Assessing the Constrained Harmonic Mean Method for Deriving the Kinematics of ICMEs with a Numerical Simulation

In this study we use a numerical simulation of an artificial coronal mass ejection (CME) to validate a method for calculating propagation directions and kinematical profiles of interplanetary CMEs (ICMEs). In this method observations from heliospheric images are constrained with in-situ plasma and field data at 1 AU. These data are used to convert measured ICME elongations into distance by applying the harmonic mean approach, which assumes a spherical shape of the ICME front. We used synthetic white-light images, similar to those observed by STEREO-A/HI, for three different separation angles between remote and in-situ spacecraft of 30^°, 60^°, and 90^°. To validate the results of the method, the images were compared to the apex speed profile of the modeled ICME, as obtained from a top view. This profile reflects the “true” apex kinematics because it is not affected by scattering or projection effects. In this way it is possible to determine the accuracy of the method for revealing ICME propagation directions and kinematics. We found that the direction obtained by the constrained harmonic mean method is not very sensitive to the separation angle (30^° sep: ?=W7; 60^° sep: ?=W12; 90^° sep: ?=W15; true dir.: E0/W0). For all three cases the derived kinematics agree relatively well with the real kinematics. The best consistency is obtained for the 30^° case, while with growing separation angle the ICME speed at 1 AU is increasingly overestimated (30^° sep: ΔV _arr≈??50 km?s^?1, 60^° sep: ΔV _arr≈+?75 km?s^?1, 90^° sep: ΔV _arr≈+?125 km?s^?1). Especially for future L₄/L₅ missions, the 60^° separation case is highly interesting in order to improve space-weather forecasts.     

An Ensemble Study of a January 2010 Coronal Mass Ejection (CME): Connecting a Non-obvious Solar Source with Its ICME/Magnetic Cloud

A distinct magnetic cloud (MC) was observed in-situ at the Solar TErrestrial RElations Observatory (STEREO)-B on 20?–?21 January 2010. About three days earlier, on 17 January, a bright flare and coronal mass ejection (CME) were clearly observed by STEREO-B, which suggests that this was the progenitor of the MC. However, the in-situ speed of the event, several earlier weaker events, heliospheric imaging, and a longitude mismatch with the STEREO-B spacecraft made this interpretation unlikely. We searched for other possible solar eruptions that could have caused the MC and found a faint filament eruption and the associated CME on 14?–?15 January as the likely solar source event. We were able to confirm this source by using coronal imaging from the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI)/EUVI and COR and Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronograph (LASCO) telescopes and heliospheric imaging from the Solar Mass Ejection Imager (SMEI) and the STEREO/Heliospheric Imager instruments. We use several empirical models to understand the three-dimensional geometry and propagation of the CME, analyze the in-situ characteristics of the associated ICME, and investigate the characteristics of the MC by comparing four independent flux-rope model fits with the launch observations and magnetic-field orientations. The geometry and orientations of the CME from the heliospheric-density reconstructions and the in-situ modeling are remarkably consistent. Lastly, this event demonstrates that a careful analysis of all aspects of the development and evolution of a CME is necessary to correctly identify the solar counterpart of an ICME/MC.     

Heliospheric Observations of STEREO-Directed Coronal Mass Ejections in 2008?–?2010: Lessons for Future Observations of Earth-Directed CMEs

We present a study of coronal mass ejections (CMEs) which impacted one of the STEREO spacecraft between January 2008 and early 2010. We focus our study on 20 CMEs which were observed remotely by the Heliospheric Imagers (HIs) onboard the other STEREO spacecraft up to large heliocentric distances. We compare the predictions of the Fixed-?? and Harmonic Mean (HM) fitting methods, which only differ by the assumed geometry of the CME. It is possible to use these techniques to determine from remote-sensing observations the CME direction of propagation, arrival time and final speed which are compared to in-situ measurements. We find evidence that for large viewing angles, the HM fitting method predicts the CME direction better. However, this may be due to the fact that only wide CMEs can be successfully observed when the CME propagates more than 100^° from the observing spacecraft. Overall eight CMEs, originating from behind the limb as seen by one of the STEREO spacecraft can be tracked and their arrival time at the other STEREO spacecraft can be successfully predicted. This includes CMEs, such as the events on 4 December 2009 and 9 April 2010, which were viewed 130^° away from their direction of propagation. Therefore, we predict that some Earth-directed CMEs will be observed by the HIs until early 2013, when the separation between Earth and one of the STEREO spacecraft will be similar to the separation of the two STEREO spacecraft in 2009??C?2010.     

