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Earth-affecting solar transients: a review of progresses in solar cycle 24

Abstract

This review article summarizes the advancement in the studies of Earth-affecting solar transients in the last decade that encompasses most of solar cycle 24. It is a part of the effort of the International Study of Earth-affecting Solar Transients (ISEST) project, sponsored by the SCOSTEP/VarSITI program (2014–2018). The Sun-Earth is an integrated physical system in which the space environment of the Earth sustains continuous influence from mass, magnetic field, and radiation energy output of the Sun in varying timescales from minutes to millennium. This article addresses short timescale events, from minutes to days that directly cause transient disturbances in the Earth’s space environment and generate intense adverse effects on advanced technological systems of human society. Such transient events largely fall into the following four types: (1) solar flares, (2) coronal mass ejections (CMEs) including their interplanetary counterparts ICMEs, (3) solar energetic particle (SEP) events, and (4) stream interaction regions (SIRs) including corotating interaction regions (CIRs). In the last decade, the unprecedented multi-viewpoint observations of the Sun from space, enabled by STEREO Ahead/Behind spacecraft in combination with a suite of observatories along the Sun-Earth lines, have provided much more accurate and global measurements of the size, speed, propagation direction, and morphology of CMEs in both 3D and over a large volume in the heliosphere. Many CMEs, fast ones, in particular, can be clearly characterized as a two-front (shock front plus ejecta front) and three-part (bright ejecta front, dark cavity, and bright core) structure. Drag-based kinematic models of CMEs are developed to interpret CME propagation in the heliosphere and are applied to predict their arrival times at 1 AU in an efficient manner. Several advanced MHD models have been developed to simulate realistic CME events from the initiation on the Sun until their arrival at 1 AU. Much progress has been made on detailed kinematic and dynamic behaviors of CMEs, including non-radial motion, rotation and deformation of CMEs, CME-CME interaction, and stealth CMEs and problematic ICMEs. The knowledge about SEPs has also been significantly improved. An outlook of how to address critical issues related to Earth-affecting solar transients concludes this article.

Introduction

Earth-affecting solar transients refer to a broad range of energetic and/or eruptive events occurring on the Sun that have direct effects on the space environment near the Earth and cause adverse space weather impact on advanced technological systems of human society. They occur near the Sun on timescales of minutes to hours, and the resulting effects on the Earth can take place in minutes to days. These transient events are commonly categorized into four different types: (1) solar flares, (2) coronal mass ejections (CMEs) and their interplanetary counterparts, Interplanetary CMEs (ICMEs), (3) solar energetic particle (SEP) events, and (4) stream interaction regions (SIRS) including corotating interaction regions (CIRs). These four types of Earth-affecting transient events differ in their observational appearances, physical origin or processes, as well as the geoeffectiveness in their own unique ways (Table 1). Other energetic events on the Sun, such as filament eruptions, coronal dimmings, waves, etc., can be usually treated as an associated phenomenon with solar flares and/or CMEs. In the following, we briefly introduce the definition of these phenomena and their possible geoeffectiveness, along with selected review articles that discuss in depth these phenomena. The detailed review of these phenomena, including theoretical interpretations and numerical modelings, is given in the subsequent sections of this article.

Table 1 Four types of Earth-affecting solar transients and their key physical processes and geoeffectiveness

Solar flares

Solar flares are probably the oldest transient phenomenon ever observed on the Sun. They were first discovered as a flash in white light by Carrington (1859) and Hodgson (1859) when observing sunspots. In the modern era, solar flares are observed as sudden enhancement in electromagnetic radiation over a broad range of wavelengths including radio, visible light, EUV, X-rays, and gamma rays. The radiation energy released during a flare is about 1028 to 1032 ergs during a timescale of minutes to hours. It is well accepted that magnetic reconnection in a configuration of current sheet is the central mechanism that converts free magnetic energy in the corona into particle acceleration and plasma heating, producing a solar flare. Shibata and Magara (2011) provided a review on solar flares with a focus on the theoretical magnetohydrodynamic process. Fletcher et al. (2011) made a review on solar flares from an observational point of view. Hudson (2011) discussed flares from the perspective of their global properties. Note that it is now well known that the process of flares is strongly coupled with that of CMEs (Harrison 1995; Zhang et al. 2001; Temmer et al. 2008). Therefore, any further discussion on the origin of flares will be included in the discussions on the origin of CMEs, which will be extensively reviewed in this article. Very often, the term solar eruptions is used to refer to transient and large-scale energy release on the Sun, and a solar eruption contains both flare and CME, along with other associated phenomena, such as coronal dimmings and global coronal waves, etc.

While the total electromagnetic radiation, or irradiance from the Sun, is nearly a constant with an amplitude of approximately 0.1% over the 11-year solar cycle that affects the long-term climate of the Earth (Lean 1991), the EUV and X-ray irradiances during solar flares can increase by many folds to orders of magnitude. One space weather effect of solar flares is from EUV radiation in particular the Lyman-alpha radiation at 121.6 nm wavelength absorbed in the Earth’s upper atmosphere causing its instantaneous heating and expansion, which results in a sudden drag and lowering of low-orbiting satellites (Schwenn 2006). Enhanced X-ray emissions from solar flares can penetrate to the bottom of the ionosphere and create an enhancement in the electron content, which may affect high-frequency radio communication.

CMEs and ICMEs

Since the discovery of solar flares by Carrington in 1859, it had long been conceived that there was a cause and effect relation between solar flares and geomagnetic activities on the Earth. Only starting from the 1980s, it became clear that the only type of solar transients that has a clear cause-effect relation to geomagnetic activity lies in CMEs, not in flares (e.g., Schwenn 1983; Sheeley Jr et al. 1985; Gosling 1993; Reames 1999; Zhang et al. 2007). It is now well accepted that CMEs are the solar transients that have the most profound effect on the space environment and inflict the most adverse space weather effect (Gopalswamy 2016).

CMEs are transient and energetic expulsion of mass and magnetic flux on a large scale from the low corona into interplanetary space. While the basic configuration of shock-driven magnetic structures from the Sun has been proposed to explain geomagnetic storm sudden commencement (Gold 1962) and various types of non-thermal solar radio bursts (Fokker 1963), CMEs were first directly imaged in white light from space by the OSO-7 coronagraph in the early 1970s (Tousey 1973). The speed of CMEs in the outer corona ranges from ~ 100 km/s to ~ 3000 km/s at maximum with an average speed from 300 to 500 km/s depending on the phase of the solar cycle (Yashiro et al. 2004). Mass of CMEs is mostly in the range from 1013 to 1016 g with a peak value at 3.4 × 1014 g, and their kinetic energy is mostly between 1027 to 1032 ergs with a peak value at 8.5 × 1029 ergs (Vourlidas et al. 2010). CMEs reach their peak speed in the time range from minutes to hours with a median value at ~ 54 min (Zhang and Dere 2006).

The following is a list of review articles on CMEs, or more generally in solar eruptions, in the last decade. Schrijver (2009) reviewed the drivers of major solar flares and eruptions with a focus on flux emergence and its interaction with the ambient field. Chen (2011) provided a comprehensive overview of theoretical models and their observational basis of CMEs. The review of Webb and Howard (2012) focused the observational aspects of CMEs. Schmieder et al. (2015) further reviewed on observational perspectives of flare-CME models. Gopalswamy et al. (2016) reviewed major discoveries on CMEs observed by spaceborne coronagraphs that show the growing significance of CMEs as the primary source of severe space weather. More recently, reviews were made focusing on magnetic structures of solar eruptions, from the perspective of magnetic flux rope (Cheng et al. 2017) and modeling of magnetic field (Guo et al. 2017). Chen (2017) made a review on the physics of erupting solar flux ropes in the aspects of both theory and observation. The origin, early evolution and predictability of solar eruptions were recently reviewed by Green et al. (2018).

The recent review of Patsourakos et al. (2020) discusses the formation and the nature of the pre-eruptive magnetic configuration of CMEs. We would also like to point out the following earlier reviews on CME models (Forbes 2000; Klimchuk 2001; Lin et al. 2003). Most recently, Lamy et al. (2019) made an extensive review on statistical properties of CMEs covering two complete solar cycles 23 and 24. Gopalswamy et al. (2020b) also reviewed how CME properties varied with the solar cycle, taking advantage of the availability of uniform and extensive observations made over two complete solar cycles.

Following the ejection from the corona, a CME largely maintains its magnetic configuration or topology that is well organized by a twisted magnetic flux rope, thus is able to continuously propagate outward through the heliosphere to a large distance, interacting with the ambient solar wind and impacting planets along its path. Its counterpart in the heliosphere is called interplanetary CME (ICME). Howard and Tappin (2009) reviewed the theory of ICMEs observed in the heliosphere. Rouillard (2011) provided a short review relating white light CMEs near the Sun and in situ ICMEs. Zhao and Dryer (2014) summarized the status of CME/shock arrival time prediction to that date. The physical processes of CME/ICME evolution are reviewed in Manchester et al. (2017). Lugaz et al.’s (2017) review focused on the interaction of successive CMEs. Shen et al. (2017) also reviewed on CME interaction with a focus on analyzing the physical nature of the interaction. More recently, Vourlidas et al. (2019) made an overview of predicting the geoeffectiveness properties of CMEs, including current status, open issues, and a path forward. The review by Kilpua et al. (2019) focused on the forecasting of magnetic structure and orientation of CMEs. The most recent review on ICMEs was by Luhmann et al. (2020).

Besides the ejecta or magnetic flux rope component, a fast CME is capable of driving a wider shock ahead and forming a thick sheath region between the eject front and the shock front. While the shock is the main source of solar energetic particles (SEPs), the sheath, like the magnetic flux rope, is also an important transient structure for causing geomagnetic storms. The properties and importance of shock, sheath regions, as well as CME ejecta, are viewed in (Kilpua et al. 2017; 2017a).

ICMEs passing the Earth can significantly distort and energize the Earth’s magnetosphere and generate a cascade of effects in the different layers of the Earth’s space environment, including in the magnetosphere, radiation belt, ionosphere and upper atmosphere, and even in the lithosphere. These are collectively defined as space weather. The term space weather refers to conditions on the Sun and in the solar wind, magnetosphere, ionosphere, and thermosphere that can influence the performance and reliability of space-borne and ground-based technological systems and that can affect human life and health (Schwenn 2006). The terrestrial perspective and impacts of space weather are summarized in Pulkkinen (2007). Space weather effects in the Earth’s radiation belts were recently reviewed in Baker et al. (2018). CMEs can cause extensive ionospheric anomalies (e.g., Wang et al. 2016a, b, c, d), and disturbances in the atmosphere-ionosphere coupling system (Yiğit et al. 2016). The cradle to grave process of some extreme space weather events is outlined in Riley et al. (2018a). Bocchialini et al. (2018) studied a large number of storm sudden commencement (SSCs), traced their origin to solar sources, identified their effects in the interplanetary medium, and investigated the corresponding response of the terrestrial ionized and neutral environment.

The impacts due to severe space weather storms caused by CMEs/ICMEs on technological systems are profound (Lanzerotti 2017). These impacts include hazards to astronauts, satellite degradation, and failure through single event upset. dielectric material charging and discharging and surface charging, error and failure in GPS navigation, effects on satellite communication, effects on high-frequency communication, effects on power grids and aviation, etc. The potential catastrophic societal effect of the May 1967 great storm is revisited by Knipp et al. (2016). The economic impact of space weather is reviewed and analyzed in Eastwood et al. (2017).

SEPs

Solar energetic particle events are enhancements of electrons, protons and heavy ion fluxes observed in the heliosphere related to both solar flares and CMEs. SEP events present energy spectra that span more than six orders of magnitude, from a few keV superthermal to GeV relativistic energies.

High energy particles from the Sun were first observed as a sudden increase in intensity in ground-based ion chambers and neutron monitors during large solar flares (Forbush 1946). Such ground-level enhancements (GLEs) consist of the strongest set of SEPs events that are mostly detected from space. For half a century following its discovery, it was generally assumed that energetic particles originated from solar flares, i.e., the point-like source in time and space. However, in the 1990s, it became clear that there are two types of SEPs: impulsive type and gradual type, whose source is of impulsive flares on the Sun and of large-scale long-lasting shocks driven by CMEs, respectively (Reames 1999). The gradual SEPs typically last for several days, while the impulsive events only last for a few hours. It is now believed that CME-driven coronal and interplanetary shocks are the most prolific producers of SEPs that pose radiation hazards for our environment and our assets on Earth and in space. Particle enhancements accompanying CME-driven interplanetary shocks that are passing near the Earth are known as energetic storm particles or ESP events, because they are often associated with “Sudden Storm Commencements.”

Besides the seminal review paper that summarized the paradigm shift on the origin of SEPs in (Reames 1999), a series of review papers were also published in the last decade (Reames 2013, 2015, 2018, 2020). Reames (2013) provided a comprehensive account on the two sources of solar energetic particles, which highlighted the early evidence from fast-drifting type III and slow-drifting type II solar radio emissions (Wild et al. 1963). Reames (2015) focused on element abundances and source plasma temperatures of SEPs. Reames (2018) extended the topics including abundances, ionization states, temperatures and FIP (First Ionization Potential) in SEPs. Most recently, Reames (2020) categorized SEPs into four basic populations and discussed the four distinct pathways, to account for the mixture of SEPs from pure impulsive and pure gradual events. Desai and Giacalone (2016) provided a comprehensive review on large gradual SEP events to date. Klein and Dalla (2017) also made a review on the acceleration and propagation of SEPs. More recently, a set of 10 review papers on SEPs are collected in a published book (Malandraki and Crosby 2018b), which built upon the 2-year HESPERIA (High Energy Solar Particle Events Forecasting and Analysis) project of the EU HORIZON 2020 program.

Like flares and CMEs, it is apparent that SEPs pose a threat to modern technology strongly relying on spacecraft and are a serious radiation hazard to humans in space (Jiggens et al. 2014; Malandraki and Crosby 2018a). High energy charged particles have been found to have damaging impacts on various components of spacecraft, including instruments, electronic components, solar arrays etc. SEPs also effect signal propagation between Earth and satellites due to Polar Cap Absorption (PCA) which results from intense ionization of the D-layer of the polar ionosphere. In the instances when SEP events reach aviation latitudes, they are also a concern for human health as the radiation dose received can increase. This applies specifically to high latitude flights and polar routes for commercial aviation. It can be a risk for frequent flyers and for aircrew. SEP forecasting is relied upon to mitigate against the effects SEP events.

SIRs/CIRs

The solar wind reveals long-term, and most often periodic, variations in terms of high speed solar wind streams that may lead to geomagnetic storms. The solar wind also transports short-term disturbances, such as CMEs. Investigating the solar wind is therefore of crucial interest for Space Weather forecasting. The interplay between fast and slow solar wind causes stream interaction regions (SIRs). SIRs are related to coronal holes (CHs), long-lived regions on the Sun with predominantly open magnetic field. Due to the quasi-stationary location of low-latitude CHs, the interaction of high and slow speed solar wind streams results in a compression of plasma and magnetic field that occurs at certain distance from the Sun. As the Sun rotates, recurring SIRs are referred to as corotating interaction regions (CIRs).

Recent reviews on solar wind high speed streams are given by Cranmer, Gibson, and Riley et al. (2017); Living review by Richardson (2018) on SIRs and corona and solar wind by Cranmer and Winebarger (2019). Cranmer et al. (2017) gives an overview of the community’s recent progress and understanding of two major problems associated with HSSs: the coronal heating and the acceleration of the fast and slow solar wind. They discuss recent observational, theoretical, model and forecasting techniques with a positive forecast to the future. The review by Richardson (2018) focuses entirely on the interaction of slow and fast solar wind leading to the formation of SIRs and discusses the acceleration processes of energetic particles in stream-stream interaction regions, modulation of the galactic cosmic ray count, resulting geomagnetic disturbances as well as MHD modeling results. The very recent review by Cranmer and Winebarger (2019) gives detailed insight into high-resolution observations of the solar corona as well as 3D numerical simulations which hint towards small-scale entangled, twisted, and braided magnetic fields. These processes, which may lead to reconnection, are, despite their limitations, thought to be a main source of heating the solar corona.

