Modelling of Solar Wind, CME Initiation and CME Propagation

Simulations of coronal mass ejections (CMEs) evolving in the interplanetary (IP) space from the Sun up to 1 AU are performed in the framework of ideal magnetohydrodynamics (MHD) by the means of a finite-volume, explicit solver. The aim is to quantify the effect of the background solar wind and of the CME initiation parameters, such as the initial magnetic polarity, on the evolution and on the geo-effectiveness of CMEs. First, three different solar wind models are reconstructed using the same numerical grid and the same numerical scheme. Then, different CME initiation models are considered: Magnetic foot point shearing and magnetic flux emergence. For the fast CME evolution studies, a very simple CME model is considered: A high-density and high-pressure magnetized plasma blob is superposed on a background steady state solar wind model with an initial velocity and launch direction. The simulations show that the initial magnetic polarity substantially affects the IP evolution of the CMEs influencing the propagation velocity, the shape, the trajectory (and thus, the geo-effectiveness).     

An Introduction to Theory and Models of CMEs, Shocks, and Solar Energetic Particles

We present a brief introduction to the essential physics of coronal mass ejections as well as a review of theory and models of CME initiation, solar energetic particle (SEP) acceleration, and shock propagation. A brief review of the history of CME models demonstrates steady progress toward an understanding of CME initiation, but it is clear that the question of what initiates CMEs has still not been solved. For illustration, we focus on the flux cancellation model and the breakout model. We contrast the similarities and differences between these models, and we examine how their essential features compare with observations. We review the generation of shocks by CMEs. We also outline the theoretical ideas behind the origin of a gradual SEP event at the evolving CME-driven coronal/interplanetary shock and the origin of “impulsive” SEP events at flare sites of magnetic reconnection below CMEs. We argue that future developments in models require focused study of “campaign events” to best utilize the wealth of available CME and SEP observations.     

CME Theory and Models

This chapter provides an overview of current efforts in the theory and modeling of CMEs. Five key areas are discussed: (1) CME initiation; (2) CME evolution and propagation; (3) the structure of interplanetary CMEs derived from flux rope modeling; (4) CME shock formation in the inner corona; and (5) particle acceleration and transport at CME driven shocks. In the section on CME initiation three contemporary models are highlighted. Two of these focus on how energy stored in the coronal magnetic field can be released violently to drive CMEs. The third model assumes that CMEs can be directly driven by currents from below the photosphere. CMEs evolve considerably as they expand from the magnetically dominated lower corona into the advectively dominated solar wind. The section on evolution and propagation presents two approaches to the problem. One is primarily analytical and focuses on the key physical processes involved. The other is primarily numerical and illustrates the complexity of possible interactions between the CME and the ambient medium. The section on flux rope fitting reviews the accuracy and reliability of various methods. The section on shock formation considers the effect of the rapid decrease in the magnetic field and plasma density with height. Finally, in the section on particle acceleration and transport, some recent developments in the theory of diffusive particle acceleration at CME shocks are discussed. These include efforts to combine self-consistently the process of particle acceleration in the vicinity of the shock with the subsequent escape and transport of particles to distant regions.     

Theoretical modeling for the stereo mission

We summarize the theory and modeling efforts for the STEREO mission, which will be used to interpret the data of both the remote-sensing (SECCHI, SWAVES) and in-situ instruments (IMPACT, PLASTIC). The modeling includes the coronal plasma, in both open and closed magnetic structures, and the solar wind and its expansion outwards from the Sun, which defines the heliosphere. Particular emphasis is given to modeling of dynamic phenomena associated with the initiation and propagation of coronal mass ejections (CMEs). The modeling of the CME initiation includes magnetic shearing, kink instability, filament eruption, and magnetic reconnection in the flaring lower corona. The modeling of CME propagation entails interplanetary shocks, interplanetary particle beams, solar energetic particles (SEPs), geoeffective connections, and space weather. This review describes mostly existing models of groups that have committed their work to the STEREO mission, but is by no means exhaustive or comprehensive regarding alternative theoretical approaches.     

Solar Sources of Heliospheric Energetic Electron Events—Shocks or Flares?

