by upgoing electrons accelerated (downward) by trapped Alfvén waves, that have mirrored above the Jupiter ionosphere. According to this theory, the S-bursts would correspond to wave modes that propagate at oblique angles with respect to the magnetic field. Oblique propagation is also inferred for the more slowly varying components of Io-Jupiter radio emissions. Previous works, mainly based on observations of the terrestrial AKR, whose generation process is closely related to those of S-bursts, showed that these waves are emitted on perpendicular wave modes. This discrepancy between the Jovian and Terrestrial cases has led to a controversy about the credibility of the S-bursts model by Hess et al. In the present paper, we show that indeed, the most unstable wave modes for Earth AKR, and Io-Jupiter S-bursts, as they are seen from ground based radio-telescopes, are not the same. Several causes are evaluated: observational bias, the different degree of plasma magnetization above Earth and Jupiter, the role of a cold plasma component and of plasma auroral cavities. Furthermore, we make predictions about what kind of radiation modes a probe crossing the low altitude Io-Jupiter flux tube will see.     

Stokes Diagnostics of Magneto-Acoustic Wave Propagation in the Magnetic Network on the Sun

The solar atmosphere is magnetically structured and highly dynamic. Owing to the dynamic nature of the regions in which the magnetic structures exist, waves can be excited in them. Numerical investigations of wave propagation in small-scale magnetic flux concentrations in the magnetic network on the Sun have shown that the nature of the excited modes depends on the value of plasma β (the ratio of gas to magnetic pressure) where the driving motion occurs. Considering that these waves should give rise to observable characteristic signatures, we have attempted a study of synthesised emergent spectra from numerical simulations of magneto-acoustic wave propagation. We find that the signatures of wave propagation in a magnetic element can be detected when the spatial resolution is sufficiently high to clearly resolve it, enabling observations in different regions within the flux concentration. The possibility to probe various lines of sight around the flux concentration bears the potential to reveal different modes of the magnetohydrodynamic waves and mode conversion. We highlight the feasibility of using the Stokes-V asymmetries as a diagnostic tool to study the wave propagation within magnetic flux concentrations. These quantities can possibly be compared with existing and new observations in order to place constraints on different wave excitation mechanisms.     

Field and flow perturbations outside the reconnected field line region in flux transfer events: Theory

We propose a simplified model of field draping in flux transfer events. To this end we investigate the perturbations in the magnetic field and plasma flow close to but outside a reconnected magnetic flux tube. Following Southwood (1985, in Physics of Ionosphere—Magnetosphere, Adv. Space Res.5, 4–7), we treat the case of incompressible flow and rigid flux tube boundary. We find that the external field perturbations are practically indistinguishable from those observed in the data and hitherto generally ascribed to actual penetration by the spacecraft of the open field line region. The magnetic signature of draping involves all three components of the magnetic field and is accompanied by changes in field strength. The perturbations in the plasma velocity are related to those in the magnetic field and there are concomitant pressure disturbances as well.The effect of magnetopause motion is to complicate the signature by introducing asymmetries and multiple extrema in the variations of the components.A discussion of observations corroborating the theory will appear separately.