Heating Diagnostics with MHD Waves

The heating of the solar atmosphere is a fundamental problem of modern solar and astrophysics. A review of the seismological aspects of magnetohydrodynamic (MHD) waves with an emphasis on standing longitudinal waves in the context of coronal heating is presented. Efforts made recently may be split into two categories: forward modelling and data inversion. Forward modelling can be applied to predict the observational footprints of various heating scenarios. A new diagnostic method based on the analysis of Doppler shift time series is outlined with specific application to solar coronal conditions. The power of the method is demonstrated and tested using synthetic data and comparing them with actual high-resolution (e.g. SoHO/SUMER) observations. Further, related recent examples of standing longitudinal oscillations in coronal loop structures observed with the new Hinode/EIS instrument are also presented. These latter observations provide an advanced ground for MHD seismology as a tool for plasma heating diagnostics in the atmosphere of the Sun.     

Standing Slow-Mode Waves in Hot Coronal Loops: Observations, Modeling, and Coronal Seismology

Strongly damped Doppler shift oscillations are observed frequently associated with flarelike events in hot coronal loops. In this paper, a review of the observed properties and the theoretical modeling is presented. Statistical measurements of physical parameters (period, decay time, and amplitude) have been obtained based on a large number of events observed by SOHO/SUMER and Yohkoh/BCS. Several pieces of evidence are found to support their interpretation in terms of the fundamental standing longitudinal slow mode. The high excitation rate of these oscillations in small- or micro-flares suggest that the slow mode waves are a natural response of the coronal plasma to impulsive heating in closed magnetic structure. The strong damping and the rapid excitation of the observed waves are two major aspects of the waves that are poorly understood, and are the main subject of theoretical modelling. The slow waves are found mainly damped by thermal conduction and viscosity in hot coronal loops. The mode coupling seems to play an important role in rapid excitation of the standing slow mode. Several seismology applications such as determination of the magnetic field, temperature, and density in coronal loops are demonstrated. Further, some open issues are discussed.     

Transverse Oscillations of Coronal Loops

On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.     

Progress, Challenges, and Perspectives of the 3D MHD Numerical Modeling of Oscillations in the Solar Corona

Recent high temporal and spatial resolution satellite observations of the solar corona provide ample evidence of oscillations in coronal structures. The observed waves and oscillations can be used as a diagnostic tool of the poorly known coronal parameters, such as magnetic field, density, and temperature. The emerging field of coronal seismology relies on the interpretation of the various coronal oscillations in terms of theoretically known wave modes, and the comparison of observed and theoretical wave mode properties for the determination of the coronal parameters. However, due to complexity of coronal structures the various modes are coupled, and the application of linear theory of idealized structures to coronal loops and active regions limits the usefulness of such methods. Improved coronal seismology can be achieved by the development of full 3D MHD dynamical model of relevant coronal structures and the oscillation phenomena. In addition to improved accuracy compared to linear analysis, 3D MHD models allow the diagnostic method to include nonlinearity, compressibility, and dissipation. The current progress made with 3D MHD models of waves in the corona is reviewed, and the challenges facing further development of this method are discussed in the perspective of future improvement that will be driven by new high resolution and high cadence satellite data, such as received from Hinode and STEREO, and expected from SDO.     

Longitudinal Waves in Coronal Loops

Outwardly propagating intensity disturbances are a common feature in large, quiescent coronal loop structures. In this paper, an overview is given of the observed properties and the theoretical modelling. As a large number of events have been observed and analysed, good statistical results on the estimated parameters have now been obtained. The theoretical modelling mainly focuses on two distinct aspects, namely the observed rapid damping of the perturbations, thought to be due to thermal conduction and the origin of the driver. Leakage of the solar surface p-modes is the main candidate to explain the observed periodicity, due to the strong correlation between loop position and period and the filamentary nature of the observed coronal intensity perturbations. Recent observational results appear to confirm the leakage and subsequent upward propagation of the solar surface 5 minute oscillations into the overlying atmospheric layers.     

