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We present a novel method to derive the shock density compression ratio of coronal shock waves that are occasionally observed as halo coronal mass ejections (CMEs). Our method uses the three-dimensional (3-D) geometry and enables us to access the reliable shock density compression ratio. We show the 3-D properties of coronal shock waves seen from multiple vantage point observations, i.e., geometry, kinematics, and compression ratio (Mach number). The significant findings are as follows: (1) Halo CMEs are the manifestation of spherically shaped fast-mode waves/shocks, rather than a matter of the projection of expanding flux ropes. The footprints of halo CMEs on the coronal base are the so-called EIT/EUV waves. (2) These spherical fronts arise from a driven shock (bow- or piston-type) close to the CME nose, and it is gradually becoming a freely propagating (decaying) fast-mode shock wave at the flank. (3) The shock density compressions peak around the CME nose and decrease at larger position angles (flank). (4) Finally, the supercritical region extends over a large area of the shock and lasts longer than past reports. These results offer a simple unified picture of the different manifestations for CME-associated (shock) waves, such as EUV waves and SEP events observed in various regimes and heliocentric distances. We conclude that CME shocks can accelerate energetic particles in the corona over extended spatial and temporal scales and are likely responsible for the wide longitudinal distribution of these particles in the inner heliosphere.

Global EUV waves remain a controversial phenomenon more than 20 yr after their discovery by SOHO/EIT. Although consensus is growing in the community that they are most likely large-amplitude waves or shocks, the wide variety of observations and techniques used to identify and analyze them have led to disagreements regarding their physical properties and interpretation. Here, we use a 3D magnetohydrodynamic (MHD) model of the solar corona to simulate an EUV wave event on 2009 February 13 to enable a detailed validation of the various commonly used detection and analysis techniques of global EUV waves. The simulated event exhibits comparable behavior to that of a real EUV wave event, with similar kinematic behavior and plasma parameter evolution. The kinematics of the wave are estimated via visual identification and profile analysis, with both approaches providing comparable results. We find that projection effects can affect the derived kinematics of the wave, due to the variation in fast-mode wave speed with height in the corona. Coronal seismology techniques typically used for estimates of the coronal magnetic field are also tested and found to estimate fast-mode speeds comparable to those of the model. Plasma density and temperature variations of the wave front are also derived using a regularized inversion approach and found to be consistent with observed wave events. These results indicate that global waves are best interpreted as large-amplitude waves and that they can be used to probe the coronal medium using well-defined analysis techniques.

Solar rotational tomography (SRT) is an important method to reconstruct the physical parameters of the three-dimensional solar corona. Here we propose an approach to apply the filtered backprojection (FBP) algorithm to the SRT. The FBP algorithm is generally not suitable for SRT due to the several issues with solar extreme ultraviolet (EUV) observations, in particular a problem caused by missing data because of the unobserved back side of corona hidden behind the Sun. We developed a method to generate a modified sinogram which resolves the blocking problem. The modified sinogram is generated by combining the EUV data at two opposite sites observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We generated the modified sinogram for about one month in 2019 February and reconstructed the three-dimensional corona under the static state assumption. In order to obtain the physical parameters of the corona, we employed a DEM inversion method. We tested the performance of the FBP algorithm with the modified sinogram by comparing the reconstructed data with the observed EUV image, electron density models, previous studies of electron temperature, and an observed coronagraph image. The results illustrate that the FBP algorithm reasonably reconstructs the bright regions and the coronal holes, and can reproduce their physical parameters. The main advantage of the FBP algorithm is that it is easy to understand and computationally efficient. Thus, it enables us to easily probe the inhomogeneous coronal electron density and temperature distribution of the solar corona., Comment: Accepted for ApJ