The geoeffectiveness and Space Weather impact of SIRs/CIRs can be observed as variations in the Earth’s magnetosphere, ionosphere, and even neutral density in the thermosphere. The solar wind delivers significant energy that causes various Space Weather phenomena. CIR-related storms are more hazardous to space-based assets, particularly at geosynchronous orbit compared to CMEs, because CIRs are of longer duration and have hotter plasma sheets causing a stronger spacecraft charging (Borovsky and Denton 2006). Details on the geoeffectiveness of SIRs/CIRs can be found in recent reviews and statistical papers (Kilpua et al. 2017; Vršnak et al. 2017; Yermolaev et al. 2018).

ISEST project

This review article is part of the collective effort made by the International Study of Earth-affecting Solar Transients (ISEST) project, which is one of the four research projects of the Variability of the Sun and Its Terrestrial Impact (VarSITI)) program, sponsored by the Scientific Committee on Solar-Terrestrial Physics (SCOSTEP) for the period of 2014 – 2018. The VarSITI program is summarized in a companion article (Shiokawa and Katya 2020 to be added). The stated overarching goal of the ISEST project is to understand the origin, propagation, and evolution of solar transients through the space between the Sun and the Earth, and develop the prediction capability of space weather. Toward this goal, the ISEST project has organized four dedicated workshops in three different geographic locations across the globe: 17 – 20 June 2013 in Hvar, Croatia, 26 – 30 October 2015 in Mexico City, Mexico, 18 – 22 September 2017 in Jeju, South Korea, and 24 – 28 September 2018 again in Hvar, Croatia. The ISEST project maintains a standing website for hosting event catalogs, data, and presentations, and offers a forum for discussion at http://solar.gmu.edu/heliophysics/index.php/Main_Page.

The ISEST project has resulted in a Topic Issue in the journal of Solar Physics with a collection of 32 articles (Zhang et al. 2018a); this collection is then converted to a published book (Zhang et al. 2018b). A similar but earlier project in the CAWSES-II era, Climate and Weather of the Sun-Earth System of SCOSTEP (2010-2014), is the project of “Short-term variability of the Sun-Earth system”; the summary of the activity from 2010-2014 is in Gopalswamy et al. (2015c).

The implementation of the ISEST project is centered around several working groups, which are (1) data, (2) theory, (3) simulation, (4) campaign study, (5) SEP, (6) Bs challenge, and (7) MiniMax24 campaign. The sections of this article largely contain the contribution of these seven working groups, respectively. We organize the articles as follows. Section 2 is on observational progress on CMEs and ICMEs. Section 3 is on theoretical progress on CMEs and ICMEs, while Section 4 summarizes the progress in simulation studies of CMEs and ICMEs. Campaign-style studies are reviewed in Section 5. SEP studies are reviewed in Section 6. Section 7 reviews stream interaction regions. Forecasting CMEs are reviewed in Section 8. Section 9 summarizes the activity of MiniMax24 campaign. The conclusion and outlook are in Section 10.

Progress in observations of CMEs/ICMEs

Introduction

The capacity of observing and studying the solar-terrestrial system has increased dramatically during solar cycle 24. We can observe and track solar eruptions nearly continuously in time and space from Sun to Earth, thanks to a large set of sensitive remote-sensing and in situ instruments onboard a fleet of spacecraft. These include the Solar Terrestrial Relations Observatory Ahead/Behind (STEREO A/B) (twin spacecraft launched in 2006; drifting along the Earth orbit) (Kaiser et al. 2008), the Solar Dynamics Observatory (SDO) (geosynchronous orbit; launched in 2010) (Pesnell et al. 2012), the Solar and Heliospheric Observatory (SOHO) (L1 point; launched in 1995) (Domingo et al. 1995), Hinode mission (polar orbit of Earth; launched in 2006) (Kosugi et al. 2007), the Advance Composition Explorer (ACE) (L1 point; launched in 1997) (Smith et al. 1998), Wind spacecraft (L1 point; launched in 1994) (Ogilvie et al. 1995), and other space-based spacecraft and ground-based observatories.

In particular, the SECCHI (Sun Earth Connection Coronal and Heliospheric Investigation) suite onboard STEREO comprised five imaging telescopes, which together observe the solar corona from the solar disk to beyond 1 AU; these telescopes are EUVI (Extreme Ultraviolet Imager: 1–1.7 Rs), COR-1 (Coronagraph 1: 1.5–4 Rs), COR-2 (Coronagraph 2: 2.5–15 Rs), HI-1 (Heliospheric Imager 1: 15–84 Rs, or 4–24° in elongation angle) and HI-2 (Heliospheric Imager 2: 66–318 Rs, or 19–89° in elongation angle ) (Howard et al. 2008). Two recent missions dedicated to solar and heliospheric physics are the Parker Solar Probe (PSP) (varying elliptical orbit around the Sun with perihelia < 10 Rs; launched in 2018) (Fox et al. 2016) and the Solar Orbiter (highly elliptical and inclined orbit around the Sun; launched in 2020) (Müller et al. 2020). These missions will provide observations of the unexplored territories of the Sun-heliosphere system, but results from these two spacecraft will not be included in this review.

The global and long-lasting nature of CMEs makes the so-called Sun-Earth connection truly meaningful. Erupting from the low corona of the Sun and propagating into the outer corona and interplanetary space, a typical fast CME largely contains two volumetric components that are persistent in time and space: the magnetic ejecta component and the shock sheath component. Each of the two volumetric components has its own unique front: the ejecta front and the shock front, respectively. This is evident in both remote-sensing imaging observations in white light as well as from in situ one-point time-series sampling when the CME passes through the spacecraft, as illustrated in Fig. 1. The ejecta contains the erupted magnetic field and plasma originating in the low corona, while the sheath region contains the magnetic field and plasma corresponding to the ambient solar wind that is disturbed and compressed by the forward shock (or forward compressing waves for slower CMEs). Through its propagation from the Sun to Earth, a CME ejecta is believed to maintain its curved flux-rope shape in a quasi-self-similar manner and keep its two legs remaining rooted on the surface of the Sun for days and even longer.

Fig. 1
figure1

A schematic of a CME and its interplanetary counterpart ICME. Top left: the CME image in white light near the Sun (an event on July 12, 2012, adopted from Hess and Zhang (2014). The red and blue curves outline the shock front and CME ejecta front, respectively. The Sun is indicated by the white circle in the center. Top right: the in situ data of the resulting ICME near the Earth (adopted from Hess and Zhang 2014). From top to bottom, the five panels show the Dst index, solar wind magnetic field, velocity, and density. The vertical red line indicates the arrival time of the shock, and two vertical blue lines indicate the beginning and ending time of the CME ejecta. Bottom: A schematic of CME/ICME illustrates its geometry and internal components including the shock front, turbulent sheath and draped ambient magnetic field, twisted magnetic field in the CME ejecta and electron heat flux along magnetic fields. (adopted from Zurbuchen and Richardson 2006)

In light of the fact that the behavior of CMEs is dominated by different kinematics and dynamics at different distances within the vast space between the Sun and Earth, we loosely divide the whole Sun-Earth domain into three sub-domains: (1) in the corona where CME evolution is dominated by its internal magnetic force; this is also the region imaged by coronagraphic instruments, (2) farther from the Sun in the interplanetary space where CME evolution is mostly dominated by the aerodynamic drag force, i.e., momentum transfer between the CME and the ambient solar wind flow; practically, this is the area observed by Heliospheric Imagers onboard STEREO, and (3) near the Earth (or other locations near 1 AU) where most in situ sampling data are taken. These in situ data provide detailed diagnostics of plasma, magnetic, and abundance properties of CME ejecta and driven shock, albeit limited at one particular point in space or a particular sampling line for a traveling ICME. Remote-sensing of the CME-driven shock has been enabled by tracking type II radio bursts with the radio instruments on board the Wind and STEREO missions. A CME in these three sub-domains can be conveniently called as CME in the traditional sense, an ICME in the interplanetary space and in situ ICME, respectively. Note that there is certainly no boundary or barrier between the aforementioned corona and interplanetary space, which can be anywhere between 4 Rs and 30 Rs. For the sake of simplicity only, one could arbitrarily adopt a value of 20 Rs (roughly coinciding with the Alfvenic critical point) to separate domains 1 and 2.

In this Section, we review the basic morphology and geometry (Section 2.2) as well as kinematic behavior of CMEs (Section 2.3) in the corona and in the interplanetary space. The properties of source regions in the low corona where CMEs originate are reviewed in Section 2.4. Section 2.5 reviews statistical properties and solar cycle variation of CMEs and ICMEs. A summary is given in Section 2.6

CME morphology, geometry and their evolution

Basic morphology of CMEs

One of the fundamental properties of CMEs is its morphology near the Sun, as obtained from the direct interpretation of outer corona images made by white-light coronagraphs. Prior to the SOHO era, the morphology of CMEs had been characterized by the so-called three-part structure: a bright frontal shell, followed by a relatively dark cavity surrounding a bright core (Illing and Hundhausen 1986). The expected shock fronts missing in this traditional structure were later routinely identified, thanks to the improved sensitivity of coronagraphs on the SOHO and STEREO spacecraft. The shock front appears as an outline or boundary of a weakly brightened region that contains displaced or kinked coronal streamers and rays (Sheeley et al. 2000; Wood and Howard 2009; Ontiveros and Vourlidas 2009; Hess and Zhang 2014; Liu et al. 2017a; Gopalswamy et al. 2009a, 2009b; Gopalswamy and Yashiro 2011). A shock fronts is expected to form when the speed of the CME ejecta in the frame of the ambient solar wind is faster than the fast mode wave speed. Figure 2 shows one example of the identification and geometrical fitting of the fronts of the ejecta (green wireframe) and the shock (red wireframe). Thus, the overall morphology of a typically large and fast CME can be characterized by two fronts: a large fuzzy shock/wave front followed by a bright loop-like ejecta front which can be interpreted as the plasma pileup at the boundary of the expanding magnetic flux rope, irrespective of whether a three-part structure can be identified following the loop-like front (Vourlidas et al. 2013).

Fig. 2
figure2

Forward model fitting of CME ejecta front and CME-driven shock front of July 12, 2012 event based on STEREO-A COR2 (left) and STEREO-B COR (right) images, along with (bottom) and without the raytrace mesh. The green mesh shows the GCS fitting to the eject front, whereas the red mesh shows the spheroid fitting to the shock front (adapted from Hess and Zhang 2014)

To quantitatively capture the 3D morphology (i.e., shape and size) and geometry (i.e., location and orientation) of a CME ejecta, the graduated cylindrical shell (GCS) model has been widely used (Thernisien et al. 2006; Thernisien et al. 2009; Thernisien 2011). This 3D geometric model, meant to reproduce flux-rope-like CMEs, consists of a tubular section forming the main body of the flux rope attached to two cones that correspond to the “legs” of the flux rope that are connected to the surface of the Sun. In this model, the bright frontal shell of the ejecta corresponds to the surface of the flux rope, and the cavity as the body of the flux rope, being consonant with the common view (e.g., Chen et al. 1997a; Cremades et al. 2006). This model contains a central axis that threads through the center of the curved tube and the conical legs. The shell surface of the flux rope exhibits rotational symmetry around the central axis at each cross section perpendicular to the axis. This axis also defines the geometric plane of the flux rope. The GCS model, as the one implemented in Solar Software (IDL), has the following six free parameters, (1) propagation longitude, (2) propagation latitude, (3) tilt angle of the curved central axis (the plane of the flux rope), (4) height of the leading edge of the front, (5) half angle between the axes of the legs and (6) aspect ratio between the radius of the circular cross section of the tubular shell and the distance to the outer edge of the shell from the Sun center; for details of the geometry and the parameters, refer to Fig. 1 in Thernisien et al. (2009). The first three parameters define the geometry, while the later three parameters define the morphology or sizes of the CME. As will be discussed below, CME geometry changes significantly close to the Sun, but is assumed to remains largely constant in the interplanetary space. On the contrary, CME morphology remains self-similar in the corona, but distorts significantly in the interplanetary space.

To capture both the ejecta and shock fronts of CMEs, Kwon et al. (2014) developed a compound model, in which the shock front is modeled as an ellipsoid, which can be spherical or ellipsoidal depending on events as well as on the evolution stage of the event of study; the ejecta front simply follows the GCS model. The ellipsoid model of the shock front also has six free parameters that define the geometry and morphology in 3D. Using this model, Kwon et al. (2014) demonstrated that the footprints of expanding shock waves seen in the outer corona correspond well to the EUV wave front observed on the solar disk in the early development of CMEs. Similar results of reconciling CME-driven shock and EUV coronal waves are obtained in other studies (Cheng et al. 2012; Veronig et al. 2018), revealing the global behavior of CME-driven shocks.

The reconstruction of shock fronts in 3D also reveals the global properties of halo CMEs. It had been widely believed that the halo appearance of a CME is caused by the geometric projection effect, i.e., a CME moves along the Sun-Earth line and project in all directions on the plane of the sky surrounding the occulter. However, Kwon et al. (2015) found that 66% of halo CMEs from 2010 to 2012 are seen as halos in all three spacecraft, SOHO, STEREO-A and STREO-B when they are in quadrature configuration. They concluded that the halo structure largely represents the shock/wave that propagates in all directions, with a lesser dependence on the projection effect of the CME ejecta that has a limited size. Shen et al. (2013a, b, c) also found that very fast (> 900 km/s) full-halo CMEs originating far from the vicinity of solar disk center have a small projection effect. This global reach of CME-driven shock, even having a component propagating in the opposite direction of the CME ejecta, helps explain that some SEP events have a wide range of helio-longitude distribution, even allowing particle intensity increase at poorly connected spacecraft (Lario et al. 2014; Liu et al. 2017a).

While the physical properties of CME-driven shocks were refined in the last decade, as discussed above, the physical nature of the core of CMEs has been recently questioned in several studies (Howard et al. 2017; Song et al. 2017; Veronig et al. 2018; Song et al. 2019). It has long been believed that the bright core inside the CME cavity originates from entrained erupting filament/prominence material which has a high density. However, through investigating source region of CMEs on the solar disk and tracking eruptions continuously into the coronagraph FOV from multiple viewpoints in space, unambiguous observational evidence shows that many “classical” three-part CMEs do not contain an erupting filament/prominence (Howard et al. 2017; Song et al. 2017). Howard et al. (2017) suggested that the core could be the result of a mathematical caustic produced by the geometric projection of a twisted/writhed flux rope, implying the same flux rope produces both the cavity and core; they also suggested another possible cause that could arise spontaneously from the eruption of a flux rope. Through investigating the well-observed highly structured CME on 2017 September 10, Veronig et al. (2018) argued that the bright core rises from the hot plasma generated through magnetic reconnection but adds onto the rim of the rising flux rope, implying that the core is the flux rope.

Song et al. (2019) suggested that the core might correspond to the entirety of the flux rope in the early phase, but expand continuously and fill-in the entire cavity at a later time. The physical nature of the observed CME core and cavity remains to be an open question.

CME morphological evolution in the corona: self-similar expansion

How does the morphology of CMEs evolve in the corona (as well as in the interplanetary space; see next subsection)? This issue is far from settled. One simple question is whether such evolution is self-similar or not. Since it is a structured 3D entity, a CME evolves along three principal directions in a 3D space. Thus, to properly answer this question, one has to define which direction the self-similarity refers to. For the clarity of discussion hereafter, we define three principal directions in the frame of the flux rope with the apex of the central axis of the flux rope at the origin: toroidal direction (T), poloidal direction (P) and radial direction (R). The radial direction is the vector line connecting the Sun center toward the apex of the central axis, the toroidal direction, which is on the plane of the flux rope, is along the direction of the central axis at the apex, while the poloidal direction is perpendicular to the plane of the flux rope. Both toroidal and poloidal directions are perpendicular to the radial direction. If the tilt angle of the flux rope is zero, the toroidal direction will be exactly along the heliographic longitude, while the poloidal direction will be along the heliographic latitude. The linear sizes of the flux ropes can be characterized by LT, LP and LR, respectively. Similarly, one can define three aspect ratios: κT = LT/dA, κP = LP/dA, κR = LR/dA, respectively, where dA is the distance of the apex of the flux rope central axis. A constant aspect ratio along one particular direction defines the self-similar evolution in that direction.