Speeds and Arrival Times of Solar Transients Approximated by Self-similar Expanding Circular Fronts

The NASA Solar TErrestrial RElations Observatory (STEREO) mission offered the possibility to forecast the arrival times, speeds, and directions of solar transients from outside the Sun–Earth line. In particular, we are interested in predicting potentially geoeffective interplanetary coronal mass ejections (ICMEs) from observations of density structures at large observation angles from the Sun (with the STEREO Heliospheric Imager instrument). We contribute to this endeavor by deriving analytical formulas concerning a geometric correction for the ICME speed and arrival time for the technique introduced by Davies et al. (Astrophys. J., 2012, in press), called self-similar expansion fitting (SSEF). This model assumes that a circle propagates outward, along a plane specified by a position angle (e.g., the ecliptic), with constant angular half-width (λ). This is an extension to earlier, more simple models: fixed-Φ fitting (λ=0°) and harmonic mean fitting (λ=90°). In contrast to previous models, this approach has the advantage of allowing one to assess clearly if a particular location in the heliosphere, such as a planet or spacecraft, might be expected to be hit by the ICME front. Our correction formulas are especially significant for glancing hits, where small differences in the direction greatly influence the expected speeds (up to 100?–?200 km?s^?1) and arrival times (up to two days later than the apex). For very wide ICMEs (2λ>120°), the geometric correction becomes very similar to the one derived by Möstl et al. (Astrophys. J. 741, 34, 2011) for the harmonic mean model. These analytic expressions can also be used for empirical or analytical models to predict the 1 AU arrival time of an ICME by correcting for effects of hits by the flank rather than the apex, if the width and direction of the ICME in a plane are known and a circular geometry of the ICME front is assumed.     

On Fields and Mass Constraints for the Uniform Propagation of Magnetic-Flux Ropes Undergoing Isotropic Expansion

An analytical 3-D magnetohydrodynamic (MHD) solution of a magnetic-flux rope (FR) is presented. This FR solution may explain the uniform propagation, beyond ～?0.05 AU, of coronal mass ejections (CMEs) commonly observed by today’s missions like The Solar Mass Ejection Imager (SMEI), Solar and Heliospheric Observatory (SOHO) and Solar Terrestrial Relations Observatory (STEREO), tracked to tens of times the radius of the Sun, and in some cases up to 1 AU, and/or beyond. Once a CME occurs, we present arguments regarding its evolution based on its mass and linear momentum conservation. Here, we require that the gravitational and magnetic forces balance each other in the framework of the MHD theory for a simple model of the evolution of a CME, assuming it interacts weakly with the steady solar wind. When satisfying these ansätze we identify a relation between the transported mechanical mass of the interplanetary CME with its geometrical parameters and the intensity of the magnetic field carried by the structure. In this way we are able to estimate the mass of the interplanetary CME (ICME) for a list of cases, from the Wind mission records of ICME encountered near Earth, at 1 AU. We obtain a range for masses of ～?10⁹ to 10¹³ kg, or assuming a uniform distribution, of ～?0.5 to 500 cm^?3 for the hadron density of these structures, a result that appears to be consistent with observations.     

Evolution of Cosmic-Ray Intensities While the Earth Was Engulfed by the Interplanetary Storm (Blob) of 1 – 3 October 2013

When a Coronal Mass Ejection (CME) is ejected by the Sun, it reaches the Earth orbit in a modified state and is called an ICME (Interplanetary CME). When an ICME blob engulfs the Earth, short-scale cosmic-ray (CR) storms (Forbush decreases, FDs) occur, sometimes accompanied by geomagnetic Dst storms, if the B _z component in the blob is negative. Generally, this is a sudden process that causes abrupt changes. However, sometimes before this abrupt change (FD) due to strong ICME blobs, there are slow, small changes in interplanetary parameters such as steady increases in solar wind speed V, which are small, but can last for several hours. In the present communication, CR changes in such an event are illustrated in the period 1?–?3 October 2013, when V increased steadily from ～?200 km?s^?1 to ～?400 km?s^?1 during 24 hours on 1 October 2013. The CR intensities decreased by 1?–?2 % during some hours of this 24-hour interval, indicating that CR intensities do respond to these weak but long-lasting increases in interplanetary solar wind speed.     

