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.     

Numerical Magnetohydrodynamic (MHD) Modeling of Coronal Mass Ejections (CMEs)

The Coronal Mass Ejection (CME) is arguably the most important discovery of solar eruptive phenomena in the 20th century. It is now also recognized that CMEs have great impact on the Earth's environment by inducing geomagnetic storms. Thus, development of simulation models to understand the physical mechanisms of CME initiation and propagation has become a challenge in the solar MHD community. In this paper we shall summarize chronologically the development of the theoretical analyses, and the successes and failures of the numerical magnetohydrodynamic (MHD) simulations of coronal mass ejections (CMEs) during the past two decades. The chronological development of numerical simulation models and the evolution of the numerical methods to treat this class of problems are presented. The most appropriate way to model CMEs is to have (i) a realistic pre-event coronal atmosphere, and (ii) realistic driving mechanisms. Details of the progress and assessment of the theoretical and modeling efforts for the understanding of the physics of the CME initiation and propagation will be presented, and the numerical methods to construct these simulation models will be discussed.     

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’’.     

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.     

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.     

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.     

Coronal mass ejections at high heliographic latitudes: Ulysses

Nine coronal mass ejections (CMEs) have been detected in the solar wind by the Ulysses plasma experiment between 31° and 61° South. One of these events, which was also a magnetic cloud, was directly associated with an event observed by the soft X-ray telescope on Yohkoh in which large magnetic loops formed in the solar corona directly beneath Ulysses. This association suggests that the flux rope topology of the magnetic cloud resulted from reconnection between the legs of neighboring magnetic loops within the rising CME. The average CME speed (740 km s^–1) at these latitudes was comparable to that of the normal solar wind there and is much greater than average CME speeds observed either in the solar wind in the ecliptic plane or in the corona close to the Sun. We suggest that the same basic acceleration process applies to both slow CMEs and the normal solar wind at any latitude.     

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.     

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.     

Coronal Observations of CMEs

CMEs have been observed for over 30 years with a wide variety of instruments. It is now possible to derive detailed and quantitative information on CME morphology, velocity, acceleration and mass. Flares associated with CMEs are observed in X-rays, and several different radio signatures are also seen. Optical and UV spectra of CMEs both on the disk and at the limb provide velocities along the line of sight and diagnostics for temperature, density and composition. From the vast quantity of data we attempt to synthesize the current state of knowledge of the properties of CMEs, along with some specific observed characteristics that illuminate the physical processes occurring during CME eruption. These include the common three-part structures of CMEs, which is generally attributed to compressed material at the leading edge, a low-density magnetic bubble and dense prominence gas. Signatures of shock waves are seen, but the location of these shocks relative to the other structures and the occurrence rate at the heights where Solar Energetic Particles are produced remains controversial. The relationships among CMEs, Moreton waves, EIT waves, and EUV dimming are also cloudy. The close connection between CMEs and flares suggests that magnetic reconnection plays an important role in CME eruption and evolution. We discuss the evidence for reconnection in current sheets from white-light, X-ray, radio and UV observations. Finally, we summarize the requirements for future instrumentation that might answer the outstanding questions and the opportunities that new space-based and ground-based observatories will provide in the future.     

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.     

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.     

CME-Driven Solar Wind Disturbances at High Heliographic Latitudes

We have identified 20 coronal mass ejections, or CMEs, in the solar wind in the Ulysses data obtained between S30° and S75° during the second polar orbit. Unlike CME-driven disturbances observed at high latitudes during Ulysses’ first polar orbit, these disturbances had plasma and magnetic field characteristics similar to those observed in the ecliptic plane near 1 AU when one allows for evolution with heliocentric distance. Here we provide a brief overview of CME observations at high latitudes both close to and far from the Sun, with emphasis on the recent Ulysses measurements on the rising portion of solar cycle 23. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Evolving Sigmoid: Evidence for Magnetic Flux Ropes in the Corona Before, During, and After CMES

It is generally accepted that the energy that drives coronal mass ejections (CMEs) is magnetic in origin. Sheared and twisted coronal fields can store free magnetic energy which ultimately is released in the CME. We explore the possibility of the specific magnetic configuration of a magnetic flux rope of field lines that twist about an axial field line. The flux rope model predicts coronal observables, including heating along forward or inverse S-shaped, or sigmoid, topological surfaces. Therefore, studying the observed evolution of such sigmoids prior to, during, and after the CME gives us crucial insight into the physics of coronal storage and release of magnetic energy. In particular, we consider (1) soft-X-ray sigmoids, both transient and persistent; (2) The formation of a current sheet and cusp-shaped post-flare loops below the CME; (3) Reappearance of sigmoids after CMEs; (4) Partially erupting filaments; (5) Magnetic cloud observations of filament material.     

