Solar coronal heating by magnetosonic waves

Solar coronal heating by magnetohydrodynamic (MHD) waves is investigated. ultraviolet (UV) and X-ray emission lines of the corona show non-thermal broadenings. The wave rms velocities inferred from these observations are of the order of 25–60 km s⁻¹ . Assuming that these values are not negligible, we solved MHD equations in a quasi-linear approximation, by retaining the lowest order non-linear term in rms velocity. Plasma density distribution in the solar corona is assumed to be inhomogeneous. This plasma is also assumed to be permeated by dipole-like magnetic loops. Wave propagation is considered along the magnetic field lines. As dissipative processes, only the viscosity and parallel (to the local magnetic field lines) heat conduction are assumed to be important. Two wave modes emerged from the solution of the dispersion relation. The fast mode magneto-acoustic wave, if originated from the coronal base can propagate upwards into the corona and dissipate its mechanical energy as heat. The damping length-scale of the fast mode is of the order of 500 km. The wave energy flux associated with these waves turned out to be of the order of 2.5×10⁵ ergs cm⁻² s⁻¹ which is high enough to replace the energy lost by thermal conduction to the transition region and by optically thin coronal emission. The fast magneto-acoustic waves prove to be a likely candidate to heat the solar corona. The slow mode is absent, in other words cannot propagate in the solar corona.     

太阳大气中动力学阿尔文波的产生与加热研究进展

动力学阿尔文波是垂直波长接近离子回旋半径或者电子惯性长度的色散阿尔文波.由于波的尺度接近粒子的动力学尺度,动力学阿尔文波在太阳和空间等离子体加热、加速等能化现象中起重要作用.因此,动力学阿尔文波通常被认为是日冕加热的候选者.本研究工作深入、系统地调研了太阳大气中动力学阿尔文波的激发和耗散机制.基于日冕等离子体环境,介绍了几种常见的动力学阿尔文波激发机制:温度各向异性不稳定性、场向电流不稳定性、电子束流不稳定性、密度非均匀不稳定性以及共振模式转换.还介绍了太阳大气中动力学阿尔文波的耗散机制,并讨论了这些耗散机制对黑子加热、冕环加热以及冕羽加热的影响.不仅为认识太阳大气中动力学阿尔文波的驱动机制、动力学演化特征以及波粒相互作用提供合理的理论依据,而且有助于揭示日冕等离子体中能量储存和释放、粒子加热等能化现象的微观物理机制.     

MHD waves and instabilities of a temperature-anisotropic plasma in the solar corona as a source of its heating

The MHD instabilities of a temperature-anisotropic coronal plasma are considered. We show that aperiodic mirror instabilities of slow MHD waves can develop under solar coronal conditions for weak magnetic fields (B < 1 G) and periodic ion-acoustic instabilities can develop for strong magnetic fields (B > 10 G). We have found the instability growth rates and estimated the temporal and spatial scales of development and decay of the periodic instability. We show that the instabilities under consideration can play a prominent role in the energy balance of the corona and may be considered as a large-scale energy source of the wave coronal heating mechanism.     

Transition region and coronal plasmas: instrumentation and spectral analysis

The plasma conditions in the solar atmosphere and, in particular, in coronal holes are summarized, before space-borne instrumentation for observing these regions in vacuum-ultraviolet light is briefly introduced with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer on the Solar and Heliospheric Observatory (SOHO) as example. Spectroscopic measurements of small plasma jets are then analyzed in detail. Magnetic reconnection is thought to be responsible for heating the corona of the Sun as well as accelerating the solar wind by converting magnetic energy into thermal and kinetic energies. The continuous outflow of the fast solar wind from coronal holes on ‘open’ field lines, which reach out into interplanetary space, then requires many reconnection events of very small scale sizes – most of them probably below the resolution capabilities of present-day instruments. Our observations of such an event have been obtained with the Solar and Heliospheric Observatory (SOHO) providing both high-resolution imaging and spectral information for structural and dynamical studies. We find whirling or rotating motions as well as jets with acceleration along their propagation paths in close spatial and temporal vicinity to the coronal jet. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Impulsive Heating Model for the Evolution of Coronal Loops

