Generation and propagation of the ULF planetary-scale electromagnetic wavy structures in the ionosphere

In the present article, the results of theoretical investigation of the dynamics of generation and propagation of planetary (with wavelength 10³ km and more) ultra-low frequency (ULF) electromagnetic wave structures in the dissipative ionosphere are given. The physical mechanism of generation of the planetary electromagnetic waves is proposed. It is established, that the global factor, acting permanently in the ionosphere—inhomogeneity (latitude variation) of the geomagnetic field and angular velocity of the earth's rotation—generates the fast and slow planetary ULF electromagnetic waves. The waves propagate along the parallels to the east as well as to the west. In E-region the fast waves have phase velocities (2-20) km s⁻¹and frequencies (10⁻¹-10⁻⁴) s⁻¹; the slow waves propagate with local winds velocities and have frequencies (10⁻⁴-10⁻⁶) s⁻¹. In F-region the fast ULF electromagnetic waves propagate with phase velocities tens-hundreds km s⁻¹ and their frequencies are in the range of (10-10⁻³) s⁻¹. The slow mode is produced by the dynamoelectric field, it represents a generalization of the ordinary Rossby-type waves in the rotating ionosphere and is caused by the Hall effect in the E-layer. The fast disturbances are the new modes, which are associated with oscillations of the ionospheric electrons frozen in the geomagnetic field and are connected with the large-scale internal vortical electric field generation in the ionosphere. The large-scale waves are weakly damped. The features and the parameters of the theoretically investigated electromagnetic wave structures agree with those of large-scale ULF midlatitude long-period oscillations (MLO) and magnetoionospheric wave perturbations (MIWP), observed experimentally in the ionosphere. It is established, that because of relevance of Coriolis and electromagnetic forces, generation of slow planetary electromagnetic waves at the fixed latitude in the ionosphere can give rise to the reverse of local wind structures and to the direction change of general ionospheric circulation. It is considered one more class of the waves, called as the slow magnetohydrodinamic (MHD) waves, on which inhomogeneity of the Coriolis and Ampere forces do not influence. These waves appear as an admixture of the slow Alfven- and whistler-type perturbations. The waves generate the geomagnetic field from several tens to several hundreds nT and more. Nonlinear interaction of the considered waves with the local ionospheric zonal shear winds is studied. It is established, that planetary ULF electromagnetic waves, at their interaction with the local shear winds, can self-localize in the form of nonlinear solitary vortices, moving along the latitude circles westward as well as eastward with velocity, different from phase velocity of corresponding linear waves. The vortices are weakly damped and long lived. They cause the geomagnetic pulsations stronger than the linear waves by one order. The vortex structures transfer the trapped particles of medium and also energy and heat. That is why such nonlinear vortex structures can be the structural elements of strong macroturbulence of the ionosphere.     

Oscillatory motions in sunspots

We observe vertical velocity oscillations in some sunspot umbrae with periods of about 180 s and peak to peak amplitudes up to 1 km s^–1. These oscillations are not visible in either the line depth, line width or the continuum intensity. No correlation seems to exist between the occurence of these oscillations and the presence of the chromospheric umbral flashes (Solar Phys. 7, 351, 1069). In the spot penumbra there is an indication of a long period oscillation, the period increasing from about 300 s in the inner penumbra to nearly 1000 s at the penumbra-photosphere boundary. An attempt has been made to interpret these oscillations in terms of gravity or acoustic waves, travelling along the magnetic field lines, taking into account the variation of scale height and magnetic field direction across the sunspot.     

Imaging Observations of X-Ray Quasi-periodic Oscillations at 3 – 6 keV in the 26 December 2002 Solar Flare

Quasi-periodic oscillations in soft X-rays (SXR) are not well known due to the instrument limitations, especially the absence of imaging observations of SXR oscillations. We explore the quasi-periodic oscillations of SXR at 3?–?6 keV in a solar flare observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) on 26 December 2002. This was a B8.1 class event and showed three X-ray sources (S₁, S₂, and S₃) at 3?–?6 keV and two sources (S₁ and S₂) at 12?–?25 keV. The light curves of the total fluxes display a two-minute oscillation at 3?–?6 keV, but not in the energy bands above 8 keV. To investigate imaging observations of the oscillations, we prepared CLEAN images at seven energy bands between 3 keV and 20 keV with an eight-second integration. The light curves of three sources were analyzed after integrating the flux of each source region. We used the Fourier method to decompose each source light curve into rapidly varying and slowly varying components. The rapidly varying components show seven individual peaks which are well fitted with a sine function. Then we used the wavelet method to analyze the periods in the rapidly varying component of each source. The results show that three sources display damped quasi-periodic oscillations with a similar two-minute period. The damped oscillations timescale varies between 2.5 to 6 minutes. Source S₁ oscillates with the same phase as S₃, but is almost in anti-phase with S₂. Analyzing the flaring images in more detail, we found that these oscillation peaks are well consistent with the appearance of S₃, which seems to split from or merge with S₂ with a period of two minutes. The flare images with a high cadence of one second at 3?–?6 keV show that source S₃ appears with a rapid period of 25 seconds. The two-minute oscillation shows the highest spectral power. Source S₃ seems to shift its position along the flare loop with a mean speed of 130 km?s^?1, which is of the same order as the local sound speed. This connection between the oscillation peaks and emission enhancement appears to be an observational constraint on the emission mechanism at 3?–?6 keV.     

