Influence of a chromospheric magnetic field on solar acoustic modes

This paper studies the effect of a magnetic atmosphere on the global solar acoustic oscillations in a simple Cartesian model. First, the influence of the ratio of the coronal and the photospheric temperature τ and the strength of the magnetic field at the base of the corona B_c on the oscillation modes is studied for a convection zone-corona model with a true discontinuity. The ratio τ seems to be an important parameter. Subsequently, the discontinuity is replaced by an intermediate chromospheric layer of thickness L and the effect of the thickness on the frequencies of the acoustic waves is studied. In addition, nonuniformity in the magnetic field, plasma density and temperature in the transition layer gives rise to continuous Alfvén and slow spectra. Modes with characteristic frequencies lying within the range of the continuum may resonantly couple to Alfvén and/or slow waves.     

Effects of the magnetic field model and wave polarisation on the estimation of proton number densities in the magnetosphere using field line resonances

The cold, core plasma mass density in the Earth's magnetosphere may be deduced from the resonant behaviour of ultra-low frequency (ULF; 1–100 mHz), magnetohydrodynamic (MHD) waves. Ground-based magnetometers are the most widely used instruments for recording the signature of ULF wave activity in the magnetosphere. For a suitable model of the background magnetic field and a functional form for the variation of the proton number density with radial distance, the resonant frequencies of ULF waves provide estimates of the equatorial plasma mass density. At high latitudes, the magnetic field model becomes critical when estimating the plasma mass density from FLR data. We show that a dipole field model is generally inadequate for latitudes greater than ∼65° geomagnetic compared with models that are keyed to magnetic activity, interplanetary magnetic field and solar wind properties. Furthermore, the method often relies on the detection of the fundamental ULF resonance, which changes frequency depending on the polarisation of the oscillation. Using idealised toroidal and poloidal oscillation modes, the range of the derived densities as the ULF wave polarisation changes is of the same order as changing the density function from a constant value throughout the magnetosphere to assuming constant Alfven speed in a dipole geometry.     

Acoustic damping of fast kink oscillations of coronal loops

The damping of fast kink oscillations of solar coronal loops attributable to the radiation of MHD waves into the surroundings is considered in the thin-tube approximation. The oscillation damping decrement is calculated both by using a new energy method and by solving the dispersion equation for magnetic-tube eigenmodes. The two approaches are in good agreement under appropriate assumptions. The damping is negligible if MHD waves are radiated perpendicular to the magnetic field. The low Q factor of the loop oscillations in active regions found with the TRACE space telescope is associated with the generation of running waves that propagate along magnetic field lines.     

Resonant oscillations in sunspot umbrae

The Uchida and Sakurai (1975), Thomas and Scheuer (1982), and Scheuer and Thomas (1981) theory of umbral oscillations as resonant modes of magneto-acoustic-gravity waves is re-examined. For an isothermal atmosphere it is found that the quasi-Alfvén approximation is not a good approximation to the complete linearized wave equations. The new results presented here show that 3 min umbral oscillation periods are fairly insensitive to magnetic field strength above some critical value. For a detailed model umbra (Thomas and Scheuer, 1982) the calculations presented here show that 3 min umbral oscillations do not depend to any great extent on the level of forcing of the oscillations for those magnetic field strengths which are observed in sunspot umbras. Modes outside the 3 min range appear, as the lowest mode, as the level of forcing is placed at deeper and deeper levels in the solar atmosphere.     

Multilevel Analysis of Oscillation Motions in Active Regions of the Sun

The nature of the three-minute and five-minute oscillations observed in sunspots is considered to be an effect of propagation of magnetohydrodynamic (MHD) waves from the photosphere to the solar corona. However, the real modes of these waves and the nature of the filters that result in rather narrow frequency bands of these modes are still far from being generally accepted, in spite of a large amount of observational material obtained in a wide range of wave bands. The significance of this field of research is based on the hope that local seismology can be used to find the structure of the solar atmosphere in magnetic tubes of sunspots. We expect that substantial progress can be achieved by simultaneous observations of the sunspot oscillations in different layers of the solar atmosphere in order to gain information on propagating waves. In this study we used a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromosphere – corona transition region in the layer with magnetic field B=2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to the optical ones. This implies an MHD wave traveling upward inside the umbral magnetic tube of the sunspot. For the five-minute oscillations the similarity in spectral details could be found only for optical oscillations at the chromospheric level in the umbral region or very close to it. The time delays seem to be similar. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records. Their nature still requires further observational and theoretical study for even a preliminary discussion.     

Rapid damping of the oscillations of coronal loops with an azimuthal magnetic field

We consider the MHD oscillations of an inhomogeneous coronal loop that consists of a dense cord surrounded by a shell. The magnetic field is longitudinal in the cord and has only an azimuthal component in the shell. The parameters of the loop are chosen to be such that there are no resonances; i.e., the resonance points are cut off. This choice is dictated by the formulated problem of considering the influence of the radiation of MHD waves into the surrounding space on the loop oscillations, thereby ruling out the possibility of resonant energy absorption. The wave radiation efficiency is high and allows low oscillation Q-factors, which are equal in order of magnitude to their observed values, to be obtained.     