Electrons with near-relativistic (E≳30 keV, NrR) and relativistic (E≳0.3 MeV) energies are often observed as discrete events in the inner heliosphere following solar transient activity. Several acceleration mechanisms have been proposed for the production of those electrons. One candidate is acceleration at MHD shocks driven by coronal mass ejections (CMEs) with speeds ≳1000 km s⁻¹. Many NrR electron events are temporally associated only with flares while others are associated with flares as well as with CMEs or with radio type II shock waves. Since CME onsets and associated flares are roughly simultaneous, distinguishing the sources of electron events is a serious challenge. On a phenomenological basis two classes of solar electron events were known several decades ago, but recent observations have presented a more complex picture. We review early and recent observational results to deduce different electron event classes and their viable acceleration mechanisms, defined broadly as shocks versus flares. The NrR and relativistic electrons are treated separately. Topics covered are: solar electron injection delays from flare impulsive phases; comparisons of electron intensities and spectra with flares, CMEs and accompanying solar energetic proton (SEP) events; multiple spacecraft observations; two-phase electron events; coronal flares; shock-associated (SA) events; electron spectral invariance; and solar electron intensity size distributions. This evidence suggests that CME-driven shocks are statistically the dominant acceleration mechanism of relativistic events, but most NrR electron events result from flares. Determining the solar origin of a given NrR or relativistic electron event remains a difficult proposition, and suggestions for future work are given.     

The Role of Magnetic Reconnection in CME Acceleration

Observations carried out from the coronagraphs on board space missions (LASCO/SOHO, Solar Maximum and Skylab) and ground-based facilities (HAO/Mauna Loa Observatory) show that coronal mass ejections (CMEs) can be classified into two classes based on their kinematics evolution. These two classes of CMEs are so-called fast and slow CMEs. The fast CME starts with a high initial speed that remains more or less constant; it is also called the constant-speed CME. On the other hand, the slow CME starts with a low initial speed, but shows a gradual acceleration; it is also called the accelerated and slow CME. Low and Zhang [Astrophys. J. 564, L53–L56, 2002] suggested that these two classes of CMEs could be a result of a difference in the initial topology of the magnetic fields associated with the underlying quiescent prominences. A normal prominence magnetic field topology will lead to a fast CME, while an inverse quiescent prominence results in a slow CME, because of the nature of the magnetic reconnection processes. In a recent study given by Wu et al. [Solar Phys. 225, 157–175, 2004], it was shown that an inverse quiescent prominence magnetic topology also could produce a fast CME. In this study, we perform a numerical MHD simulation for CMEs occurring in both normal and inverse quiescent prominence magnetic topology. This study demonstrates three major physical processes responsible for destabilization of these two types of prominence magnetic field topologies that can launch CMEs. These three initiation processes are identical to those used by Wu et al. [Solar Phys. 225, 157–175, 2004]. The simulations show that both fast and slow CMEs can be initiated from these two different types of magnetic topologies. However, the normal quiescent prominence magnetic topology does show the possibility for launching a reconnection island (or secondary O-line) that might be thought of as a “CME’’.     

The Pre-CME Sun

The coronal mass ejection (CME) phenomenon occurs in closed magnetic field regions on the Sun such as active regions, filament regions, transequatorial interconnection regions, and complexes involving a combination of these. This chapter describes the current knowledge on these closed field structures and how they lead to CMEs. After describing the specific magnetic structures observed in the CME source region, we compare the substructures of CMEs to what is observed before eruption. Evolution of the closed magnetic structures in response to various photospheric motions over different time scales (convection, differential rotation, meridional circulation) somehow leads to the eruption. We describe this pre-eruption evolution and attempt to link them to the observed features of CMEs. Small-scale energetic signatures in the form of electron acceleration (signified by nonthermal radio bursts at metric wavelengths) and plasma heating (observed as compact soft X-ray brightening) may be indicative of impending CMEs. We survey these pre-eruptive energy releases using observations taken before and during the eruption of several CMEs. Finally, we discuss how the observations can be converted into useful inputs to numerical models that can describe the CME initiation.     