On the possibility of heating of local solar chromospheric regions by magnetoacoustic-gravity waves in a thin flux tube

The response of an isothermal atmosphere of a thin vertical magnetic flux tube to the presence of an acoustic-gravity wave field in the external medium is considered. The Laplace transform method is used to solve a problem with initial conditions. The structure of the solution for disturbances in the tube is a superposition of forced oscillations at the source frequency and oscillations decaying as ～ t ^?3/2 (the so-called wave wake). Both components are analogues of the corresponding disturbances in an external medium with a modified amplitude. The excitation under consideration is shown to be effective in the ranges of external oscillation frequencies 0 mHz ≤ v ≤ 3.3 mHz and v ≥ 6.5 mHz. The time-averaged energy flux density for high-frequency magnetoacoustic-gravity waves in the tube is estimated to be ∝ 3.0 × 10⁷ erg cm^?2 s^?1, a value of the same order of magnitude as that required for heating local regions in the solar chromosphere, ∝ 10⁷ erg cm^?2 s^?1.     

Spatial variations in parameters of quasi-hourly sunspot fragment oscillations and a singular penumbra oscillator

We obtained three-dimensional interpolated portraits for the radial and torsional oscillations of fragments of 12 sunspots in the form of deviations of their polar coordinates from drift as functions of the time and distance from the sunspot center. We performed a wavelet analysis of the two orthogonal components and determined the dominant oscillation modes; the period varies between 40 and 100 min for different sunspots. We revealed two types of dominant modes, one is associated with the sunspot and the other is associated with its surrounding pores: the central-mode frequency depends on the maximum field strength of the sunspot and decreases from its center toward the boundary, while the peripheral-mode frequency depends on the heliographic latitude and decreases toward the sunspot boundary from the far periphery. We revealed radial variations in frequency and amplitude with a spatial period of 0.8 sunspot radius. The types of dominant modes and the radial variations in oscillation parameters are linked with the subphotospheric structure of an active region—with two types of spiral waves and concentric magnetic-field waves. We estimated the mean pore oscillation energy to be ～10³⁰ erg and found a singular oscillator with a mean energy of ～10³¹ erg in the penumbra at a distance of 0.8 sunspot radius. We argue that the singular penumbra oscillator is the source of solar flares.     

Gaussian process modelling of asteroseismic data

The measured properties of stellar oscillations can provide powerful constraints on the internal structure and composition of stars. To begin this process, oscillation frequencies must be extracted from the observational data, typically time series of the star's brightness or radial velocity. In this paper, a probabilistic model is introduced for inferring the frequencies and amplitudes of stellar oscillation modes from data, assuming that there is some periodic character to the oscillations, but that they may not be exactly sinusoidal. Effectively, we fit damped oscillations to the time series, and hence the mode lifetime is also recovered. While this approach is computationally demanding for large time series (>1500 points), it should at least allow improved analysis of observations of solar-like oscillations in subgiant and red giant stars, as well as sparse observations of semiregular stars, where the number of points in the time series is often low. The method is demonstrated on simulated data and then applied to radial velocity measurements of the red giant star  ξ Hydrae  , yielding a mode lifetime between 0.41 and 2.65 d with 95 per cent posterior probability. The large frequency separation between modes is ambiguous, however we argue that the most plausible value is 6.3 μHz, based on the radial velocity data and the star's position in the Hertzsprung–Russell diagram.     

On the oscillatory behaviour of kinematic mean-field dynamos

The paper considers the question after the circumstances in which kinematic mean-field dynamos can have oscillatory magnetic field modes. The conducting fluid body is allowed to be of almost arbitrary shape; its surroundings are vacuum. A general relation for the frequency of oscillation is derived. This relation is discussed more closely for models with pure α²-mechanism. Proof is given that no oscillations can occur for constant α. The investigations published so far on spherical models with pure α²-mechanism call up the question whether there is a chance for axisymmetric modes to be oscillatory. For both spherical models and disk models the possibility of oscillatory axisymmetric modes is demonstrated by examples.     