Since the advent of multi-viewpoint observations of CMEs, the aforementioned GCS model is widely used to determine CME morphology in 3D for a large number of CMEs (e.g., Poomvises et al. 2010; Kilpua et al. 2012; Colaninno et al. 2013; Subramanian et al. 2014; Hess and Zhang 2014; Veronig et al. 2018; Chi et al. 2018b). These studies found good agreement between GCS-generated flux rope shells and the observed CME appearances. One particular interesting result, relevant to the morphology, is that the constant aspect ratio and angular width can be adopted for a particular CME observed in different times, implying a self-similar evolution of the morphology in all three principle directions. Note that the aspect ratio in the GCS model is the same as κP and κR defined above, and κP = κR since the GCS flux rope has a circular cross section perpendicular to the central axis. The angular width in the GCS model is equivalent to κT defined above. In other words, CME angular widths along both toroidal and poloidal directions remain constant as it evolves, and in the meantime, the CME expands radially at the same rate as along the two lateral directions, maintaining a circular cross section, or constant κR. However, the constant aspect ratio along the radial direction will not be true in the interplanetary space as discussed in the next subsection.

A more robust examination of self-similarity can be carried out by comparing expansion speed and bulk speed of CMEs, and a constant ratio with time indicates the self-similarity. Through a statistical study of 475 CMEs from 2007 -2014 that are geometrically well structured and whose geometric centroid and boundary can be well determined from single-viewpoint images (Vourlidas et al. 2017; Balmaceda et al. 2018), Balmaceda et al. (2020) found that (1) the relationship between lateral expansion and radial expansion speeds is linear and does not change with height, and (2) the ratio of the bulk propagation speed to the lateral expansion speed is a function of the angular width that follows the description of self-similar evolution. They also found that most CMEs achieve a self-similar evolution above 4 Rs, which is especially applicable to impulsively accelerated events.

However, in the inner corona (e.g., < 4 Rs), CMEs would not evolve in a self-similar manner and experience the so-called over-expansion, i.e., the aspect ratio increases with height and consequently the angular width also increases with height (Patsourakos et al. 2010; Balmaceda et al. 2020; Cremades et al. 2020). Studying a sizeable number of CMEs that could be tracked from their inception in the EUV low corona to the outer corona from multiple viewpoints, Cremades et al. (2020) found that CME angular widths, along both toroidal and poloidal directions, increase considerably with height below ~ 3 Rs, and the growth rate along the toroidal direction is higher than that along the poloidal direction. They also found that the ratio of the two expansion speeds is nearly constant after ~ 4 Rs, implying that CMEs there reach a state of self-similar expansion.

CME geometric change in the corona: deflection and rotation

On the top of morphological expansion of CMEs discussed above, the geometry of CMEs evolves in a manner that deviates from the simplest behavior of straight radial motion near the Sun: (1) deflection or non-radial motion, (2) rotation resulting in the change of the tilt angle of the CME. Both deviations pose a challenge for predicting hits or misses for Earth-directed CMEs and eventually whether a given CME would be geoeffective (Kay et al. 2017).

CME deflection has long been noticed (MacQueen et al. 1986; Gopalswamy et al. 2003; Cremades and Bothmer 2004). The deflection found in these observations was restricted along the latitude only, since they were made from single viewpoint observations from spacecraft along the Sun-Earth line. The deflection has a tendency that changes the direction of motion of CMEs from high latitude toward the low latitude equator during the solar minimum. This tendency implies that the deflection during solar minimum is related to the large-scale magnetic field from polar coronal holes (Gopalswamy et al. 2003; Cremades and Bothmer 2004). However, during the solar maximum, the directions of deflection can be complex, i.e., toward both higher and lower latitudes from the original position angle of CMEs.

Multiple viewpoint observations from STEREO provide much improved diagnostics of CME deflections, including the time evolution of deflections along both latitudinal and longitudinal directions. (Gopalswamy et al. 2003) found that a slow CME during solar minimum was deflected toward a lower latitude region by ~30°, and demonstrated that such a deflection is caused by a non-uniform distribution of the background magnetic field, and the CME tended to propagate to the region with lower magnetic-energy density. A follow-up study on a larger sample of events further confirmed that the background magnetic field quantitatively described by the magnetic energy density control the deflection of CMEs along both longitude and latitude (Gui et al. 2011). Kilpua et al. (2009) showed that a CME originating in a high latitude crown prominence was guided by polar coronal hole fields to the equator and produced a clear ICME in the near-ecliptic solar wind at in situ. Such a scenario of large latitude deflection (e.g., >30°) of a high-latitude CME moving toward the equator and intercepting the Earth was also reported in Byrne et al. (2010). Besides being influenced by coronal holes, Liewer et al. (2015) attributed the rapid initial asymmetric expansion or deflection of some CMEs in the inner corona (< 1.5 Rs in EUVI FOV) to the magnetic pressure of active regions fields in the immediate vicinity of the eruption.

CME deflections in longitude were also recognized and studied, but to a lesser extent than in latitude. One of the earlier clues came from the fact that there was an east-west asymmetry of solar source regions of geoeffective CMEs, i.e., more geoeffective CMEs originated from the western hemisphere than from the eastern hemisphere (Zhang et al. 2003; Wang et al. 2004), thus favoring an interpretation of longitudinal deflection (Wang et al. 2004). Another line of evidence is related to the finding of “driverless” shocks found at 1 AU whose solar sources were near the solar disk center, indicating that the CME ejecta were deflected away from the Sun-Earth line (Gopalswamy et al. 2009b).

Direct measurements of longitudinal deflection only became possible with the advent of STEREO (Isavnin et al. 2013, 2014; Möstl et al. 2015; Mays et al. 2015). Based on a sample of 14 events, Isavnin et al. (2014) showed that most longitudinal and latitudinal deflections happened within 30 Rs, and a large part of the latitudinal deflection occurred within a few Rs. Möstl et al. (2015) studied a particularly interesting case of the January 7, 2014, CME, which originated near the disk center but was deflected toward the west by ~ 37° in longitude. Thus, this major CME (projected speed of ~ 2400 km/s and associated with an X1.2 flare) almost entirely missed the Earth and causing a false alarm of prediction by various space weather prediction centers. They also found that such a large longitudinal direction was attained very close to the Sun (< 2.1 Rs), likely caused in this particular case by the channeling of nearby active region magnetic fields rather than coronal holes. Such a surprising geomagnetic non-event from a major disk center eruption highlights the importance of knowing the true directionality of CMEs for space weather prediction (Mays et al. 2015).

Another very relevant geometric evolution of CMEs is the rotation, or the change of the tilt angle of the entrained magnetic flux rope. The tilt angle is zero if the toroidal axis of CMEs lies on the equatorial plane of the Sun, and 90° if perpendicular to the equatorial plane. The tilt angle is critically important in deciding how much of the southward magnetic field will encounter the Earth for a given impacting CME, thus determining its expected intensity of geoeffectiveness (e.g., Bothmer and Schwenn 1998). Prior to the STEREO era, the evidence of rotation resided on the observations of erupting filaments in EUV coronal images (Ji et al. 2003; Zhou et al. 2006; Green et al. 2007). Using the orientation of the elongation of halo CMEs from single viewpoint LASCO observations as a proxy and assuming that the orientation of the post-eruption arcade in the source region is the CME orientation at the beginning of the eruption, Yurchyshyn et al. (2009) found that most CMEs appeared to rotate by 10°, but up to 30–50° in some events.

Multiple viewpoint STEREO observations provide direct measurements of CME rotations in the coronagraphic field of view (Vourlidas et al. 2011; Isavnin et al. 2013, 2014; Liu et al. 2018d; Chen et al. 2019). Using the GCS model to define and track the 3D geometry of a slow CME on 2010 June 16, Vourlidas et al. (2011) found that the CME had an initial tilt of about 30° at 2–3 Rs, very similar to the orientation of the neutral line on the surface source, but later rotated by about 60° when the CME traveled from 2 to 15 Rs. Liu et al. (2018d) studied a CME on 2015 December 16 and found that the tilt from the GCS model rotated by almost 95° compared with the orientation on the source region; the same CME was also deflected by 45° in longitude and 35° in latitude. Such an extremely large rotation of the main structural axis was also found in an erupting filament based on STEREO observations in Song et al. (2018), who reported a counter-clockwise rotation of about 135° of the filament in ~ 26 min and then reversed to the clockwise rotation of 45° in about 15 min. Based on a statistical study of geometry of CMEs, Isavnin et al. (2014) noted that the rotation largely occurred below 5 Rs, but continued in the outer corona and the interplanetary space.

Geometry of ICMEs in the interplanetary space

As discussed above, in the inner corona (~ < 4 Rs), a CME usually undergoes a super-expansion or non-self-similar increase of sizes in comparison with its distance from the Sun, and also experiences most geometric changes as defined by radial deflection and rotation of tilt angles. In the outer corona (e.g., from ~ 4 Rs to 20 Rs), on the other hand, a CME usually undergoes a self-similar expansion in all three principle directions and some relatively smaller changes in propagation direction and tilt angle. What about morphological and geometric evolution of CMEs in the interplanetary space, i.e., from ~ 20 Rs to 1 AU? Much progress has been made in the last one and half decades, thanks to the Heliospheric Imager (HI) (Eyles et al. 2009) onboard STEREO A/B. Nevertheless, the knowledge that has been gathered is largely limited, as discussed below.

Studies of using HI images from a single spacecraft usually assume that CMEs have a constant propagation direction and speed in HI FOVs. Having expanded into a huge volume thus becoming extremely faint, CMEs in HI images have a much lower signal-to-noise ratio than in coronagraphic images. Instead of forward-fitting CME appearances using a 3D geometric model such as the GCS model, HI studies often make use of time-elongation maps, or so-called J-maps (Sheeley et al. 1999), which are stack plots of slices taken along a given position angle (often along the ecliptic plane) from consecutive images of a single STEREO spacecraft (Lugaz et al. 2009; Davies et al. 2012). The slice provides a direct measure of elongation angles from the inner to the outer edges of HI FOV (Fig. 3). Such time-elongation maps show enhanced tracks of the leading edges of a CME, but at the expense of its 3D geometry such as aspect ratios and tilt angles. The time-elongation curve of the tracked feature in the map is then used to determine the propagation longitude and speed of the feature along the selected latitude/slice. This assumption of constant propagation longitude and speed, imposed by this time-elongation map method from a single spacecraft, is not unrealistic, since it is known that most changes have occurred near the Sun in coronagraphic FOVs.

Fig. 3
figure3

An example of measuring CME (July 12–14, 2012 CME) leading fronts using slice-stacking plot or J-map and geometric models. a The density track of the CME viable in a J-map from STEREO-A. b Fits of the extracted CME track with the SSEF (Self-Similar Expansion Fitting) model. c The resulting geometry of the event, with propagation directions derived from FP (dot-dashed red line, 0° full width), SSEF (solid green line, 90° full width), and HM (dotted blue line, 180° full width) geometric assumption of the CME. Adopted from Möstl et al. (2014)

The orbital configuration of STEREO A/B is such that the degree to which the same CMEs are imaged by the HI cameras on both spacecraft critically depends on the mission phase (Harrison et al. 2018). The percentage of such so-called coincident events by HI-1 ranges between 40% and 90%. Note that the percentage of coincident events by COR2 is about 80% in total (Vourlidas et al. 2017). For coincident events of HI observations, one can apply a geometric triangulation technique on the time-elongation data from two spacecraft to extract instantaneous propagation longitude and distance at each time of the observation, thus allowing the time variation of propagation longitude and velocity of CMEs (Liu et al. 2010; Lugaz 2010; Davies et al. 2013). Using stereoscopic time-elongation methods and theoretical arguments, several studied suggested possible non-radial motions of CMEs over a large distance in the heliosphere (Lugaz et al. 2010a; Wang et al. 2014; Isavnin et al. 2014).

Nevertheless, caution is needed as the time-elongation methods do not provide a converging result on the propagation longitude when different geometric assumption of CMEs are made (Liu et al. 2013; Davies et al. 2013) and different spacecraft are used (Barnes et al. 2020). Note that a set of commonly used time-elongation methods have been developed, which differ in the assumption of CME geometry on the plane containing the selected slice and the observing spacecraft: as a point or compact source (the fixed-φ, or FP method) (Sheeley et al. 1999; Rouillard et al. 2008), as a circle with the feature at the tangent front and the bottom attached to Sun-center (harmonic mean, or HM method) (Lugaz 2010), or as a generalized circle of certain half angle λ (generalized self-expansion, or SEE method) (Davies et al. 2012); the FP and HM geometries form the limiting cases with λ equals 0° and 90° respectively, while λ can be chosen between 0° and 90° in the SEE method (Fig. 3). Davies et al. (2013) found that the derived CME longitude is a function depending on the choice of λ, and the disparity in longitudes can be significant between the two limiting cases. In a statistical study of 273 coincident events, Barnes et al. (2020) noted that the longitude derived from single-spacecraft are in fairly poor agreement with each other, and moreover, neither agree well with the results from stereoscopic analysis. Such systematic disparity may indicate the incorrectness of the underlying assumption, i.e., the assumed circular front of CMEs may deviate significantly from the actual morphology, which will be discussed below.

Morphology of ICMEs in the interplanetary space

In contrast to the largely self-similar expansion pattern of CMEs in the corona, CMEs may undergo significant deformation in the interplanetary space, thanks to the enhanced effect of structured solar wind flows on CMEs (Odstrčil and Pizzo 1999a; Riley and Crooker 2004). It is understood that, in the regime of high plasma beta where plasma pressure dominates magnetic pressure, the magnetic structure of CMEs will be strongly modulated by the pattern of plasma flow. In the interplanetary space, the solar wind plasma flows along the radial direction but in a spherically diverging geometry. Consequently, such a flow pattern introduces the following kinematic effects on the structure of CMEs: (1) self-similar expansion along lateral directions, or directions on the spherical surface (2) no expansion at all along the radial direction that is perpendicular to the spherical surface, leading to the thinning or pancaking of the overall CME morphology (Riley and Crooker 2004). In the following, we discuss the self-similarity of CME evolution along lateral and radial directions respectively.

Observations in HI FOVs show that CMEs maintain a nearly constant angular width, indicating a self-similar expansion or constant aspect ratios along lateral directions with respect to the distance of CMEs (Wood et al. 2009; Wood et al. 2017). Note that the two principal lateral directions for a flux rope CME are along the toroidal and poloidal directions, respectively. To reproduce the observed two-dimensional loop of CME leading fronts in a flexible way, Wood et al. (2009) adopted a geometric shape described by a quasi-Gaussian equation in polar coordinates with a variable power index α regulating the shape of the loop; the shape is a perfect Gaussian for α = 2, while higher values of α result in loops with flatter tops. Using a statistical survey study of 48 events, Wood et al. (2017) noted that self-similar expansion is a decent, albeit not perfect, approximation for CMEs expanding into the interplanetary space. Such self-similar expansion along lateral directions should have continued from coronagraphic FOVs into HI FOVs.

Nevertheless, the self-similar evolution breaks down for the dimension along the radial direction. The cross section of the CME flux rope can be initially well described by a circle, as in the highly successful GCS models. Into the interplanetary space, the circular shape may evolve into a highly flattened and distorted shape, which has been described as a convex-outward pancake shape (Riley and Crooker 2004), elliptical shape (Savani et al. 2011), or even a concave shape (Savani et al. 2010). As an example of one extreme case, (Savani et al. 2010) clearly showed the observation that a circular-shaped CME in the coronagraphic FOV evolved into a concaved structure in the HI FOV, and suggested that the kinematic effect of a bimodal speed solar wind caused such distortion. Therefore, the shape of the leading front of a CME can deviate significantly from a circular shape, and caution needs to be taken when a circular-shape assumption is assumed in modeling ICMEs.

