Spherically-shaped coronal shock waves associated with Coronal Mass Ejections

Knowing the three-dimensional (3D) geometry of Coronal mass ejections (CMEs) and associated shock waves is crucial for interpretations of in-situ measurements close to the Sun that will be carried out by Solar Probe Plus and Solar Orbiter. Here, we obtain the 3D geometries of three CMEs and associated shock waves using multiple perspective observations from STEREO-Ahead, -Behind, SDO, and SOHO. These CMEs appeared as halo CMEs in all three viewing perspectives and were accompanied by solar energetic particle (SEP) events. The 3D structures and kinematics of the halo fronts were determined by applying a forward modeling method. We find that the angular widths of the halos are at least 192 degrees while those of the CMEs are at most 100 degrees, implying the presence of a spherically-shaped wave, extending out much further than the CME. The peak speeds of the CMEs are in the range of 1355- 2157 km/s, but the speeds of the halo flanks seem to reach the local fast-mode speed of the coronal medium 500 km/s. To further investigate the physical nature of the halo flanks, we compare the 3D properties of the halos with a fast-mode wave model given in Uchida (1970). The model reproduced the halo flanks with the local fast-mode speed profiles of the coronal medium. The modeled waves refract toward the lower altitudes as propagating through the inhomogeneous medium, and these fast-mode waves lead to the spherically-shaped fronts. In addition, the azimuthal extents of the halos are consistent with the SEP injection sites far away from the flare sites, supporting that the halo fronts are truly the signatures of the fast-mode wave. Our results suggest that the halo-shaped fronts are likely spherically-shaped fast-mode waves, extending out much further than the CMEs. The unprecedented in-situ measurements of Solar Probe Plus and Solar Orbiter will probe into the detailed physical properties of such large-scale disturbances in the corona.