Large Amplitude Oscillations in Prominences

Since the first reports of oscillations in prominences in the 1930s, there have been major theoretical and observational developments to understand the nature of these oscillatory phenomena, leading to the whole new field of the so-called “prominence seismology”. There are two types of oscillatory phenomena observed in prominences; “small-amplitude oscillations” (2–3 km?s^?1), which are quite common, and “large-amplitude oscillations” (>20 km?s^?1) for which observations are scarce. Large-amplitude oscillations have been found as “winking filament” in Hα as well as motion in the plane-of-sky in Hα, EUV, micro-wave and He 10830 observations. Historically, it has been suggested that the large-amplitude oscillations in prominences were triggered by disturbances such as fast-mode MHD waves (Moreton wave) produced by remote flares. Recent observations show, in addition, that near-by flares or jets can also create such large-amplitude oscillations in prominences. Large-amplitude oscillations, which are observed both in transverse as well as longitudinal direction, have a range of periods varying from tens of minutes to a few hours. Using the observed period of oscillation and simple theoretical models, the obtained magnetic field in prominences has shown quite a good agreement with directly measured one and, therefore, justifies prominence seismology as a powerful diagnostic tool. On rare occasions, when the large-amplitude oscillations have been observed before or during the eruption, the oscillations may be applied to diagnose the stability and the eruption mechanism. Here we review the recent developments and understanding in the observational properties of large-amplitude oscillations and their trigger mechanisms and stability in the context of prominence seismology.     

EIT Waves: A Changing Understanding over a Solar Cycle

We present here a review of observations and the current theories that attempt to explain coronal EIT waves. EIT waves were first observed by SOHO-EIT in 1996. Since then, careful analysis has shown that they are related to various other phenomena, such as: CMEs, coronal dimming regions, Moreton waves, and transverse coronal loop oscillations. Over the years, myriad theories have been proposed to explain EIT waves. Early attempts, while elegant, relied heavily on theories based on pre-coronal observations. More recent work, which tends to consider a larger data pool, has led to two competing theoretical camps: wave vs. non-wave models; in many cases, proposed hypotheses flatly contradict each other. Sifting through these seemingly-incongruous models requires a thorough understanding of the available data, as some observations make certain theories more difficult to justify. However, some questions still do not appear resolvable with current data and will likely require help from the next generation of coronal telescopes.     

Observational evidence for non-equilibrium ionization in the solar corona

We investigate whether temperature sensitive EUV line ratios can be used as observational signatures for the presence of non-equilibrium ionization in transition region plasma. We compute the total intensity of some EUV lines of carbon and oxygen expected from coronal loop models with a steady-state flow and which are known to have significant departures from ionization equilibrium, selecting lines whose intensity ratios are useful for deducing the electron temperature in the coronal plasma. We calculate the intensity ratios with and without the approximation of ionization equilibrium, in order to determine the effects of any deviations from equilibrium on the numerical values of the line ratios examined.     

Seismology of Prominence-Fine structures: Observations and Theory

Prominence seismology is a rapidly developing topic which seeks to infer the internal structure and properties of solar prominences from the study of its oscillations. Two-dimensional high-resolution observations suggest that filaments can be considered as made by small scale fibrils, having a cool region, stacked one after another in the vertical and horizontal directions. An extense observational background about oscillations in filaments has been gathered during the last 20 years and these observations point out that fibrils or groups of fibrils can oscillate independently. From the theoretical point of view, small amplitude oscillations in single and multifibril configurations have been studied as a first step to explain observational features.     