Note that, besides the studies based on coronal and heliospheric imaging observations mentioned above, the geometry and morphology of CMEs can also be inferred from in situ observations. There is a vast amount of work of fitting in situ data to infer the structure of shocks and magnetic flux ropes, and such studies are partially reviewed in Section 3.5. In the next sub-section, we provide a review on the studies of kinematic properties of CMEs and ICMEs, which are mostly based on the time tracking of the leading fronts of the CME, instead of the 3D extension of the structure.

Kinematics of CMEs and ICMEs

Our knowledge about the whole kinematic evolution of CMEs from the Sun to the Earth has improved significantly in the last decade, largely thanks to the wide-angle observations of STEREO. Rising from locations above magnetic polarity inversion lines near the surface of the Sun, CMEs accelerate and reach speeds in the outer corona with a wide range of values from tens of km/s up to ~ 4000 km/s. The subsequent evolution of CMEs depends on their initial speeds in the outer corona relative to the speed of ambient solar wind: faster CMEs decelerate, while slower CMEs accelerate. As CMEs propagate further into the interplanetary space, their speeds tend to equalize with that of the solar wind due to the effect of aerodynamic drag (or more precisely, magnetohydrodynamic drag). For a large fraction of CMEs, the balance in speed and pressure is not established at the distance of 1 AU. The speed of ICMEs at 1 AU ranges from ~ 300 km/s to ~ 1000 km/s, meaning that it can be much faster than the ambient solar wind at 1 AU. In the following, we provide a review on the Sun-to-Earth kinematic evolution, including the phases of evolution, peak velocity, terminal velocity, cessation distance and others. The topic on the prediction of CME Time of Arrival at 1 AU will be given in Section 8.2.

Based on tens of thousands of CMEs observed, it is found that CME speed (i.e., average projected speed measured in LASCO FOV) has a very broad distribution ranging from ~ 10 km/s to ~ 3000 km/s (Yashiro et al. 2004; Robbrecht et al. 2009a; Olmedo and Zhang 2010; Webb and Howard 2012; Lamy et al. 2019). The average speed of all CMEs in the various observed periods is about 300 km/s during the solar minimum and about 500 km/s during the solar maximum. Further, halo CMEs, which are the ones likely hitting the Earth, have an average speed of about 950 km/s, or about twice of that of all CMEs. Slow CMEs are quite common, as about half of CMEs in the LASCO FOV are slower or near the speed of the ambient solar wind. On the other hand, fast CMEs are equally common. Nevertheless, extremely fast CMEs, i.e., > 1500 km/s, are rather rare, occupying ~0.5% of all CMEs (Wang and Zhang 2007). The highest CME speed on the record is ~4400 km/s (Gopalswamy et al. 2018a, b, c, d, e).

Recently, Barnes et al. (2019) made a statistical study of CME kinematics in the STEREO HI-1 FOV and compared with that in the LASCO FOV. They found that the velocity distributions are similar in both areas: a sharp peak at the low end of the distribution and a long tail of high-speed CMEs. The yearly mean speeds in HI-1 FOV are consistently higher than that in LASCO; however, the two types of speeds are very similar after projecting HI speeds onto the plane of the sky. In the HI FOV, the range of CME speeds is from ~ 100 km/s to ~ 2000 km/s. It is noticed that there are very few CMEs with speeds less than 200 km/s in the HI FOV, which is of a distinct contrast with that of LASCO CMEs. This difference is certainly not surprising, as slow CMEs in the corona are picked up by the drag of ambient solar wind.

A large number of studies on individual events have provided detailed kinematic evolution of CMEs from corona and far into the inner heliosphere (Wood and Howard 2009; Poomvises et al. 2010; Liu et al. 2010; Colaninno et al. 2013; Hess and Zhang 2014; Liu et al. 2016; Wang et al. 2016a, b, c, d; Wood et al. 2017). The observed speed profiles of three typical CMEs, which are of slow, intermediate and fast initial speeds respectively, are shown in Fig. 4 (adopted from Liu et al. 2016). Clearly, faster CMEs decelerate and slower CMEs accelerate, as also shown in earlier studies (Sheeley et al. 1999; Gopalswamy et al. 2000). One of the interesting results from observational studies is that there appears the existence of a cessation distance, at which a CME reaches its terminal velocity; after this distance, the CME moves at a nearly constant speed, or too small to be measured by existing imaging instruments. Note that we are cautious on the usage of the term “terminal speed,” as CME speeds will continue to change, albeit in a relatively small rate (e.g., < 1 m/s2). Poomvises et al. (2010) showed that this cessation distance was at about 50 Rs for several events including very fast ones. Using a kinematic model that divides the CME evolution into 2–4 phases of constant acceleration and constant velocity (Wood and Howard 2009), a recent statistical study by Wood et al. (2017) showed that the cessation distance ranged from ~ 10 Rs to ~ 100 Rs, and the terminal velocity ranged from ~ 300 km/s to ~ 1200 km/s. Similar result was found in an earlier study based on Type II radio observations (Reiner et al. 2007).

Fig. 4
figure4

Sun to Earth velocity profiles of a typical fast CME (upper), a typical intermediate-speed one (middle), and a typical slow one (lower). The horizontal dashed line indicates the observed speed at the Earth. Adopted from Liu et al. (2016)

CMEs reach their peak velocity at varying heights from the Sun. In general, fast CMEs reach their peak velocity at a low height, thanks to strong and impulsive acceleration, while slow CMEs reach their peak velocity at a relatively high height (Zhang and Dere 2006; Bein et al. 2011, 2012; Wood et al. 2017). Based on a statistical study of 95 events, Bein et al. (2011) found that the heights of peak velocity distribute from a very low height of 1.17 Rs (from disk center) to ~ 10.5 Rs (close to the border height of STEREO COR2 used in this study). A continued study by Bein et al. (2012) found that CMEs associated with flares, in comparison with CMEs associated with filaments, have on average significantly higher peak acceleration and lower height of peak velocities. Wood et al. (2017) found that the average peak velocity height was ~ 3.2 Rs for fast CMEs that were associated with flares, ~ 13.9 Rs for intermediate velocity CME associated with erupting filaments, and ~ 29.4 Rs for slow CMEs that were not associated with any apparent surface source regions.

The full Sun-to-Earth evolution of CMEs can be largely divided into four phases, each of which depends how the velocity varies and what forces drive the velocity change. Near the surface and in the corona, the full kinematic evolution of a CME can be characterized by three distinct phases: (1) a slow rise phase, or initiation phase, (2) a fast acceleration phase, or main phase, (3) a propagation phase with no or small variation of velocity (Zhang et al. 2001); this third phase is called residual acceleration phase in Zhang and Dere (2006). During the first two phases, a CME should be mainly driven by the Lorentz force. However, following the main acceleration, the Lorentz force may become significantly weaker, and the aerodynamic drag force sets in and become important. During this third phase, a CME likely experiences a combined effect of both Lorentz force and aerodynamic drag force, leading to the observed residual acceleration which can be either positive or negative (Zhang and Dere 2006). Further moving out, the Lorentz force eventually diminishes and the aerodynamic drag force will dominate; this phase can be considered the 4th phase of the full evolution, or the drag phase. When only the aerodynamic drag force is considered, the kinematic evolution of a CME can be modeled in a relatively straightforward way (Cargill 2004; Vršnak et al. 2013). As the aerodynamic drag force is proportional to the square of the difference between the CME velocity and the ambient solar wind velocity, the CME velocity will asymptotically approach the velocity of the ambient solar wind. In other words, a faster CME decelerates and a slower CME accelerates, and the acceleration rate is not a constant but asymptotically approaches zero. For a slow CME, the full evolution may be reduced to only two phases, a gradual acceleration out to about 20-30 Rs, followed by a nearly constant speed near the solar wind level (Liu et al. 2016). A detailed review on theories of CMEs propagation is given in Section 3.

Coronal sources of solar eruptions

The initiation and early evolution of CMEs cannot be observed using traditional coronagraphic observations, due to the blockage of the eruption region by the occulting disk. Therefore, various associated phenomena in H⍺, extreme-ultraviolet (EUV), X-rays, and microwaves on solar disk are linked to specific properties of the eruption and used to infer the origin of CMEs (Gopalswamy et al. 1999; Hudson and Cliver 2001; Harra 2009; Webb and Howard 2012). Over the course of the eruption, the associated activities can be a combination of filament eruptions, solar flares, large-scale coronal EIT waves, post-eruptive arcades, and coronal dimmings. For example, the CME onset is often accompanied with the eruption of filaments/prominences that later form the inner bright core of CMEs observed in coronagraphic data (Gopalswamy et al. 2003; Parenti 2014). The relationship between eruptive prominences and CMEs was investigated in several statistical studies (Munro et al. 1979; Webb and Hundhausen 1987; Hori and Culhane 2002; Gopalswamy et al. 2003), where an association rate of up to 90% was found.

Low coronal observations also revealed the close relationship between solar flares and CMEs

(Schmieder et al. 2015; Vršnak 2016). Strong and powerful flares tend to be associated with fast and massive CMEs (Moon et al. 2002; Burkepile et al. 2004; Vršnak et al. 2005; Bein et al. 2012), which results in a 90% correspondence for flares above X-class (Yashiro et al. 2006). However, there exist flares without CMEs (i.e., confined flares (e.g., Pallavicini et al. 1977; Wang and Zhang 2007; Sun et al. 2015) and vice versa, CMEs without flares (e.g., stealth CMEs) (Robbrecht et al. 2009b; Ma et al. 2010; Howard and Harrison 2013; D’Huys et al. 2014). A recent study by Nitta and Mulligan (2017) showed that stealth CMEs can result in significant geoeffective disturbances at 1 AU, highlighting their importance in space weather research.

If CMEs and flares occur together, they are interpreted to be different parts of the same magnetically driven event (Harrison 1995; Priest and Forbes 2002; Webb and Howard 2012; Green et al. 2018).

Over the past years, it was shown that CMEs and flares are closely related in time; i.e., the SXR peak and the main acceleration phase of the CME are nearly synchronized (Zhang et al. 2001; Neupert et al. 2001; Shanmugaraju et al. 2003; Maričić et al. 2004; Vršnak et al. 2004; Zhang et al. 2004; Zhang and Dere 2006; Cheng et al. 2020). The main acceleration phase of the CME is correlated with the time evolution of the flare-related hard X-ray burst (Temmer et al. 2008; Gou et al. 2020) and a close relationship between their onset times was found in statistical studies (Maričić et al. 2007; Bein et al. 2012). Further evidence for a close flare/CME relationship is provided by the strong correlation between characteristic CME parameters, such as the velocity, the acceleration, and its kinetic energy with the SXR peak flux, indicating the flare strength, or the integrated flux of the associated flare (Vršnak et al. 2005; Maričić et al. 2007; Yashiro and Gopalswamy 2009).

Since the flare energy release rate is closely related to the magnetic reconnection rate (Miklenic et al. 2009), a feedback relationship between the CME and its associated flare is established (Zhang et al. 2001; Vršnak 2008; Temmer et al. 2010; Welsch 2018). Increasing reconnection rates enhance CME acceleration, and vice versa, enhanced acceleration provides more efficient reconnection. Studies showed the correlation between CME velocities and the total reconnection flux supporting this interpretation (Qiu and Yurchyshyn 2005; Miklenic et al. 2009; Tschernitz et al. 2018; Gopalswamy et al. 2018a, b, c, d; Pal et al. 2018). The most recent study by Zhu et al. (2020) even directly proves this interpretation observationally by reporting on a strong correlation between the reconnection rates, estimated by flare ribbons and CME accelerations (c > 0.7). Interestingly, they also report on a positive correlation between the maximum speed of CMEs and the total reconnection flux but only for fast CMEs (v > 600 km/s). For slow CMEs with weak reconnection, other physical processes may play a more important role during acceleration than magnetic reconnection.

The initial lateral expansion of the CME also drives fast-mode magneto-sonic waves observed as large-scale perturbations of enhanced EUV emission, so-called EIT waves (Thompson et al. 1999; Patsourakos and Vourlidas 2009; Long et al. 2016). Their speeds typically range from 200 to 400 km/s (Klassen et al. 2000; Thompson and Myers 2009; Muhr et al. 2014), but also EIT waves with speeds up to 1000 km/s have been reported (Nitta et al. 2013; Seaton and Darnel 2018). Statistical studies revealed that fast and wide CMEs are in general accompanied with well-observed EIT waves often associated with shocks and therefore also related with type-II radio bursts (Biesecker et al. 2002; Cliver et al. 2005; Nitta et al. 2013, 2014; Muhr et al. 2014; Warmuth 2015). Combining type II radio burst observations with EUV waves observed by SOHO and STEREO, Gopalswamy et al. (2013b) found that the EUV waves are shocks forming very close to the Sun - as low as 0.2 Rs above the solar surface. For the physical mechanisms leading to the shock wave formation and coronal and chromospheric response, see, e.g., Vršnak et al. (2016) and references therein.

After the CME has erupted, bright post-eruptive arcades or post-flare loops appear in soft X-ray and EUV (Kahler 1977; McAllister and Hundhausen 1996; Tripathi et al. 2004) as a consequence of magnetic reconnection processes (Kopp and Pneuman 1976). Tripathi et al. (2004) statistically analyzed post-eruptive arcades using data from SOHO/EIT. They found that the majority of post-eruptive arcades (92%) were associated with CMEs identified in SOHO/LASCO.

Due to the expansion of the CME volume and evacuation of plasma during the eruption, regions of decreased emission in soft X-rays and EUV are formed, so-called coronal dimmings (Hudson et al. 1996; Thompson et al. 2000; Harra and Sterling 2001; Vanninathan et al. 2018). As they represent the lower footprint of CMEs in the low corona, their properties are closely related to the initial properties of the observed CME later on. For instance, several studies tried to relate the mass loss within coronal dimming regions to the CME mass measured from coronagraphic observations (Harrison and Lyons 2000; Zhukov and Auchère 2004; Aschwanden et al. 2009; López et al. 2019).

Recently performed statistical studies confirm the close connection between coronal dimmings and CMEs and found that the dimming area, its total magnetic flux, and its brightness are strongly correlated with the CME mass (Dissauer et al. 2018, 2019; Sindhuja and Gopalswamy 2020). Dimming parameters, describing its dynamics, such as the area growth rate, brightness change rate, and magnetic flux change rate, are tightly related to the CME speed. This is in agreement with the results of Mason et al. (2016) who studied coronal dimmings extracted from full-disk irradiance light curves of SDO/EVE (EUV Variability Experiment).

A number of studies also successfully compared magnetic flux rope properties, such as the magnetic flux, the chirality, and its helicity sign determined from post-eruptive arcades, flare ribbons, and coronal dimmings measured close to the Sun with magnetic cloud properties at 1 AU (Qiu et al. 2007; Yurchyshyn 2008; Hu et al. 2014; Marubashi et al. 2015; Gopalswamy et al. 2017b; Palmerio et al. 2017, 2018; James et al. 2017; Aparna and Martens 2020). The total amount of magnetic flux ejected during an eruption is estimated by the total reconnection flux in the wake of the CME or sometimes also by the magnetic flux involved in coronal dimming regions, which form the footprint of CMEs in the low corona (Mandrini et al. 2005; Attrill et al. 2006; Qiu et al. 2007; Hu et al. 2014). Especially the total reconnection flux strongly correlates with the magnetic flux of magnetic clouds (Qiu et al. 2007; Hu et al. 2014).

The helicity sign and the total amount of helicity of magnetic clouds at 1 AU seem to be strongly controlled by the location and properties of the solar source region (Cho et al. 2013; Hu et al. 2014; Marubashi et al. 2015). CMEs erupting in the southern (northern) hemisphere tend to have a positive (negative) helicity sign (hemispheric helicity rule, e.g., Pevtsov et al. 2003). Recently, Aparna and Martens (2020) investigated the directionality (chirality) of 86 CMEs-ICME pairs by comparing the orientation of their flux rope axes close to the Sun with the direction of the interplanetary magnetic field near Earth at L1. An agreement between the northward/southward orientation of Bz between ICMEs and their CME source regions was found in 85% of the cases, which is comparable to earlier results by Palmerio et al. (2018) and Yurchyshyn (2008), which found agreement for 55% and 77% of their cases.

