Coronal streamers' theories

Some theoretical aspects of solar coronal streamers are discussed with emphasis on the current sheet and reconnection processes going on along the axis of the streamer. The dynamics of the streamer is a combination of MHD and transport, with acceleration of particles due to reconnection and leakage of plasma outwards as a slow solar wind as the observable results. The presence of the almost-closed magnetic bottles of streamers that can store high-energy particles for significant times provides the birdcage for solar cosmic rays, the reconnection in the sheet feeds medium-energy protons into the corona for the large-scale storage needed for certain flare models, and the build-up of excess density sets the stage for coronal mass ejections.     

MHD ANALYSIS OF PETSCHEK-TYPE RECONNECTION IN NON-UNIFORM FIELD AND FLOW GEOMETRIES

Analytical studies of reconnection have, for the most part, been confined to steady and uniform current sheet geometries. In contrast to these implifications, natural phenomena associated with the presence of current sheets indicate highly non-uniform structure and time-varying behaviour. Examples include the violent outbursts of energy on the Sun known as solar flares, and magnetospheric phenomena such as flux transfer events, plasmoids, and auroral activity. Unlike the theoretical models, reconnection therefore occurs in a highly dynamic and structured plasma environment. In this article we review the mathematical tools and techniques which are available to formulate models capable of describing the effects of reconnection in such situations. We confine attention to variants of the reconnection model first discussed by Petschek in the 1960s, in view of its successful application in predicting and interpreting phenomena in the terrestrial magnetosphere. The analysis of Petschek-type reconnection is based on the equations of ideal magnetohydrodynamics (MHD), which describe the large-scale behaviour of the magnetic field and plasma flow outside the diffusion region, which we determine as a localised part of the current sheet in which reconnection is initiated. The approach we adopt here is to transform the MHD equations into a Lagrangian or so-called 'frozen-in' coordinate system. In this coordinate system, the equation of motion transforms into a set of coupled nonlinear equations, in which the presence of inhomogeneous magnetic fields and/or plasma flows gives rise to a term similar to that which appears in the study of the ordinary string equation in a non-homogeneous medium. As demonstrated here, this approach not only clarifies and highlights the effects of such non-uniformities, it also simplifies the solution of the original set of MHD equations. In particular, this is true for those types of problem in which the total pressure can be considered as a known quantity from the outset. To illustrate the method, we solve several 2D problems involving magnetic field and flow non-uniformities: reconnection in a stagnation-point flow geometry with antiparallel magnetic fields; reconnection in a Y-type magnetic field geometry with and without velocity shear across the current sheet; and reconnection in a force-free magnetic field geometry with field lines of the form xy = const. These case examples, chosen for their tractability, each incorporate some aspects of the field and flow geomtries encountered in solar-terrestrial applications, and they provide a starting point for further analytical as well as numerical studies of reconnection.     

Quasi-Periodic Pulsations in Solar Flares

Quasi-periodic pulsations (QPP) are a common feature of flaring energy releases in the solar atmosphere, observed in all bands, from radio to hard X-ray. In this review we concentrate on QPP with the periods longer than one second. Physical mechanisms responsible for the generation of long QPP split into two groups: “load/unload” mechanisms and MHD oscillations. Load/unload mechanisms are repetitive regimes of flaring energy releases by magnetic reconnection or by other means. MHD oscillations can affect all elements of the flaring emission generation: triggering of reconnection and modulation of its rate, acceleration and dynamics of non-thermal electrons, and physical conditions in the emitting plasmas. In the case of MHD oscillations, the periodicity of QPP is determined either by the presence of some resonances, e.g. standing modes of plasma structures, or by wave dispersion. Periods and other parameters of QPP are linked with properties of flaring plasmas and their morphology. Observational investigation of the QPP generation mechanisms based upon the use of spatial information, broadband spectral coverage and multi-periodicity is discussed.     

Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media

Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here.     

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.     