It was suggested by Parker that the solar corona is heated by many small energy release events generally called microflares or nanoflares. More and more observations showed flows and intensity variations in nonflaring loops. Both theories and observations have indicated that the heating of coronal loops should actually be unsteady. Using SOLFTM (Solar Flux Tube Model), we investigate the hydrodynamics of coronal loops undergoing different manners of impulsive heating with the same total energy deposition. The half length of the loops is 110 Mm, a typical length of active region loops. We divide the loops into two categories: loops that experience catastrophic cooling and loops that do not. It is found that when the nanoflare heating sources are in the coronal part, the loops are in non-catastrophic-cooling state and their evolutions are similar. When the heating is localized below the transition region, the loops evolve in quite different ways. It is shown that with increasing number of heating pulses and inter-pulse time, the catastrophic cooling is weakened, delayed, or even disappears altogether.     

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.     

Magneto‐seismology of the solar atmosphere

Magnetohydrodynamic (MHD) waves in solar coronal loops, which were previously only predicted by theory have actually been detected with space‐borne instruments. These observations have given an important and novel tool to measure fundamental parameters in the magnetically embedded solar corona. This paper will illustrate how information about the magnetic and density structure along coronal loops can be determined by measuring the frequency or amplitude profiles of standing fast kink mode oscillations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

宁静日冕和冕洞研究现状

主要论述宁静日冕洞，以及日冕加热问题的研究现状。讨论了宁静日冕的理论模型、观测模型和混合模型，以及冕洞区大气模型和太阳风加热问题。最后对计划中的日冕空间探测作了简要介绍。     

Waves and Oscillations in the Corona – (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earth's crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.     

Observational Features of Large-Scale Structures as Revealed by the Catastrophe Model of Solar Eruptions

Large-scale magnetic structures are the main carrier of major eruptions in the solar atmosphere. These structures are rooted in the photosphere and are driven by the unceas-ing motion of the photospheric material through a series of equilibrium configurations. The motion brings energy into the coronal magnetic field until the system ceases to be in equilib-rium. The catastrophe theory for solar eruptions indicates that loss of mechanical equilibrium constitutes the main trigger mechanism of major eruptions, usually shown up as solar flares, eruptive prominences, and coronal mass ejections (CMEs). Magnetic reconnection which takes place at the very beginning of the eruption as a result of plasma instabilities/turbulence inside the current sheet, converts magnetic energy into heating and kinetic energy that are responsible for solar flares, and for accelerating both plasma ejecta (flows and CMEs) and energetic particles. Various manifestations are thus related to one another, and the physics behind these relationships is catastrophe and magnetic reconnection. This work reports on re- cent progress in both theoretical research and observations on eruptive phenomena showing the above manifestations. We start by displaying the properties of large-scale structures in the corona and the related magnetic fields prior to an eruption, and show various morphological features of the disrupting magnetic fields. Then, in the framework of the catastrophe theory, we look into the physics behind those features investigated in a succession of previous works, and discuss the approaches they used.     

Numerical simulations for MHD coronal seismology

Magnetohydrodynamic（MHD） processes are important for the transfer of energy over large scales in plasmas and so are essential to understanding most forms of dynamical activity in the solar atmosphere. The introduction of transverse structuring into models for the corona modifies the behavior of MHD waves through processes such as dispersion and mode coupling. Exploiting our understanding of MHD waves with the diagnostic tool of coronal seismology relies upon the development of sufficiently detailed models to account for all the features in observations. The development of realistic models appropriate for highly structured and dynamical plasmas is often beyond the domain of simple mathematical analysis and so numerical methods are employed. This paper reviews recent numerical results for seismology of the solar corona using MHD.     

