A Self-Similar Expansion Model for Use in Solar Wind Transient Propagation Studies

Abstract

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single-and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed φ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed φ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient's speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient's angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.

Assessing the Effect of Spacecraft Motion on Single-Spacecraft Solar Wind Tracking Techniques

“…Davies et al (2012) found that the two models described so far can be considered as two extremes of a common geometry. They use a more generalised HMF-like analysis, in which the circular CME front is not fixed to the Sun, which they call a self-similar expansion (SSE).…”

“…This diagram follows the notation used by Davies et al (2012) and Möstl et al (2011) and uses d 0 instead of r sc .…”

“…A development of this technique assumes that the feature is more extended in cross section -indeed that it forms an expanding circle with its rear end fixed to Sun centre. Figure 2 ( Figure 1a from Davies et al, 2012) illustrates the viewing geometries of both the fixed-φ and the harmonic mean fitting techniques. It is assumed that the leading edge of the feature observed in a J-map is the tangent to the circle.…”

Using Coordinated Observations in Polarized White Light and Faraday Rotation to Probe the Spatial Position and Magnetic Field of an Interplanetary Sheath

“…Even for an observer at a fixed longitude, a different part of the CME will contribute to the imaged radiance at any given time (Xiong et al 2013). Various techniques have been developed that enable the spatial locations and propagation directions of CMEs to be inferred, based on fitting their moving radiance patterns (e.g., Sheeley et al 2008;Rouillard et al 2008;Thernisien et al 2009;Liu et al 2010;Lugaz et al 2010;Möstl et al 2011;Davies et al 2012). However, the determination of interplanetary CME kinematics, and propagation direction in particular, is somewhat ambiguous (Howard & Tappin 2009;Davis et al 2010;Davies et al 2012;Howard & DeForest 2012;Xiong et al 2013;Lugaz & Kintner 2013).…”

“…Time-elongation maps (J-maps) are usually constructed by stacking differenced radiance between observed sky maps along a fixed position angle (sometimes background subtracted images are used instead of difference images). Using such J-maps, transients such as CMEs are manifested as inclined streaks (e.g., Sheeley et al 2008;Rouillard et al 2008;Xiong et al 2011;Harrison et al 2012;Davies et al 2012;Xiong et al 2013). As a propagating transient is viewed at larger elongations, its WL signatures become fainter.…”