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.     

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.     

The Localization of Particle Acceleration Sites in Solar Flares and CMES

We review the particular aspect of determining particle acceleration sites in solar flares and coronal mass ejections (CMEs). Depending on the magnetic field configuration at the particle acceleration site, distinctly different radiation signatures are produced: (1) If charged particles are accelerated along compact closed magnetic field lines, they precipitate to the solar chromosphere and produce hard X-rays, gamma rays, soft X-rays, and EUV emission; (2) if they are injected into large-scale closed magnetic field structures, they remain temporarily confined (or trapped) and produce gyrosynchrotron emission in radio and bremsstrahlung in soft X-rays; (3) if they are accelerated along open field lines they produce beam-driven plasma emission with a metric starting frequency; and (4) if they are accelerated in a propagating CME shock, they can escape into interplanetary space and produce beam-driven plasma emission with a decametric starting frequency. The latter two groups of accelerated particles can be geo-effective if suitably connected to the solar west side. Particle acceleration sites can often be localized by modeling the magnetic topology from images in different wavelengths and by measuring the particle velocity dispersion from time-of-flight delays.     

A Comparison of Ground Level Event e/p and Fe/O Ratios with Associated Solar Flare and CME Characteristics

Solar energetic particle (SEP) events reaching rigidities >1 GV are observed at 1?AU as ground-level events (GLEs). They are considered to be extreme cases of gradual SEP events, produced by shocks driven by wide and fast CMEs that are usually associated with long-duration (>1 hour) soft X-ray (SXR) flares. However, some large gradual SEP events, including GLEs, are associated with flares of short-duration (<1 hour) timescales comparable to those of flares seen with impulsive, low-energy SEP events with enhanced charge states, heavy-element abundances, and e/p ratios. The association of some GLEs with short-duration SXR events challenges us to understand the GLE event-to-event variation with SXR durations and whether it truly reflects the nature of the particle acceleration processes or simply the characteristics of the solar regions from which large, fast CMEs arise. We examine statistically the associated flare, active region (AR), and CME characteristics of ～40?GLEs observed since 1976 to determine how the GLE e/p and Fe/O ratios, each measured in two energy ranges, depend on those characteristics. The abundance ratios trend weakly to lower, more coronal, and less scattered values with increasing flare timescales, thermal and nonthermal peak fluxes, and measures of source AR sizes. These results and the wide range of solar longitude connections for GLEs with high abundance ratios argue against a significant role for flare effects in the GLEs. We suggest that GLE SEPs are accelerated predominately in CME-driven shocks and that a coupling of flare size and timescales with CME properties could explain the SEP abundance correlations with flare properties.     

Hybrid Simulations of Wave Propagation and Ion Cyclotron Heating in the Expanding Solar Wind

We present results from hybrid (particle ions, fluid electrons) simulations of the evolution of Alfvén waves close to the ion cyclotron frequency in the solar wind, which take into account the basic properties of the background solar wind flow, i.e., the spherical expansion and the consequent decrease in magnetic field and cyclotron frequency with increasing distance from the Sun. We follow the evolution of a plasma parcel in a frame of reference moving with the solar wind using a 1D expanding box hybrid model; use of the hybrid model yields a fully self-consistent treatment of the resonant cyclotron wave-particle interaction. This model is related to a previous MHD model (Velli et al. 1992), which allows the use of a simple Cartesian geometry with periodic boundary conditions. The use of stretched expanding coordinates in directions transverse to the mean radial solar wind flow naturally introduces an anisotropic damping effect on velocity and magnetic field. We present results for the case of a single circularly polarized Alfvén wave propagating radially outward. Initially, the wave is below the cyclotron frequency for both the alpha partcles and protons. As the wind expands, the wave frequency (as seen in the solar wind frame) decreases more slowly than the cyclotron frequencies and the wave comes into resonance. With only protons, heating occurs as the wave frequency approaches the proton cyclotron frequency. With both alphas and protons, the alphas, which come into resonance first, are observed to be preferentially heated and accelerated. This revised version was published online in June 2006 with corrections to the Cover Date.