We present general considerations regarding the derivation of the radial
distances of coronal mass ejections (CMEs) from elongation angle measurements
such as those provided by SECCHI and SMEI, focusing on measurements in the
Heliospheric Imager 2 (HI-2) field of view (i.e. past 0.3 AU). This study is
based on a three-dimensional (3-D) magneto-hydrodynamics (MHD) simulation of
two CMEs observed by SECCHI on January 24-27, 2007. Having a 3-D simulation
with synthetic HI images, we are able to compare the two basic methods used to
derive CME positions from elongation angles, the so-called "Point-P" and
"Fixed-Phi" approximations.
We confirm, following similar works, that both methods, while valid in the
most inner heliosphere, yield increasingly large errors in HI-2 field of view
for fast and wide CMEs. Using a simple model of a CME as an expanding
self-similar sphere, we derive an analytical relationship between elongation
angles and radial distances for wide CMEs. This relationship is simply the
harmonic mean of the "Point-P" and "Fixed-Phi'' approximations and it is aimed
at complementing 3-D fitting of CMEs by cone models or flux rope shapes. It
proves better at getting the kinematics of the simulated CME right when we
compare the results of our line-of-sights to the MHD simulation. Based on this
approximation, we re-analyze the J-maps (time-elongation maps) in January
26-27, 2007 and present the first observational evidence that the merging of
CMEs is associated with a momentum exchange from the faster ejection to the
slower one due to the propagation of the shock wave associated with the fast
eruption through the slow eruption.Comment: 10 pages, 4 figures, accepted in Annales Geophysicae (Special Issue:
Three eyes on the Sun - multi-spacecraft studies of the corona and impacts on
the heliosphere