In recent years, several studies also focused on Sun-to-Earth analysis of CMEs by linking the low coronal behavior and properties of the eruption with its observed in situ signature (Möstl et al. 2015; Patsourakos et al. 2016; D’Huys et al. 2017; Temmer et al. 2017a). A number of studies also compared magnetic flux rope properties, such as the magnetic flux, the chirality, and its helicity sign determined from post-eruptive arcades, flare ribbons, and coronal dimmings measured close to the Sun with magnetic cloud properties at 1 AU (Qiu et al. 2007; Gopalswamy et al. 2017b; Palmerio et al. 2017; James et al. 2017). Scolini et al. (2019b) used proxies of magnetic flux estimates determined from post-flare arcades (Gopalswamy et al. 2017b), flare ribbons (Kazachenko et al. 2017; Tschernitz et al. 2018) as well as coronal dimmings (Dissauer et al. 2018), as initial input for the global heliospheric EUHFORIA model, to study the geoeffectiveness of the famous 2017 September events. Good agreement with the observed Dst profile was found for simulations using the optimized input and including CME-CME interactions.

Solar cycle variations of CMEs and ICMEs

Solar cycle 24 is known to be weaker than previous several solar cycles, which is the focus of many studies during the VarSITI program. A weak solar cycle 24 is understood to be due to the weak polar magnetic field in the preceding solar minimum according to the Babcock Leighton Mechanism of the solar cycle (see e.g., Petrovay 2010). A weak cycle implies mild space weather that helps satellites in Earth orbit live longer. A weak cycle also means less total solar irradiance reaching Earth (e.g., Krivova and Solanki 2008). Here, we focus on the effect of a weak solar cycle on solar wind magnetic structures originating from the Sun and their space weather consequences.

Both solar source and impact of CMEs showed significant variations in cycle 24. The overall rate of CMEs increased in solar cycle 24 relative to cycle 23, although the rate of fast and wide CMEs decreased. Accordingly, the phenomena that are linked to fast and wide (FW) CMEs appeared subdued in cycle 24. The rate of occurrence of CMEs is known to be correlated with the sunspot number (SSN) for a long time. However, the slope of the regression line is significantly different in cycle 24. The relation between CME width and speed is also different in cycle 24: for a given speed, cycle-24 CMEs are significantly wider. CMEs are the main source of severe space weather. Weakened solar activity is reflected in the weak heliospheric state in terms of magnetic field strength, temperature, density, speed, and consequently the total pressure. The backreaction of the weakened heliosphere had led to the changed properties of CMEs and hence affected the space weather consequences. Marked reductions are observed in the number of intense (Dst ≤ − 100 nT) geomagnetic storms and high-energy (≥ 500 MeV) solar energetic particle (SEP) events. The number of halo CMEs in cycle 24 did not decrease significantly. In fact, the number of halo CMEs normalized to the sunspot number is larger in cycle 24. One would have expected enhanced geomagnetic activity in cycle 24 because of the higher abundance of halo CMEs, but it did not occur. In this section, we summarize some of the key observational results that describe the compound effect of the weak solar activity and heliospheric backreaction on CME properties.

Solar activity and eruption properties

Figure 5 shows the solar-cycle variation of CMEs and flares compared to SSN cycles 23 and 24 updated from (Gopalswamy et al. 2020a; Gopalswamy et al. 2020b). We can readily infer the following: (i) the daily rate of the general population of CMEs (width ≥ 30°) and that of the soft X-ray flares (size ≥ C1.0) did not decline in cycle 24, (ii) the FW CME rate declines significantly in cycle 24 (as opposed to the general population), (iii) the CME daily rates have a different relationship with SSN in the two cycles, (iv) the variation in the number of FW CMEs is similar to that of major soft X-ray flares (M- and X-class flares), and (v) the CME rate increases more rapidly as the activity increased, indicated by the steeper slope in the cycle-23 CME rate—SSN scatter plot. The reduction in FW CMEs is significant because they are the ones that are relevant for space weather consequences (geomagnetic storms and SEP events).

Fig. 5
figure5

Solar cycle variation of eruptive phenomena (flares and CMEs): a daily CME rate for the general population (width ≥30°) in red and the number of soft X-ray flares with size ≥C1.0 in blue, b fast and wide CMEs (speed ≥ 900 km/s; width ≥ 60°) in red and major (M- and X-class) soft X-ray flares in blue, and c scatter plots between the sunspot number (SSN, V2.0) and the daily CME rate (general population) for cycle 23 (red) and 24 (blue). In (a) and (b), SSN is shown in gray background. The CME and flare rates are averaged over the Carrington rotation (CR) periods. The flare rates are multiplied by 0.5 to fit the scale. Updated from Gopalswamy et al. (2020a); Gopalswamy et al. (2020b)

Petrie (2015) studied SOHO/LASCO CMEs with angular widths > 30° listed in the manual (CDAW) and automatic (CACTus and SEEDS) catalogs. He found that the CME rate relative to the sunspot number began an upward divergence with respect to the SSN in 2004 after the polar field reversal, while the interplanetary magnetic field decreased by ~ 30% around the same time (see Fig. 3a). These results are consistent with the enhanced halo CME detections due to the increased CME expansion in a heliosphere with diminished total pressure (Gopalswamy et al. 2015a). Petrie (2015) also showed that the increased CME rate in cycle 24 is not due to the LASCO cadence change that occurred in August 2010 (Wang and Colaninno 2014; Hess and Colaninno 2017). The cadence change was also found to be not important for halo CME rates (Gopalswamy et al. 2015a). Michalek et al. (2019) showed that the higher rate of the narrow CMEs can be attributed to the global magnetic structure in cycle 24 coupled with the reduced total pressure in the heliosphere, in agreement with Petrie (2015).

Phenomena associated with energetic CMEs

Figure 6 shows the solar cycle variation of the numbers of halo CMEs, intense geomagnetic storms, large SEP events, and decameter-hectometric (DH) type II bursts. All the numbers are summed over Carrington rotation periods. The properties of halo CMEs have a good overlap with FW CMEs, although some halos are wide, but not fast. Halo CMEs, when front-sided, are important because they can affect space weather. Intense geomagnetic storms are mostly due to energetic CMEs heading toward Earth containing southward magnetic field components either in the ejecta part or in the shock sheath. On the other hand, the shock at the leading edge of CMEs accelerates electrons and ions. The accelerated electrons produce type II radio bursts that are a good indicator of shock-driving CMEs near the Sun and in the interplanetary medium. Accelerated particles traveling along interplanetary field lines are detected as SEP events. We see that the number of events in each case generally follows the solar cycle with more events occurring during solar maxima. A notable exception is the number of intense geomagnetic storms in cycle 24 that remained flat.

Fig. 6
figure6

Solar cycle variation of the key CME-related phenomena during cycles 23 and 24 (from 1996 to the end of 2019): a SOHO/LASCO halo CME number from https://cdaw.gsfc.nasa.gov/CME_list/halo/halo.html. b the number of large geomagnetic storms (Dst ≤ − 100 nT), c the number of large solar energetic particle events (SEPEs) detected in the > 10 MeV GOES channel with intensity exceeding 10 pfu, and d the number of decameter-hectometric (DH) type II radio bursts from Wind/WAVES. For comparison with the solar cycle, the sunspot number averaged over Carrington rotation (CR) periods is also shown. Updated from Gopalswamy et al. (2015a, b, c)

Halo CMEs in solar cycle 24

As reported in (Gopalswamy et al. 2015a; Gopalswamy et al. 2020b; Gopalswamy et al. 2020), the halo CME rate in cycle 24 did not decline commensurate with the SSN. There are roughly the same number of halos in the two cycles. When normalized to SSN, cycle 24 has ~ 30% more halos (per SSN). As with the general population of CMEs, the halo CMEs are slower in cycle 24. Furthermore, CMEs in cycle 24 become halos at shorter heliocentric distances than in cycle 23. These authors attributed the peculiar behavior of halo CMEs to the diminished heliospheric total pressure in cycle 24 that made relatively slower CMEs and those originating at larger central meridian distances become halos. Solar wind parameters measured at Sun-Earth L1 confirm that most of the parameters have lower values in cycle 24. In particular, the decline in the heliospheric field strength resulted in the diminished total pressure and the Alfven speed (Gopalswamy et al. 2020a).

Interplanetary CMEs in solar cycle 24

The reduction in the number of FW CMEs in cycle 24 is expected to be reflected in the number of interplanetary CMEs (ICMEs) observed at 1 AU because the latter are known to be associated with energetic CMEs. The annual number of ICMEs in Fig. 7 shows clear solar-cycle variation, similar to other phenomena. The total number of ICMEs declined from 307 in cycle 23 to 208 in cycle 24, representing a reduction of 32%. The decline is smaller than that in SSN. One possible explanation is that ICMEs also originate from non-spot regions where quiescent filaments erupt and the associated CMEs become ICMEs. When normalized to the cycle-averaged SSN in each cycle (81 in cycle 23 dropping to 49 in cycle 24), we see a 12% increase in the number of ICMEs. If we separate the ICMEs into magnetic clouds (MCs) and non-cloud ejecta (EJ), we see a similar trend, but the decline in EJ (37%) is steeper than in MCs (25%). When normalized to SSN, we see an increase of 4% and 25% for EJs and MCs, respectively. This behavior was noted previously for MCs detected during the rise and maximum phases of cycles 23 and 24 (Gopalswamy et al. 2015a, b, c). The fraction of MCs is also slightly higher in cycle 24: 37% (114 out of 397 ICMEs) vs. 41% (86 out of 208 ICMEs) in cycle 23.

Fig. 7
figure7

a Solar cycle variation of the annual number of ICMEs (magnetic clouds—MCs and non-cloud ejecta—EJs) observed near Earth as compiled in http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm. The total number of ICMEs in cycles 23 (307) and 24 (208) are noted on the plot. b Annual number of EJs and MCs shown separately. The number of EJs and MCs is noted on the plot

Stream interaction regions

While CMEs cause most of the intense geomagnetic storms, stream interaction regions (SIRs) and especially co-rotating interaction regions (CIR) can cause relatively weaker but more frequent geomagnetic storms. The solar sources of SIRs and CIRs also have been shown to be different in cycles 23 and 24. Nakagawa et al. (2019) studied the temporal and spatial variations of the low-latitude coronal hole (CH) area related to high-speed solar (HSS) wind during solar cycles 23 (1996–2008) and 24 (2009–2016). They found that (i) the CHs in solar cycle 24 appeared over a wider latitude range than in solar cycle 23, and (ii) the maximum values of the CH area and the solar wind speed in solar cycle 24 were smaller than those in solar cycle 23. Jian et al. (2019) compared the annual occurrence rates of SIRs and CIRs using Wind/ACE and STEREO in situ observations from 1995 to 2016 as displayed in Fig. 8. They found a higher occurrence rate of SIRs in cycle 24, which they attribute to the presence of persistent equatorial coronal holes as well as weaker CMEs in that cycle. The fraction of CIRs is higher in the declining minimum phase of each cycle. Grandin et al. (2019) developed a catalog of 588 HSS and SIR events that occurred during the interval 1995 to 2017. Their list is largely in agreement with the list of SIRs identified manually by Jian et al. (2019).

Fig. 8
figure8

Monthly sunspot number (top), number of SIR/CIR (middle), and CIR rate (bottom) in solar cycles 23 and 24. Corresponding epochs in cycles 23 and 24 are indicated by the cyan bars at the top (adapted from Jian et al. 2019)

Geoeffectiveness

A severe reduction in the geoeffectiveness of CMEs in cycle 24 as measured by the number of intense (Dst ≤ − 100 nT) geomagnetic storms has been reported (Gopalswamy et al. 2014a, b; Gopalswamy et al. 2015a, b, c) in the rise to the maximum phases. In the updated version covering two full cycles shown in Fig. 4b, we see that there are 86 intense storms in cycle 23 compared to just 22 in cycle 24. These include 11 CIR storms in cycle 23 and 2 in cycle 24 (an 82% reduction). The first intense geomagnetic storm occurred during the maximum phase of cycle 24 on 2013 June 1 due to a low-latitude coronal hole that was at the central meridian on 2013 May 30 (Gopalswamy et al. 2015c). The second storm occurred on 2015 October 6 due to a coronal hole that was present at the central meridian on 2015 October 5 (Watari 2018). The number of intense storms due to CMEs declined by ~ 73% from 75 to 20. Both these reductions can be attributed to the dilution of the CME and CIR magnetic content.

Considering MCs that occurred during the first 6 years in each of cycles 23 and 24, it was found that the MC-associated storms were weaker in cycle 24: the average value of Dst increased from − 66 to − 55 nT. Scolini et al. (2018b) investigated the geoeffectiveness of halo CMEs in cycles 23 and 24. They found that during the first 85 months of Cycle 23 the geoeffectiveness rate of the disk-center full-halo CMEs was 58% compared to 35% in cycle 24. The average minimum value of the Dst index was − 146 nT in cycle 23 compared to − 97 nT in cycle 24. These results are consistent with the reduced geoeffectiveness of cycle-24 MCs (Gopalswamy et al. 2015a, b, c). Hess and Zhang (2017) studied 70 Earth-affecting ICMEs in Solar Cycle 24 and found the lack of events resulting in extreme geomagnetic storms.

Selvakumaran et al. (2016) considered the moderate and intense geomagnetic storms that occurred during the first 77 months of solar cycles 23 and 24. While they confirmed an 80% reduction in the occurrence of intense storms, they found that the number of moderate storms decreased by only ~ 40%. When moderate storms from CIRs are considered separately, these authors found that the reduction in the number of geomagnetic storms is more drastic (see also Grandin et al. 2019). In cycle 23, there were 43 CIR storms during the first 77 months of cycle 23 compared to 15 in cycle 24, amounting to a reduction of 63%. This is about the same when the CIR storms are separated into moderate and intense storms. Chi et al. (2018a) studied the geoeffectiveness of SIRs from 1995 to 2016 and found that about 52% of the SIRs caused geomagnetic storms with Dst ≤ − 30 nT, but only 3% of them caused intense geomagnetic storms (Dst ≤ − 100 nT). They also reported that the possibility of SIR-ICME interaction structures causing geomagnetic storms is significantly higher than that of isolated SIRs or isolated ICMEs.

Solar cycle variation of large SEP events

As of December 2019, there were 46 large SEP events (> 10 MeV proton intensity ≥ 10 pfu) in cycle 24 compared to 102 in cycle 23 (see Fig. 4c). This is a 55% reduction, more than the reduction in the SSN. Considering the period up to the middle of the maximum phase, the reduction reported previously was smaller (~ 26%, Gopalswamy et al. 2015c), most likely due to the lower Alfven speed in the rising phase of cycle 24. If we consider the highest energy particle events, viz., the ground level enhancement (GLE) events, the reduction is very drastic: there were 16 GLE events in cycle 23 compared to just 2 in cycle 24, amounting to a reduction of 88%. All large SEP events are associated with DH Type II bursts because the same CME-driven shock accelerates electrons (producing type II bursts) and ions (observed in space as SEP events). CMEs associated with SEP events and DH type II bursts are typically fast and wide (Gopalswamy et al. 2019). Not all DH type II bursts are associated with SEP events because of connectivity issues, high particle background, and < 10 pfu events. The number of DH type II bursts decreased from 339 in cycle 23 to 181 in cycle 24 (see Fig. 6d), indicating a decline by 47%, very similar to the reduction in FW CMEs (50%) because most of the type II bursts are due to FW CMEs.