A Parallel Adaptive 3D MHD Scheme for Modeling Coronal and Solar Wind Plasma Flows

A parallel adaptive mesh refinement (AMR) scheme is described for solving the governing equations of ideal magnetohydrodynamics (MHD) in three space dimensions. This solution algorithm makes use of modern finite-volume numerical methodology to provide a combination of high solution accuracy and computational robustness. Efficient and scalable implementations of the method have been developed for massively parallel computer architectures and high performance achieved. Numerical results are discussed for a simplified model of the initiation and evolution of coronal mass ejections (CMEs) in the inner heliosphere. The results demonstrate the potential of this numerical tool for enhancing our understanding of coronal and solar wind plasma processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.     

Magnetic Flux Emergence, Activity, Eruptions and Magnetic Clouds: Following Magnetic Field from the Sun to the Heliosphere

We present an overview of how the principal physical properties of magnetic flux which emerges from the toroidal fields in the tachocline through the turbulent convection zone to the solar surface are linked to solar activity events, emphasizing the effects of magnetic field evolution and interaction with other magnetic structures on the latter. We compare the results of different approaches using various magnetic observables to evaluate the probability of flare and coronal mass ejection (CME) activity and forecast eruptive activity on the short term (i.e. days). Then, after a brief overview of the observed properties of CMEs and their theoretical models, we discuss the ejecta properties and describe some typical magnetic and composition characteristics of magnetic clouds (MCs) and interplanetary CMEs (ICMEs). We review some individual examples to clarify the link between eruptions from the Sun and the properties of the resulting ejecta. The importance of a synthetic approach to solar and interplanetary magnetic fields and activity is emphasized.     

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.     

Synthesis of CME-Associated Moreton and EIT Wave Features from MHD Simulations

Soft X-ray (SXR) waves, EIT waves, and Hα Moreton waves are all associated with coronal mass ejections (CMEs). The knowledge of the characteristics about these waves is crucial for the understanding of CMEs, and hence for the space weather researches. MHD numerical simulation is performed, with the consideration of the quiet Sun atmosphere, to investigate the CME/flare processes. On the basis of the numerical results, SXR, EUV, and Hα images of the eruption are synthesized, where SXR waves, EIT waves, and Hα Moreton waves are identified. It confirms that the EIT waves, which border the expanding dimmming region, are produced by the successive opening (or stretching) of the closed magnetic field lines. Hα Moreton waves are found to propagate outward synchronously with the SXR waves, lagging behind the latter spatially by ～27 Mm in the simulated scenario. However, the EIT wave velocity is only a third of the Moreton wave velocity. The synthesized results also suggest that Hα± 0.45Å would be the best off-band for the detection of Hα Moreton waves.     

Modeling coronal streamers and their eruption

Numerical solutions of the time-dependent MHD equations are used to generate ambient coronal streamer structures in a corona characteristic of that near solar minimum. The streamers are then disrupted by slow photospheric shear motion at the base of magnetic field lines within the closed field region, which is currently believed to be responsible for producing at least some CMEs. In contrast to several other simulations of this phenomena, the polytropic index is maintained at a value of 5/3 through the addition of coronal heating. Observations are used as a guide in determining the thermodynamic structure and plasma beta in the ambient corona. For a shear speed of 2.5 km/sec, the streamer configuration evolves slowly for about 65 hours before erupting outward with the formation of a CME. The bright CME leading edge travels outward at a speed of about 240 km/sec, and the sheared field lines follow at a somewhat slower speed. A closed magnetic field region is ejected as the magnetic field lines that were opened by the CME reconnect and reform the streamer.     