Kinematics of Interacting ICMEs and Related Forbush Decrease: Case Study

We study heliospheric propagation and some space weather aspects of three Earth-directed interplanetary coronal mass ejections (ICMEs), successively launched from the active region AR 11158 in the period 13?–?15 February 2011. From the analysis of the ICME kinematics, morphological evolution, and in situ observations, we infer that the three ICMEs interacted on their way to Earth, arriving together at 1 AU as a single interplanetary disturbance. Detailed analysis of the in situ data reveals complex internal structure of the disturbance, where signatures of the three initially independent ICMEs could be recognized. The analysis also reveals compression and heating of the middle ICME, as well as ongoing magnetic reconnection between the leading and the middle ICME. We present evidence showing that the propagation of these two, initially slower ICMEs, was boosted by the fastest, third ICME. Finally, we employ the ground-based cosmic ray observations, to show that this complex disturbance produced a single cosmic ray event, i.e., a simple Forbush decrease (FD). The results presented provide a better understanding of the ICME interactions and reveal effects that should be taken into account in forecasting of the arrival of such compound structures.     

From the Sun to the Earth: The 13 May 2005 Coronal Mass Ejection

We report the results of a multi-instrument, multi-technique, coordinated study of the solar eruptive event of 13 May 2005. We discuss the resultant Earth-directed (halo) coronal mass ejection (CME), and the effects on the terrestrial space environment and upper Earth atmosphere. The interplanetary CME (ICME) impacted the Earth’s magnetosphere and caused the most-intense geomagnetic storm of 2005 with a Disturbed Storm Time (Dst) index reaching ?263 nT at its peak. The terrestrial environment responded to the storm on a global scale. We have combined observations and measurements from coronal and interplanetary remote-sensing instruments, interplanetary and near-Earth in-situ measurements, remote-sensing observations and in-situ measurements of the terrestrial magnetosphere and ionosphere, along with coronal and heliospheric modelling. These analyses are used to trace the origin, development, propagation, terrestrial impact, and subsequent consequences of this event to obtain the most comprehensive view of a geo-effective solar eruption to date. This particular event is also part of a NASA-sponsored Living With a Star (LWS) study and an on-going US NSF-sponsored Solar, Heliospheric, and INterplanetary Environment (SHINE) community investigation.     

Effect of Electron Pressure on the Grad–Shafranov Reconstruction of Interplanetary Coronal Mass Ejections

We investigate the effect of electron pressure on the Grad–Shafranov (GS) reconstruction of Interplanetary Coronal Mass Ejection (ICME) structures. The GS method uses in situ magnetic field and plasma measurements to solve for a magnetohydrostatic quasi-equilibrium state of space plasmas. For some events, a magnetic flux-rope structure embedded within the ICME can be reconstructed. The electron temperature contributes directly to the calculation of the total plasma pressure, and in ICMEs its contribution often substantially exceeds that of proton temperature. We selected ICME events observed with the Wind spacecraft at 1 AU and applied the GS reconstruction method to each event for cases with and without electron temperature measurements. We sorted them according to the proton plasma β (the ratio of proton plasma pressure to magnetic pressure) and the electron-to-proton temperature ratio. We present case studies of three representative events, show the cross sections of GS reconstructed flux-rope structure, and discuss the electron pressure contribution to key quantities in the numerical reconstruction procedure. We summarize and compare the geometrical and physical parameters derived from the GS reconstruction results for cases with and without electron temperature contribution. We conclude that overall the electron pressure effect on the GS reconstruction results contributes to a 10?–?20 % discrepancy in some key physical quantities, such as the magnetic flux content of the ICME flux rope observed at 1 AU.     