Summary of solar cycle variation

Table 2 summarizes the Earth-affecting events in solar cycles 23 and 24 in comparison with the SSN. In addition to SSN, we have shown major soft X-ray flares, regular CMEs, fast and wide CMEs, halo CMEs, and ICMEs followed by the heliospheric consequences (DH type II bursts, large SEP events, and major geomagnetic storms). The decline in solar activity in cycle 24 is represented by the 39% drop in the cycle-averaged SSN. Most events declined more than the SSN did in cycle 24, except for ICMEs (declined by 32%), halo CMEs (declined by 21%), and the general population (W ≥ 30°) of CMEs (increased by 1%). When the numbers are normalized to SSN, these three types of events show a clear increase in cycle 24. Fast and wide CMEs declined in cycle 24 by ~ 47%, slightly more than the SSN did. When normalized to SSN, the number of FW CMEs per SSN declined only by 17% in cycle 24, somewhat similar to the decline in major soft X-ray flares and DH type II bursts. The general population of CMEs with width > 30° clearly showed no decrease in number; when normalized to SSN, the average number of CMEs per SSN increased by 66%. The two phenomena that showed the deepest decline are the major geomagnetic storms (74%) and GLE events (88%). Both these events are related to the heliospheric magnetic field strength, which significantly declined in cycle 24. The reduced heliospheric magnetic field results in the weaker heliospheric pressure leading to the anomalous expansion of CMEs and the attendant magnetic dilution in CMEs. In the case of SEP events, the particle acceleration efficiency depends on the strength of the heliospheric magnetic field, hence a reduction in the latter results in less efficient acceleration, and hence, particles do not attain high energies (Gopalswamy et al. 2014a, b). The reduction in the heliospheric magnetic field is also likely to be responsible for weaker CIR storms: the decreased MHD compression of the weaker field does not increase it to high levels.

Table 2 Earth-affecting events in solar cycles 23 and 24 in comparison with the SSN

Summary

To conclude this section, we provide a list of catalogs of Earth-affecting transient events that have been compiled and maintained online by many workers in the past (Table 3). The catalogs include lists of observed solar flares, CMEs, ICMEs in the inner heliosphere, ICMEs at in situ, interplanetary shocks, ICMEs with solar sources, SIRs, and SEPs. These event catalogs are useful resources for facilitating research for the wide community.

Table 3 Catalogs of Earth-affecting solar transients, including flares, CMEs, ICMEs-IH (inner heliosphere), ICMEs-IS (in situ), shocks, SIRs and SEPs

Progress in theories of CMEs and ICMEs

Introduction

It is generally accepted that CMEs are driven by the free magnetic energy stored in the non-potential magnetic fields. There is a general consensus that the erupted structure is twisted, where the most common magnetic structure employed in modeling is a flux rope, i.e., a cylindrical plasma structure with a magnetic field draped around the central axis (Lepping et al. 1990). The eruption of the twisted magnetic structure is interrelated with the magnetic reconnection of the surrounding coronal magnetic field, releasing both thermal and non-thermal energy and producing a number of effects (Priest and Forbes 2002). The magnetic dips of the flux rope can support cool plasma, in which case also an eruptive filament can be observed. The whole process is known as “the standard flare-CME model” and is sketched in the left panel of Fig. 9. In “the standard magnetic cloud model,” the erupting flux rope propagates away from the Sun, expanding at the same time, but stays attached to the Sun, i.e., remains a closed structure, as shown in the right panel of Fig. 9.

Fig. 9
figure9

Cartoon describing three different stages of CME evolution based on “the standard CME-flare model” and “the standard magnetic cloud model”: the onset (left), post-eruption phase (middle), and interplanetary propagation (right)

In order to understand the full picture of the CMEs, i.e., the magnetic structure of CMEs and processes involved in its initiation, evolution and propagation, we need theories to explain the observed properties of CMEs. Both numerical and analytical models need to be employed to reach deeper understanding of the origin and evolution of CMEs and provide a theoretical basis to the CME/ICME observations. The numerical modeling will be addressed in Section 4, while this section is devoted to analytical models and divided into subsections related to CME initiation, propagation, forward modeling, fitting to in situ measurements and finally interactions with other magnetic structures.

Mechanisms, processes, and forces governing the CME take-off

Comprehensive theoretical work on solar eruptive events started in the 1970s and early 1980s of the past century (Green et al. 2018). Many models were focused on the flux-rope configurations and their instabilities (see references in Chen 1989; Vršnak 1990), identifying Lorentz force as the main driving element of the eruption, and emphasizing the importance of the amount of the magnetic field twist. For example, using the analytical approach, Chen (1989) and Vršnak (1990), independently considered in their semi-toroidal flux-rope models a number of effects that were before taken only partially or were neglected. The flux-rope models progressively developed, becoming more sophisticated. A particular important step was the analytical model presented by Titov and Demoulin (1999), which took into account relevant effects and provides an idealized, but quite realistic configuration of a semi-toroidal flux rope embedded in a coronal arcade. This model was later on included in a number of analytical studies, or numerical simulations of the loss of equilibrium in general, and in particular, in studies of kink and torus instabilities (Török and Kliem 2003, 2005; Török et al. 2004; Török et al. 2010; Kliem and Török 2006; Kliem et al. 2014).

More recently in the past decade, which includes also the VarSITI/ISEST era, there was significant progress in physical understanding of solar eruptions. A number of papers were published considering the pre-eruptive storage of free energy and helicity, processes that cause the evolution of the system towards an unstable state, criteria defining stable/unstable configurations, initiation of the eruption, the dynamics of the eruption itself, as well as the analysis of the effects of the eruption in the ambient corona (see recent reviews by Aulanier 2013; Schmieder et al. 2015; Green et al. 2018; Patsourakos et al. 2020). Although it was clearly demonstrated that the active region magnetic complexity and its dynamics, free-energy, and helicity content are essential parameters, a number of open questions appeared. All of them can be summarized in the fact that we still do not understand why active regions that are quite similar according to the mentioned basic characteristics sometimes produce an eruption and sometimes not. Obviously, some key parameters are still missing, and consequently, this makes the eruption forecasting still highly unreliable.

The aforementioned standard CME-flare model was realized and investigated in detail in 3D using a zero-β MHD simulation of an initially potential bipolar field, which evolves by means of line-tied shearing motions in the photosphere (Aulanier et al. 2010; Aulanier et al. 2012). This 3D standard model has been exploited to investigate the properties of 3D slip-running reconnection in eruption regions (Janvier et al. 2013a, b), evolution of localized currents in flare ribbons (Janvier et al. 2014; Barczynski et al. 2020), vortex and sink flows related to coronal implosion (Zuccarello et al. 2017), and downward Lorentz force in the Sun’s photosphere during eruptions (Barczynski et al. 2019). (2018) made a review on the electric currents in the pre-eruption state and in the course of the eruption of solar magnetic structures.

Apart from general theoretical, numerical, or observational considerations regarding the mentioned pre-eruption configurations, a number of papers were published being focused more on specific processes that lead to the eruption than to general properties of active regions. For example, Török et al. (2013) analyzed in detail the consequences of rotational motions at the footpoints of a flux rope in one well-observed event. The analysis provided a very detailed physical interpretation of characteristics of the pre-eruptive evolution of the magnetic configuration, the initiation of the eruption, the dynamics of the eruption, as well as the evolution of an ambient magnetic system. On the other hand, Vršnak (2019) considered the rotating flux-rope leg process in more general terms and showed that except in quite extreme cases, such as considered by Török et al. (2013), the twisting motion does not allow for poloidal flux injection sufficient to explain the observed speeds of the slow rise of the flux rope in the gradual pre-eruptive stage. On the other hand, it was shown that the emerging flux process is viable to cause rising speed close to that observed in the pre-eruptive phase. Let us note that both processes eventually lead to a loss of equilibrium of the system if persistent long enough (Green et al. 2018).

In the last decade, special attention was paid to the role of the reconnection below the erupting flux rope in the dynamics of the eruption, primarily based on a number of observational results directly relating the eruption-related flare energy release and the eruption acceleration. This type of reconnection has three very important consequences. First, it reduces the tension of the overlying field, which tries to prevent the eruption and, in some cases, can cause a failed eruption. Second, it supplies the flux rope with a fresh poloidal flux that has a twofold effect. One is a direct enhancement of the upward-directed component of the hoop-force. The other is weakening of the self-inductive effect of the expanding structure that should lead to fast electric-current decrease, and thus a weakening of the Lorentz force. In this respect, it is worth mentioning the paper by Vršnak et al. (2016), where it was clearly demonstrated that the peak acceleration of the flux rope is dependent on the reconnection rate and the peak velocity is proportional to the total reconnected flux. Moreover, it was shown that the flux-rope acceleration time profile, as well as the velocity time profile, are closely synchronized with the time evolution of the reconnection rate. These theoretical results are able to fully explain the effects observed in the CME-flare relationship, as discussed in Section 2.4.

CME propagation from corona through interplanetary space

The kinematical evolution of CMEs can be divided into three phases: (1) slow rising phase during the CME initiation; (2) impulsive or main acceleration phase; (3) interplanetary propagation phase (Zhang and Dere 2006; Temmer 2016). There are three competing forces governing CME kinematical evolution, the gravitational force, Lorentz force and the MHD drag.

The Lorentz force mainly provided by the magnetic field in the corona is introduced in Section 3.2, while the MHD drag can be well represented by the aerodynamic drag equation and is believed to be dominant in the interplanetary propagation phase (Cargill 2004; Vršnak and Žic 2007). The latter is supported by observations showing deceleration of fast CMEs and acceleration of slow CMEs (Sheeley et al. 1999; Gopalswamy et al. 2020; Sachdeva et al. 2015). This concept was previously introduced into a simple Empirical Shock Arrival (ESA) model (Gopalswamy et al. 2001a, b), Expansion Speed Model (ESM) (Schwenn et al. 2005), and more recently in an Effective Acceleration Model (EAM) (Paouris and Mavromichalaki 2017), an analytical observation-driven model by (Liu et al. 2017a) and an empirically driven piston shock model by (Corona-Romero et al. 2017). Based on the concept of CME propagation being governed by MHD drag, an analytical drag-based model (DBM) was introduced by (Vršnak et al. 2013). DBM was found to very successfully describe heliospheric propagation of CMEs (Vršnak et al. 2014; Hess and Zhang 2014), therefore it was expanded to different geometries in recent years: most notably using a 2D-Cone geometry (Žic et al. 2015) and 2D ellipse front (Möstl et al. 2015). Note that the interplanetary acceleration obtained by Gopalswamy et al. (2001a, b) is proportional to CME speed and hence related to the Stokes drag, as opposed to the aerodynamic drag proportional to the square of the CME speed.

Observations by STEREO-HI instrument lent support to empirical models. The elongation conversion models were previously typically combined with fitting algorithms to determine CME arrival, assuming constant speed, as discussed in Section 2.2.4. However, the constant speed assumption was recently substituted with DBM and combined with a newly developed Ellipse Conversion method for the HI observations into the ElEvoHI model (Rollett et al. 2016).

CMEs typically propagate radially, although deviations were found, namely rotations (Lynch et al. 2009; Vourlidas et al. 2011) and deflections (Wang et al. 2004; Lugaz et al. 2010b; Isavnin et al. 2014). Deflections by coronal holes have been previously modeled empirically, where a deflection from the original direction by a certain angle was quantified by the so-called coronal hole influence parameter (CHIP), assuming that CME continues to propagate radially (Gopalswamy et al., 2009; Mohamed et al. 2012). Interplanetary deflections were regarded previously as well, in a kinematic model assuming interplanetary spiral magnetic field and the background solar wind. As a result, CMEs faster than background solar wind are deflected to the east, whereas CMEs slower than background solar wind are deflected to the west (Wang et al. 2004, 2006). Recently, both deflections and rotations were included in a 3D CME propagation model, where the CME flux rope is represented with a rigid, un-deformable torus and deflections and rotations are calculated using the magnetic tension and magnetic pressure gradients calculated from magnetometer input (Kay et al. 2013, 2020b; Kay and Opher 2015).

Analytical models are easy to run and are not time consuming and therefore ideal for ensemble modeling (for details on ensemble modeling see Section 4). Therefore, it is not surprising that several recently developed analytical models have their ensemble version (see Table 4). Finally, recently a novel approach was adapted in semi-empirical CME propagation modeling, machine learning (Sudar et al. 2016; Liu et al. 2018d), which in the future might prove to be a powerful predictive tool.

Table 4 List of recent analytical and semi-empirical models of CMEs/ICMEs

Forward modeling of CMEs

Recently, there has been quite a development in the forward modeling of the magnetic structures using physics-based empirical models. The forward models typically assume a specific morphology of a magnetic structure, i.e., flux rope, and evolve it, assuming specific propagation and expansion. For instance, Wood et al. (2017) use the croissant-like morphology described by Wood and Howard (2009), apply self-similar expansion and propagate it to Earth using either the Harmonic mean or Fixed Phi method as a kinematic model. With this method, it is possible to obtain a global shape of the structure, as well as its local size and orientation.

A step further is to include a specific flux rope magnetic field topology. Möstl et al. (2018) in their 3-Dimensional COronal Rope Ejection (3DCORE) model used a tapered torus geometry and a Gold-Hoyle magnetic field topology (Gold and Hoyle 1960) and evolve it using DBM and self-similar expansion. They constrain the magnetic field values using measurements at Mercury. In their Flux Rope from Eruption Data (FRED) method, Gopalswamy et al. (2018c) evolve self-similarly a croissant shaped flux rope obtained by the Graduated Cylindrical Shell (GCS) model and assume a Lundquist-type magnetic field topology (Lundquist 1951) constrained using reconnection flux computed from the area under post-eruption arcades (Gopalswamy et al. 2017b; Pal et al. 2018; Sarkar et al. 2020). It should be noted that a similar approach was studied previously by Savani et al. (2015) and Temmer et al. (2017), where several options were regarded to constrain the magnetic field (reconnection flux computed from H-alpha ribbons, dimming flux, and non-linear force-free modeling). Kay et al. (2017, 2020b) also use a Lundquist-type magnetic structure along with the shape and size represented with a rigid, un-deformable torus, which is the output of their ForeCAT model. Their ForeCAT In situ Data Observer (FIDO) model primarily assumes self-similar expansion and constant time-shift; however, with the addition of some free parameters, they are able to also simulate distortion, i.e., pancaking. They also extensively study the sensitivity of the model using ensembles (Kay and Gopalswamy 2018), although in its current form the magnetic structure is free-fitted to the in situ measurements. Recently, the FIDO model is improved by incorporating the forward model of the CME-driven shock and sheath, as FIDO-SIT (Sheath Induced by Transient) (Kay et al. 2020a, b). Flux rope in the 3D (FRi3D) model by Isavnin (2016) uses a croissant-like shape, but allows it to deform while expanding due to front flattening, pancaking, and skewing. The assumed magnetic structure is of Gold-Hoyle type and the whole FR is free-fitted to the in situ measurements. Finally, probably the most extensive forward modeling study was performed by Patsourakos et al. (2016), who used GCS croissant for the CME shape, propagated it using DBM, and then applied several different combinations for estimating the magnetic structure topology (including non-force free magnetic structures by Hidalgo et al. 2000 and Cid et al. 2002), as well as the initial helicity and expansion.

Although most of the forward modeling procedures are focused on reproducing the magnetic structure at a certain heliospheric distance, other applications might be noteworthy as well. A similar procedure was recently adopted in the Forbush decrease model (ForbMod) by (Dumbović et al. 2018a, b), who expanded the GCS croissant using empirical power-law relations for size and magnetic field, assuming constant-speed propagation and homogeneous magnetic field in order to derive galactic cosmic ray counts. The evolution of the internal properties (e.g., the plasma temperature, density, velocity, and heating) of CMEs is also one of the important research aspects, but it is limited to a certain position or a certain time by using remote sensing and in situ observations (e.g., Wang et al. 2005; Liu et al. 2006; Bemporad and Mancuso 2010; Susino et al. 2013; Susino and Bemporad 2016). In a novel approach, GCS is used to calculate the CME volume and density to derive the evolution of the magnetic ejecta and sheath density from Sun to Earth (M. Temmer et al. 2021). To continuously figure out the internal state of an individual CME during its heliospheric propagation, a self-similar flux rope internal state (FRIS) model was proposed by Wang, et al. (2009), providing the variations of the polytropic index of the CME plasma, the average Lorentz force and the thermal pressure force inside a CME with heliocentric distance. Recently, Mishra and Wang (2018) improved the FRIS model, by constraining it with the observed propagation and expansion behavior of a CME and deriving a few additional parameters (absorbed heat, entropy, heating rate, and entropy changing rate). This model was then implemented to a slow (Mishra and Wang 2018) and fast (Mishra et al. 2020) CME respectively, which showed that during the propagation (1) the expansion was driven by the thermal force inside the CME but prevented by the Lorentz force, (2) the slow CME released heat before it reached an adiabatic state and then absorbed heat, and (3) the fast CME was in the heat-releasing state throughout its journey.

