Elements with finite Coxeter part in an affine Weyl group

Let $W_a$ be an affine Weyl group and $\eta:W_a\longrightarrow W_0$ be the natural projection to the corresponding finite Weyl group. We say that $w\in W_a$ has finite Coxeter part if $\eta(w)$ is conjugate to a Coxeter element of $W_0$. The elements with finite Coxeter part is a union of conjugacy classes of $W_a$. We show that for each conjugacy class $\mathcal{O}$ of $W_a$ with finite Coxeter part there exits a unique maximal proper parabolic subgroup $W_J$ of $W_a$, such that the set of minimal length elements in $\mathcal{O}$ is exactly the set of Coxeter elements in $W_J$. Similar results hold for twisted conjugacy classes.Comment: 9 page

Effects of Coronal Density and Magnetic Field Distributions on a Global Solar EUV Wave

We investigate a global extreme-ultraviolet (EUV) wave associated with a coronal mass ejection (CME)-driven shock on 2017 September 10. The EUV wave is transmitted by north- and south-polar coronal holes (CHs), which is observed by the Solar Dynamics Observatory (SDO) and Solar Terrestrial Relations Observatory A (STEREO-A) from opposite sides of the Sun. We obtain key findings on how the EUV wave interacts with multiple coronal structures, and on its connection with the CME-driven shock: (1) the transmitted EUV wave is still connected with the shock that is incurvated to the Sun, after the shock has reached the opposite side of the eruption; (2) the south CH transmitted EUV wave is accelerated inside an on-disk, low-density region with closed magnetic fields, which implies that an EUV wave can be accelerated in both open and closed magnetic field regions; (3) part of the primary EUV wavefront turns around a bright point (BP) with a bipolar magnetic structure when it approaches a dim, low-density filament channel near the BP; (4) the primary EUV wave is diffused and apparently halted near the boundaries of remote active regions (ARs) that are far from the eruption, and no obvious AR related secondary waves are detected; (5) the EUV wave extends to an unprecedented scale of ~360{\deg} in latitudes, which is attributed to the polar CH transmission. These results provide insights into the effects of coronal density and magnetic field distributions on the evolution of an EUV wave, and into the connection between the EUV wave and the associated CME-driven shock.Comment: 16 pages, 8 figures, and 3 animations available at http://doi.org/10.13140/RG.2.2.12408.29442 , http://doi.org/10.13140/RG.2.2.25830.06723 , and http://doi.org/10.13140/RG.2.2.19119.18088 ; published in Ap

Sun-to-Earth Characteristics of Two Coronal Mass Ejections Interacting near 1 AU: Formation of a Complex Ejecta and Generation of a Two-Step Geomagnetic Storm

On 2012 September 30 - October 1 the Earth underwent a two-step geomagnetic storm. We examine the Sun-to-Earth characteristics of the coronal mass ejections (CMEs) responsible for the geomagnetic storm with combined heliospheric imaging and in situ observations. The first CME, which occurred on 2012 September 25, is a slow event and shows an acceleration followed by a nearly invariant speed in the whole Sun-Earth space. The second event, launched from the Sun on 2012 September 27, exhibits a quick acceleration, then a rapid deceleration and finally a nearly constant speed, a typical Sun-to-Earth propagation profile for fast CMEs \citep{liu13}. These two CMEs interacted near 1 AU as predicted by the heliospheric imaging observations and formed a complex ejecta observed at Wind, with a shock inside that enhanced the pre-existing southward magnetic field. Reconstruction of the complex ejecta with the in situ data indicates an overall left-handed flux rope-like configuration, with an embedded concave-outward shock front, a maximum magnetic field strength deviating from the flux rope axis and convex-outward field lines ahead of the shock. While the reconstruction results are consistent with the picture of CME-CME interactions, a magnetic cloud-like structure without clear signs of CME interactions \citep{lugaz14} is anticipated when the merging process is finished.Comment: 15 pages, 5 figures. Accepted for publication in ApJ Letter

Global explicit particle-in-cell simulations of the nonstationary bow shock and magnetosphere

We carry out two-dimensional global particle-in-cell simulations of the interaction between the solar wind and a dipole field to study the formation of the bow shock and magnetosphere. A self-reforming bow shock ahead of a dipole field is presented by using relatively high temporal-spatial resolutions. We find that (1) the bow shock and the magnetosphere are formed and reach a quasi-stable state after several ion cyclotron periods, and (2) under the Bz southward solar wind condition the bow shock undergoes a self-reformation for low \b{eta}i and high MA. Simultaneously, a magnetic reconnection in the magnetotail is found. For high \b{eta}i and low MA, the shock becomes quasi-stationary, and the magnetotail reconnection disappears. In addition, (3) the magnetopause deflects the magnetosheath plasmas. The sheath particles injected at the quasi-perpendicular region of the bow shock can be convected to downstream of an oblique shock region. A fraction of these sheath particles can leak out from the magnetosheath at the wings of the bow shock. Hence, the downstream situation is more complicated than that for a planar shock produced in local simulations.Comment: in ApJS, 201

On Sun-to-Earth Propagation of Coronal Mass Ejections: 2. Slow Events and Comparison with Others

As a follow-up study on Sun-to-Earth propagation of fast coronal mass ejections (CMEs), we examine the Sun-to-Earth characteristics of slow CMEs combining heliospheric imaging and in situ observations. Three events of particular interest, the 2010 June 16, 2011 March 25 and 2012 September 25 CMEs, are selected for this study. We compare slow CMEs with fast and intermediate-speed events, and obtain key results complementing the attempt of \citet{liu13} to create a general picture of CME Sun-to-Earth propagation: (1) the Sun-to-Earth propagation of a typical slow CME can be approximately described by two phases, a gradual acceleration out to about 20-30 solar radii, followed by a nearly invariant speed around the average solar wind level, (2) comparison between different types of CMEs indicates that faster CMEs tend to accelerate and decelerate more rapidly and have shorter cessation distances for the acceleration and deceleration, (3) both intermediate-speed and slow CMEs would have a speed comparable to the average solar wind level before reaching 1 AU, (4) slow CMEs have a high potential to interact with other solar wind structures in the Sun-Earth space due to their slow motion, providing critical ingredients to enhance space weather, and (5) the slow CMEs studied here lack strong magnetic fields at the Earth but tend to preserve a flux-rope structure with axis generally perpendicular to the radial direction from the Sun. We also suggest a "best" strategy for the application of a triangulation concept in determining CME Sun-to-Earth kinematics, which helps to clarify confusions about CME geometry assumptions in the triangulation and to improve CME analysis and observations.Comment: 37 pages, 13 figures, accepted for publication in ApJ Supplemen