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.     

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.     

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.     

MHD waves in coronal flux tubes

The basic MHD waves of a coronal flux loop are investigated for the rectangular box model of a plasma with oblique magnetic field and line-tied at the ends. The waves found are completely different from those in a periodic box, representative for tokamaks. They consist of a mixture of Alfvén components with a ballooning factor, favouring minimal field line bending, and fast components without such a factor. Pure Alfvén modes are only found as singular limiting cases of cluster spectra of Alfvén-fast waves, where the fast components are localised in a photospheric boundary layer which is dictated by the requirements of line-tying. This justifies the assumption of continuous spectra in coronal loops, required for the mechanism of resonant Alfvén wave heating. The waves consist of large amplitude Alfvén components in the corona and fast components with a small but rapidly varying amplitude in the boundary layer, so that they appear to have the right signature for effective transfer of energy from the photosphere to the corona.     

Working Group 1 Report: Solar Wind Models from the Sun to 1 AU: Constraints by "in situ" and Remote Sensing Measurements

The goal of Working Group 1 was to discuss constraints on solar wind models. The topics for discussion, outlined by Eckart Marsch in his introduction, were: (1) what heats the corona, (2) what is the role of waves, (3) what determines the solar wind mass flux, (4) can stationary, multi-fluid models describe the fast and slow solar wind, or (5) do we need time dependent fluid models, kinetic models, and/or MHD models to describe solar wind acceleration. The discussion in the working group focused on observations of "temperatures" in the corona, mainly in coronal holes, and whether the observations of line broadening should be interpreted as thermal broadening or wave broadening. Observations of the coronal electron density and the flow speed in coronal holes were also discussed. There was only one contribution on observations of the distant solar wind, but we can place firm constraints on the solar wind particle fluxes and asymptotic flow speeds from observations with Ulysses and other spacecraft. Theoretical work on multi-fluid models, higher-order moment fluid models, and MHD models of the solar wind were also presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Review Article: MHD Wave Propagation Near Coronal Null Points of Magnetic Fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a ??=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.     

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.     

The 3D Geometry, Motion, and Hydrodynamic Aspects of Oscillating Coronal Loops

We transition from two-dimensional (2D) imaging observations of kink-mode loop oscillations in the solar corona to three-dimensional (3D) reconstructions by exploring two new methods: (1) De-projection of 2D loop tracings using the strategy of curvature radius maximization in 3D space, based on the assumption of force-free magnetic fields; and (2) stereoscopic triangulation of epipolar loop coordinates using coaligned images from the STEREO EUVI/A and B spacecraft. Both methods reveal new features of oscillating loops: non-circularity, non-planarity, and helical geometries. We extend the 3D reconstruction techniques into the time domain and find indications of circularly polarized (helical) kink-mode oscillations, in contrast to linearly polarized modes assumed previously. We discuss also hydrodynamic effects of coronal loops in non-equilibrium state that are essential for the detection and modeling of kink-mode oscillations.     

Alfvén wave heating

This review discusses Alfvén wave heating in non-uniform plasmas as a possible means for explaining the heating of the solar corona. It focusses on recent analytical results that enable us to understand the basic physics of Alfvén wave heating and help us with the interpretation of results of numerical simulations. First we consider the singular wave solutions that are found in linear ideal MHD at the resonant magnetic surface where the frequency of the wave equals the local Alfvén frequency. Next, we use linear resistive MHD for describing the waves in the dissipative region and explain how dissipation modifies the singular solutions found in linear ideal MHD.     

Short Quasi-Periodic MHD Waves in Coronal Structures

The possibility of remote diagnostics of coronal structures with impulsively-generated short-period fast magnetoacoustic wave trains is demonstrated. An initially broad-band, aperiodic fast magnetoacoustic perturbation guided by a 1D plasma inhomogeneity develops into a quasi-periodic wave train with a well-pronounced frequency and amplitude modulation. The quasi-periodicity results from the geometrical dispersion of the modes, determined by the transverse profile of the loop, and hence contains information about the profile. Wavelet images of the wave train demonstrate that their typical spectral signature is of a “crazy tadpole’’ shape: a narrow spectrum tail precedes a broad-band head. The instantaneous period of the oscillations in the wave train decreases gradually with time, with a mean value of several seconds for typical coronal values. The period and the spectral amplitude evolution are determined by the steepness of the transverse density profile and the density contrast ratio in the loop, which offers a tool for estimation of the sub-resolution structuring of the corona.     

Self-consistent Simulations of Alfv��n Wave Driven Winds from the Sun and Stars

We review our recent results of Alfvén wave-driven winds. First, we present the result of self-consistent 1D MHD simulations for solar winds from the photosphere to interplanetary region. Here, we emphasize the importance of the reflection of Alfvén waves in the density stratified corona and solar winds. We also introduce the recent Hinode observation that might detect the reflection signature of transverse (Alfvénic) waves by Fujimura and Tsuneta (Astrophys. J. 702:1443, 2009). Then, we show the results of Alfvén wave-driven winds from red giant stars. As a star evolves to the red giant branch, the properties of stellar winds drastically change from steady coronal winds to intermittent chromospheric winds. We also discuss how the stellar evolution affects the wave reflection in the stellar atmosphere and similarities and differences of accretion disk winds by MHD turbulence.     

