Finite amplitude transverse oscillations of a magnetic rope

The effects of finite amplitudes on the transverse oscillations of a quiescent prominence represented by a magnetic rope are investigated in terms of the model proposed by Kolotkov et al. 2016. We consider a weakly nonlinear case governed by a quadratic nonlinearity, and also analyse the fully nonlinear equations of motion. We treat the prominence as a massive line current located above the photosphere and interacting with the magnetised dipped environment via the Lorentz force. In this concept the magnetic dip is produced by two external current sources located at the photosphere. Finite amplitude horizontal and vertical oscillations are found to be strongly coupled between each other. The coupling is more efficient for larger amplitudes and smaller attack angles between the direction of the driver and the horizontal axis. Spatial structure of oscillations is represented by Lissajous-like curves with the limit cycle of a hourglass shape, appearing in the resonant case, when the frequency of the vertical mode is twice the horizontal mode frequency. A metastable equilibrium of the prominence is revealed, which is stable for small amplitude displacements, and becomes horizontally unstable, when the amplitude exceeds a threshold value. The maximum oscillation amplitudes are also analytically derived and analysed. Typical oscillation periods are determined by the oscillation amplitude, prominence current, its mass and position above the photosphere, and the parameters of the magnetic dip. The main new effects of the finite amplitude are the coupling of the horizontally and vertically polarised transverse oscillations (i.e. the lack of a simple, elliptically polarised regime) and the presence of metastable equilibria of prominences

Transverse oscillations and stability of prominences in a magnetic field dip

Aims. An analytical model of the global transverse oscillations and mechanical stability of a quiescent prominence in the magnetised environment with a magnetic field dip, accounting for the mirror current effect, is developed. Methods. The model is based upon the interaction of line currents through the Lorentz force. Within this concept the prominence is treated as a straight current-carrying wire, and the magnetic dip is provided by two photospheric current sources. Results. Properties of both vertical and horizontal oscillations are determined by the value of the prominence current, its density and height above the photosphere, and the parameters of the magnetic dip. The prominence can be stable in both horizontal and vertical directions simultaneously when the prominence current dominates in the system and its height is less than the half-distance between the photospheric sources

Empirical mode decomposition analysis of random processes in the solar atmosphere

Context. Coloured noisy components with a power law spectral energy distribution are often shown to appear in solar signals of various types. Such a frequency-dependent noise may indicate the operation of various randomly distributed dynamical processes in the solar atmosphere. Aims. We develop a recipe for the correct usage of the empirical mode decomposition (EMD) technique in the presence of coloured noise, allowing for clear distinguishing between quasi-periodic oscillatory phenomena in the solar atmosphere and superimposed random background processes. For illustration, we statistically investigate extreme ultraviolet (EUV) emission intensity variations observed with SDO/AIA in the coronal (171 Å), chromospheric (304 Å), and upper photospheric (1600 Å) layers of the solar atmosphere, from a quiet sun and a sunspot umbrae region. Methods. EMD has been used for analysis because of its adaptive nature and essential applicability to the processing non-stationary and amplitude-modulated time series. For the comparison of the results obtained with EMD, we use the Fourier transform technique as an etalon. Results. We empirically revealed statistical properties of synthetic coloured noises in EMD, and suggested a scheme that allows for the detection of noisy components among the intrinsic modes obtained with EMD in real signals. Application of the method to the solar EUV signals showed that they indeed behave randomly and could be represented as a combination of different coloured noises characterised by a specific value of the power law indices in their spectral energy distributions. On the other hand, 3-min oscillations in the analysed sunspot were detected to have energies significantly above the corresponding noise level. Conclusions. The correct accounting for the background frequency-dependent random processes is essential when using EMD for analysis of oscillations in the solar atmosphere. For the quiet sun region the power law index was found to increase with height above the photosphere, indicating that the higher frequency processes are trapped deeper in the quiet sun atmosphere. In contrast, lower levels of the sunspot umbrae were found to be characterised by higher values of the power law index, meaning the domination of lower frequencies deep inside the sunspot atmosphere. Comparison of the EMD results with those obtained with the Fourier transform showed good consistency, justifying the applicability of EMD

Nonlinear oscillations of coalescing magnetic flux ropes

An analytical model of highly nonlinear oscillations occurring during a coalescence of two magnetic flux ropes, based upon two-fluid hydrodynamics, is developed. The model accounts for the effect of electric charge separation, and describes perpendicular oscillations of the current sheet formed by the coalescence. The oscillation period is determined by the current sheet thickness, the plasma parameter β, and the oscillation amplitude. The oscillation periods are typically greater or about the ion plasma oscillation period. In the nonlinear regime, the oscillations of the ion and electron concentrations have a shape of a narrow symmetric spikes

The origin of the modulation of the radio emission from the solar corona by a fast magnetoacoustic wave

Observational detection of quasi-periodic drifting fine structures in a type III radio burst associated with a solar flare SOL2015-04-16T11:22, with the LOw Frequency ARray (LOFAR), is presented. Although similar modulations of the type III emission have been observed before and were associated with the plasma density fluctuations, the origin of those fluctuations was unknown. Analysis of the striae of the intensity variation in the dynamic spectrum allowed us to reveal two quasi-oscillatory components. The shorter component has an apparent wavelength of ~2 Mm, phase speed of ~657 km s−1, which gives an oscillation period of ~3 s, and a relative amplitude of ~0.35%. The longer component has a wavelength of ~12 Mm and relative amplitude of ~5.1%. The short frequency range of the detection does not allow us to estimate its phase speed. However, the properties of the shorter oscillatory component allowed us to interpret it as a fast magnetoacoustic wave guided by a plasma nonuniformity along the magnetic field outwards from the Sun. The assumption that the intensity of the radio emission is proportional to the amount of plasma in the emitting volume allowed us to show that the superposition of the plasma density modulation by a fast wave and a longer-wavelength oscillation of an unspecified nature could readily reproduce the fine structure of the observed dynamic spectrum. The observed parameters of the fast wave give an absolute value for the magnetic field in the emitting plasma of ~1.1 G, which is consistent with the radial magnetic field model

