An Application of the Stereoscopic Self-similar-Expansion Model to the Determination of CME-Driven Shock Parameters

We present an application of the stereoscopic self-similar-expansion model (SSSEM) to Solar Terrestrial Relations Observatory (STEREO)/Sun–Earth Connection Coronal and Heliospheric Investigation (SECCHI) observations of the CME on 3 April 2010 and its associated shock. The aim is to verify whether CME-driven shock parameters can be inferred from the analysis of j-maps. For this purpose, we used the SSSEM to derive the CME and the shock kinematics. Arrival times and speeds, inferred assuming either propagation at constant speed or with uniform deceleration, agree well with Advanced Composition Explorer (ACE) measurements. The shock standoff distance [Δ]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[\Delta]$\end{document}, the density compression [ρdρu]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[\frac{\rho_{\mathrm{d}}}{\rho_{\mathrm{u}}}]$\end{document}, and the Mach number [M]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[M]$\end{document} were calculated by combining the results obtained for the CME and shock kinematics with models for the shock location. Their values were extrapolated to L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{L}_{1}$\end{document} and compared to in-situ data. The in-situ standoff distance was obtained from ACE solar-wind measurements, and the Mach number and compression ratio were provided by the interplanetary shock database of the Harvard–Smithsonian Center for Astrophysics. They are ρdρu=2.84\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{\rho_{\mathrm{d}}}{\rho_{\mathrm{u}}} =2.84$\end{document} and M=2.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M = 2.2$\end{document}. The best fit to observations was obtained when the SSSEM half-width λ=40∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda= 40^{\circ}$\end{document}, and the CME and shock propagate with uniform deceleration. In this case we found Δ=23R⊙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta= 23~\mathrm{R}_{\odot}$\end{document}, ρdρu=2.61\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{\rho_{\mathrm{d}}}{\rho_{\mathrm{u}}} =2.61$\end{document}, and M=2.93\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M = 2.93$\end{document}. The study shows that CME-driven shock parameters can be estimated from the analysis of time–elongation plots and can be used to predict their in-situ values.