A study of motions in the winter mesosphere using the partial reflection drift technique

Intensive partial reflection drift observations were made at Adelaide (35°S) for a seven day period in June 1973. The results have been analysed to isolate the prevailing motion and oscillations of various time scales: planetary, 24 hr, 12 hr and gravity waves. Each is discussed in turn with particular emphasis on the variability of energy from day to day and as a function of height. Evidence is presented for the local generation of planetary waves, the presence of the evanescent S_?2¹ mode in the 24 hr oscillation, the influence of the S₄² mode in the 12 hr oscillation and a definite polarization of gravity waves. The energies of all the forms of motion are shown to decay exponentially with increasing height and the deposition of energy and momentum in the upper mesosphere and lower thermosphere is discussed.     

MAG Waves in Sunspots Umbrae: Slow Waves Leaking to the Corona

The linear oscillations of a stratified atmosphere embedded in a uniform vertical magnetic field are studied here. We use a simple theoretical model, formed by the superposition of two isothermal layers, representing, respectively, i) the photosphere and the chromosphere, and ii) the corona. The bottom layer behaves, for some modes, as a resonant cavity where MAG waves are semi-trapped. We find the existence of two types of modes: 1) Fast modes which are trapped below the transition layer, 2) Mixed modes which are resonant modes in the first layer and leak part of the energy to the corona. These mixed modes have been found to be damped in the horizontal direction and can explain the observed slow modes in the corona.     

A model explaining type IV continuum bursts by coherent nonlinear interaction of Bernstein waves

The investigated model supposes Bernstein waves emerging from Harris instabilities at a definite coronal level. The nonlinear process is considered for a higher region, where the quasimonochromatic waves forming the primary spectrum are reflected. Spatial dispersion takes place corresponding to the decreasing magnetic field. Thus each quasimonochromatic wave can be treated separately. According to the nonlinear resonance condition there result electromagnetic waves of twice the primary frequency, the power density of which is calculated. Assuming a coherence time of 480 periods and an oscillation velocity of the electrons of 10^-3 times the thermal velocity the effective radiation temperature 10¹¹ K of a type IVmA-burst is obtained at about 180 MHz, if the range of the nonlinear interaction is about 3.9 km long. In the discussion the interpretation of occurring zebra patterns is treated.     

Oscillations of coronal loops and second pulsations of solar radio emission

The dispersion properties of the sausage eigenmodes of oscillations in a thin magnetic flux tube are numerically analyzed in terms of ideal magnetohydrodynamics (MHD). The period of the modes accompanied by the emission of MHD waves into the surrounding medium, which leads to acoustic damping of oscillations, is determined by the radius of the tube, not by its length. The dissipation of the sausage oscillations in comparatively high (?0.7R _⊙) and tenuous (?6 × 10⁸ cm^?3) coronal loops is considered. Their Q factor has bound found to be determined by the acoustic damping mechanism. The ratio of the plasma densities outside and inside the loop and the characteristic height of the emission source have been estimated by assuming the quasi-periodic pulsations of meter-wavelength radio emission to be related to the sausage oscillations.     

Magneto-atmospheric waves

The nature and properties of magneto-atmospheric (MA) waves are discussed here. A simple model atmosphere, isothermal and permeated by a uniform vertical magnetic field, was used to find that there are two type of modes with avoided crossing of the eigencurves in a K - diagram. The properties of these waves are found to be identical to the uncoupled fast and slow MA waves away from the crossings (specially for small horizontal wave number K 1). The energy density for the fast modes is found to vanish with height and is responsible for the 3-min umbral oscillations, while the slow mode energy density is harmonic.     

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.     

Short-Wave Oscillations of Coronal Magnetic Arcades

We investigate MHD waves in potential and force-free magnetic arcades describing bipolar active regions. The eikonal method allows us to study analytically the short waves, which are divided into Alfvén and magnetosonic waves. The eigen-modes of magnetic arcades are formed as a result of their reflection at the photosphere. The Alfvén mode oscillations of a certain frequency take place on magnetic surfaces. The fast-mode oscillations also take place on some surfaces but they are not magnetic surfaces. Both the Alfvén and fast-mode eigen-frequencies change continuously from one such surface to another. Each oscillation surface has a discrete set of eigen-frequencies.     

Torsional oscillations of magnetized relativistic stars

Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.     