Multi-mode quasi-periodic pulsations in a solar flare

Context. Quasi-periodic pulsations (QPP) of the electromagnetic radiation emitted in solar and stellar flares are often detected in microwave, white light, X-ray, and gamma-ray bands. Mechanisms for QPP are intensively debated in the literature. Previous studies revealed that QPP may manifest non-linear, non-stationary and, perhaps, multi-modal processes operating in flares. Aims. We study QPP of the microwave emission generated in an X3.2-class solar flare on 14 May, 2013, observed with the Nobeyama Radioheliograph (NoRH), aiming to reveal signatures of the non-linear, non-stationary, and multi-modal processes in the signal. Methods. The NoRH correlation signal obtained at the 17 GHz intensity has a clear QPP pattern. The signal was analysed with the Hilbert-Huang transform (HHT) that allows one to determine its instant amplitude and frequency, and their time variation. Results. It was established that the QPP consists of at least three well-defined intrinsic modes, with the mean periods of 15, 45, and 100 s. All the modes have quasi-harmonic behaviour with different modulation patterns. The 100 s intrinsic mode is a decaying oscillation, with the decay time of 250 s. The 15 s intrinsic mode shows a similar behaviour, with the decay time of 90 s. The 45 s mode has a wave-train behaviour. Conclusions. Dynamical properties of detected intrinsic modes indicate that the 100 s and 15 s modes are likely to be associated with fundamental kink and sausage modes of the flaring loop, respectively. The 100 s oscillation could also be caused by the fundamental longitudinal mode, while this interpretation requires the plasma temperature of about 30 million K and hence is not likely. The 45 s mode could be the second standing harmonics of the kink mode

Kinetic model of force-free current sheets with non-uniform temperature

The kinetic model of a one-dimensional force-free current sheet (CS) developed recently by Harrison and Neukirch [Phys. Rev. Lett. 102(13), 135003 (2009)] predicts uniform distributions of the plasma temperature and density across the CS. However, in realistic physical systems, inhomogeneities of these plasma parameters may arise quite naturally due to the boundary conditions or local plasma heating. Moreover, as the CS spatial scale becomes larger than the characteristic kinetic scales (the regime often referred to as the MHD limit), it should be possible to set arbitrary density and temperature profiles. Thus, an advanced model has to allow for inhomogeneities of the macroscopic plasma parameters across the CS, to be consistent with the MHD limit. In this paper, we generalise the kinetic model of a force-free current sheet, taking into account the inhomogeneity of the density and temperature across the CS. In the developed model, the density may either be enhanced or depleted in the CS central region. The temperature profile is prescribed by the density profile, keeping the plasma pressure uniform across the CS. All macroscopic parameters, as well as the distribution functions for the protons and electrons, are determined analytically. Applications of the developed model to current sheets observed in space plasmas are discussed

A blueprint of state-of-the-art techniques for detecting quasi-periodic pulsations in solar and stellar flares

Quasi-periodic pulsations (QPPs) appear to be a common feature observed in the light curves of both solar and stellar ares. However, their quasi-periodic nature, along with the facts that they can be small in amplitude and short-lived, make QPPs difficult to unequivocally detect. In this paper, we test the strengths and limitations of state-of-the-art methods for detecting QPPs using a series of hare-and-hounds exercises. The hare simulated a set of ares, both with and without QPPs of a variety of forms, while the hounds attempted to detect QPPs in blind tests. We use the results of these exercises to create a blueprint for anyone who wishes to detect QPPs in real solar and stellar data. We present eight, clear recommendations to be kept in mind for future QPP detections, with the plethora of solar and stellar are data from new and future satellites. These recommendations address the key pitfalls in QPP detection, including detrending, trimming data, accounting for coloured noise, detecting stationary-period QPPs, detecting QPP with non-stationary periods, and ensuring detections are robust and false detections are minimized. We find that QPPs can be detected reliably and robustly by a variety of methods, which are clearly identied and described, if the appropriate care and due diligence is taken

Magnetohydrodynamic oscillations in the solar corona and Earth's magnetosphere : towards consolidated understanding

Magnetohydrodynamic (MHD) oscillatory processes in different plasma systems, such as the corona of the Sun and the Earth’s magnetosphere, show interesting similarities and differences, which so far received little attention and remain underexploited. The successful commissioning within the past ten years of THEMIS, Hinode, STEREO and SDO spacecraft, in combination with matured analysis of data from earlier spacecraft (Wind, SOHO, ACE, Cluster, TRACE and RHESSI) makes it very timely to survey the breadth of observations giving evidence for MHD oscillatory processes in solar and space plasmas, and state-of-the-art theoretical modelling. The paper reviews several important topics, such as Alfv´enic resonances and mode conversion; MHD waveguides, such as the magnetotail, coronal loops, coronal streamers; mechanisms for periodicities produced in energy releases during substorms and solar flares, possibility of Alfv´enic resonators along open field lines; possible drivers of MHD waves; diagnostics of plasmas with MHD waves; interaction of MHD waves with partlyionised boundaries (ionosphere and chromosphere). The review is mainly oriented to specialists in magnetospheric physics and solar physics, but not familiar with specifics of the adjacent research fields