The STEREO Mission: An Introduction

The twin STEREO spacecraft were launched on October 26, 2006, at 00:52 UT from Kennedy Space Center aboard a Delta 7925 launch vehicle. After a series of highly eccentric Earth orbits with apogees beyond the moon, each spacecraft used close flybys of the moon to escape into orbits about the Sun near 1 AU. Once in heliospheric orbit, one spacecraft trails Earth while the other leads. As viewed from the Sun, the two spacecraft separate at approximately 44 to 45 degrees per year. The purposes of the STEREO Mission are to understand the causes and mechanisms of coronal mass ejection (CME) initiation and to follow the propagation of CMEs through the inner heliosphere to Earth. Researchers will use STEREO measurements to study the mechanisms and sites of energetic particle acceleration and to develop three-dimensional (3-D) time-dependent models of the magnetic topology, temperature, density and velocity of the solar wind between the Sun and Earth. To accomplish these goals, each STEREO spacecraft is equipped with an almost identical set of optical, radio and in situ particles and fields instruments provided by U.S. and European investigators. The SECCHI suite of instruments includes two white light coronagraphs, an extreme ultraviolet imager and two heliospheric white light imagers which track CMEs out to 1 AU. The IMPACT suite of instruments measures in situ solar wind electrons, energetic electrons, protons and heavier ions. IMPACT also includes a magnetometer to measure the in situ magnetic field strength and direction. The PLASTIC instrument measures the composition of heavy ions in the ambient plasma as well as protons and alpha particles. The S/WAVES instrument uses radio waves to track the location of CME-driven shocks and the 3-D topology of open field lines along which flow particles produced by solar flares. Each of the four instrument packages produce a small real-time stream of selected data for purposes of predicting space weather events at Earth. NOAA forecasters at the Space Environment Center and others will use these data in their space weather forecasting and their resultant products will be widely used throughout the world. In addition to the four instrument teams, there is substantial participation by modeling and theory oriented teams. All STEREO data are freely available through individual Web sites at the four Principal Investigator institutions as well as at the STEREO Science Center located at NASA Goddard Space Flight Center.     

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.     

On the Coronal Magnetic Field Configuration and Solar Flare/CME Process

The coronal magnetic field configuration is important for understanding the energy storage and release processes that account for flares and/or CMEs. Here we present a model which is based on the work for potential magnetic field problems that only applies the condition at infinity with the boundary condition on the solar surface specified. We also discuss some recent progress on general force-free field models. For some event analyses, we have employed MDI/SOHO longitudinal magnetogram insected into the synoptic magnetogram to obtain whole boundary condition over the solar surface. Globally, the extrapolated global magnetic field structures effectively demonstrate the case for the disk signature of the radio CMEs and the evolution of the radio sources during the CME/flare processes.     

Multi-Wavelength Observations of CMEs and Associated Phenomena

This chapter reviews how our knowledge of CMEs and CME-associated phenomena has been improved, since the launch of the SOHO mission, thanks to multi-wavelength analysis. The combination of data obtained from space-based experiments and ground based instruments allows us to follow the space-time development of an event from the bottom of the corona to large distances in the interplanetary medium. Since CMEs originate in the low solar corona, understanding the physical processes that generate them is strongly dependant on coordinated multi-wavelength observations. CMEs display a large diversity in morphology and kinematic properties, but there is presently no statistical evidence that those properties may serve to group them into different classes. When a CME takes place, the coronal magnetic field undergoes restructuring. Much of the current research is focused on understanding how the corona sustains the stresses that allow the magnetic energy to build up and how, later on, this magnetic energy is released during eruptive flares and CMEs. Multi-wavelength observations have confirmed that reconnection plays a key role during the development of CMEs. Frequently, CMEs display a rather simple shape, exhibiting a well known three-part structure (bright leading edge, dark cavity and bright knot). These types of events have led to the proposal of the ‘`standard model’' of the development of a CME, a model which predicts the formation of current sheets. A few recent coronal observations provide some evidence for such sheets. Other more complex events correspond to multiple eruptions taking place on a time scale much shorter than the cadence of coronagraph instruments. They are often associated with large-scale dimming and coronal waves. The exact nature of these waves and the physical link between these different manifestations are not yet elucidated. We also discuss what kind of shocks are produced during a flare or a CME. Several questions remain unanswered. What is the nature of the shocks in the corona (blast-wave or piston-driven?) How they are related to Moreton waves seen in Hα? How they are related to interplanetary shocks? The last section discusses the origin of energetic electrons detected in the corona and in the interplanetary medium. “Complex type III-like events,”which are detected at hectometric wavelengths, high in the corona, and are associated with CMEs, appear to originate from electrons that have been accelerated lower in the corona and not at the bow shock of CMEs. Similarly, impulsive energetic electrons observed in the interplanetary medium are not the exclusive result of electron acceleration at the bow shocks of CMEs; rather they have a coronal origin.     