Damped Oscillations of Coronal Loops

A mechanism of damped oscillations of a coronal loop is investigated. The loop is treated as a thin toroidal flux rope with two stationary photospheric footpoints, carrying both toroidal and poloidal currents. The forces and the flux-rope dynamics are described within the framework of ideal magnetohydrodynamics (MHD). The main features of the theory are the following: i) Oscillatory motions are determined by the Lorentz force that acts on curved current-carrying plasma structures and ii) damping is caused by drag that provides the momentum coupling between the flux rope and the ambient coronal plasma. The oscillation is restricted to the vertical plane of the flux rope. The initial equilibrium flux rope is set into oscillation by a pulse of upflow of the ambient plasma. The theory is applied to two events of oscillating loops observed by the Transition Region and Coronal Explorer (TRACE). It is shown that the Lorentz force and drag with a reasonable value of the coupling coefficient (c _d ) and without anomalous dissipation are able to accurately account for the observed damped oscillations. The analysis shows that the variations in the observed intensity can be explained by the minor radial expansion and contraction. For the two events, the values of the drag coefficient consistent with the observed damping times are in the range c _d ≈2 – 5, with specific values being dependent on parameters such as the loop density, ambient magnetic field, and the loop geometry. This range is consistent with a previous MHD simulation study and with values used to reproduce the observed trajectories of coronal mass ejections (CMEs).     

Electron plasma oscillations associated with type III radio emissions and solar electrons

An extensive study of the IMP-6 and IMP-8 plasma and radio wave data has been performed to try to find electron plasma oscillations associated with type III radio noise bursts and low-energy solar electrons. This study shows that electron plasma oscillations are seldom observed in association with solar electron events and type III radio bursts at 1.0 AU. In nearly four years of observations only one event was found in which electron plasma oscillations are clearly associated with solar electrons. For this event the plasma oscillations appeared coincident with the development of a secondary maximum in the electron velocity distribution functions due to solar electrons streaming outwards from the Sun. Numerous cases were found in which no electron plasma oscillations with field strengths greater than 1 μV m^?1 could be detected even though electrons from the solar flare were clearly detected at the spacecraft. For the one case in which electron plasma oscillations are definitely produced by the electrons ejected by the solar flare the electric field strength is relatively small, only about 100 μV m^?1. This field strength is about a factor of ten smaller than the amplitude of electron plasma oscillations generated by electrons streaming into the solar wind from the bow shock. Electromagnetic radiation, believed to be similar to the type III radio emission, is also observed coming from the region of the more intense electron plasma oscillations upstream of the bow shock. Quantitative calculations of the rate of conversion of the plasma oscillation energy to electromagnetic radiation are presented for plasma oscillations excited by both solar electrons and electrons from the bow shock. These calculations show that neither the type III radio emissions nor the radiation from upstream of the bow shock can be adequately explained by a current theory for the coupling of electron plasma oscillations to electromagnetic radiation. Possible ways of resolving these difficulties are discussed.     

On the determination of the photospheric velocity distribution from profiles of weak Fraunhofer lines

The steady-state vertical-velocity response of an isothermal atmosphere to pressure fluctuations of arbitrary period and horizontal wavelength at its base is derived in the approximation of dissipationless polytropic motion in the atmosphere. It is pointed out that, since only upward modes can be excited in an isothermal atmosphere perturbed from below, the infinite response found by Worrall (1972) at the critical frequency _g does not occur. The correct behavior of the response is presented in some detail.Comparison of the response of the model, for the case of isothermal osculations, with observed features of the photospheric oscillations indicates that, in addition to the evanescent photospheric oscillations which occur at the compression-wave propagation cut-off frequencies and which have horizontal wavelengths 3000 km, in the lower photosphere there are also smaller-scale evanescent oscillations which have horizontal wavelengths 1000 km, periods ranging from 200 to 400 s, amplitudes comparable to that of the larger-scale oscillations, and in which the phase of the vertical velocity oscillation leads the phase of the pressure oscillation.     

Seismic signatures of strange stars with crust

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.     

Oscillations and waves in a sunspot

Observations have been made in H of the vertical velocity distribution in a sunspot. Over the umbra the pattern consists of structures of scale-size 2–3. The velocity distribution undergoes oscillations with a period of about 165 s and typical amplitude ±3 km s^–1, but the pattern breaks down after one or two cycles because the period of oscillation varies typically by ±20 s from place to place. Transverse waves develop in the outer 0.1 of the umbral radius and propagate outwards with a velocity of about 20 km s^–1, becoming gradually invisible by or before the outer penumbral boundary; the amplitude is about ±1 km s^–1 at the umbra-penumbra border.The penumbral waves are believed to be basically of the Alfvén type, with 3 × 10^–8 g cm^–3. The umbral oscillations presumably represent gravity waves. In both cases the fluxes are inadequate by two orders of magnitude to account for the sunspot energy deficit.