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).     

Oscillatory Modes of a Prominence – PCTR – Corona Slab Model

Oscillations of magnetic structures in the solar corona have often been interpreted in terms of magnetohydrodynamic waves. We study the adiabatic magnetoacoustic modes of a prominence plasma slab with a uniform longitudinal magnetic field, surrounded by a prominence – corona transition region (PCTR) and a coronal medium. Considering linear small-amplitude oscillations, we deduce the dispersion relation for the magnetoacoustic slow and fast modes by assuming evanescentlike perturbations in the coronal medium. In the system without PCTR, a classification of the oscillatory modes according to the polarisation of their eigenfunctions is made to distinguish modes with fastlike or slowlike properties. Internal and external slow modes are governed by the prominence and coronal properties, respectively, and fast modes are mostly dominated by prominence conditions for the observed wavelengths. In addition, the inclusion of an isothermal PCTR does not substantially influence the mode frequencies, but new solutions (PCTR slow modes) are present.     

On Solar Intermediate Drift Radio Bursts at Decimeter and Meter Wavelength

Fiber – or intermediate drift – bursts are a continuum fine structure in some complex solar radio events. We present the analysis of such bursts in the X17 flare on 28 Oct. 2003. Based on the whistler wave model of fiber bursts we derive the 3D magnetic field structures that carry the radio sources in different stages of the event and obtain insight into the energy release evolution in the main flare phase, the related paths of nonthermal particle propagation in the corona, and the involved magnetic field structures. Additionally, we test the whistler wave model of fiber bursts for the meter and the decimeter wave range. Radio spectral data (Astrophysikalisches Institut Potsdam, Astronomical Observatory Ond?ejov) show a continuum with fibers for ≈?6 min during the main flare phase. Radio imaging data (Nançay Radio Heliograph) yield source centroid positions of the fibers at three frequencies in the spectrometer band. We compare the radio positions with the potential coronal magnetic field extrapolated from SOHO/MDI data. Given the detected source site configuration and evolution, and the change of the fiber burst frequency range with time, we can also extract those coronal flux tubes where the high-frequency fiber bursts are situated even without decimeter imaging data. To this aim we use a kinetic simulation of whistler wave growth in sample flux tubes modeled by selected potential field lines and a barometric density model. The whistler wave model of fiber bursts accurately explains the observations on 28 Oct. 2003. A laterally extended system of low coronal loops is found to guide the whistler waves. It connects several neighboring active regions including the flaring AR 10486. For varying source sites the fiber bursts are emitted at the fundamental mode of the plasma frequency over the whole range (1200?–?300 MHz). The present event can be understood without assuming two different generation mechanisms for meter and decimeter wave fiber bursts. It gives new insight into particle acceleration and propagation in the low flare and post-CME corona.     

On Solving the Coronal Heating Problem

The question of what heats the solar corona remains one of the most important problems in astrophysics. Finding a definitive solution involves a number of challenging steps, beginning with an identification of the energy source and ending with a prediction of observable quantities that can be compared directly with actual observations. Critical intermediate steps include realistic modeling of both the energy release process (the conversion of magnetic stress energy or wave energy into heat) and the response of the plasma to the heating. A variety of difficult issues must be addressed: highly disparate spatial scales, physical connections between the corona and lower atmosphere, complex microphysics, and variability and dynamics. Nearly all of the coronal heating mechanisms that have been proposed produce heating that is impulsive from the perspective of elemental magnetic flux strands. It is this perspective that must be adopted to understand how the plasma responds and radiates. In our opinion, the most promising explanation offered so far is Parker's idea of nanoflares occurring in magnetic fields that become tangled by turbulent convection. Exciting new developments include the identification of the “secondary instability” as the likely mechanism of energy release and the demonstration that impulsive heating in sub-resolution strands can explain certain observed properties of coronal loops that are otherwise very difficult to understand. Whatever the detailed mechanism of energy release, it is clear that some form of magnetic reconnection must be occurring at significant altitudes in the corona (above the magnetic carpet), so that the tangling does not increase indefinitely. This article outlines the key elements of a comprehensive strategy for solving the coronal heating problem and warns of obstacles that must be overcome along the way.     