GeV Particle Acceleration in Solar Flares and Ground Level Enhancement (GLE) Events

Ground Level Enhancement (GLE) events represent the most energetic class of solar energetic particle (SEP) events, requiring acceleration processes to boost ?1?GeV ions in order to produce showers of secondary particles in the Earth’s atmosphere with sufficient intensity to be detected by ground-level neutron monitors, above the background of cosmic rays. Although the association of GLE events with both solar flares and coronal mass ejections (CMEs) is undisputed, the question arises about the location of the responsible acceleration site: coronal flare reconnection sites, coronal CME shocks, or interplanetary shocks? To investigate the first possibility we explore the timing of GLE events with respect to hard X-ray production in solar flares, considering the height and magnetic topology of flares, the role of extended acceleration, and particle trapping. We find that 50% (6 out of 12) of recent (non-occulted) GLE events are accelerated during the impulsive flare phase, while the remaining half are accelerated significantly later. It appears that the prompt GLE component, which is observed in virtually all GLE events according to a recent study by Vashenyuk et al. (Astrophys. Space Sci. Trans. 7(4):459–463, 2011), is consistent with a flare origin in the lower corona, while the delayed gradual GLE component can be produced by both, either by extended acceleration and/or trapping in flare sites, or by particles accelerated in coronal and interplanetary shocks.     

Relationship of coronal transients to interplanetary shocks: 3D aspects

More than 1000 coronal mass ejections (CMEs) caused by different types of coronal transients have been analyzed up to now, based on the images from white light coronagraphs on board the OSO 7, Skylab, P78-1, and SMM spacecraft. In many cases, the CME images lead us to the impression of loop-like, more planar structures, similar to those of prominence structures often seen in H pictures. There is increasing evidence, though, for a three-dimensional bubble- or cloud-like structure of CMEs. In several cases, CMEs directed toward the earth (or away from it) were identified, as their outer fronts emerged on all sides of the coronagraph's occulting disk, thus suggesting a bubble-like appearance.There now appears to be unanimity about the crucial role that magnetic reconnection plays during the transient process. Recently, direct evidence was found for the pinch-off of CMEs, both from optical observations and from in situ measurements of isolated magnetic clouds' following transient shock waves. However, the detailed sequence of events during the generation of a CME is still unclear.Interplanetary shock waves associated with the CMEs are usually restricted in latitudinal extent to about the angular width of the optically observed CMEs. They may be somewhat less restricted in longitudinal extent. A nearly 1 1 association between CMEs and shock waves measured in situ from spacecraft (Helios 1 and 2, IMP 7 and 8, ISEE 3, Pioneer Venus) can be established, provided the CME and the spacecraft were in the same longitudinal and latitudinal range and the CME speed exceeds 400 km s^–1. Around the past solar activity minimum all CMEs observed were centered at solar latitudes of less than 60°. Around solar maximum, a significant fraction of CMEs also originated from the polar regions. Thus, there is a good chance that the Ulysses spaceprobe will encounter many shocks caused by both low- and high-latitude CMEs, when it finally starts its journey over the Sun's poles.     

Towards a new paradigm: from a quasi-steady description to a dynamical description of the magnetosphere

A great deal of the research done on the dynamical process of the solar wind- magnetosphere interaction is based on large-scale, quasi-steady theoretical models, such as the classical reconnection model. However, it can be argued that the theoretical and observational foundations of these commonly believed paradigms are not always strong, and support for these models is sometimes weak, controversial or inconsistent. This paper discusses the need for a transition from an oversimplified quasi-steady paradigm towards a more realistic one including the dynamics of MHD waves and wave packets. The effects of localized wave packets may be most important in active plasma regions, where ideal MHD breaks down and localized, time-dependent processes become dominant. New insights into the theories of field-aligned current generation, auroral particle acceleration and the concept of reconnection may be found by including MHD wave propagation and wave packet dynamics.