直升机非线性的稳定性分析

建立了直升机的描述函数,分析和研究了非线性条件下直升机稳定性和极限环振荡情况,导出了极限环振荡情况下纵向操纵位移计算公式和稳定裕度计算公式,并根据Z—8飞机飞行试验数据进行了验证计算和误差分折。计算结果表明,本文的方法可用于各种直升机的设计估算和飞行试验数据处理,是一种非线性闭环分析方法。     

Mass flows in coronal loops

Although static loop models are often used to describe the structure of coronal loops, it is evident on both observational and theoretical grounds that mass motions play a crucial role in the physics of the corona and transition region. First we review the observations of emission-line broadening and wavelength shifts, which imply the presence of random motions and systematic downflows in coronal loops. Some discrepancies in the observations are discussed. It is argued that velocities due to gas pressure gradients are the most likely explanation for the observed flows. A number of models that have been proposed for these motions are reviewed. The implications of the various models on observations of the corona and transition region by SOHO are discussed.     

Thermal cyclotron radiation from a hot coronal loop with helical magnetic field

The spectral and polarization properties of thermal cyclotron radio emission from a hot coronal loop with a current along the axis are computed. The magnetic field is supposed to have a component along the loop axis as well as a poloidal part due to the current, both components being of comparable magnitude. In this specific configuration a helical magnetic field is present with a remarkable minimum of its absolute value along the loop axis and a maximum at its periphery. The presence of one or two maxima of magnetic field value along the line of sight results in increasing optical thickness of the gyroresonance layers at appropriate frequencies in the microwave band and, therefore, in enhanced radio emission at those harmonics which are optically thin (for example,s=4). These cannot be observed in models with the commonly employed magnetic field configuration (longitudinal along the loop axis).We show that the frequency spectrum of thermal cyclotron radiation from a hot coronal loop with a helical magnetic field differs from that of the standards-component source (with smooth frequency characteristics and polarization corresponding toe-mode) in that plenty of fine structures (line-like features and cut-offs) are present and theo-mode is prevalent in some frequency intervals. The enhanced radio emission at high harmonics and the complicated form of frequency spectrum in the model considered imply that some microwave sources, which are poorly explained in traditional models of solar active regions, may be associated with helical magnetic fields in hot coronal loops. Computations allow one to indicate spectral and polarizational peculiarities of local sources testifying to the presence of a helical magnetic field.     

The analysis of energy release in solar flares based on X-ray observations

Extended review of selected papers which deal with the problem of flare heating in solar coronal loops is presented. Discussed methods of the analysis of flare heating based on the X-ray observations have been worked out using the Palermo-Harvard hydrodynamic code. The case is presented when the assumption of the uniform heating across the loop is made. The existence of multiple elementary heating episodes is postulated as well. Next the possibility of the non-uniform heating across the loop is assumed and its manifestation in the X-ray observations is investigated. The application of proposed methods of the analysis to the observations of solar flares in X-rays is presented.     

The Effect of Loop Curvature on Coronal Loop Kink Oscillations

We will review analytical and numerical efforts in modelling the influence of curvature on coronal loop oscillations. We will mainly focus our attention on fast kink mode oscillations. A curved slab model will be presented, where it becomes clear that curvature introduces wave leakage into the system, because of changes in the equilibrium. The importance of leakage will be assessed through the use of a slab and cylindrical model where lateral leakage is allowed. A full analytical model for a semi-toroidal loop will be constructed for a system with no leaking waves but with an inhomogeneous layer that introduces damping due to the process of resonant absorption. The model for a semi-toroidal loop will be extended to also include leakage, and will be studied numerically. The numerical results will be compared to the analytical model.     

Coronal heating by dissipation of magnetic structure

Coronal loops are heated by the release of stored magnetic energy and by the dissipation of MHD waves. Both of these processes rely on the presence of internal structure in the loop. Tangled or sheared fields dissipate wave energy more efficiently than smooth fields. Also, a highly structured field contains a large reservoir of free magnetic energy which can be released in small reconnection events (microflares and nanoflares). The typical amount of internal structure in a loop depends on the balance between input at the photosphere and dissipation. This paper describes measures of magnetic structure, how these measures relate to the magnetic energy, and how photospheric motions affect the structure of a loop.The magnetic energy released during a reconnection event. can be estimated if one knows the equilibrium energy before and after the event. For a loop with highly tangled field lines, a direct solution of the equilibrium equations may be difficult. However, lower bounds can be placed on the energy of the equilibrium field, given a measure of the tangling known as the crossing number. These bounds lead to an estimate of the buildup of energy in a coronal loop caused by random photospheric motions. Parker's topological dissipation model can plausibly supply the 10⁷ erg cm^–2 s^–1 needed to heat the active region corona. The heating rate can be greatly enhanced by fragmentation of flux tubes, for example by the breakup of photospheric footpoints and the formation of new footpoints.     