Structure of reconnection layers in the magnetosphere

Magnetic reconnection can lead to the formation of observed boundary layers at the dayside magnetopause and in the nightside plasma sheet of the earth's magnetosphere. In this paper, the structure of these reconnection layers is studied by solving the one-dimensional Riemann problem for the evolution of a current sheet. Analytical method, resistive MHD simulations, and hybrid simulations are used. Based on the ideal MHD formulation, rotational discontinuities, slow shocks, slow expansion waves, and contact discontinuity are present in the dayside reconnection layer. Fast expansion waves are also present in the solution of the Riemann problem, but they quickly propagate out of the reconnection layer. Our study provides a coherent picture for the transition from the reconnection layer with two slow shocks in Petschek's model to the reconnection layer with a rotational discontinuity and a slow expansion wave in Levy et al's model. In the resistive MHD simulations, the rotational discontinuities are replaced by intermediate shocks or time-dependent intermediate shocks. In the hybrid simulations, the time-dependent intermediate shock quickly evolves to a steady rotational discontinuity, and the contact discontinuity does not exist. The magnetotail reconnection layer consists of two slow shocks. Hybrid simulations of slow shocks indicate that there exists a critical number,M _c, such that for slow shocks with an intermediate Mach numberM _IM _c, a large-amplitude rotational wavetrain is present in the downstream region. For slow shocks withM _I<M _c, the downstream wavetrain does not exist. Chaotic ion orbits in the downstream wave provide an efficient mechanism for ion heating and wave damping and explain the existence of the critical numberM _c in slow shocks.     

Emerging Parameter Space Map of Magnetic Reconnection in Collisional and Kinetic Regimes

In large-scale systems of interest to solar physics, there is growing evidence that magnetic reconnection involves the formation of extended current sheets which are unstable to plasmoids (secondary magnetic islands). Recent results suggest that plasmoids may play a critical role in the evolution of reconnection, and have raised fundamental questions regarding the applicability of resistive MHD to various regimes. In collisional plasmas, where the thickness of all resistive layers remain larger than the ion gyroradius, simulations results indicate that plasmoids permit reconnection to proceed much faster than the slow Sweet-Parker scaling. However, it appears these rates are still a factor of ～10× slower than observed in kinetic regimes, where the diffusion region current sheet falls below the ion gyroradius and additional physics beyond MHD becomes crucially important. Over a broad range of interesting parameters, the formation of plasmoids may naturally induce a transition into these kinetic regimes. New insights into this scenario have emerged in recent years based on a combination of linear theory, fluid simulations and fully kinetic simulations which retain a Fokker-Planck collision operator to allow a rigorous treatment of Coulomb collisions as the reconnection electric field exceeds the runaway limit. Here, we present some new results from this approach for guide field reconnection. Based upon these results, a parameter space map is constructed that summarizes the present understanding of how reconnection proceeds in various regimes.     

Basic Physical Mechanism of Fast Reconnection Evolution in Space Plasmas

Large dissipative events, such as solar flares and geomagnetic substorms, may result from sudden onset of fast (explosive) magnetic reconnection. Hence, it is a long-standing problem to find the physical mechanism that makes magnetic reconnection explosive; in particular, how can the fast magnetic reconnection explosively evolve in space plasmas? In this respect, we have proposed the spontaneous fast reconnection model as a nonlinear instability that grows by the positive feedback between plasma microphysics (anomalous resistivity) and macrophysics (global reconnection flow). On the basis of MHD simulations, we demonstrate for a variety of physical situations that the fast reconnection mechanism involving slow shocks in fact evolves explosively as a nonlinear instability and is sustained quasi-steadily on the nonlinear saturation phase. Also, distinct plasma processes, such as large-scale plasmoid propagation, magnetic loop development and loop-top heating, and asymmetric fast reconnection evolution, directly result from the spontaneous fast reconnection model. Obviously, MHD simulations are very useful in understanding the basic physics of explosive fast reconnection evolution in space plasmas. However, they cannot treat the details of microphysics near an X neutral point, which should be precisely studied in the coming 21st century.     

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.     