Intermittent heating in a model of solar coronal loops

X-ray and EUV observations of the solar corona reveal a very complex and dynamic environment where there are many examples of structures that are believed to outline the Sun's magnetic field. In this present study, the authors investigate the temporal response of the temperature, density and pressure of a solar coronal plasma contained within a magnetic loop to an intermittent heating source generated by Ohmic dissipation. The energy input is produced by a one-dimensional MHD flare model. This model is able to reproduce some of the statistical properties derived from X-ray flare observations. In particular the heat deposition consists of both a sub-flaring background and much larger, singular dissipative events. Two different heating profiles are investigated: (a) the spatial average of the square of the current along the loop and (b) the maximum of the square of the current along the loop. For case (a), the plasma parameters appear to respond more to the global variations in the heat deposition about its average value rather than to each specific event. For case (b), the plasma quantities are more intermittent in their evolution. In both cases the density response is the least bursty signal. It is found that the time-dependent energy input can maintain the plasma at typical coronal temperatures. Implications of these results upon the latest coronal observations are discussed.     

耦合热传导的磁重联的数值模拟

磁重联被认为是太阳耀斑的产生机制,本文数值模拟在日冕中发生在磁重联过程,结果表明耀斑环的表观运动是磁重联的自洽结果;由重联点发出的慢激波对耀斑环的加热有贡献;耀斑环的上升并不意味着重联点的上升。     

日冕磁场重建方法在研究太阳爆发活动中的应用

太阳是与地球关系最为密切的天体.发生在日面上的剧烈爆发性活动可能对人类的生存环境产生巨大影响甚至是灾难性后果.包含太阳耀斑、暗条爆发和日冕物质抛射在内的太阳爆发活动是同一物理过程的不同表现形式,其能量来源于爆发前储存在日冕中的磁场自由能.因此,了解日冕磁场的3维结构是理解太阳爆发的触发机制以及活动区的稳定性等现象的前提.由于观测技术限制,目前尚无法对日冕磁场进行常规观测,因此发展了多种利用可常规观测的光球磁场来重建日冕磁场的方法.主要评述近10 yr来各种日冕磁场重建方法在研究太阳爆发活动中的应用.     

The solar corona as a minimum energy system?

This paper is an exploration of the possibility that the large-scale equilibrium of plasma and magnetic fields in the solar corona is a minimum energy state. Support for this conjecture is sought by considering the simplest form of that equilibrium in a dipole solar field, as suggested by the observed structure of the corona at times of minimum solar activity. Approximate, axisymmetric solutions to the MHD equations are constructed to include both a magnetically closed, hydrostatic region and a magnetically open region where plasma flows along field lines in the form of a transonic, thermally-driven wind. Sequences of such solutions are obtained for various degrees of magnetic field opening, and the total energy of each solution is computed, including contributions from both the plasma and magnetic field. It is shown that along a sequence of increasingly closed coronal magnetic field, the total energy curve is a non-monotonic function of the parameter measuring the degree of magnetic field opening, with a minimum occurring at moderate field opening.For reasonable choices of model parameters (coronal temperature, base density, base magnetic field strength, etc.), the morphology of the minimum energy solution resembles the observed quiet, solar minimum corona. The exact location energy minimum along a given sequence depends rather sensitively on some of the adopted parameter values. It is nevertheless argued that the existence of an energy minimum along the sequences of solutions should remain a robust property of more realistic coronal wind models that incorporate the basic characteristics of the equilibrium corona- the presence of both open and closed magnetic regions.The National Center for Atmospheric Research is sponsored by the National Science Foundation.