On the propagation of magneto-acoustic-gravity waves

An analysis of magneto-acoustic-gravity waves in the case of an isothermal atmosphere permeated by a uniform magnetic field is presented. The general solution is expressed in terms of generalized hypergeometric functions. It can be used in numerical simulation of oscillations in a magnetic atmosphere.

It is shown that the elliptically polarized magneto-acoustic-gravity waves consist of a pair of surface waves and a pair of body waves above the cut-off frequency. The body waves along the magnetic field are similar to acoustic waves in an atmosphere and their cut-off frequency is unaffected by magnetic field. The transverse oscillation decreases with height. For the usual boundary condition, the longitudinal oscillation decreases with height; however, in some cases, it may contain terms that increase with height. The solution is singular on a family of ellipses in the frequency - horizontal wave number plane. Near these ellipses, the wave components grow indefinitely.     

Modeling helioseismic modes in the magnetic atmosphere of the Sun

The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The magnetohydrodynamics model of twin kilohertz quasi-periodic oscillations in low-mass X-ray binaries

We suggest an explanation for the twin kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) based on magnetohydrodynamics (MHD) oscillation modes in neutron star magnetospheres. Including the effect of the neutron star spin, we derive several MHD wave modes by solving the dispersion equations, and propose that the coupling of the two resonant MHD modes may lead to the twin kHz QPOs. This model naturally relates the upper, lower kHz QPO frequencies with the spin frequencies of the neutron stars, and can well account for the measured data of six LMXBs.     

On mode conversion and wave reflection in magnetic Ap stars

We investigate the effect of a strong large-scale magnetic field on the reflection of high-frequency acoustic modes in rapidly oscillating Ap stars. To that end, we consider a toy model composed of an isothermal atmosphere matched on to a polytropic interior and determine the numerical solution to the set of ideal magnetohydrodynamic equations in a local plane-parallel approximation with constant gravity. Using the numerical solution in combination with approximate analytical solutions that are valid in the limits where the magnetic and acoustic components are decoupled, we calculate the relative fraction of energy flux that is carried away in each oscillation cycle by running acoustic waves in the atmosphere and running magnetic waves in the interior. For oscillation frequencies above the acoustic cut-off, we show that most energy losses associated with the presence of running waves occur in regions where the magnetic field is close to vertical. Moreover, by considering the depth dependence of the energy associated with the magnetic component of the wave in the atmosphere we show that a fraction of the wave energy is kept in the oscillation every cycle. For frequencies above the acoustic cut-off frequency, such energy is concentrated in regions where the magnetic field is significantly inclined in relation to the local vertical. Even though our calculations were aimed at studying oscillations with frequencies above the acoustic cut-off frequency, based on our results we discuss what results may be expected for oscillations of lower frequency.     

Resonant Absorption of Alfvén Waves in Steady Coronal Loops

The effect of equilibrium flow on linear Alfvén resonances in coronal loops is studied in the compressible viscous MHD model. By means of a finite element code, the full set of linearised driven MHD equations are solved for a one-dimensional equilibrium model in which the equilibrium quantities depend only on the radial coordinate. Computations of resonant absorption of Alfvén waves for two classes of coronal loop models show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We find that a steady equilibrium shear flow can also significantly influence the resonant absorption of Alfvén waves in coronal magnetic flux tubes. The presence of an equilibrium flow may therefore be important for resonant Alfvén waves and coronal heating. A parametric analysis also shows that the resonant absorption can be strongly enhanced by the equilibrium flow, even up to total dissipation of the incoming wave.     

The continuous spectrum of MHD waves in 2D solar loops and arcades. First results on poloidal mode coupling for poloidal magnetic fields

A first attempt is made to study the continuous spectrum of linear ideal MHD for 2D solar loops and to understand how 2D effects change the continuum eigenfrequencies and continuum eigenfunctions. The continuous spectrum is computed for 2D solar loops with purely poloidal magnetic fields and it is investigated how non-circularity of the cross-sections of the poloidal magnetic surfaces and variations of density along the poloidal magnetic field lines change the continuous spectrum and induce poloidal wave number coupling in the eigenfunctions. Approximate analytical results and numerical results are obtained for the eigenfrequencies and the eigenfunctions and the poloidal wave number coupling is clearly illustrated. It is found that the continuum frequencies are substantially increased, that the ranges of the continuum frequencies are considerably enlarged and that the derivatives of the continuum frequencies normal to the magnetic surfaces are substantially increased. The eigenfunctions are strongly influenced by poloidal wave number coupling. Implications of these findings for the heating mechanisms of resonant absorption and phase mixing are briefly considered.Research Assistant of the Belgian National Fund for Scientific Research.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