Statistical Analysis of Large-Scale EUV Waves Observed by STEREO/EUVI

We statistically analyzed the kinematical evolution and wave pulse characteristics of 60 strong large-scale EUV wave events that occurred during January 2007 to February 2011 with the STEREO twin spacecraft. For the start velocity, the arithmetic mean is 312±115 km?s^?1 (within a range of 100?–?630 km?s^?1). For the mean (linear) velocity, the arithmetic mean is 254±76 km?s^?1 (within a range of 130?–?470 km?s^?1). 52 % of all waves under study show a distinct deceleration during their propagation (a≤?50 m?s^?2), the other 48 % are consistent with a constant speed within the uncertainties (?50≤a≤50 m?s^?2). The start velocity and the acceleration are strongly anticorrelated with c≈?0.8, i.e. initially faster events undergo stronger deceleration than slower events. The (smooth) transition between constant propagation for slow events and deceleration in faster events occurs at an EUV wave start-velocity of v≈230 km?s^?1, which corresponds well to the fast-mode speed in the quiet corona. These findings provide strong evidence that the EUV waves under study are indeed large-amplitude fast-mode MHD waves. This interpretation is also supported by the correlations obtained between the peak velocity and the peak amplitude, impulsiveness, and build-up time of the disturbance. We obtained the following association rates of EUV wave events with other solar phenomena: 95 % are associated with a coronal mass ejection (CME), 74 % to a solar flare, 15 % to interplanetary type II bursts, and 22 % to coronal type II bursts. These findings are consistent with the interpretation that the associated CMEs are the driving agents of the EUV waves.     

Observations of the X-ray burster MX 0836-42 by the INTEGRAL and RXTE orbiting observatories

We present the results of our study of the emission from the transient burster MX 0836-42 using its observations by the INTEGRAL and RXTE X-ray and gamma-ray observatories in the period 2003–2004. The source’s broadband X-ray spectrum in the energy range 3–120 keV has been obtained and investigated for the first time. We have detected 39 X-ray bursts from this source. Their analysis shows that the maximum 3–20-keV flux varies significantly from burst to burst, F ～ (0.5–1.5) × 10^?8 erg cm^?2 s^?1. Using the flux at the maximum of the brightest detected burst, we determined an upper limit for the distance to the source, D ? 8 kpc.     

Propagation Characteristics of CMEs Associated with Magnetic Clouds and Ejecta

We have investigated the characteristics of magnetic cloud (MC) and ejecta (EJ) associated coronal mass ejections (CMEs) based on the assumption that all CMEs have a flux rope structure. For this, we used 54 CMEs and their interplanetary counterparts (interplanetary CMEs: ICMEs) that constitute the list of events used by the NASA/LWS Coordinated Data Analysis Workshop (CDAW) on CME flux ropes. We considered the location, angular width, and speed as well as the direction parameter, D. The direction parameter quantifies the degree of asymmetry of the CME shape in coronagraph images, and shows how closely the CME propagation is directed to Earth. For the 54 CDAW events, we found the following properties of the CMEs: i) the average value of D for the 23 MCs (0.62) is larger than that for the 31 EJs (0.49), which indicates that the MC-associated CMEs propagate more directly toward the Earth than the EJ-associated CMEs; ii) comparison between the direction parameter and the source location shows that the majority of the MC-associated CMEs are ejected along the radial direction, while many of the EJ-associated CMEs are ejected non-radially; iii) the mean speed of MC-associated CMEs (946 km?s^?1) is faster than that of EJ-associated CMEs (771 km?s^?1). For seven very fast CMEs (≥?1500 km?s^?1), all CMEs with large D (≥?0.4) are associated with MCs and the CMEs with small D are associated with EJs. From the statistical analysis of CME parameters, we found the superiority of the direction parameter. Based on these results, we suggest that the CME trajectory essentially determines the observed ICME structure.     

Multi-Wavelength Eclipse Observations of a Quiescent Prominence

We construct the maps of temperatures, geometrical thicknesses, electron densities and gas pressures in a quiescent prominence. For this we use the RGB signal of the prominence visible-light emission detected during the total solar eclipse of 1 August 2008 in Mongolia and quasi-simultaneous Hα spectra taken at Ond?ejov Observatory. The method of disentangling the electron density and geometrical (effective) thickness was described by Jej?i? and Heinzel (Solar Phys. 254, 89?–?100, 2009) and is used here for the first time to analyse the spatial variations of prominence parameters. For the studied prominence we obtained the following range of parameters: temperature 6000?–?15?000 K, effective thickness 200?–?15000 km, electron density 5×10⁹?–?10¹¹ cm^?3 and gas pressure 0.02?–?0.2 dyn?cm^?2 (assuming a fixed ionisation degree n _p/n _H=0.5). The electron density increases towards the bottom of the prominence, which we explain by an enhanced photoionisation due to the incident solar radiation. To confirm this, we construct a two-dimensional radiative-transfer model with realistic prominence illumination.     