The measurements of magnetic twist of EUV coronal loops for 14 loops are presented here. EUV coronal loops are thin, EUV-emitting structures of hot plasma tracing magnetic field lines in the corona. The constriction of plasma into a loop without dispersion may be explained if the magnetic field of the loop is twisted. On the basis of this idea, Chae and Moon developed a method of determining magnetic twist of coronal loops by analyzing coronal images and photospheric magnetograms together. By applying this method to as many coronal loops observed by TRACE 171 A as possible, we attempt to determine a statistically meaningful value of magnetic twist of coronal loops for the first time. We have selected a number of conspicuous loops which are bright enough and well separated from other adjacent loops on TRACE EUV images. We have constructed and examined coronal magnetic fields of selected active regions containing the loops with consideration of the projection effect, and we can identify 14 coronal loops whose magnetic field lines are well represented by a linear force-free field. We have found that these loops have absolute twist values from 0.22π to 1.73π, which suggests that the absolute winding number of EUV coronal loop may be mostly less than one turn. Our results support the idea that EUV coronal loops may be a product of magnetic reconnection of magnetic flux tubes.

We present a new method to extract the three-dimensional electron density profile and density compression ratio of shock fronts associated with Coronal Mass Ejections (CMEs) observed in white light coronagraph images. We demonstrate the method with two examples of fast halo CMEs ($\sim$ 2000 km s$^{-1}$) observed on 2011 March 7 and 2014 February 25. Our method uses the ellipsoid model to derive the three-dimensional (3D) geometry and kinematics of the fronts. The density profiles of the sheaths are modeled with double-Gaussian functions with four free parameters and the electrons are distributed within thin shells behind the front. The modeled densities are integrated along the lines of sight to be compared with the observed brightness in COR2-A, and a $\chi^2$ approach is used to obtain the optimal parameters for the Gaussian profiles. The upstream densities are obtained from both the inversion of the brightness in a pre-event image and an empirical model. Then the density ratio and Alfv\'{e}nic Mach number are derived. We find that the density compression peaks around the CME nose, and decreases at larger position angles. The behavior is consistent with a driven shock at the nose and a freely-propagating shock wave at the CME flanks. Interestingly, we find that the supercritical region extends over a large area of the shock and last longer (several tens of minutes) than past reports. It follows that CME shocks are capable of accelerating energetic particles in the corona over extended spatial and temporal scales and are likely responsible for the wide longitudinal distribution of these particles in the inner heliosphere. Our results also demonstrate the power of multi-viewpoint coronagraphic observations and forward modeling in remotely deriving key shock properties in an otherwise inaccessible regime., Comment: Accepted for publication in the Journal of Space Weather and Space Climate

Bright rays are often observed after coronal mass ejections (CMEs) erupt. These rays are dynamical structures along which plasmas move outward. We investigated the outflows along the post-CME rays observed by the COR2 on board STEREO Behind on 2013 September 21 and 22. We tracked two CMEs, two ray tips, and seven blobs using the NAVE optical flow technique. As a result, we found that the departure times of blobs and ray tips from the optimally chosen starting height of coincided with the occurrence times of the corresponding recurrent small flares within 10 minutes. These small flares took place many hours after the major flares. This result supports a magnetic reconnection origin of the outward flows along the post-CME ray and the importance of magnetic islands for understanding the process of magnetic reconnection. The total energy of magnetic reconnection maintaining the outflows for 40 hr is estimated at erg. Further investigations of plasma outflows along post-CME rays will shed much light on the physical properties of magnetic reconnection occurring in the solar corona.

We analyze one of the first solar energetic particle (SEP) events of solar cycle 24 observed at widely separated spacecraft in order to assess the reliability of models currently used to determine the connectivity between the sources of SEPs at the Sun and spacecraft in the inner heliosphere. This SEP event was observed on 2010 August 14 by near-Earth spacecraft, STEREO-A (∼80° west of Earth) and STEREO-B (∼72° east of Earth). In contrast to near-Earth spacecraft, the footpoints of the nominal magnetic field lines connecting STEREO-A and STEREO-B with the Sun were separated from the region where the parent fast halo coronal mass ejection (CME) originated by ∼88° and ∼47° in longitude, respectively. We discuss the properties of the phenomena associated with this solar eruption. Extreme ultraviolet and white-light images are used to specify the extent of the associated CME-driven coronal shock. We then assess whether the SEPs observed at the three heliospheric locations were accelerated by this shock or whether transport mechanisms in the corona and/or interplanetary space provide an alternative explanation for the arrival of particles at the poorly connected spacecraft. A possible scenario consistent with the observations indicates that the observation of SEPs at STEREO-B and near Earth resulted from particle injection by the CME shock onto the field lines connecting to these spacecraft, whereas SEPs reached STEREO-A mostly via cross-field diffusive transport processes. The successes, limitations, and uncertainties of the methods used to resolve the connection between the acceleration sites of SEPs and the spacecraft are evaluated.

