Expected in situ velocities from a hierarchical model for expanding interplanetary coronal mass ejections

DÉMOULIN, P.; NAKWACKI, M.S.; DASSO, S.; MANDRINI, C.H.

SOLAR PHYSICS

Springer

Año: 2008 vol. 250 p. 347 - 374

0038-0938

In situ data provide only a one dimensional sample of the plasmavelocity along the spacecraft trajectory crossing an Interplanetary Coronal MassEjection (ICME). Then, to understand the dynamics of ICMEs it is necessary toconsider some model to describe it. We derive a series of equations in a hierarchicalorder, from more general to more specific cases, to provide a general theoreticalbasis for the interpretation of in situ observations, extending and generalizingprevious studies. The main hypothesis is a self-similar expansion, but with the freedomof possible different expansion rate in three orthogonal directions. The mostdetailed application of the equations is though for a subset of ICMEs, MagneticClouds (MCs), where a magnetic flux rope can be identified. The main conclusionsare the following ones. First, we obtain theoretical expressions showing that theobserved velocity gradient within an ICME is not a direct characteristic of itsexpansion, but that it depends also on other physical quantities such as its globalvelocity and acceleration. The derived equations quantify these dependencies forthe three components of the velocity. Second, using three different types of datawe show that the global acceleration of ICMEs has, at most, a small contributionto the in situ measurements of the velocity. This eliminates practically onecontribution to the observed velocity gradient within ICMEs. Third, we provide amethod to quantify the expansion rate from velocity data. We apply it to a set of26 MCs observed by Wind or ACE spacecrafts. They are typical MCs, their mainphysical parameters cover the typical range observed in MCs in previous statisticalstudies. Though the velocity difference between their front and back includes abroad range of values, we find a narrow range for the determined expansion rate.This implies that MCs are expanding at a comparable rate, independently of theirsize or field strength, despite very different magnitudes in their velocity profiles. Furthermore, the equations derived provide a base to further analyze the dynamicsof MCs/ICMEs.