Kinematic Properties of Slow ICMEs and an Interpretation of a Modified Drag Equation for Fast and Moderate ICMEs

We report kinematic properties of slow interplanetary coronal mass ejections (ICMEs) identified by SOHO/LASCO, interplanetary scintillation, and in situ observations and propose a modified equation for the ICME motion. We identified seven ICMEs between 2010 and 2011 and compared them with 39 events reported in our previous work. We examined 15 fast (V _SOHO?V _bg>500 km?s^?1), 25 moderate (0 km?s^?1≤V _SOHO?V _bg≤500 km?s^?1), and 6 slow (V _SOHO?V _bg<0 km?s^?1) ICMEs, where V _SOHO and V _bg are the initial speed of ICMEs and the speed of the background solar wind. For slow ICMEs, we found the following results: i) They accelerate toward the speed of the background solar wind during their propagation and reach their final speed by 0.34±0.03 AU. ii) The acceleration ends when they reach 479±126 km?s^?1; this is close to the typical speed of the solar wind during the period of this study. iii) When γ ₁ and γ ₂ are assumed to be constants, a quadratic equation for the acceleration a=?γ ₂(V?V _bg)|V?V _bg| is more appropriate than a linear one a=?γ ₁(V?V _bg), where V is the propagation speed of ICMEs, while the latter gives a smaller χ ² value than the former. For the motion of the fast and moderate ICMEs, we found a modified drag equation a=?2.07×10^?12(V?V _bg)|V?V _bg|?4.84×10^?6(V?V _bg). From the viewpoint of fluid dynamics, we interpret this equation as indicating that ICMEs with 0 km?s^?1≤V?V _bg≤2300 km?s^?1 are controlled mainly by the hydrodynamic Stokes drag force, while the aerodynamic drag force is a predominant factor for the propagation of ICME with V?V _bg>2300 km?s^?1.     

Shock acceleration of solar cosmic rays

The solar cosmic ray (SCR) acceleration by the shocks driven by coronal mass ejections is studied by taking into account the generation of Alfvén waves by accelerated particles. Detailed numerical calculations of the SCR spectra produced during the shock propagation through the solar corona have been performed within a quasi-linear approach with a realistic set of coronal parameters. The resultant SCR energy spectrum is shown to include a power-law part N ∝ ?^-γ with an index γ = 1.7–3.5 that ends with an exponential tail. The maximum SCR energy lies within the range ? _max = 0.01–10 GeV, depending on the shock velocity V _S = 750–2500 km s^?1. The decrease of the shock Alfvénic Mach number due to the increase Alfvén velocity with heliocentric distance r leads to the end of the efficient SCR acceleration when the shock size reaches R _S ≈ 4R _⊙. In this case, the diffusive SCR propagation begins to exceed the shock velocity; as a result, SCRs escape intensively from the shock vicinity. The self-consistent generation of Alfvén waves by accelerated particles is accompanied by a steepening of the particle spectrum and an increase of their maximum energy. Comparison of the calculated SCR fluxes expected near the Earth’s orbit with the available experimental data shows that the theory explains the main observed features.     

Kinematics of the Gould Belt based on open clusters

We have redetermined the kinematic parameters of the Gould Belt using currently available data on the motion of nearby young (log t < 7.91) open clusters, OB associations, and moving stellar groups. Our modeling shows that the residual velocities reach their maximum values of ?4 km s^?1 for rotation (in the direction of Galactic rotation) and +4 km s^?1 for expansion at a distance from the kinematic center of ≈300 pc. We have taken the following parameters of the Gould Belt center: R ₀ = 150 pc and l ₀ = 128°. The whole structure is shown to move relative to the local standard of rest at a velocity of 10.7 ± 0.7 km s^?1 in the direction l = 274° ± 4° and b = ?1° ± 3°. Using the derived rotation velocity, we have estimated the virial mass of the Gould Belt to be 1.5 × 10⁶ M _⊙.     