Magnetic Reconnection in Extreme Astrophysical Environments

Magnetic reconnection is a fundamental plasma physics process in which ideal-MHD??s frozen-in constraints are broken and the magnetic field topology is dramatically re-arranged, which often leads to a violent release of the free magnetic energy. Most of the magnetic reconnection research done to date has been motivated by the applications to systems such as the solar corona, Earth??s magnetosphere, and magnetic confinement devices for thermonuclear fusion. These environments have relatively low energy densities and the plasma is adequately described as a mixture of equal numbers of electrons and ions and where the dissipated magnetic energy always stays with the plasma. In contrast, in this paper I would like to introduce a different, new direction of research??reconnection in high energy density radiative plasmas, in which photons play as important a role as electrons and ions; in particular, in which radiation pressure and radiative cooling become dominant factors in the pressure and energy balance. This research is motivated in part by rapid theoretical and experimental advances in High Energy Density Physics, and in part by several important problems in modern high-energy astrophysics. I first discuss some astrophysical examples of high-energy-density reconnection and then identify the key physical processes that distinguish them from traditional reconnection. Among the most important of these processes are: special-relativistic effects; radiative effects (radiative cooling, radiation pressure, and radiative resistivity); and, at the most extreme end??QED effects, including pair creation. The most notable among the astrophysical applications are situations involving magnetar-strength fields (10¹⁴?C10¹⁵ G, exceeding the quantum critical field B _??4×10¹³ G). The most important examples are giant flares in soft gamma repeaters (SGRs) and magnetic models of the central engines and relativistic jets of Gamma Ray Bursts (GRBs). The magnetic energy density in these environments is so high that, when it is suddenly released, the plasma is heated to ultra-relativistic temperatures. As a result, electron-positron pairs are created in copious quantities, dressing the reconnection layer in an optically thick pair coat, thereby trapping the photons. The plasma pressure inside the layer is then dominated by the combined radiation and pair pressure. At the same time, the timescale for radiation diffusion across the layer may, under some conditions, still be shorter than the global (along the layer) Alfvén transit time, and hence radiative cooling starts to dominate the thermodynamics of the problem. The reconnection problem then becomes essentially a radiative transfer problem. In addition, the high pair density makes the reconnection layer highly collisional, independent of the upstream plasma density, and hence radiative resistive MHD applies. The presence of all these processes calls for a substantial revision of our traditional physical picture of reconnection when applied to these environments and thus opens a new frontier in reconnection research.     

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.     

Cusp dynamics and ionospheric outflow

One of the IMAGE mission science goals is to understand the dayside auroral oval and its dynamic relationship to the magnetosphere. Two ways the auroral oval is dynamically coupled to the magnetosphere are through the injection of magnetosheath plasma into the magnetospheric cusps and through the ejection of ionospheric plasma into the magnetosphere. The ionospheric footpoints of the Earth's magnetospheric cusps are relatively narrow regions in invariant latitude that map magnetically to the magnetopause. Monitoring the cusp reveals two important aspects of magnetic reconnection at the magnetopause. Continuous cusp observations reveal the relative contributions of quasi-steady versus impulsive reconnection to the overall transfer of mass, energy, and momentum across the magnetopause. The location of the cusp is used to determine where magnetic reconnection is occurring on the magnetopause. Of particular interest is the distinction between anti-parallel reconnection, where the magnetosheath and magnetospheric field lines are strictly anti-parallel, and component merging, where the magnetosheath and magnetospheric field lines have one component that is anti-parallel. IMAGE observations suggest that quasi-steady, anti-parallel reconnection is occurring in regions at the dayside magnetopause. However, it is difficult to rule out additional component reconnection using these observations. The ionospheric footpoint of the cusp is also a region of relatively intense ionospheric outflow. Since outflow also occurs in other regions of the auroral oval, one of the long-standing problems has been to determine the relative contributions of the cusp/cleft and the rest of the auroral oval to the overall ionospheric ion content in the Earth's magnetosphere. While the nature of ionospheric outflow has made it difficult to resolve this long-standing problem, the new neutral atom images from IMAGE have provided important evidence that ionospheric outflow is strongly controlled by solar wind input, is `prompt' in response to changes in the solar wind, and may have very narrow and distinct pitch angle structures and charge exchange altitudes.     