Coronal Seismology by Means of Kink Oscillation Overtones

The detection of overtones of coronal loop kink oscillations has been an important advance in the development of coronal seismology. It has significantly increased the potential of coronal seismology and has thus initiated important theoretical and observational improvements. New detections of overtones have been made and a reduction of the error bars has been obtained. The efforts of theoreticians to extend eigenmode studies to more general coronal loop models is no longer a matter of checking the robustness of the model but now also allows for the estimation of certain equilibrium parameters. The frequencies of the detected (longitudinal) overtones are in particular sensitive to changes in the equilibrium properties along the loop, especially the density and the magnetic field expansion. Also, attempts have been made to use the limited longitudinal resolution in combination with the theoretical eigenmodes as an additional seismological tool.     

Numerical simulation of magnetohydrodynamic shock propagation in the corona

Recent developments in the field of numerical simulation models for the study of shock wave propagation in the corona are presented. These models are based on gasdynamic (GD) and ideal (that is, dissipationless, except at shocks) magnetohydrodynamic (MHD) theories. The characteristics and physical interpretations of the results derived from these models are discussed in some detail.The most significant physical results obtained to date are provided by the two-dimensional non-planar, time-dependent, MHD numerical simulation model. In this model, the non-linear interaction among the three essential MHD waves, i.e., fast-, slow-, and Alfvén waves are demonstrated. Finally, the physical relevance of these numerical simulation models in relation to observed solar activity is presented.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

Spectroscopic Constraints on Models of Ion-cyclotron Resonance Heating in the Polar Solar Corona

Using empirical velocity distributions derived from UVCS and SUMER ultraviolet spectroscopy, we construct theoretical models of anisotropic ion temperatures in the polar solar corona. The primary energy deposition mechanism we investigate is the dissipation of high frequency (10-10000 Hz) ion-cyclotron resonant Alfvén waves which can heat and accelerate ions differently depending on their charge and mass. We find that it is possible to explain the observed high perpendicular temperatures and strong anisotropies with relatively small amplitudes for the resonant waves. There is suggestive evidence for steepening of the Alfvén wave spectrum between the coronal base and the largest heights observed spectroscopically. Because the ion-cyclotron wave dissipation is rapid, even for minor ions like O⁵⁺, the observed extended heating seems to demand a constantly replenished population of waves over several solar radii. This indicates that the waves are generated gradually throughout the wind rather than propagated up from the base of the corona. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.     

Slow Solar Wind: Observations and Modeling

While it is certain that the fast solar wind originates from coronal holes, where and how the slow solar wind (SSW) is formed remains an outstanding question in solar physics even in the post-SOHO era. The quest for the SSW origin forms a major objective for the planned future missions such as the Solar Orbiter and Solar Probe Plus. Nonetheless, results from spacecraft data, combined with theoretical modeling, have helped to investigate many aspects of the SSW. Fundamental physical properties of the coronal plasma have been derived from spectroscopic and imaging remote-sensing data and in situ data, and these results have provided crucial insights for a deeper understanding of the origin and acceleration of the SSW. Advanced models of the SSW in coronal streamers and other structures have been developed using 3D MHD and multi-fluid equations.However, the following questions remain open: What are the source regions and their contributions to the SSW? What is the role of the magnetic topology in the corona for the origin, acceleration and energy deposition of the SSW? What are the possible acceleration and heating mechanisms for the SSW? The aim of this review is to present insights on the SSW origin and formation gathered from the discussions at the International Space Science Institute (ISSI) by the Team entitled “Slow solar wind sources and acceleration mechanisms in the corona” held in Bern (Switzerland) in March 2014 and 2015.     

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.     

Alfvén Waves in the Solar Atmosphere

Alfvén waves are considered to be viable transporters of the non-thermal energy required to heat the Sun’s quiescent atmosphere. An abundance of recent observations, from state-of-the-art facilities, have reported the existence of Alfvén waves in a range of chromospheric and coronal structures. Here, we review the progress made in disentangling the characteristics of transverse kink and torsional linear magnetohydrodynamic (MHD) waves. We outline the simple, yet powerful theory describing their basic properties in (non-)uniform magnetic structures, which closely resemble the building blocks of the real solar atmosphere.     

Characteristics of shocks in the solar corona,as inferred from radio,optical, and theoretical investigations

Solar radio bursts of spectral type II provide one of the chief diagnostics for the propagation of shocks through the solar corona. Radio data on the shocks are compared with computer models for propagation of fast-mode MHD shocks through the solar corona. Data on coronal shocks and high-velocity ejecta from solar flares are then discussed in terms of a general model consisting of three main velocity regimes.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

On the Role of Interchange Reconnection in the Generation of the Slow Solar Wind

The heating of the solar corona and therefore the generation of the solar wind, remain an active area of solar and heliophysics research. Several decades of in situ solar wind plasma observations have revealed a rich bimodal solar wind structure, well correlated with coronal magnetic field activity. Therefore, the reconnection processes associated with the large-scale dynamics of the corona likely play a major role in the generation of the slow solar wind flow regime. In order to elucidate the relationship between reconnection-driven coronal magnetic field structure and dynamics and the generation of the slow solar wind, this paper reviews the observations and phenomenology of the solar wind and coronal magnetic field structure. The geometry and topology of nested flux systems, and the (interchange) reconnection process, in the context of coronal physics is then explained. Once these foundations are laid out, the paper summarizes several fully dynamic, 3D MHD calculations of the global coronal system. Finally, the results of these calculations justify a number of important implications and conclusions on the role of reconnection in the structural dynamics of the coronal magnetic field and the generation of the solar wind.