The Relationship Between the Expansion Speed and Radial Speed of CMEs   Confirmed Using Quadrature Observations of the 2011 February 15 CME
  It is difficult to measure the true speed of Earth-directed CMEs from a coronagraph located along the Sun-Earth line because of the occulting disk. However, the expansion speed (the speed with which the CME appears to spread in the sky plane) can be measured by such a coronagraph. In order to convert the expansion speed to radial speed (which is important for space weather applications) one can use an empirical relationship between the two that assumes an average width for all CMEs. If we have the width information from quadrature observations, we can confirm the relationship between expansion and radial speeds derived by Gopalswamy et al. (2009a). The STEREO spacecraft were in qudrature with SOHO (STEREO-A ahead of Earth by 87o and STEREO-B 94o behind Earth) on 2011 February 15, when a fast Earth-directed CME occurred. The CME was observed as a halo by the Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO. The sky-plane speed was measured by SOHO/LASCO as the expansion speed, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images provided the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (Vexp) and radial speed (Vrad) derived previously from geometrical considerations (Gopalswamy et al. 2009a): Vrad = 1/2 (1 + cot w)Vexp, where w is the half width of the CME. STEREO-B images of the CME, we found that CME had a full width of 76o, so w = 38o. This gives the relation as Vrad = 1.14 Vexp. From LASCO observations, we measured Vexp = 897 km/s, so we get the radial speed as 1023 km/s. Direct measurement of radial speed yields 945 km/s (STEREO-A) and 1058 km/s (STEREO-B). These numbers are different only by 7.6% and 3.4% (for STEREO-A and STEREO-B, respectively) from the computed value. 
Nat Gopalswamy, Pertti M\"akel\"a, Seiji Yashiro, and Joseph M. Davila
astro-ph.SR