In situ fitting of ICMEs

ICMEs can be identified by a number of typical properties that differ from those of the ambient solar wind (Gosling 1990; Wimmer-Schweingruber et al. 2006; Zurbuchen and Richardson 2006; Rouillard 2011; Kilpua et al. 2017). Among ICMEs there is a subset, called magnetic clouds (MCs), which were first identified by Burlaga et al. (1981), and then studied widely in the past decades. MCs exhibit a smooth rotation of the magnetic field direction through a large angle, an enhanced magnetic field strength, and a low proton temperature (Burlaga et al. 1981). MCs play an important role in understanding the evolution of CMEs in the heliosphere and are one of the main drives of space weather events (Wilson 1987; Gopalswamy et al. 2008; Gopalswamy et al. 2015a, b, c; Tsurutani et al. 1988; Huttunen et al. 2002; Wu and Lepping 2002; Cane and Richardson 2003; Zhang et al. 2007; Hidalgo 2011; Li et al. 2018).

MCs are believed to have a magnetic flux rope structure with two ends rooting on the Sun (Burlaga et al. 1981; Larson et al. 1997; Janvier et al. 2013a, b). So far, the observations about MCs could only rely on the in situ data along the MC pass path. To reconstruct the global configuration of MCs in 2D or 3D space, a variety of techniques has been developed. Based on the idea of force-free ( × B = αB) magnetic configuration of MCs (Goldstein 1983), the symmetric-cylindrical models, with linear (Burlaga 1988; Lepping et al. 1990; Lepping 2003) and non-linear (Farrugia et al. 1999) force-free fields, were proposed. Other models were also developed by adopting different assumptions, e.g., (1) the expanding model (Farrugia et al. 1993; Vandas et al. 2006), (2) the models with distorted cross section (Romashets and Vandas 2003; Vandas et al. 2006; Démoulin and Dasso 2009), and (3) the torus model (Romashets and Vandas 2003; Marubashi and Lepping 2007). Based on the observations of pressure gradients inside MCs, some non-force-free models were proposed and then improved (Hidalgo 2002; Mulligan and Russell 2001; Hidalgo et al. 2002; Cid et al. 2002; Hidalgo 2003).

Nowadays, with our deeper understanding about MCs, several new models have emerged, which are still based on the well-developed description of (non-)force-free magnetic configuration, but can provide extra information about MCs.

Force-free magnetic field

The assumptions of the cross section and the symmetry along the MC axis are two keys in the models. Keeping the cylindrical symmetry and the circular cross section, Wang et al., (Wang et al. 2015; Wang et al. 2016a, b, c, d) developed the velocity-modified force-free flux rope models, which can provide the MC kinetic information by incorporating the linear propagating motion away from the Sun, the expanding, and the poloidal motion of the plasma inside MCs with respect to the MC axis. Recently, Lepping et al. (2018) improved their previous model (Lepping et al. 1990) by modifying the magnetic field magnitude based on a B-modification scheme presented by Lepping et al. (2017). This model improves the fitted B-profile, but is applicable for use with data originating only at/near 1 AU. The models of linear force-free field with different boundary pitch-angle treatments and of non-linear force-free field with varying prescribed twist were derived by Nishimura et al. and Vandas and Romashets, respectively. Discarding the assumption of locally straight MC axis, the non-cylindrical models were developed. For example, Owens et al. (2012) developed a curved flux rope (CFR) model, assuming a circular cross section but bending the axial field in a similar manner to a Parker spiral magnetic field. This allows the radius of curvature of the axis and the cross-sectional extent of the MC to vary along the length of the axis. To model irregularities in MCs, Romashets and Vandas (2013) added a local irregularity in the form of a compact toroid into a cylindrical linear force-free magnetic structure. Furthermore, MCs in toroidal geometry can also be constructed by the constant-alpha force-free magnetic field with elliptical cross sections (Vandas and Romashets 2017a) or uniform-twist force-free field with circular cross sections (Vandas and Romashets 2017b).

Non-force-free magnetic field

Inherited from Hidalgo (2003), a much more complicated model was improved in series (Hidalgo and Nieves-Chinchilla 2012; Hidalgo 2013). Hidalgo and Nieves-Chinchilla described MC topology with torus geometry and a non-uniform cross section. They established an intrinsic coordinate system for that topology, and then analytically solved the Maxwell equations in terms of it. The model was tested by applying it to the observations of multiple spacecraft by Hidalgo (2013). The model was further improved with inclusion of the plasma pressure (Hidalgo) and the proton current density (Hidalgo). Extending the concept of Hidalgo et al. (2002), Nieves-Chinchilla et al. (2016) presented a circular-cylindrical flux-rope model by introducing a general form for the radial dependence of the current density, which can give the information on the force distribution inside MCs. The circular cross section was later improved to an ellipse (new elliptic-cylindrical flux rope model, Nieves-Chinchilla et al. 2018b), which, for the first time, allows us to completely describe MCs by nonorthogonal geometry.

Different from the above introduced techniques, the Grad-Shafranov (GS) reconstruction technique (Hu and Sonnerup 2001, 2002) doesn’t presume a specific magnetic structure or cross section of MCs. It assumes that an asymmetric-cylindrical MC is in an approximately magnetostatic equilibrium with an invariant direction, and uses the GS equation to recover the magnetic field as well as the plasma pressure. With this technique, the boundaries of the MC need not first be identified in the data. Recently, trying to approach a more real flux rope topology, the GS reconstruction of MCs in toroidal geometry with rotational symmetry was developed (Hu 2017; Hu et al. 2017).

The development of all the introduced techniques provides invaluable tools for extracting information about the properties of MCs and leads to our understanding of the underlying physics of MCs. However, it was shown that assessing their accuracy based on in situ data is challenging. Different comparisons of the MC properties have been performed between: (1) MHD simulations and fitting techniques (Riley et al. 2004; Vandas et al. 2010; Al-Haddad et al. 2011, 2019) and (2) different fitting models (Al-Haddad et al. 2013; Démoulin et al. 2013; Hu et al. 2013; Vandas et al. 2015; Vandas and Romashets 2015; Lepping et al.; Nishimura et al. 2019). While these studies largely support the applicability of examined techniques and methods to gain insight into the MC structure, they also reveal their limitations as well as reliability issues, which should be tackled in the future.

CME-CME interactions

Erupting from the Sun, coronal mass ejections (CMEs) will interact with different structures. The interaction between a CME and the magnetic fields in the corona and interplanetary space, and the solar wind govern the propagation and evolution of the CME itself (see Section 3.3 and 3.4). Magnetic reconnection between CMEs and ambient solar wind can lead to the peeling-off of the magnetic field lines and the erosion of the axial magnetic flux from the CMEs (Dasso et al. 2006; Gosling 2012; Ruffenach et al. 2012, 2015; Manchester et al. 2014; Lavraud et al. 2014; Wang et al. 2018). Furthermore, CMEs were found to be interacting with other CMEs by many observations (e.g., Gopalswamy et al. 2001a; Lugaz et al. 2012; Shen et al. 2012; Harrison et al. 2012; Liu et al. 2012; Liu et al. 2014; Oliveros et al. 2012; Möstl et al. 2012; Temmer et al. 2012, 2014; Webb et al. 2013; Shanmugaraju et al. 2014; Colaninno and Vourlidas 2015; Mishra et al. 2014, 2015, 2017), involving complicated physical processes, resulting in the changes of CME properties, forming complex structures, and playing an important role in leading to large solar energetic particle events (see Section 6) and intense geomagnetic storms. CME-CME interaction can result in the changes in CME speed, propagation direction (Xiong et al. 2009; Lugaz et al. 2012; Shen et al. 2012; Mishra et al.), radial extent as well as internal magnetic strength (Schmidt and Cargill 2004; Xiong et al. 2006; Lugaz et al. 2005, 2012, 2013). The speed change, or more physical, the natures of the collision of one CME by another, were widely studied, namely, inelastic (Lugaz et al. 2012; Maričić et al. 2004; Mishra et al. 2015) vs. elastic (Mishra et al. 2014, 2015) vs. super-elastic collision (Shen et al. 2012; Shen et al. 2013a, b, c; Colaninno and Vourlidas 2015). Note that the term of collision used here refers to that the main bodies of two CMEs are touching.

In determining the nature of collisions, most of the earlier studies have used a simplistic approach that CMEs are propagating exactly in the same direction, i.e., 1D head-on collision (with momentum conservation constraint, Mishra and Srivastava 2014). However, a relatively more precise analysis should be performed in 3D space. For the first time, Shen et al. (2012) studied an oblique collision of CMEs in 3D using imaging observations (Fig. 10a) and took several uncertainties into consideration, but did not constrain the conservation of momentum instead of indirectly evaluating it by analyzing the effect of the solar wind on the acceleration of the first CME. Recently, Mishra et al. addressed previous limitation and proposed a method for the 3D oblique collision (Fig. 10b), in which the post-collision directions and speeds are theoretically measured with different pre-set restitution coefficients, together satisfying the momentum conservation law, and the best-matched parameters with the observations are extracted. Based on this, Mishra et al. (2017) calculated the uncertainties in determining the nature of collisions quantitively, with different CME observed parameters considered, which then emphasized the possibility of a large uncertainty (see one example in Fig. 10c). Furthermore, Shen et al. (2017) presented four definitions of different types of collisions, i.e., a classical Newtonian definition, an energy definition, Poissons definition, and Stronges definition, helping with a deeper understanding of the determination of collisions in theory. They focused on the first two used in observational and numerical studies, and found out that these two definitions are not equivalent to each other when the colliding objects are expanding or contracting with a changing rate.

Fig. 10
figure10

a The super-elastic collision of two interacting CMEs observed in STEREO/HI (Shen et al. 2012). b Oblique collision of two CMEs assumed as spherical bubbles (Mishra et al.,). c The variation of the restitution coefficient with the uncertainties of pre-collision longitudes of CMEs considered (Mishra et al.,)

Including collision, CME-CME interaction could be involved in four forms: (1) the two-CME driven shock waves interact without the ejecta interacting, (2) one shock wave interacts with preceding magnetic ejecta, (3) the direct interaction between two ejecta, and (4) the reconnection between successive magnetic ejecta. The last three may result in a variety of complex structures at 1 AU: from 1) partial ongoing interaction of the preceding ejecta with a shock wave inside (Lugaz et al. 2015a, b; Wang 2003; Liu et al. 2018c; Wang et al. 2018; Xu et al. 2019), to full interaction of 2) the multiple magnetic cloud (MC) events (Wang et al. 2002; Wang 2003; Shen et al. 2011c; Lugaz et al. 2013), 3) a complex ejecta or compound stream (Burlaga et al. 2003), and 4) long-duration events (Dasso et al. 2009; Lugaz et al. 2013), leading to a hard understanding of the undisturbed conditions by in situ observations. Wang et al. (2018) proposed a recovery model based on Rankine-Hugoniot jump conditions to recover the shocked structure back to the uncompressed state in the first type of the interacted structure, which was later used to estimate the related interacting effects in causing geoeffectiveness (Shen et al. 2018a; Xu et al. 2019). The resulting structure from CME-CME interaction was discussed in detail in the review of Lugaz et al. (2017).

Summary of recent analytical and semi-empirical models

Table 4 shows the analytical and semi-empirical models of CMEs/ICMEs introduced above, which were proposed roughly during the VarSITI period (ca. 2014-2018). Models are listed according to their type: P = propagation, EC = elongation conversion, FM = forward modeling, FIT = in situ fitting, GS = Grad-Shafranov reconstruction.

Progress in numerical modeling of CMEs/ICMEs

Magnetohydrodynamic (MHD) simulations have proved to be one of the most important tools to study the evolution of a coronal mass ejection (CME) in both corona and interplanetary space, and the modeled results can be used to analyze the initiation and propagation characteristics observed by ground-based and space-based instruments. Lugaz and Roussev (2011) gave a detailed review and discussion on the efforts to use numerical simulations of ICMEs to investigate the magnetic topology, density structure, energetics, and kinematics of ICMEs in the interplanetary space. In the book of Feng (2020), the author has provided a recent in-depth review of the field focusing primarily on the current status of MHD modeling for space weather with a thorough collection at the time of writing the book. Here, the review is devoted to recent progress of time-dependent MHD space weather modeling with the focus on such topics: the ambient solar wind, CME initiation and CME propagation, CME-solar-wind interaction, and CME-CME interaction, especially on the work performed in the second half of the 2010s.

Modeling the background solar wind

Numerical simulations have shown the importance of an accurate modeling of the background medium in which the disturbances propagate (Odstrčil and Pizzo 1999a, 1999b; Chané et al. 2005; Shen et al. 2007). In the past decade, due to the vast improvement in computational resources, the usage of 3D MHD models for reconstructing the solar corona and interplanetary solar wind has become almost routine. Moreover, based on much improved observations, it is possible to produce more realistic simulations, e.g., by the inclusion of the observational data through the boundary conditions or through data assimilation. Hayashi (2012) presented a treatment of observation-based time-dependent boundary conditions for the inner boundary sphere in the 3D MHD simulations of the global co-rotating solar wind structures. In order to adjust the model to the time-varying magnetic field on the bottom boundary, developed the model of the confined differential potential field (CDPF) to prescribe the bottom boundary condition, In addition, a modified version of this model was adopted as the module of the time-dependent 3D MHD simulation at the Joint Science Operation Center (JSOC) of SDO (Hayashi et al. 2015). The module could routinely generate 3D data of the time-relaxed minimum-energy state of the solar corona using the full-disk magnetogram data from HMI/SDO.

In parallel, data assimilation has been included in the WSA model through ADAPT (Hickmann et al. 2015), which allows photospheric simulations to agree better with available observations from magnetograms. This model has been coupled to the 3D MHD LFM-Helio (Merkin et al. 2016a) to perform time-dependent simulations of the background solar wind. These simulations are able to reproduce more accurate details of small-scale of the heliospheric current sheet and corotating interaction regions.

Recently, by using magnetogram synoptic map images from GONG and theoretical/empirical models such as the PFSS model and WSA model, Shen et al. (2018a, b) applied a new boundary treatment to the 3D MHD simulation of solar wind and established the 3D IN (INterplanetary)-TVD-MHD model. The boundary conditions depend on five tunable parameters when simulating the solar wind for different phases of the solar cycle, and the simulated solar wind parameters are in good agreement with the observations most of the time. However, we know that models tend to fail when solar activity increases. The comparison of their modeled results with the in situ data throughout 2007 is shown in Fig. 11, which demonstrates that the simulation retrieves most of the high-speed streams (HSSs), and the duration time and the magnitude of the HSSs are largely consistent with those of the observations. Later, Yang and Shen (2019) presented a new method to construct the global distribution of solar wind parameters at the source surface using multiple observations and the ANN (Artificial Neural Network) technique, which could be used to provide a more realistic boundary condition for 3D MHD solar wind modeling.

Fig. 11
figure11

Modeled (red lines) and observed (blue lines) time profiles of solar wind parameters at 1.0 au through all of 2007. From the top to the bottom, the panels show the speed Vr, number density N, temperature T, and total magnetic field strength B (From Shen et al. 2018b). Besides the improvement in the treatment of the inner boundary condition, there have been significant improvements in other aspects of background solar wind simulations in recent years. Some of these are detailed below

By using CORHEL (CORona-HELiosphere), Linker et al. (2016) further developed a time-dependent study of the solar wind empirically driven by magnetic maps at a daily cadence using ADAPT. Their simulation showed both classic features of stream structure in the interplanetary medium often seen in steady-state models and evolutionary features unable to be captured in a steady-state approach. Their model results also compared reasonably well with 1 AU OMNI observations. As a rather mature space weather model, CORHEL is a coupled suite of models for simulating the solar corona and solar wind in 3D space, which provides three solar coronal models at present, including the Magnetohydrodynamic Algorithm outside a Sphere (MAS) polytropic model, MAS thermodynamic model, and the potential field source surface and Wang-Sheeley-Arge (PFSS-WSA) model. The heliospheric models involved in CORHEL are ENLIL (Odstrcil et al. 2004), the MAS-Heliosphere (MAS-H) models (Lionello et al. 2013), and the LFM-Helio (Merkin et al. 2016b).