Magnetic turbulence at the magnetopause, a key problem for understanding the solar wind/ magnetosphere exchanges

According to ideal MHD, the magnetopause boundary should split the terrestrial environment in two disconnected domains: outside, the solar wind (including its shocked part, the magnetosheath), and inside, the magnetosphere. This view is at variance with the experimental data, which show that the magnetopause is not tight and that a net transfer of matter exists from the solar wind to the magnetosphere; it implies that the frozen-in condition must break down on the magnetopause, either over the whole boundary or at some points. In the absence of ordinary collisions, only short scale phenomena (temporal and/or spatial) can be invoked to explain this breakdown, and the best candidates in this respect appear to be the ULF magnetic fluctuations which show very strong amplitudes in the vicinity of the magnetopause boundary. It has been shown that these fluctuations are likely to originate in the magnetosheath, probably downstream of the quasi-parallel shock region, and that they can get amplified by a propagation effect when crossing the magnetopause. When studying the propagation across the magnetopause boundary, several effects are to be taken into account simultaneously to get reliable results: the magnetopause density gradient, the temperature effects, and the magnetic field rotation can be introduced while remaining in the framework of ideal MHD. In these conditions, the magnetopause amplification has been interpreted in term of Alfvén and slow resonances occurring in the layer. When, in addition, one takes the ion inertia effects into account, by the way of the Hall-MHD equations, the result appears drastically different: no resonance occurs, but a strong Alfvén wave can be trapped in the boundary between the point where it is converted from the incident wave and the point where it stops propagating back, i.e., the point where k _\|=0, which can exist thanks to the magnetic field rotation. This effect can bring about a new interpretation to the magnetopause transfers, since the Hall effect can allow reconnection near this particular point. The plasma transfer through the magnetopause could then be interpreted in terms of a reconnection mechanism directly driven by the magnetosheath turbulence, which is permanent, rather than due to any local instability of the boundary, for instance of the tearing type, which should be subject to an instability threshold and thus, as far as it exists, more sporadic.     

Reconnection and Waves: A Review with a Perspective

This review is intended to help prepare a new stage of wave studies in the context of magnetic reconnection. Various results that have accumulated would not let the two-dimensional, steady and laminar magnetic reconnection to remain as the standard model. Emphasis on three-dimensional, temporally varying, and turbulent effects is growing and this fact tells that the effects of waves in various frequency ranges deserve further attention in the context of magnetic reconnection. In this review, by setting a perspective, selected recent topics are reviewed and the ways in which these can be viewed as the stepping stones towards a new research horizon of magnetic reconnection are discussed.     

Dayside Proton Aurora: Comparisons between Global MHD Simulations and IMAGE Observations

The IMAGE mission provides a unique opportunity to evaluate the accuracy of current global models of the solar wind interaction with the Earth's magnetosphere. In particular, images of proton auroras from the Far Ultraviolet Instrument (FUV) onboard the IMAGE spacecraft are well suited to support investigations of the response of the Earth's magnetosphere to interplanetary disturbances. Accordingly, we have modeled two events that occurred on June 8 and July 28, 2000, using plasma and magnetic field parameters measured upstream of the bow shock as input to three-dimensional magnetohydrodynamic (MHD) simulations. This paper begins with a discussion of images of proton auroras from the FUV SI-12 instrument in comparison with the simulation results. The comparison showed a very good agreement between intensifications in the auroral emissions measured by FUV SI-12 and the enhancement of plasma flows into the dayside ionosphere predicted by the global simulations. Subsequently, the IMAGE observations are analyzed in the context of the dayside magnetosphere's topological changes in magnetic field and plasma flows inferred from the simulation results. Finding include that the global dynamics of the auroral proton precipitation patterns observed by IMAGE are consistent with magnetic field reconnection occurring as a continuous process while the IMF changes in direction and the solar wind dynamic pressure varies. The global simulations also indicate that some of the transient patterns observed by IMAGE are consistent with sporadic reconnection processes. Global merging patterns found in the simulations agree with the antiparallel merging model, though locally component merging might broaden the merging region, especially in the region where shocked solar wind discontinuities first reach the magnetopause. Finally, the simulations predict the accretion of plasma near the bow shock in the regions threaded by newly open field lines on which plasma flows into the dayside ionosphere are enhanced. Overall the results of these initial comparisons between global MHD simulation results and IMAGE observations emphasize the interplay between reconnection and dynamic pressure processes at the dayside magnetopause, as well as the intricate connection between the bow shock and the auroral region.     

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.     

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.