Elliptical approximation for the fronts of ICMEs and application to STEREO events in August 2010 and February 2011

Geo-effective solar eruptions can now be followed continuously from the Sun to 1 AU from a viewpoint far away from the Sun-Earth line (with STEREO/SECCHI), thus making it possible to link solar, heliospheric and in situ observations unambiguously. A very basic problem is that only the elongation of the interplanetary coronal mass ejection's (ICME) density enhancements, and not the radial distances, are measured by an observer when the ICME is propagating at large angles to the Sun. Additionally, this is complicated by the effects of Thomson scattering. Nevertheless, the community has worked so far with increasingly realistic geometrical approximations to convert the observed elongations to radial distance, such as Point-P (a circle around the Sun), Fixed-Phi (a point), Harmonic Mean (a circle always attached to the Sun at one end), and Self-Similar Expansion (a circle with a given angular width). We add to this an analytical formula which is based on an elliptical geometry (abbreviated EL), with the assumption, similar to HM and SSE, that the observer looks along the tangent of the ellipse which approximates the ICME front. In this way we still ignore Thomson-scattering, but otherwise the free parameters direction, angular width and aspect ratio allow more freedom to derive ICME radial distances and speeds from heliospheric imager observations, which should improve the consistency with in situ ICME observations and the CME directions and speeds in coronagraphs. An application to combined STEREO heliospheric imager and multi-point in situ observations of the multiple ICME events on 1-4 August 2010 and 15-17 February 2011 is presented, and the possibility of using EL for real-time forecasts by means of inverse fitting and triangulation is discussed.