Three-Dimensional (3-D) Reconstructions of EISCAT IPS Velocity Data in the Declining Phase of Solar Cycle 23

The European Incoherent SCATter (EISCAT) radar has been used for remote-sensing observations of interplanetary scintillation (IPS) for a quarter of a century. During the April/May 2007 observing campaign, a large number of observations of IPS using EISCAT took place to give a reasonable spatial and temporal coverage of solar wind velocity structure throughout this time during the declining phase of Solar Cycle 23. Many co-rotating and transient features were observed during this period. Using the University of California, San Diego three-dimensional (3-D) time-dependent computer assisted tomography (C.A.T.) solar-wind reconstruction analysis, we show the velocity structure of the inner heliosphere in three dimensions throughout the time interval of 20 April through 20 May 2007. We also compare to white-light remote-sensing observations of an interplanetary coronal mass ejection (ICME) seen by the STEREO Ahead spacecraft inner Heliospheric Imager on 16 May 2007, as well as to in-situ solar-wind measurements taken with near-Earth spacebourne instrumentation throughout this interval. The reconstructions show clear co-rotating regions during this period, and the time-series extraction at spacecraft locations compares well with measurements made by the STEREO, Wind, and ACE spacecraft. This is the first time such clear structures have been revealed using this 3-D technique with EISCAT IPS data as input.     

Visibility-Graph Analysis of the Solar Wind Velocity

We analyze in situ measurements of the solar wind velocity obtained by the Advanced Composition Explorer (ACE) and the Helios spacecraft during the years 1998?–?2012 and 1975?–?1983, respectively. The data mainly belong to solar cycles 23 (1996?–?2008) and 21 (1976?–?1986). We used the directed horizontal-visibility-graph (DHVg) algorithm and estimated a graph functional, namely, the degree distance (D), which is defined using the Kullback–Leibler divergence (KLD) to understand the time irreversibility of solar wind time-series. We estimated this degree-distance irreversibility parameter for these time-series at different phases of the solar activity cycle. The irreversibility parameter was first established for known dynamical data and was then applied to solar wind velocity time-series. It is observed that irreversibility in solar wind velocity fluctuations show a similar behavior at 0.3 AU (Helios data) and 1 AU (ACE data). Moreover, the fluctuations change over the phases of the activity cycle.     

Correlation of ICME Magnetic Fields at Radially Aligned Spacecraft

The magnetic field structures of two interplanetary coronal mass ejections (ICMEs), each observed by a pair of spacecraft close to radial alignment, have been analysed. The ICMEs were observed in situ by MESSENGER and STEREO-B in November 2010 and November 2011, while the spacecraft were separated by more than 0.6 AU in heliocentric distance, less than 4° in heliographic longitude, and less than 7° in heliographic latitude. Both ICMEs took approximately two days to travel between the spacecraft. The ICME magnetic field profiles observed at MESSENGER have been mapped to the heliocentric distance of STEREO-B and compared directly to the profiles observed by STEREO-B. Figures that result from this mapping allow for easy qualitative assessment of similarity in the profiles. Macroscale features in the profiles that varied on timescales of one hour, and which corresponded to the underlying flux rope structure of the ICMEs, were well correlated in the solar east–west and north–south directed components, with Pearson’s correlation coefficients of approximately 0.85 and 0.95, respectively; microscale features with timescales of one minute were uncorrelated. Overall correlation values in the profiles of one ICME were increased when an apparent change in the flux rope axis direction between the observing spacecraft was taken into account. The high degree of similarity seen in the magnetic field profiles may be interpreted in two ways. If the spacecraft sampled the same region of each ICME (i.e. if the spacecraft angular separations are neglected), the similarity indicates that there was little evolution in the underlying structure of the sampled region during propagation. Alternatively, if the spacecraft observed different, nearby regions within the ICMEs, it indicates that there was spatial homogeneity across those different regions. The field structure similarity observed in these ICMEs points to the value of placing in situ space weather monitors well upstream of the Earth.