Microscopic structure of the solar wind

As the solar wind flows out from the coronal base the coulomb collision frequencies rapidly become small and particle-particle collisions can no longer maintain local statistical equilibrium. At 1 AU the particle distribution functions have important non-Maxwellian characteristics and the firehose instability, a cyclotron resonance whistler-mode instability, and several heat flux current instabilities should be operative. Superthermal particle populations also provide large wave levels, and other forms of enhanced plasma turbulence develop at shock fronts and discontinuities. This report contains a review of the theoretical concepts and a progress report on the experimental study of interplanetary wave-particle interactions.Prepared for Space Science Reviews.     

MHD Waves and Heating in Coronal Holes

Coronal holes have been identified as source regions of the fast solar wind, and MHD wave activity has been detected in coronal holes by remote sensing, and in situ in fast solar wind streams. I review some of the most suggestive wave observations, and discuss the theoretical aspects of MHD wave heating and solar wind acceleration in coronal holes. I review the results of single fluid 2.5D MHD, as well as multi-fluid 2.5D MHD models of waves in coronal holes, the heating, and the acceleration of the solar wind be these waves.     

Loop Models from SOHO Observations

The Coronal Diagnostic Spectrometer (CDS) on SOHO is a grazing/normal incidence spectrograph, aimed to produce stigmatic spectra of selected regions of the solar surface in six spectral windows of the extreme ultraviolet from 150 Å to 785 Å (Harrison et al. 1995). In the present work, CDS, EIT, MDI and Yohkoh observations of active region lops have been analyzed. These observations are part of JOP 54. CDS monochromatic images from lines at different temperatures have been co-aligned with EIT and MDI images, and loop structures have been clearly identified using Fe XVI emission lines. Density sensitive lines and lines from adjacent stages of ionization of Fe ions have been used to measure electron density and temperature along the loop length; these measurements have been used to determine the electron pressure along the loop and test the constant pressure assumption commonly used in loop modeling. The observations have been compared with a static, isobaric loop model (Landini and Monsignori Fossi 1975) assuming a temperature-constant heating function in the energy balance equation. Good agreement is found for the temperature distribution along the loop at the coronal level. The model pressure is somewhat higher than obtained from density sensitive line ratios.     

Dynamics of Coronal Loop Oscillations Recent Improvements and Computational Aspects

We will discuss the observed, heavily damped transversal oscillations of coronal loops. These oscillations are often modeled as transversal kink oscillations in a cylinder. Several features are added to the classical cylindrical model. In our models we include loop curvature, longitudinal density stratification, and highly inhomogeneous radial density profiles. In this paper, we will first give an overview of recently obtained results, both analytically and numerically. After that, we shed a light on the computational aspects of the modeling process. In particular, we will focus on the parallellization of the numerical codes.     

Theoretical Advances in Prominence Seismology

Prominence seismology is a rapidly developing topic which seeks to infer the internal structure and properties of solar prominences from the study of its oscillations. An extensive observational background about oscillations in quiescent solar prominences has been gathered during the last 70 years. These observations point out the existence of two different types of oscillations: Flare-induced oscillations (winking filaments) which affect the whole prominence and are of large amplitude and small amplitude oscillations which seem to be of local nature. From the theoretical point of view, few models have been set up to explain the phenomenon of winking filaments while, on the contrary, for small amplitude oscillations a large number of models trying to explain the observed features have been proposed.