Based on the SWMF (Space Weather Modeling Framework), van der Holst et al. (2014) developed the Alfvén wave solar model named AWSoM, which is a 3D MHD model that considers the anisotropy of ion temperature in the solar corona and the inner heliosphere. In Meng et al. (2015), the AWSoM model has been applied to simulate the steady solar wind from the solar corona to 1 AU of CRs 2107 and 2123. Figure 12 a shows the simulated proton pressure anisotropy ratio and the simulated solar wind speed in the Y = 0 and Z = 0 planes for CR2107. The simulation results also show a reasonable agreement with in situ observations at 1 AU, as shown in Fig. 12b. Together with a coronal charge state evolution model, the Michigan Ionization Code (MIC, see Landi et al. 2012), Oran et al. (2015) employed the AWSoM model to calculate the elemental charge state evolution along the modeled open magnetic field lines. The charge state evolution model was initiated with the electron density, temperature, and speed simulated by the AWSoM wind model, and provided the first charge state calculation covering all latitudes in a realistic magnetic field. Evans et al. (2012) self-consistently coupled the Alfvén wave energy transport with the MHD equations. In this solar wind model, they introduced an additional dissipation mechanism: surface Alfvén wave (SAW) damping, which was weak in the polar regions, and strong in subpolar latitudes and the boundaries of open and closed magnetic fields. Their simulated results showed that SAW damping could reproduce regions of enhanced temperature at the boundaries of open and closed magnetic fields seen in both tomographic reconstructions in the low corona and Ulysses data in the heliosphere. Sokolov et al. (2013) presented a combined global model of the solar corona, the low corona, the transition region, and the top of the chromosphere. Their model used MHD Alfvén wave turbulence as the only momentum and energy source to heat the coronal plasma and drive the solar wind with different turbulence dissipation efficiencies in coronal holes and closed field regions. Recent developments include further validations of the AWSoM model (Gombosi et al. 2018; Sachdeva et al. 2019). It is known that the SWMF couples the models of Lower Corona (LC), Solar Corona (SC), Inner Heliosphere (IH), and other integrated components (Tóth et al. 2012). The models of SC, IH, and several other components are modeled by the BATS-R-US code. In the SC model, van der Holst et al. (2010) solved the two-temperature MHD equations with Alfvén wave heating and heat conduction on either Cartesian or spherical grid in a frame corotating with the Sun.

Fig. 12
figure12

a The simulated proton pressure anisotropy ratio p/p_ and the simulated solar wind speed in the Y = 0 and Z = 0 planes for CR2107 by the AWSoM model, and the plot on the right bottom panel also shows the trajectories of the Earth, STEREO-A and B satellites projected to the Z = 0 plane; b The simulated solar wind properties along the WIND orbit and the WIND data during CR2107 (From Meng et al. 2015)

Feng et al. (2010) employed the SIP-CESE MHD model within a six-component overset grid for solar wind simulation. They numerically investigated the large-scale structures of interplanetary solar wind and the evolution of the heliospheric magnetic field. Feng et al. (2012) carried out the numerical studies for the solar wind background of different solar-activity phases by using the SIP-AMR-CESE MHD model, and their modeled results could reproduce many features near the Sun and in interplanetary space, e.g., the changing trends of the solar-wind parameters for the selected CRs, and the IMF polarities and their changes. Furthermore, Feng et al. (2015) investigated the solar wind evolution between the solar surface to the Earth’s orbit from 1 July to 11 August 2008 with the SIP-AMR-CESE MHD model driven by the consecutive synoptic maps from GONG. Similarly, Li and Feng (2018) simulated the evolution of solar wind from the solar surface to the Earth’s orbit during the year 2008, and evaluated simulated results quantitatively by comparison with in situ measurements.

Merkin et al. (2011) adapted the Lyon-Fedder-Mobarry (LFM) model for the inner heliosphere, which was referred to as the LFM-helio model. They simulated the solar wind and heliospheric magnetic field between 0.1 and 2 AU to study the disruption of a heliospheric current sheet fold during CR 1892 in the decline phase of solar cycle 22. (Merkin et al. 2016a) also presented a simulation study exploring heliospheric consequences of time-dependent changes at the Sun during a 2-month period in the beginning of the year 2008, in which they used the Air Force Data Assimilate Photospheric Flux Transport (ADAPT) model to obtain daily updated photospheric magnetograms and drive the WSA model of the corona. The results of the WSA model were used as a time-dependent boundary condition for the LFM-helio model. They compared the simulation results with ACE, STEREO-A and B near 1 AU, and MESSENGER spacecraft orbiting between 0.35 and 0.6 AU and their simulations showed that time-dependent simulations could reproduce the gross-scale structure of the heliosphere.

The CRONOS model was employed to solve the equations of ideal MHD in a one-fluid model and to obtain realistic modeling solar wind conditions from 0.1 AU to 2 AU (Wiengarten et al. 2013, 2014). Additionally, Wiengarten et al. (2015) incorporated turbulence transport into the Reynolds-averaged MHD equations in the framework of the CRONOS, which was used to investigate the effects on the turbulence evolution for transient events from 0.1 AU to 1 AU by injecting a CME from the inner boundary.

Shiota et al. (2014) developed the SUSANOO model (also see Shiota and Kataoka 2016), and they used it to simulate the ambient solar wind structure from 25 to 425 Rs covering 3 years (2007–2009). Their numerical results were in reasonable agreement with in situ measurements at Venus and Mars by Venus Express and Mars Express, respectively (Shiota et al. 2014).

The “European heliospheric forecasting information asset” (EUHFORIA) is another space weather forecasting model focus on the inner heliosphere, which is capable to provide MHD modeling of the ambient solar wind and the CME eruptions from 0.1 AU to 2 AU (Moschou et al. 2017; Pomoell and Poedts 2018). EUHFORIA consists of an empirical coronal model and an MHD heliosphere model. The coronal model provides plasma and magnetic field parameters at Rb = 0.1AU, which was then used as a boundary condition to drive the heliospheric model. The performance of the solar wind model was recently performed in the study of Hinterreiter et al. (2019).

Usmanov et al. (2018) presented a fully 3D MHD model of the solar corona and solar wind by coupling Reynolds-averaged solar wind equations with transport equations for turbulence energy, cross helicity, and correlation scale, from the coronal base to 5 AU. Their simulation results showed that the model could reproduce most of the solar wind parameters compared with Ulysses data during its first and third fast latitude transits.

Piantschitsch et al. (2017) developed a 2.5D MHD code to simulate the corona wave propagation and its interaction with a low-density region, such as the coronal hole (CH). By using this new code, they also made a comprehensive analysis on the dependence on different Alfvén speeds inside the CH and initial amplitude of the incoming wave (Piantschitsch et al. 2018a, b). Their results depicted that the density value inside the CH influenced the phase speed and the amplitude values of density and magnetic field for all different secondary waves and there existed a correlation between the initial amplitude of the incoming wave and the amplitudes of the secondary waves as well as the peak values of the stationary features.

Modeling CME initiation and propagation

Jacobs and Poedts (2011) gave a detailed review about the state-of-the-art models for CME simulation before 2011. Here, we focus on the progress on the CME initiation, propagation, CME-CME interaction, and CME-solar wind interaction, mainly after 2011, especially from years 2014 to 2019. The review by Manchester et al. (2017) includes a section about simulations and additional information about the main physical processes occurring during CME evolution in the inner heliosphere.

Modeling CME initialization

Most of the existing CME models are candidates for mimicking the morphology near the Sun, with the purpose of reproducing the plasma parameters comparable with 1 AU observations, with the stated goal for many of them to move towards real-time space weather forecasting simulations. Presently, significant progress has been made towards improving the performance of the existing CME initialization models.

Cone model

The cone model ((Fisher and Munro 1984; Zhao et al. 2002; Zhao et al. 2016a; Xie et al. 2004) is one of the popular CME initiation models because of its simplicity and relatively good match with CME arrival time observations. In most implementations of the model, the CME does not possess an internal magnetic field, but the input size, speed, and location are determined from coronal observations, typically from coronagraphs. In addition, due to its geometry and lack of internal magnetic field, the initiation does not include parameters related to CME orientation. By using cone model as CME initialization, Odstrcil et al. (2005) applied the 3D MHD simulation to the 12 May 1997 interplanetary event to analyze possible interactions of the ICME propagating in various steady-state and evolving configurations of the background solar wind.

Taktakishvili et al. (2011) reported the simulated results of selected well-observed halo CME events using a combined model of the WSA/ENLIL and the cone models. Their simulation results demonstrated that the combination of numerical models with the observations from coronagraph as input could give reasonably good results for the CMEs’ arrival times for the selected set of “geoeffective” CME events. Bain et al. (2016) also combined the WSA-ENLIL and cone models to discuss shock connectivity in the August 2010 and July 2012 events. Dewey et al. (2015) integrated the cone model into the WSA-ENLIL model to study the CME-related solar wind perturbations on the Mercury system. Their simulation results demonstrated that the modeled results could be compared with the observations by the spacecraft of MErcury Surface, Space ENvironment, GEochemistry and Ranging (MESSENGER) during the period from March 2011 to December 2012.

Pomoell and Poedts (2018) integrated the cone model into the EUHRORIA model to simulate the CME events in the inner heliosphere during 17–29 July 2015. Also by combining the cone model and the EUHRORIA model, Scolini et al. (2018a, b) tested the effect of different CME shapes on the simulation results, and their simulation results showed that all the parameters specifying the CME shape in the model significantly affect simulation results at 1 AU as well as the predicted CME geoeffectiveness.

Flux rope models

Flux rope models have been shown to self-consistently reproduce many observed properties of CMEs, including the three-part density structure (Manchester et al. 2017). Contrary to the cone models, they include an internal magnetic field and may therefore reproduce not only the arrival time but also the magnetic field components when a CME impacts Earth. Due to their more complex nature, additional parameters are required to initialize such models, including the internal magnetic field strength or flux and the orientation of the flux rope. These models were first implemented in 3D MHD simulations by Roussev et al. (2003).

Lionello et al. (2013) improved the MAS-ENLIL model by inserting an out-of-equilibrium flux rope in the coronal model within 7 Rs as CME initiation model, and they simulated the propagation of an interplanetary CME (ICME) from 18 Rs to 1.1 AU. Their simulation results showed that the improved model could follow the propagation of the CME accurately. By using the MAS/MAS-H model combined the modified Titov-Démoulin (TDm) model (Titov et al. 2014), Török et al. (2018) inserted a magnetically stable flux rope to generate a CME close to the observed properties of the 2000 July 14 “Bastille Day” eruption. The properties of the CME as it propagates were studied based on MHD simulations of solar eruptions from near the Sun to the Earth. Figure 13 a shows the initial flux-rope field lines, (b) depicts the field lines of the flux-rope core at t = 164.10, shortly after eruption onset, and (c) and (d) demonstrates the interplanetary magnetic field and ICME flux rope at t = 256, shortly before it reached 1 AU.

Fig. 13
figure13

a Initial flux-rope field lines with zero-β relaxation; b field lines of the flux-rope core at t = 164.10; c Interplanetary magnetic field and ICME flux rope at t = 256; d close-up view on (c), showing two flux bundles at the core of the flux rope (From Török et al. 2018)

Using the Titov-Démoulin (TD) flux-rope model to initiate the CME, Jin et al. (2013) simulated a fast CME erupted from active region NOAA AR 11164 during CR2107. Simulations of this CME event were conducted with 1T (one-temperature) and 2T (two-temperature: coupled electron and proton) MHD models. The authors compared the propagation of this fast CME and the thermodynamics of CME-driven shocks in both the 1T and 2T CME simulations, and their results demonstrated the importance of the electron heat conduction in conjunction with proton shock heating in order to produce the physically correct CME structures and CME-driven shocks.

Based on the solar wind background constructed by the AWSoM SC model (van der Holst et al. 2014), Jin et al. (2016) presented a numerical simulation on the CME which occurred at 00:04 UT on 15 February 2011, which was initiated by using the analytical Gibson-Low (GL) flux rope model (Gibson and Low 1998) with different parameters. Their simulation results showed that a CME’s impact on the surrounding solar wind structures would be influenced by the magnetic strength of these structures, their distance to the source region, and the interaction between the CME with the large-scale magnetic field. Jin et al. (2017a) developed a new data-driven tool called Eruptive Event Generator Gibson-Low (EEGGL) to automatically determine the GL flux rope parameters using synoptic magnetogram data from GONG and CME speed derived from the observations of SOHO/LASCO. By combining the EEGGL model and the AWSoM solar wind model, Jin et al. (2017a) conducted a comprehensive study of CME propagation on 7 March 2011 by performing a simulation from the chromosphere to 1 AU. Their simulated results could reproduce many of the observed features both near the Sun and in the heliosphere. Figure 14 a depicts the initial GL flux rope configuration for 7 March 2011 CME event with the central plane showing the radial velocity, and Fig. 14 b compares EUV waves in the simulation and in the SDO/AIA observation.

Fig. 14
figure14

a Initial GL flux rope configuration for 7 March 2011 CME; b EUV waves in the simulation (left) and in the SDO/AIA observation (right) (From Jin et al. 2017a)

The Versatile Advection Code (VAC) is a general tool for solving MHD and hydrodynamical problems with astrophysical applications. A variety of numerical schemes are available for users to solve hyperbolic differential equations, including, e.g., TVD-Roe, TVDLF, and flux correction of transport (FCT) method. By using the VAC model, Jacobs and Poedts (2012) solved the MHD equations with the inner boundary of the domain locating at the low solar corona. They investigated the effect of new flux emergence on a magnetic system that possessed a 3D topology favorable for the breakout scenario, which was suitable for the ‘breakout’ CME scenario to work. Keppens et al. (2012) implemented a block-based AMR on the parallel VAC model using the Message Passing Interface library (MPI-AMRVAC), which has been used to provide interplanetary space weather forecasting models with relative accurate time-dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Pagano et al. (2015) performed a 3D MHD simulation of a flux rope ejection where a CME was produced by using the MPI-AMRVAC. Their results showed that the polarization ratio technique could reproduce the position of the center of mass along the line of sight with a relative high accuracy and studied the propagation of the CME in the real 3D direction.

Singh et al. (2019, 2020) modified the Gibson-Low flux rope by constraining the poloidal and toroidal fluxes of the initial flux rope using eruption data such as total reconnected flux (Gopalswamy et al. 2018c) and flux in the core dimming regions (Webb et al. 2000; Dissauer et al. 2018; Kay and Gopalswamy 2018). The modified spheromak has the option to control the helicity sign of flux ropes, which can be derived from line-of-sight magnetograms. Singh et al. (2020) simulated the 2012 July 12 CME and showed that they can reproduce the properties of the CME in the coronagraph FOV. They created a solar wind background from 1.03 Rs to 30 Rs using solar synoptic magnetograms. Then the flux rope model is inserted into the domain, allowing it to erupt as a CME due to pressure imbalance. They used the Multi-Scale Fluid Kinetic Simulation Suite (MS-FLUKSS, Yalim et al. 2017), which is a highly parallelized code suitable for MHD treatment of plasma and fluid.

Wu et al. (2016c) presented a 3D MHD simulation based on an observed eruptive twisted flux rope deduced from solar vector magnetograms. They combined a data-driven flux rope model for the CME initiation and a global coronal-heliosphere evolution model to track the propagation of the CME. They selected the CME event on 6 September 2011 to test this model, and their simulation results suggested that the flux rope evolution model produced the physical properties of a CME, and the morphology resembled the observations made by STEREO/COR1.

By using the 3D IN-TVD-MHD model (Shen et al. 2018b), Liu et al. (2019a) established a CME flux rope model based on the graduated cylindrical shell (GCS) model and applied it into the numerical simulation on the propagation and deflection of the fast CMEs in the interplanetary space from 0.1 AU to 1 AU.

Spherical plasmoid/magnetized plasma blob

Besides the cone model and the flux rope models, the spherical plasmoid model and the magnetized plasma blob are also popular CME initialization models used in recent years (Shen et al. 2011a; Shen et al.