We investigate the solar phenomena associated with the origin of the solar energetic particle (SEP) event observed on 2013 April 11 by a number of spacecraft distributed in the inner heliosphere over a broad range of heliolongitudes. We use Extreme UltraViolet (EUV) and white-light coronagraph observations from the Solar Dynamics Observatory (SDO), the SOlar and Heliospheric Observatory (SOHO) and the twin Solar TErrestrial RElations Observatory spacecraft (STEREO-A and STEREO-B) to determine the angular extent of the EUV wave and coronal mass ejection (CME) associated with the origin of the SEP event. We compare the estimated release time of SEPs observed at each spacecraft with the arrival time of the structures associated with the CME at the footpoints of the field lines connecting each spacecraft with the Sun. Whereas the arrival of the EUV wave and CME-driven shock at the footpoint of STEREO-B is consistent, within uncertainties, with the release time of the particles observed by this spacecraft, the EUV wave never reached the footpoint of the field lines connecting near-Earth observers with the Sun, even though an intense SEP event was observed there. We show that the west flank of the CME-driven shock propagating at high altitudes above the solar surface was most likely the source of the particles observed near Earth, but it did not leave any EUV trace on the solar disk. We conclude that the angular extent of the EUV wave on the solar surface did not agree with the longitudinal extent of the SEP event in the heliosphere. Hence EUV waves cannot be used reliably as a proxy for the solar phenomena that accelerates and injects energetic particles over broad ranges of longitudes.

We present new insights into the physical nature of coronal mass ejections (CMEs) and associated shock waves within the framework of the three-dimensional (3D) structure. We have developed a compound model in order to determine the 3D structure of multiple fronts composing a CME, using data sets taken from STEREO, SDO, and SOHO. We applied the method to time series observations of a CME on 2012 March 7. From the analyses, we revealed that a CME could consist of two different fronts: one is represented well with the ellipsoid model, implying that CMEs are bubble-shaped structures, and the other is reproduced well with the graduated cylindrical shell model, indicating that CMEs are flux rope-shaped structures. The bubble-shaped structure is seen as the outermost front of the CME, and the flux rope-shaped structure is seen as the bright frontal loop or three-part morphology. From our results, we conclude that (1) a CME could consist of two distinct structures, a bubble-shaped structure and a flux rope-shaped structure, (2) the bubble-shaped structure is a fast magnetosonic shock wave, while the flux rope-shaped structure is the mass carried outward by the underlying magnetic structure, (3) the driven shock front could be either a piston-shock type or a bow-shock type, (4) the observed EUV wave in the low corona is the footprint of the bubble-shaped wave, and (5) the halo CME is primarily the projection of the bubble-shaped shock wave but not the underlying flux rope.

We present global coronal seismology for the first time, which allows us to determine inhomogeneous magnetic field strength in the extended corona. From the measurements of the propagation speed of a fast magnetosonic wave associated with a coronal mass ejection (CME) and the coronal background density distribution derived from the polarized radiances observed by the STEREO SECCHI COR1, we determined the magnetic field strengths along the trajectories of the wave at different heliocentric distances. We found that the results have an uncertainty less than 40%, and are consistent with values determined with a potential field model and reported in previous works. The characteristics of the coronal medium we found are that (1) the density, magnetic field strength, and plasma β are lower in the coronal hole region than in streamers; (2) the magnetic field strength decreases slowly with height but the electron density decreases rapidly so that the local fast magnetosonic speed increases while plasma β falls off with height; and (3) the variations of the local fast magnetosonic speed and plasma β are dominated by variations in the electron density rather than the magnetic field strength. These results imply that Moreton and EIT waves are downward-reflected fast magnetosonic waves from the upper solar corona, rather than freely propagating fast magnetosonic waves in a certain atmospheric layer. In addition, the azimuthal components of CMEs and the driven waves may play an important role in various manifestations of shocks, such as type II radio bursts and solar energetic particle events.