Resonantly damped oscillations of elliptically shaped stratified emerging coronal loops

The effects of both elliptical shape and stage of emergence of the coronal loop on the resonant absorption of standing kink oscillations are studied. To do so, a typical coronal loop is modeled as a zero-beta longitudinally stratified cylindrical magnetic flux tube. We developed the connection formulae for the resonant absorption of standing transversal oscillations of a coronal loop with an elliptical shape, at various stages of its emergence. Using the connection formulae, the dispersion relation is derived and solved numerically to obtain the frequencies and damping rates of the fundamental and first-overtone kink modes. Our numerical results show that both the elliptical shape and stage of emergence of the loop alter the frequencies and damping rates of the tube as well as the ratio of frequencies of the fundamental and its first-overtone modes. However, the ratio of the oscillation frequency to the damping rate is not affected by the tube shape and stage of its emergence and also is independent of the density stratification parameter.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

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.     

The global structure of the solar wind in June 1991

A numerical simulation of the global solar wind structure for Carrington rotation 1843 (31 May–28 June, 1991) is performed based on a fully three-dimensional, steady-state MHD model of the solar wind (Usmanov, 1993b). A self-consistent solution for 3-D MHD equations is constructed for the spherical shell extending from the solar photosphere up to 10 AU. Solar magnetic field observations are used to prescribe boundary conditions. The computed distribution of the magnetic field is compared with coronal hole observations and with the IMF measurements made by IMP-8 spacecraft at the Earth's orbit.     

Magnetohydrodynamic behaviour of a finite amplitude disturbance in the solar magnetic field

In this paper, dynamic processes in the solar atmosphere are studied numerically from a complete set of MHD equations. Dynamic evolution of the non-linear magnetic field is produced by the finite amplitude of the azimuthai magnetic field at the base of the flux tube of the solar atmosphere. It is assumed that the initial configuration of the magnetic field is a force-free and potential field, the magnetic field is disturbed at the base, the plasma is driven and a part of the magnetic energy is transformed into the kinetic energy of the plasma.The compressed flow of the plasma has the features of fast MHD waves. The computation results give quantitatively the non-linear evolution of strong magnetic fields. These results could be used in an explanation of coronal transients, surge, spray and eruptive prominence events in the solar atmosphere, as well as in a modelling of plasma behaviour in high-β structure experiments in the laboratory.     

Automated Detection of Oscillating Regions in the Solar Atmosphere

Recently observed oscillations in the solar atmosphere have been interpreted and modeled as magnetohydrodynamic wave modes. This has allowed for the estimation of parameters that are otherwise hard to derive, such as the coronal magnetic-field strength. This work crucially relies on the initial detection of the oscillations, which is commonly done manually. The volume of Solar Dynamics Observatory (SDO) data will make manual detection inefficient for detecting all of the oscillating regions. An algorithm is presented that automates the detection of areas of the solar atmosphere that support spatially extended oscillations. The algorithm identifies areas in the solar atmosphere whose oscillation content is described by a single, dominant oscillation within a user-defined frequency range. The method is based on Bayesian spectral analysis of time series and image filtering. A Bayesian approach sidesteps the need for an a-priori noise estimate to calculate rejection criteria for the observed signal, and it also provides estimates of oscillation frequency, amplitude, and noise, and the error in all of these quantities, in a self-consistent way. The algorithm also introduces the notion of quality measures to those regions for which a positive detection is claimed, allowing for simple post-detection discrimination by the user. The algorithm is demonstrated on two Transition Region and Coronal Explorer (TRACE) datasets, and comments regarding its suitability for oscillation detection in SDO are made.     

On the formation of coronal cavities

We present a theoretical study of the formation of a coronal cavity and its relation to a quiescent prominence. We argue that the formation of a coronal cavity is initiated by the condensation of plasma which is trapped by the coronal magnetic field in a closed streamer and which then flows down to the chromosphere along the field lines due to lack of stable magnetic support against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength; with low strength, the plasma density is not high enough for condensation to occur. Furthermore, we suggest that prominence and cavity material is supplied from the chromospheric level. Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration; a prominence requires stable magnetic support.We initiate the study by considering the stability of condensation modes of a plasma in the coronal streamer model obtained by Steinolfson et al. (1982) using a 2-D, time dependent, ideal MHD computer simulation; they calculated the dynamic interaction between outward flowing solar wind plasma and a global coronal magnetic field. In the final steady state, they found a density enhancement in the closed field region with the enhancement increasing with increasing strength of the magnetic field. Our stability calculation shows that if the density enhancement is higher than a critical value, the plasma is unstable to condensation modes. We describe how, depending on the magnetic field configuration, the condensation may produce a coronal cavity and/or initiate the formation of a prominence.NRC Research Associate.