We report white-light observations of a fast magnetosonic wave associated with a coronal mass ejection observed by STEREO/SECCHI/COR1 inner coronagraphs on 2011 August 4. The wave front is observed in the form of density compression passing through various coronal regions such as quiet/active corona, coronal holes, and streamers. Together with measured electron densities determined with STEREO COR1 and Extreme UltraViolet Imager (EUVI) data, we use our kinematic measurements of the wave front to calculate coronal magnetic fields and find that the measured speeds are consistent with characteristic fast magnetosonic speeds in the corona. In addition, the wave front turns out to be the upper coronal counterpart of the EIT wave observed by STEREO EUVI traveling against the solar coronal disk; moreover, stationary fronts of the EIT wave are found to be located at the footpoints of deflected streamers and boundaries of coronal holes, after the wave front in the upper solar corona passes through open magnetic field lines in the streamers. Our findings suggest that the observed EIT wave should be in fact a fast magnetosonic shock/wave traveling in the inhomogeneous solar corona, as part of the fast magnetosonic wave propagating in the extended solar corona.

We report on the determination of radial magnetic field strength in the heliocentric distance range from 6 to 120 solar radii (R-solar) using data from Coronagraph 2 (COR2) and Heliospheric Imager I (HI1) instruments on board the Solar Terrestrial Relations Observatory spacecraft following the standoff-distance method of Gopalswamy & Yashiro. We measured the shock standoff distance of the 2008 April 5 coronal mass ejection (CME) and determined the flux-rope curvature by fitting the three-dimensional shape of the CME using the Graduated Cylindrical Shell model. The radial magnetic field strength is computed from the Alfven speed and the density of the ambient medium. We also compare the derived magnetic field strength with in situ measurements made by the Helios spacecraft, which measured the magnetic field at the heliocentric distance range from 60 to 215 R-solar.We found that the radial magnetic field strength decreases from 28 mG at 6 R-solar to 0.17 mG at 120 R-solar. In addition, we found that the radial profile can be described by a power law.

We unveil the three-dimensional structure of quiet-Sun EUV bright points and their temporal evolution by applying a triangulation method to time series of images taken by SECCHI/EUVI on board the STEREO twin spacecraft. For this study we examine the heights and lengths as the components of the three-dimensional structure of EUV bright points and their temporal evolutions. Among them we present three bright points which show three distinct changes in the height and length: decreasing, increasing, and steady. We show that the three distinct changes are consistent with the motions (converging, diverging, and shearing, respectively) of their photospheric magnetic flux concentrations. Both growth and shrinkage of the magnetic fluxes occur during their lifetimes and they are dominant in the initial and later phases, respectively. They are all multi-temperature loop systems which have hot loops (approx. 10(exp 6.2) K) overlying cooler ones (approx 10(exp 6.0) K) with cool legs (approx 10(exp 4.9) K) during their whole evolutionary histories. Our results imply that the multi-thermal loop system is a general character of EUV bright points. We conclude that EUV bright points are flaring loops formed by magnetic reconnection and their geometry may represent the reconnected magnetic field lines rather than the separator field lines.

For almost 20 years the physical nature of globally propagating waves in the solar corona (commonly called "EIT waves") has been controversial and subject to debate. Additional theories have been proposed over the years to explain observations that did not fit with the originally proposed fast-mode wave interpretation. However, the incompatibility of observations made using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory with the fast-mode wave interpretation was challenged by differing viewpoints from the twin Solar Terrestrial Relations Observatory spacecraft and higher spatial/temporal resolution data from the Solar Dynamics Observatory. In this article, we reexamine the theories proposed to explain "EIT waves" to identify measurable properties and behaviours that can be compared to current and future observations. Most of us conclude that "EIT waves" are best described as fast-mode large-amplitude waves/shocks that are initially driven by the impulsive expansion of an erupting coronal mass ejection in the low corona., Comment: 26 pages, 2 figures, accepted for publication in Solar Physics